diff --git a/go.mod b/go.mod index c12a003626e..eb016f214f6 100644 --- a/go.mod +++ b/go.mod @@ -98,7 +98,7 @@ require ( github.com/schollz/peerdiscovery v1.7.0 github.com/status-im/extkeys v1.4.0 github.com/status-im/go-wallet-sdk v0.0.0-20250924175027-d5faf23a5ef7 - github.com/waku-org/go-waku v0.8.1-0.20250825172353-0c3d6dc0a8cc + github.com/waku-org/go-waku v0.10.0 github.com/waku-org/waku-go-bindings v0.0.0-20250714110306-6feba5b0df4d github.com/wk8/go-ordered-map/v2 v2.1.7 go.lsp.dev/jsonrpc2 v0.10.0 @@ -300,7 +300,7 @@ require ( github.com/tklauser/numcpus v0.6.1 // indirect github.com/urfave/cli/v2 v2.27.5 // indirect github.com/wadey/gocovmerge v0.0.0-20160331181800-b5bfa59ec0ad // indirect - github.com/waku-org/go-discover v0.0.0-20240506173252-4912704efdc5 // indirect + github.com/waku-org/go-discover v0.0.0-20251002230139-b9b5a06121c6 // indirect github.com/waku-org/go-libp2p-rendezvous v0.0.0-20240110193335-a67d1cc760a0 // indirect github.com/waku-org/go-zerokit-rln v0.1.14-0.20240102145250-fa738c0bdf59 // indirect github.com/waku-org/go-zerokit-rln-apple v0.0.0-20230916172309-ee0ee61dde2b // indirect diff --git a/go.sum b/go.sum index 25f587936a5..fa2c8343ae7 100644 --- a/go.sum +++ b/go.sum @@ -686,7 +686,6 @@ github.com/creack/pty v1.1.9/go.mod h1:oKZEueFk5CKHvIhNR5MUki03XCEU+Q6VDXinZuGJ3 github.com/creack/pty v1.1.11/go.mod h1:oKZEueFk5CKHvIhNR5MUki03XCEU+Q6VDXinZuGJ33E= github.com/cruxic/go-hmac-drbg v0.0.0-20170206035330-84c46983886d h1:bE1UyBQ5aE6FjhNY4lbPtMqh7VDldoVkvZMtFEbd+CE= github.com/cruxic/go-hmac-drbg v0.0.0-20170206035330-84c46983886d/go.mod h1:HAe1wsCrwH2uFnFaCC2vlcyEohnxs8KeShAFqGIHvmM= -github.com/cyberdelia/templates v0.0.0-20141128023046-ca7fffd4298c/go.mod h1:GyV+0YP4qX0UQ7r2MoYZ+AvYDp12OF5yg4q8rGnyNh4= github.com/cyphar/filepath-securejoin v0.2.2/go.mod h1:FpkQEhXnPnOthhzymB7CGsFk2G9VLXONKD9G7QGMM+4= github.com/cyphar/filepath-securejoin v0.2.3/go.mod h1:aPGpWjXOXUn2NCNjFvBE6aRxGGx79pTxQpKOJNYHHl4= github.com/cznic/b v0.0.0-20180115125044-35e9bbe41f07/go.mod h1:URriBxXwVq5ijiJ12C7iIZqlA69nTlI+LgI6/pwftG8= @@ -714,7 +713,6 @@ github.com/dchest/siphash v1.2.3 h1:QXwFc8cFOR2dSa/gE6o/HokBMWtLUaNDVd+22aKHeEA= github.com/dchest/siphash v1.2.3/go.mod h1:0NvQU092bT0ipiFN++/rXm69QG9tVxLAlQHIXMPAkHc= github.com/deckarep/golang-set v0.0.0-20180603214616-504e848d77ea/go.mod h1:93vsz/8Wt4joVM7c2AVqh+YRMiUSc14yDtF28KmMOgQ= github.com/deckarep/golang-set v1.7.1/go.mod h1:93vsz/8Wt4joVM7c2AVqh+YRMiUSc14yDtF28KmMOgQ= -github.com/deckarep/golang-set v1.8.0/go.mod h1:5nI87KwE7wgsBU1F4GKAw2Qod7p5kyS383rP6+o6qqo= github.com/deckarep/golang-set/v2 v2.6.0 h1:XfcQbWM1LlMB8BsJ8N9vW5ehnnPVIw0je80NsVHagjM= github.com/deckarep/golang-set/v2 v2.6.0/go.mod h1:VAky9rY/yGXJOLEDv3OMci+7wtDpOF4IN+y82NBOac4= github.com/decred/dcrd/crypto/blake256 v1.0.0/go.mod h1:sQl2p6Y26YV+ZOcSTP6thNdn47hh8kt6rqSlvmrXFAc= @@ -724,9 +722,8 @@ github.com/decred/dcrd/dcrec/secp256k1/v4 v4.0.1/go.mod h1:hyedUtir6IdtD/7lIxGeC github.com/decred/dcrd/dcrec/secp256k1/v4 v4.3.0 h1:rpfIENRNNilwHwZeG5+P150SMrnNEcHYvcCuK6dPZSg= github.com/decred/dcrd/dcrec/secp256k1/v4 v4.3.0/go.mod h1:v57UDF4pDQJcEfFUCRop3lJL149eHGSe9Jvczhzjo/0= github.com/decred/dcrd/lru v1.0.0/go.mod h1:mxKOwFd7lFjN2GZYsiz/ecgqR6kkYAl+0pz0tEMk218= +github.com/deepmap/oapi-codegen v1.6.0 h1:w/d1ntwh91XI0b/8ja7+u5SvA4IFfM0UNNLmiDR1gg0= github.com/deepmap/oapi-codegen v1.6.0/go.mod h1:ryDa9AgbELGeB+YEXE1dR53yAjHwFvE9iAUlWl9Al3M= -github.com/deepmap/oapi-codegen v1.8.2 h1:SegyeYGcdi0jLLrpbCMoJxnUUn8GBXHsvr4rbzjuhfU= -github.com/deepmap/oapi-codegen v1.8.2/go.mod h1:YLgSKSDv/bZQB7N4ws6luhozi3cEdRktEqrX88CvjIw= github.com/denisenkom/go-mssqldb v0.0.0-20190515213511-eb9f6a1743f3/go.mod h1:zAg7JM8CkOJ43xKXIj7eRO9kmWm/TW578qo+oDO6tuM= github.com/denisenkom/go-mssqldb v0.10.0/go.mod h1:xbL0rPBG9cCiLr28tMa8zpbdarY27NDyej4t/EjAShU= github.com/denverdino/aliyungo v0.0.0-20190125010748-a747050bb1ba/go.mod h1:dV8lFg6daOBZbT6/BDGIz6Y3WFGn8juu6G+CQ6LHtl0= @@ -737,7 +734,6 @@ github.com/dgryski/go-sip13 v0.0.0-20181026042036-e10d5fee7954/go.mod h1:vAd38F8 github.com/dhui/dktest v0.3.0/go.mod h1:cyzIUfGsBEbZ6BT7tnXqAShHSXCZhSNmFl70sZ7c1yc= github.com/dhui/dktest v0.3.10/go.mod h1:h5Enh0nG3Qbo9WjNFRrwmKUaePEBhXMOygbz3Ww7Sz0= github.com/dlclark/regexp2 v1.2.0/go.mod h1:2pZnwuY/m+8K6iRw6wQdMtk+rH5tNGR1i55kozfMjCc= -github.com/dlclark/regexp2 v1.4.1-0.20201116162257-a2a8dda75c91/go.mod h1:2pZnwuY/m+8K6iRw6wQdMtk+rH5tNGR1i55kozfMjCc= github.com/dnaeon/go-vcr v1.0.1/go.mod h1:aBB1+wY4s93YsC3HHjMBMrwTj2R9FHDzUr9KyGc8n1E= github.com/docker/cli v0.0.0-20191017083524-a8ff7f821017/go.mod h1:JLrzqnKDaYBop7H2jaqPtU4hHvMKP+vjCwu2uszcLI8= github.com/docker/distribution v0.0.0-20190905152932-14b96e55d84c/go.mod h1:0+TTO4EOBfRPhZXAeF1Vu+W3hHZ8eLp8PgKVZlcvtFY= @@ -760,8 +756,6 @@ github.com/docker/libtrust v0.0.0-20150114040149-fa567046d9b1/go.mod h1:cyGadeNE github.com/docker/spdystream v0.0.0-20160310174837-449fdfce4d96/go.mod h1:Qh8CwZgvJUkLughtfhJv5dyTYa91l1fOUCrgjqmcifM= github.com/docopt/docopt-go v0.0.0-20180111231733-ee0de3bc6815/go.mod h1:WwZ+bS3ebgob9U8Nd0kOddGdZWjyMGR8Wziv+TBNwSE= github.com/dop251/goja v0.0.0-20200721192441-a695b0cdd498/go.mod h1:Mw6PkjjMXWbTj+nnj4s3QPXq1jaT0s5pC0iFD4+BOAA= -github.com/dop251/goja v0.0.0-20211011172007-d99e4b8cbf48/go.mod h1:R9ET47fwRVRPZnOGvHxxhuZcbrMCuiqOz3Rlrh4KSnk= -github.com/dop251/goja_nodejs v0.0.0-20210225215109-d91c329300e7/go.mod h1:hn7BA7c8pLvoGndExHudxTDKZ84Pyvv+90pbBjbTz0Y= github.com/dustin/go-humanize v0.0.0-20171111073723-bb3d318650d4/go.mod h1:HtrtbFcZ19U5GC7JDqmcUSB87Iq5E25KnS6fMYU6eOk= github.com/dustin/go-humanize v0.0.0-20180421182945-02af3965c54e/go.mod h1:HtrtbFcZ19U5GC7JDqmcUSB87Iq5E25KnS6fMYU6eOk= github.com/dustin/go-humanize v1.0.0/go.mod h1:HtrtbFcZ19U5GC7JDqmcUSB87Iq5E25KnS6fMYU6eOk= @@ -803,7 +797,6 @@ github.com/etcd-io/bbolt v1.3.3/go.mod h1:ZF2nL25h33cCyBtcyWeZ2/I3HQOfTP+0PIEvHj github.com/ethereum/c-kzg-4844/v2 v2.1.0 h1:gQropX9YFBhl3g4HYhwE70zq3IHFRgbbNPw0Shwzf5w= github.com/ethereum/c-kzg-4844/v2 v2.1.0/go.mod h1:TC48kOKjJKPbN7C++qIgt0TJzZ70QznYR7Ob+WXl57E= github.com/ethereum/go-ethereum v1.10.4/go.mod h1:nEE0TP5MtxGzOMd7egIrbPJMQBnhVU3ELNxhBglIzhg= -github.com/ethereum/go-ethereum v1.10.16/go.mod h1:Anj6cxczl+AHy63o4X9O8yWNHuN5wMpfb8MAnHkWn7Y= github.com/ethereum/go-ethereum v1.16.3 h1:nDoBSrmsrPbrDIVLTkDQCy1U9KdHN+F2PzvMbDoS42Q= github.com/ethereum/go-ethereum v1.16.3/go.mod h1:Lrsc6bt9Gm9RyvhfFK53vboCia8kpF9nv+2Ukntnl+8= github.com/ethereum/go-verkle v0.2.2 h1:I2W0WjnrFUIzzVPwm8ykY+7pL2d4VhlsePn4j7cnFk8= @@ -848,8 +841,6 @@ github.com/garyburd/redigo v0.0.0-20150301180006-535138d7bcd7/go.mod h1:NR3MbYis github.com/gballet/go-libpcsclite v0.0.0-20190607065134-2772fd86a8ff/go.mod h1:x7DCsMOv1taUwEWCzT4cmDeAkigA5/QCwUodaVOe8Ww= github.com/gballet/go-libpcsclite v0.0.0-20191108122812-4678299bea08 h1:f6D9Hr8xV8uYKlyuj8XIruxlh9WjVjdh1gIicAS7ays= github.com/gballet/go-libpcsclite v0.0.0-20191108122812-4678299bea08/go.mod h1:x7DCsMOv1taUwEWCzT4cmDeAkigA5/QCwUodaVOe8Ww= -github.com/getkin/kin-openapi v0.53.0/go.mod h1:7Yn5whZr5kJi6t+kShccXS8ae1APpYTW6yheSwk8Yi4= -github.com/getkin/kin-openapi v0.61.0/go.mod h1:7Yn5whZr5kJi6t+kShccXS8ae1APpYTW6yheSwk8Yi4= github.com/getsentry/raven-go v0.2.0/go.mod h1:KungGk8q33+aIAZUIVWZDr2OfAEBsO49PX4NzFV5kcQ= github.com/getsentry/sentry-go v0.29.1 h1:DyZuChN8Hz3ARxGVV8ePaNXh1dQ7d76AiB117xcREwA= github.com/getsentry/sentry-go v0.29.1/go.mod h1:x3AtIzN01d6SiWkderzaH28Tm0lgkafpJ5Bm3li39O0= @@ -863,7 +854,6 @@ github.com/glycerine/go-unsnap-stream v0.0.0-20210130063903-47dfef350d96/go.mod github.com/glycerine/goconvey v0.0.0-20180728074245-46e3a41ad493/go.mod h1:Ogl1Tioa0aV7gstGFO7KhffUsb9M4ydbEbbxpcEDc24= github.com/glycerine/goconvey v0.0.0-20190315024820-982ee783a72e/go.mod h1:Ogl1Tioa0aV7gstGFO7KhffUsb9M4ydbEbbxpcEDc24= github.com/glycerine/goconvey v0.0.0-20190410193231-58a59202ab31/go.mod h1:Ogl1Tioa0aV7gstGFO7KhffUsb9M4ydbEbbxpcEDc24= -github.com/go-chi/chi/v5 v5.0.0/go.mod h1:BBug9lr0cqtdAhsu6R4AAdvufI0/XBzAQSsUqJpoZOs= github.com/go-errors/errors v1.0.1/go.mod h1:f4zRHt4oKfwPJE5k8C9vpYG+aDHdBFUsgrm6/TyX73Q= github.com/go-errors/errors v1.4.2 h1:J6MZopCL4uSllY1OfXM374weqZFFItUbrImctkmUxIA= github.com/go-errors/errors v1.4.2/go.mod h1:sIVyrIiJhuEF+Pj9Ebtd6P/rEYROXFi3BopGUQ5a5Og= @@ -917,7 +907,6 @@ github.com/go-playground/locales v0.14.0/go.mod h1:sawfccIbzZTqEDETgFXqTho0QybSa github.com/go-playground/universal-translator v0.18.0 h1:82dyy6p4OuJq4/CByFNOn/jYrnRPArHwAcmLoJZxyho= github.com/go-playground/universal-translator v0.18.0/go.mod h1:UvRDBj+xPUEGrFYl+lu/H90nyDXpg0fqeB/AQUGNTVA= github.com/go-sourcemap/sourcemap v2.1.2+incompatible/go.mod h1:F8jJfvm2KbVjc5NqelyYJmf/v5J0dwNLS2mL4sNA1Jg= -github.com/go-sourcemap/sourcemap v2.1.3+incompatible/go.mod h1:F8jJfvm2KbVjc5NqelyYJmf/v5J0dwNLS2mL4sNA1Jg= github.com/go-sql-driver/mysql v1.4.0/go.mod h1:zAC/RDZ24gD3HViQzih4MyKcchzm+sOG5ZlKdlhCg5w= github.com/go-sql-driver/mysql v1.4.1/go.mod h1:zAC/RDZ24gD3HViQzih4MyKcchzm+sOG5ZlKdlhCg5w= github.com/go-sql-driver/mysql v1.5.0/go.mod h1:DCzpHaOWr8IXmIStZouvnhqoel9Qv2LBy8hT2VhHyBg= @@ -1035,7 +1024,6 @@ github.com/golang/snappy v0.0.3/go.mod h1:/XxbfmMg8lxefKM7IXC3fBNl/7bRcc72aCRzEW github.com/golang/snappy v0.0.4/go.mod h1:/XxbfmMg8lxefKM7IXC3fBNl/7bRcc72aCRzEWrmP2Q= github.com/golang/snappy v0.0.5-0.20220116011046-fa5810519dcb h1:PBC98N2aIaM3XXiurYmW7fx4GZkL8feAMVq7nEjURHk= github.com/golang/snappy v0.0.5-0.20220116011046-fa5810519dcb/go.mod h1:/XxbfmMg8lxefKM7IXC3fBNl/7bRcc72aCRzEWrmP2Q= -github.com/golangci/lint-1 v0.0.0-20181222135242-d2cdd8c08219/go.mod h1:/X8TswGSh1pIozq4ZwCfxS0WA5JGXguxk94ar/4c87Y= github.com/google/btree v0.0.0-20180124185431-e89373fe6b4a/go.mod h1:lNA+9X1NB3Zf8V7Ke586lFgjr2dZNuvo3lPJSGZ5JPQ= github.com/google/btree v0.0.0-20180813153112-4030bb1f1f0c/go.mod h1:lNA+9X1NB3Zf8V7Ke586lFgjr2dZNuvo3lPJSGZ5JPQ= github.com/google/btree v1.0.0/go.mod h1:lNA+9X1NB3Zf8V7Ke586lFgjr2dZNuvo3lPJSGZ5JPQ= @@ -1122,7 +1110,6 @@ github.com/gorilla/mux v1.7.1/go.mod h1:1lud6UwP+6orDFRuTfBEV8e9/aOM/c4fVVCaMa2z github.com/gorilla/mux v1.7.2/go.mod h1:1lud6UwP+6orDFRuTfBEV8e9/aOM/c4fVVCaMa2zaAs= github.com/gorilla/mux v1.7.3/go.mod h1:1lud6UwP+6orDFRuTfBEV8e9/aOM/c4fVVCaMa2zaAs= github.com/gorilla/mux v1.7.4/go.mod h1:DVbg23sWSpFRCP0SfiEN6jmj59UnW/n46BH5rLB71So= -github.com/gorilla/mux v1.8.0/go.mod h1:DVbg23sWSpFRCP0SfiEN6jmj59UnW/n46BH5rLB71So= github.com/gorilla/securecookie v1.1.1 h1:miw7JPhV+b/lAHSXz4qd/nN9jRiAFV5FwjeKyCS8BvQ= github.com/gorilla/securecookie v1.1.1/go.mod h1:ra0sb63/xPlUeL+yeDciTfxMRAA+MP+HVt/4epWDjd4= github.com/gorilla/sessions v1.2.1 h1:DHd3rPN5lE3Ts3D8rKkQ8x/0kqfeNmBAaiSi+o7FsgI= @@ -1206,7 +1193,6 @@ github.com/huandu/xstrings v1.3.2 h1:L18LIDzqlW6xN2rEkpdV8+oL/IXWJ1APd+vsdYy4Wdw github.com/huandu/xstrings v1.3.2/go.mod h1:y5/lhBue+AyNmUVz9RLU9xbLR0o4KIIExikq4ovT0aE= github.com/hudl/fargo v1.3.0/go.mod h1:y3CKSmjA+wD2gak7sUSXTAoopbhU08POFhmITJgmKTg= github.com/huin/goupnp v1.0.1-0.20210310174557-0ca763054c88/go.mod h1:nNs7wvRfN1eKaMknBydLNQU6146XQim8t4h+q90biWo= -github.com/huin/goupnp v1.0.2/go.mod h1:0dxJBVBHqTMjIUMkESDTNgOOx/Mw5wYIfyFmdzSamkM= github.com/huin/goupnp v1.3.0 h1:UvLUlWDNpoUdYzb2TCn+MuTWtcjXKSza2n6CBdQ0xXc= github.com/huin/goupnp v1.3.0/go.mod h1:gnGPsThkYa7bFi/KWmEysQRf48l2dvR5bxr2OFckNX8= github.com/huin/goutil v0.0.0-20170803182201-1ca381bf3150/go.mod h1:PpLOETDnJ0o3iZrZfqZzyLl6l7F3c6L1oWn7OICBi6o= @@ -1229,9 +1215,8 @@ github.com/influxdata/influxdb1-client v0.0.0-20220302092344-a9ab5670611c h1:qSH github.com/influxdata/influxdb1-client v0.0.0-20220302092344-a9ab5670611c/go.mod h1:qj24IKcXYK6Iy9ceXlo3Tc+vtHo9lIhSX5JddghvEPo= github.com/influxdata/influxql v1.1.1-0.20200828144457-65d3ef77d385/go.mod h1:gHp9y86a/pxhjJ+zMjNXiQAA197Xk9wLxaz+fGG+kWk= github.com/influxdata/line-protocol v0.0.0-20180522152040-32c6aa80de5e/go.mod h1:4kt73NQhadE3daL3WhR5EJ/J2ocX0PZzwxQ0gXJ7oFE= +github.com/influxdata/line-protocol v0.0.0-20200327222509-2487e7298839 h1:W9WBk7wlPfJLvMCdtV4zPulc4uCPrlywQOmbFOhgQNU= github.com/influxdata/line-protocol v0.0.0-20200327222509-2487e7298839/go.mod h1:xaLFMmpvUxqXtVkUJfg9QmT88cDaCJ3ZKgdZ78oO8Qo= -github.com/influxdata/line-protocol v0.0.0-20210311194329-9aa0e372d097 h1:vilfsDSy7TDxedi9gyBkMvAirat/oRcL0lFdJBf6tdM= -github.com/influxdata/line-protocol v0.0.0-20210311194329-9aa0e372d097/go.mod h1:xaLFMmpvUxqXtVkUJfg9QmT88cDaCJ3ZKgdZ78oO8Qo= github.com/influxdata/promql/v2 v2.12.0/go.mod h1:fxOPu+DY0bqCTCECchSRtWfc+0X19ybifQhZoQNF5D8= github.com/influxdata/roaring v0.4.13-0.20180809181101-fc520f41fab6/go.mod h1:bSgUQ7q5ZLSO+bKBGqJiCBGAl+9DxyW63zLTujjUlOE= github.com/influxdata/tdigest v0.0.0-20181121200506-bf2b5ad3c0a9/go.mod h1:Js0mqiSBE6Ffsg94weZZ2c+v/ciT8QRHFOap7EKDrR0= @@ -1344,7 +1329,6 @@ github.com/k0kubun/colorstring v0.0.0-20150214042306-9440f1994b88/go.mod h1:3w7q github.com/k0kubun/pp v2.3.0+incompatible/go.mod h1:GWse8YhT0p8pT4ir3ZgBbfZild3tgzSScAn6HmfYukg= github.com/karalabe/usb v0.0.0-20190919080040-51dc0efba356/go.mod h1:Od972xHfMJowv7NGVDiWVxk2zxnWgjLlJzE+F4F7AGU= github.com/karalabe/usb v0.0.0-20210518091819-4ea20957c210/go.mod h1:Od972xHfMJowv7NGVDiWVxk2zxnWgjLlJzE+F4F7AGU= -github.com/karalabe/usb v0.0.2/go.mod h1:Od972xHfMJowv7NGVDiWVxk2zxnWgjLlJzE+F4F7AGU= github.com/kardianos/osext v0.0.0-20190222173326-2bc1f35cddc0/go.mod h1:1NbS8ALrpOvjt0rHPNLyCIeMtbizbir8U//inJ+zuB8= github.com/karrick/godirwalk v1.8.0/go.mod h1:H5KPZjojv4lE+QYImBI8xVtrBRgYrIVsaRPx4tDPEn4= github.com/karrick/godirwalk v1.10.3/go.mod h1:RoGL9dQei4vP9ilrpETWE8CLOZ1kiN0LhBygSwrAsHA= @@ -1402,8 +1386,6 @@ github.com/kshvakov/clickhouse v1.3.5/go.mod h1:DMzX7FxRymoNkVgizH0DWAL8Cur7wHLg github.com/ktrysmt/go-bitbucket v0.6.4/go.mod h1:9u0v3hsd2rqCHRIpbir1oP7F58uo5dq19sBYvuMoyQ4= github.com/kylelemons/godebug v1.1.0 h1:RPNrshWIDI6G2gRW9EHilWtl7Z6Sb1BR0xunSBf0SNc= github.com/kylelemons/godebug v1.1.0/go.mod h1:9/0rRGxNHcop5bhtWyNeEfOS8JIWk580+fNqagV/RAw= -github.com/labstack/echo/v4 v4.2.1/go.mod h1:AA49e0DZ8kk5jTOOCKNuPR6oTnBS0dYiM4FW1e6jwpg= -github.com/labstack/gommon v0.3.0/go.mod h1:MULnywXg0yavhxWKc+lOruYdAhDwPK9wf0OL7NoOu+k= github.com/ladydascalie/currency v1.6.0 h1:r5s/TMCYcpn6jPRHLV3F8nI7YjpY8trvstfuixxiHns= github.com/ladydascalie/currency v1.6.0/go.mod h1:C9eil8e6tthhBb5yhwoH1U0LT5hm1BP/g+v/V82KYjY= github.com/lann/builder v0.0.0-20180802200727-47ae307949d0 h1:SOEGU9fKiNWd/HOJuq6+3iTQz8KNCLtVX6idSoTLdUw= @@ -1480,14 +1462,11 @@ github.com/marten-seemann/tcp v0.0.0-20210406111302-dfbc87cc63fd h1:br0buuQ854V8 github.com/marten-seemann/tcp v0.0.0-20210406111302-dfbc87cc63fd/go.mod h1:QuCEs1Nt24+FYQEqAAncTDPJIuGs+LxK1MCiFL25pMU= github.com/mat/besticon v0.0.0-20210314201728-1579f269edb7 h1:nxEXqXZcqWABJ8BudZJwrkdfKqCsSsGeo5IPQCbDKTw= github.com/mat/besticon v0.0.0-20210314201728-1579f269edb7/go.mod h1:RucRlHZcJbj2wwfsa5Vf6sZW5oIYv9ID65evx+CzUrw= -github.com/matryer/moq v0.0.0-20190312154309-6cfb0558e1bd/go.mod h1:9ELz6aaclSIGnZBoaSLZ3NAl1VTufbOrXBPvtcy6WiQ= github.com/mattn/go-colorable v0.0.9/go.mod h1:9vuHe8Xs5qXnSaW/c/ABM9alt+Vo+STaOChaDxuIBZU= github.com/mattn/go-colorable v0.1.0/go.mod h1:9vuHe8Xs5qXnSaW/c/ABM9alt+Vo+STaOChaDxuIBZU= github.com/mattn/go-colorable v0.1.1/go.mod h1:FuOcm+DKB9mbwrcAfNl7/TZVBZ6rcnceauSikq3lYCQ= github.com/mattn/go-colorable v0.1.2/go.mod h1:U0ppj6V5qS13XJ6of8GYAs25YV2eR4EVcfRqFIhoBtE= github.com/mattn/go-colorable v0.1.6/go.mod h1:u6P/XSegPjTcexA+o6vUJrdnUu04hMope9wVRipJSqc= -github.com/mattn/go-colorable v0.1.7/go.mod h1:u6P/XSegPjTcexA+o6vUJrdnUu04hMope9wVRipJSqc= -github.com/mattn/go-colorable v0.1.8/go.mod h1:u6P/XSegPjTcexA+o6vUJrdnUu04hMope9wVRipJSqc= github.com/mattn/go-colorable v0.1.13 h1:fFA4WZxdEF4tXPZVKMLwD8oUnCTTo08duU7wxecdEvA= github.com/mattn/go-colorable v0.1.13/go.mod h1:7S9/ev0klgBDR4GtXTXX8a3vIGJpMovkB8vQcUbaXHg= github.com/mattn/go-ieproxy v0.0.0-20190610004146-91bb50d98149/go.mod h1:31jz6HNzdxOmlERGGEc4v/dMssOfmp2p5bT/okiKFFc= @@ -2207,9 +2186,6 @@ github.com/urfave/cli v1.22.2/go.mod h1:Gos4lmkARVdJ6EkW0WaNv/tZAAMe9V7XWyB60NtX github.com/urfave/cli/v2 v2.3.0/go.mod h1:LJmUH05zAU44vOAcrfzZQKsZbVcdbOG8rtL3/XcUArI= github.com/urfave/cli/v2 v2.27.5 h1:WoHEJLdsXr6dDWoJgMq/CboDmyY/8HMMH1fTECbih+w= github.com/urfave/cli/v2 v2.27.5/go.mod h1:3Sevf16NykTbInEnD0yKkjDAeZDS0A6bzhBH5hrMvTQ= -github.com/valyala/bytebufferpool v1.0.0/go.mod h1:6bBcMArwyJ5K/AmCkWv1jt77kVWyCJ6HpOuEn7z0Csc= -github.com/valyala/fasttemplate v1.0.1/go.mod h1:UQGH1tvbgY+Nz5t2n7tXsz52dQxojPUpymEIMZ47gx8= -github.com/valyala/fasttemplate v1.2.1/go.mod h1:KHLXt3tVN2HBp8eijSv/kGJopbvo7S+qRAEEKiv+SiQ= github.com/viant/assertly v0.4.8/go.mod h1:aGifi++jvCrUaklKEKT0BU95igDNaqkvz+49uaYMPRU= github.com/viant/toolbox v0.24.0/go.mod h1:OxMCG57V0PXuIP2HNQrtJf2CjqdmbrOx5EkMILuUhzM= github.com/vishvananda/netlink v0.0.0-20181108222139-023a6dafdcdf/go.mod h1:+SR5DhBJrl6ZM7CoCKvpw5BKroDKQ+PJqOg65H/2ktk= @@ -2222,14 +2198,14 @@ github.com/vishvananda/netns v0.0.0-20200728191858-db3c7e526aae/go.mod h1:DD4vA1 github.com/vishvananda/netns v0.0.0-20210104183010-2eb08e3e575f/go.mod h1:DD4vA1DwXk04H54A1oHXtwZmA0grkVMdPxx/VGLCah0= github.com/wadey/gocovmerge v0.0.0-20160331181800-b5bfa59ec0ad h1:W0LEBv82YCGEtcmPA3uNZBI33/qF//HAAs3MawDjRa0= github.com/wadey/gocovmerge v0.0.0-20160331181800-b5bfa59ec0ad/go.mod h1:Hy8o65+MXnS6EwGElrSRjUzQDLXreJlzYLlWiHtt8hM= -github.com/waku-org/go-discover v0.0.0-20240506173252-4912704efdc5 h1:4K3IS97JryAEV8pRXB//qPcg+8bPXl/O+AOLt3FeCKc= -github.com/waku-org/go-discover v0.0.0-20240506173252-4912704efdc5/go.mod h1:eBHgM6T4EG0RZzxpxKy+rGz/6Dw2Nd8DWxS0lm9ESDw= +github.com/waku-org/go-discover v0.0.0-20251002230139-b9b5a06121c6 h1:c9ZwkW26T0+8pjevhUwWTZs+cujXTNur9MdnPnvwaL4= +github.com/waku-org/go-discover v0.0.0-20251002230139-b9b5a06121c6/go.mod h1:oVHZeHiB/OJpc0k4r+Iq+5bJXvOV3Mpz1gPQh8Vswps= github.com/waku-org/go-libp2p-pubsub v0.13.1-gowaku h1:ovXh1m76i0yPWXt95Z9ZRyEk0+WKSuPt5e4IddgwUrY= github.com/waku-org/go-libp2p-pubsub v0.13.1-gowaku/go.mod h1:MKPU5vMI8RRFyTP0HfdsF9cLmL1nHAeJm44AxJGJx44= github.com/waku-org/go-libp2p-rendezvous v0.0.0-20240110193335-a67d1cc760a0 h1:R4YYx2QamhBRl/moIxkDCNW+OP7AHbyWLBygDc/xIMo= github.com/waku-org/go-libp2p-rendezvous v0.0.0-20240110193335-a67d1cc760a0/go.mod h1:EhZP9fee0DYjKH/IOQvoNSy1tSHp2iZadsHGphcAJgY= -github.com/waku-org/go-waku v0.8.1-0.20250825172353-0c3d6dc0a8cc h1:dSkSI7rF3ScUB0zNNPgUHFGHqylIwYx1uTFwTBf9W/E= -github.com/waku-org/go-waku v0.8.1-0.20250825172353-0c3d6dc0a8cc/go.mod h1:vwUjxXV8Sd4S6ptZ750ZW1LSYP52Yre7jqjBRvprykQ= +github.com/waku-org/go-waku v0.10.0 h1:FWezOAZdgsIzNBUuN8U9rHJJ5QrSYwCOgGfzwa8YfXE= +github.com/waku-org/go-waku v0.10.0/go.mod h1:ZCkxxfqhZ+//gXw+BNs5Y58HnGXPObLdfxABrKtncTs= github.com/waku-org/go-zerokit-rln v0.1.14-0.20240102145250-fa738c0bdf59 h1:jisj+OCI6QydLtFq3Pyhu49wl9ytPN7oAHjMfepHDrA= github.com/waku-org/go-zerokit-rln v0.1.14-0.20240102145250-fa738c0bdf59/go.mod h1:1PdBdPzyTaKt3VnpAHk3zj+r9dXPFOr3IHZP9nFle6E= github.com/waku-org/go-zerokit-rln-apple v0.0.0-20230916172309-ee0ee61dde2b h1:KgZVhsLkxsj5gb/FfndSCQu6VYwALrCOgYI3poR95yE= @@ -2415,7 +2391,6 @@ golang.org/x/crypto v0.0.0-20200602180216-279210d13fed/go.mod h1:LzIPMQfyMNhhGPh golang.org/x/crypto v0.0.0-20200622213623-75b288015ac9/go.mod h1:LzIPMQfyMNhhGPhUkYOs5KpL4U8rLKemX1yGLhDgUto= golang.org/x/crypto v0.0.0-20200709230013-948cd5f35899/go.mod h1:LzIPMQfyMNhhGPhUkYOs5KpL4U8rLKemX1yGLhDgUto= golang.org/x/crypto v0.0.0-20200728195943-123391ffb6de/go.mod h1:LzIPMQfyMNhhGPhUkYOs5KpL4U8rLKemX1yGLhDgUto= -golang.org/x/crypto v0.0.0-20200820211705-5c72a883971a/go.mod h1:LzIPMQfyMNhhGPhUkYOs5KpL4U8rLKemX1yGLhDgUto= golang.org/x/crypto v0.0.0-20201002170205-7f63de1d35b0/go.mod h1:LzIPMQfyMNhhGPhUkYOs5KpL4U8rLKemX1yGLhDgUto= golang.org/x/crypto v0.0.0-20201016220609-9e8e0b390897/go.mod h1:LzIPMQfyMNhhGPhUkYOs5KpL4U8rLKemX1yGLhDgUto= golang.org/x/crypto v0.0.0-20201221181555-eec23a3978ad/go.mod h1:jdWPYTVW3xRLrWPugEBEK3UY2ZEsg3UU495nc5E+M+I= @@ -2428,7 +2403,6 @@ golang.org/x/crypto v0.0.0-20210817164053-32db794688a5/go.mod h1:GvvjBRRGRdwPK5y golang.org/x/crypto v0.0.0-20210921155107-089bfa567519/go.mod h1:GvvjBRRGRdwPK5ydBHafDWAxML/pGHZbMvKqRZ5+Abc= golang.org/x/crypto v0.0.0-20211215153901-e495a2d5b3d3/go.mod h1:IxCIyHEi3zRg3s0A5j5BB6A9Jmi73HwBIUl50j+osU4= golang.org/x/crypto v0.0.0-20220131195533-30dcbda58838/go.mod h1:IxCIyHEi3zRg3s0A5j5BB6A9Jmi73HwBIUl50j+osU4= -golang.org/x/crypto v0.0.0-20220331220935-ae2d96664a29/go.mod h1:IxCIyHEi3zRg3s0A5j5BB6A9Jmi73HwBIUl50j+osU4= golang.org/x/crypto v0.8.0/go.mod h1:mRqEX+O9/h5TFCrQhkgjo2yKi0yYA+9ecGkdQoHrywE= golang.org/x/crypto v0.12.0/go.mod h1:NF0Gs7EO5K4qLn+Ylc+fih8BSTeIjAP05siRnAh98yw= golang.org/x/crypto v0.14.0/go.mod h1:MVFd36DqK4CsrnJYDkBA3VC4m2GkXAM0PvzMCn4JQf4= @@ -2716,7 +2690,6 @@ golang.org/x/sys v0.0.0-20200728102440-3e129f6d46b1/go.mod h1:h1NjWce9XRLGQEsW7w golang.org/x/sys v0.0.0-20200803210538-64077c9b5642/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs= golang.org/x/sys v0.0.0-20200814200057-3d37ad5750ed/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs= golang.org/x/sys v0.0.0-20200817155316-9781c653f443/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs= -golang.org/x/sys v0.0.0-20200826173525-f9321e4c35a6/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs= golang.org/x/sys v0.0.0-20200828194041-157a740278f4/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs= golang.org/x/sys v0.0.0-20200831180312-196b9ba8737a/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs= golang.org/x/sys v0.0.0-20200905004654-be1d3432aa8f/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs= diff --git a/vendor/github.com/ethereum/c-kzg-4844/v2/bindings/go/blst_headers/blst.h b/vendor/github.com/ethereum/c-kzg-4844/v2/bindings/go/blst_headers/blst.h new file mode 100644 index 00000000000..8d90abf017f --- /dev/null +++ b/vendor/github.com/ethereum/c-kzg-4844/v2/bindings/go/blst_headers/blst.h @@ -0,0 +1,490 @@ +/* + * Copyright Supranational LLC + * Licensed under the Apache License, Version 2.0, see LICENSE for details. + * SPDX-License-Identifier: Apache-2.0 + */ +#ifndef __BLST_H__ +#define __BLST_H__ + +#ifdef __SIZE_TYPE__ +typedef __SIZE_TYPE__ size_t; +#else +#include +#endif + +#if defined(__UINT8_TYPE__) && defined(__UINT32_TYPE__) \ + && defined(__UINT64_TYPE__) +typedef __UINT8_TYPE__ uint8_t; +typedef __UINT32_TYPE__ uint32_t; +typedef __UINT64_TYPE__ uint64_t; +#else +#include +#endif + +#ifdef __cplusplus +extern "C" { +#elif !defined(__STDC_VERSION__) || __STDC_VERSION__<202311 +# if defined(__BLST_CGO__) +typedef _Bool bool; /* it's assumed that cgo calls modern enough compiler */ +# elif !defined(bool) +# if defined(__STDC_VERSION__) && __STDC_VERSION__>=199901 +# define bool _Bool +# else +# define bool int +# endif +# define __blst_h_bool__ +# endif +#endif + +#ifdef SWIG +# define DEFNULL =NULL +#elif defined __cplusplus +# define DEFNULL =0 +#else +# define DEFNULL +#endif + +typedef enum { + BLST_SUCCESS = 0, + BLST_BAD_ENCODING, + BLST_POINT_NOT_ON_CURVE, + BLST_POINT_NOT_IN_GROUP, + BLST_AGGR_TYPE_MISMATCH, + BLST_VERIFY_FAIL, + BLST_PK_IS_INFINITY, + BLST_BAD_SCALAR, +} BLST_ERROR; + +typedef uint8_t byte; +typedef uint64_t limb_t; + +typedef struct { byte b[256/8]; } blst_scalar; +typedef struct { limb_t l[256/8/sizeof(limb_t)]; } blst_fr; +typedef struct { limb_t l[384/8/sizeof(limb_t)]; } blst_fp; +/* 0 is "real" part, 1 is "imaginary" */ +typedef struct { blst_fp fp[2]; } blst_fp2; +typedef struct { blst_fp2 fp2[3]; } blst_fp6; +typedef struct { blst_fp6 fp6[2]; } blst_fp12; + +void blst_scalar_from_uint32(blst_scalar *out, const uint32_t a[8]); +void blst_uint32_from_scalar(uint32_t out[8], const blst_scalar *a); +void blst_scalar_from_uint64(blst_scalar *out, const uint64_t a[4]); +void blst_uint64_from_scalar(uint64_t out[4], const blst_scalar *a); +void blst_scalar_from_bendian(blst_scalar *out, const byte a[32]); +void blst_bendian_from_scalar(byte out[32], const blst_scalar *a); +void blst_scalar_from_lendian(blst_scalar *out, const byte a[32]); +void blst_lendian_from_scalar(byte out[32], const blst_scalar *a); +bool blst_scalar_fr_check(const blst_scalar *a); +bool blst_sk_check(const blst_scalar *a); +bool blst_sk_add_n_check(blst_scalar *out, const blst_scalar *a, + const blst_scalar *b); +bool blst_sk_sub_n_check(blst_scalar *out, const blst_scalar *a, + const blst_scalar *b); +bool blst_sk_mul_n_check(blst_scalar *out, const blst_scalar *a, + const blst_scalar *b); +void blst_sk_inverse(blst_scalar *out, const blst_scalar *a); +bool blst_scalar_from_le_bytes(blst_scalar *out, const byte *in, size_t len); +bool blst_scalar_from_be_bytes(blst_scalar *out, const byte *in, size_t len); + +#ifndef SWIG +/* + * BLS12-381-specific Fr operations. + */ +void blst_fr_add(blst_fr *ret, const blst_fr *a, const blst_fr *b); +void blst_fr_sub(blst_fr *ret, const blst_fr *a, const blst_fr *b); +void blst_fr_mul_by_3(blst_fr *ret, const blst_fr *a); +void blst_fr_lshift(blst_fr *ret, const blst_fr *a, size_t count); +void blst_fr_rshift(blst_fr *ret, const blst_fr *a, size_t count); +void blst_fr_mul(blst_fr *ret, const blst_fr *a, const blst_fr *b); +void blst_fr_sqr(blst_fr *ret, const blst_fr *a); +void blst_fr_cneg(blst_fr *ret, const blst_fr *a, bool flag); +void blst_fr_eucl_inverse(blst_fr *ret, const blst_fr *a); +void blst_fr_inverse(blst_fr *ret, const blst_fr *a); + +void blst_fr_from_uint64(blst_fr *ret, const uint64_t a[4]); +void blst_uint64_from_fr(uint64_t ret[4], const blst_fr *a); +void blst_fr_from_scalar(blst_fr *ret, const blst_scalar *a); +void blst_scalar_from_fr(blst_scalar *ret, const blst_fr *a); + +/* + * BLS12-381-specific Fp operations. + */ +void blst_fp_add(blst_fp *ret, const blst_fp *a, const blst_fp *b); +void blst_fp_sub(blst_fp *ret, const blst_fp *a, const blst_fp *b); +void blst_fp_mul_by_3(blst_fp *ret, const blst_fp *a); +void blst_fp_mul_by_8(blst_fp *ret, const blst_fp *a); +void blst_fp_lshift(blst_fp *ret, const blst_fp *a, size_t count); +void blst_fp_mul(blst_fp *ret, const blst_fp *a, const blst_fp *b); +void blst_fp_sqr(blst_fp *ret, const blst_fp *a); +void blst_fp_cneg(blst_fp *ret, const blst_fp *a, bool flag); +void blst_fp_eucl_inverse(blst_fp *ret, const blst_fp *a); +void blst_fp_inverse(blst_fp *ret, const blst_fp *a); +bool blst_fp_sqrt(blst_fp *ret, const blst_fp *a); + +void blst_fp_from_uint32(blst_fp *ret, const uint32_t a[12]); +void blst_uint32_from_fp(uint32_t ret[12], const blst_fp *a); +void blst_fp_from_uint64(blst_fp *ret, const uint64_t a[6]); +void blst_uint64_from_fp(uint64_t ret[6], const blst_fp *a); +void blst_fp_from_bendian(blst_fp *ret, const byte a[48]); +void blst_bendian_from_fp(byte ret[48], const blst_fp *a); +void blst_fp_from_lendian(blst_fp *ret, const byte a[48]); +void blst_lendian_from_fp(byte ret[48], const blst_fp *a); + +/* + * BLS12-381-specific Fp2 operations. + */ +void blst_fp2_add(blst_fp2 *ret, const blst_fp2 *a, const blst_fp2 *b); +void blst_fp2_sub(blst_fp2 *ret, const blst_fp2 *a, const blst_fp2 *b); +void blst_fp2_mul_by_3(blst_fp2 *ret, const blst_fp2 *a); +void blst_fp2_mul_by_8(blst_fp2 *ret, const blst_fp2 *a); +void blst_fp2_lshift(blst_fp2 *ret, const blst_fp2 *a, size_t count); +void blst_fp2_mul(blst_fp2 *ret, const blst_fp2 *a, const blst_fp2 *b); +void blst_fp2_sqr(blst_fp2 *ret, const blst_fp2 *a); +void blst_fp2_cneg(blst_fp2 *ret, const blst_fp2 *a, bool flag); +void blst_fp2_eucl_inverse(blst_fp2 *ret, const blst_fp2 *a); +void blst_fp2_inverse(blst_fp2 *ret, const blst_fp2 *a); +bool blst_fp2_sqrt(blst_fp2 *ret, const blst_fp2 *a); + +/* + * BLS12-381-specific Fp12 operations. + */ +void blst_fp12_sqr(blst_fp12 *ret, const blst_fp12 *a); +void blst_fp12_cyclotomic_sqr(blst_fp12 *ret, const blst_fp12 *a); +void blst_fp12_mul(blst_fp12 *ret, const blst_fp12 *a, const blst_fp12 *b); +void blst_fp12_mul_by_xy00z0(blst_fp12 *ret, const blst_fp12 *a, + const blst_fp6 *xy00z0); +void blst_fp12_conjugate(blst_fp12 *a); +void blst_fp12_inverse(blst_fp12 *ret, const blst_fp12 *a); +/* caveat lector! |n| has to be non-zero and not more than 3! */ +void blst_fp12_frobenius_map(blst_fp12 *ret, const blst_fp12 *a, size_t n); +bool blst_fp12_is_equal(const blst_fp12 *a, const blst_fp12 *b); +bool blst_fp12_is_one(const blst_fp12 *a); +bool blst_fp12_in_group(const blst_fp12 *a); +const blst_fp12 *blst_fp12_one(void); +#endif // SWIG + +/* + * BLS12-381-specific point operations. + */ +typedef struct { blst_fp x, y, z; } blst_p1; +typedef struct { blst_fp x, y; } blst_p1_affine; + +void blst_p1_add(blst_p1 *out, const blst_p1 *a, const blst_p1 *b); +void blst_p1_add_or_double(blst_p1 *out, const blst_p1 *a, const blst_p1 *b); +void blst_p1_add_affine(blst_p1 *out, const blst_p1 *a, + const blst_p1_affine *b); +void blst_p1_add_or_double_affine(blst_p1 *out, const blst_p1 *a, + const blst_p1_affine *b); +void blst_p1_double(blst_p1 *out, const blst_p1 *a); +void blst_p1_mult(blst_p1 *out, const blst_p1 *p, const byte *scalar, + size_t nbits); +void blst_p1_cneg(blst_p1 *p, bool cbit); +void blst_p1_to_affine(blst_p1_affine *out, const blst_p1 *in); +void blst_p1_from_affine(blst_p1 *out, const blst_p1_affine *in); +bool blst_p1_on_curve(const blst_p1 *p); +bool blst_p1_in_g1(const blst_p1 *p); +bool blst_p1_is_equal(const blst_p1 *a, const blst_p1 *b); +bool blst_p1_is_inf(const blst_p1 *a); +const blst_p1 *blst_p1_generator(void); + +bool blst_p1_affine_on_curve(const blst_p1_affine *p); +bool blst_p1_affine_in_g1(const blst_p1_affine *p); +bool blst_p1_affine_is_equal(const blst_p1_affine *a, const blst_p1_affine *b); +bool blst_p1_affine_is_inf(const blst_p1_affine *a); +const blst_p1_affine *blst_p1_affine_generator(void); + +typedef struct { blst_fp2 x, y, z; } blst_p2; +typedef struct { blst_fp2 x, y; } blst_p2_affine; + +void blst_p2_add(blst_p2 *out, const blst_p2 *a, const blst_p2 *b); +void blst_p2_add_or_double(blst_p2 *out, const blst_p2 *a, const blst_p2 *b); +void blst_p2_add_affine(blst_p2 *out, const blst_p2 *a, + const blst_p2_affine *b); +void blst_p2_add_or_double_affine(blst_p2 *out, const blst_p2 *a, + const blst_p2_affine *b); +void blst_p2_double(blst_p2 *out, const blst_p2 *a); +void blst_p2_mult(blst_p2 *out, const blst_p2 *p, const byte *scalar, + size_t nbits); +void blst_p2_cneg(blst_p2 *p, bool cbit); +void blst_p2_to_affine(blst_p2_affine *out, const blst_p2 *in); +void blst_p2_from_affine(blst_p2 *out, const blst_p2_affine *in); +bool blst_p2_on_curve(const blst_p2 *p); +bool blst_p2_in_g2(const blst_p2 *p); +bool blst_p2_is_equal(const blst_p2 *a, const blst_p2 *b); +bool blst_p2_is_inf(const blst_p2 *a); +const blst_p2 *blst_p2_generator(void); + +bool blst_p2_affine_on_curve(const blst_p2_affine *p); +bool blst_p2_affine_in_g2(const blst_p2_affine *p); +bool blst_p2_affine_is_equal(const blst_p2_affine *a, const blst_p2_affine *b); +bool blst_p2_affine_is_inf(const blst_p2_affine *a); +const blst_p2_affine *blst_p2_affine_generator(void); + +/* + * Multi-scalar multiplications and other multi-point operations. + */ + +void blst_p1s_to_affine(blst_p1_affine dst[], const blst_p1 *const points[], + size_t npoints); +void blst_p1s_add(blst_p1 *ret, const blst_p1_affine *const points[], + size_t npoints); + +size_t blst_p1s_mult_wbits_precompute_sizeof(size_t wbits, size_t npoints); +void blst_p1s_mult_wbits_precompute(blst_p1_affine table[], size_t wbits, + const blst_p1_affine *const points[], + size_t npoints); +size_t blst_p1s_mult_wbits_scratch_sizeof(size_t npoints); +void blst_p1s_mult_wbits(blst_p1 *ret, const blst_p1_affine table[], + size_t wbits, size_t npoints, + const byte *const scalars[], size_t nbits, + limb_t *scratch); + +size_t blst_p1s_mult_pippenger_scratch_sizeof(size_t npoints); +void blst_p1s_mult_pippenger(blst_p1 *ret, const blst_p1_affine *const points[], + size_t npoints, const byte *const scalars[], + size_t nbits, limb_t *scratch); +void blst_p1s_tile_pippenger(blst_p1 *ret, const blst_p1_affine *const points[], + size_t npoints, const byte *const scalars[], + size_t nbits, limb_t *scratch, + size_t bit0, size_t window); + +void blst_p2s_to_affine(blst_p2_affine dst[], const blst_p2 *const points[], + size_t npoints); +void blst_p2s_add(blst_p2 *ret, const blst_p2_affine *const points[], + size_t npoints); + +size_t blst_p2s_mult_wbits_precompute_sizeof(size_t wbits, size_t npoints); +void blst_p2s_mult_wbits_precompute(blst_p2_affine table[], size_t wbits, + const blst_p2_affine *const points[], + size_t npoints); +size_t blst_p2s_mult_wbits_scratch_sizeof(size_t npoints); +void blst_p2s_mult_wbits(blst_p2 *ret, const blst_p2_affine table[], + size_t wbits, size_t npoints, + const byte *const scalars[], size_t nbits, + limb_t *scratch); + +size_t blst_p2s_mult_pippenger_scratch_sizeof(size_t npoints); +void blst_p2s_mult_pippenger(blst_p2 *ret, const blst_p2_affine *const points[], + size_t npoints, const byte *const scalars[], + size_t nbits, limb_t *scratch); +void blst_p2s_tile_pippenger(blst_p2 *ret, const blst_p2_affine *const points[], + size_t npoints, const byte *const scalars[], + size_t nbits, limb_t *scratch, + size_t bit0, size_t window); + +/* + * Hash-to-curve operations. + */ +#ifndef SWIG +void blst_map_to_g1(blst_p1 *out, const blst_fp *u, const blst_fp *v DEFNULL); +void blst_map_to_g2(blst_p2 *out, const blst_fp2 *u, const blst_fp2 *v DEFNULL); +#endif + +void blst_encode_to_g1(blst_p1 *out, + const byte *msg, size_t msg_len, + const byte *DST DEFNULL, size_t DST_len DEFNULL, + const byte *aug DEFNULL, size_t aug_len DEFNULL); +void blst_hash_to_g1(blst_p1 *out, + const byte *msg, size_t msg_len, + const byte *DST DEFNULL, size_t DST_len DEFNULL, + const byte *aug DEFNULL, size_t aug_len DEFNULL); + +void blst_encode_to_g2(blst_p2 *out, + const byte *msg, size_t msg_len, + const byte *DST DEFNULL, size_t DST_len DEFNULL, + const byte *aug DEFNULL, size_t aug_len DEFNULL); +void blst_hash_to_g2(blst_p2 *out, + const byte *msg, size_t msg_len, + const byte *DST DEFNULL, size_t DST_len DEFNULL, + const byte *aug DEFNULL, size_t aug_len DEFNULL); + +/* + * Zcash-compatible serialization/deserialization. + */ +void blst_p1_serialize(byte out[96], const blst_p1 *in); +void blst_p1_compress(byte out[48], const blst_p1 *in); +void blst_p1_affine_serialize(byte out[96], const blst_p1_affine *in); +void blst_p1_affine_compress(byte out[48], const blst_p1_affine *in); +BLST_ERROR blst_p1_uncompress(blst_p1_affine *out, const byte in[48]); +BLST_ERROR blst_p1_deserialize(blst_p1_affine *out, const byte in[96]); + +void blst_p2_serialize(byte out[192], const blst_p2 *in); +void blst_p2_compress(byte out[96], const blst_p2 *in); +void blst_p2_affine_serialize(byte out[192], const blst_p2_affine *in); +void blst_p2_affine_compress(byte out[96], const blst_p2_affine *in); +BLST_ERROR blst_p2_uncompress(blst_p2_affine *out, const byte in[96]); +BLST_ERROR blst_p2_deserialize(blst_p2_affine *out, const byte in[192]); + +/* + * Specification defines two variants, 'minimal-signature-size' and + * 'minimal-pubkey-size'. To unify appearance we choose to distinguish + * them by suffix referring to the public key type, more specifically + * _pk_in_g1 corresponds to 'minimal-pubkey-size' and _pk_in_g2 - to + * 'minimal-signature-size'. It might appear a bit counterintuitive + * in sign call, but no matter how you twist it, something is bound to + * turn a little odd. + */ +/* + * Secret-key operations. + */ +void blst_keygen(blst_scalar *out_SK, const byte *IKM, size_t IKM_len, + const byte *info DEFNULL, size_t info_len DEFNULL); +void blst_sk_to_pk_in_g1(blst_p1 *out_pk, const blst_scalar *SK); +void blst_sign_pk_in_g1(blst_p2 *out_sig, const blst_p2 *hash, + const blst_scalar *SK); +void blst_sk_to_pk_in_g2(blst_p2 *out_pk, const blst_scalar *SK); +void blst_sign_pk_in_g2(blst_p1 *out_sig, const blst_p1 *hash, + const blst_scalar *SK); + +/* + * Pairing interface. + */ +#ifndef SWIG +void blst_miller_loop(blst_fp12 *ret, const blst_p2_affine *Q, + const blst_p1_affine *P); +void blst_miller_loop_n(blst_fp12 *ret, const blst_p2_affine *const Qs[], + const blst_p1_affine *const Ps[], + size_t n); +void blst_final_exp(blst_fp12 *ret, const blst_fp12 *f); +void blst_precompute_lines(blst_fp6 Qlines[68], const blst_p2_affine *Q); +void blst_miller_loop_lines(blst_fp12 *ret, const blst_fp6 Qlines[68], + const blst_p1_affine *P); +bool blst_fp12_finalverify(const blst_fp12 *gt1, const blst_fp12 *gt2); +#endif + +#ifdef __BLST_CGO__ +typedef limb_t blst_pairing; +#elif defined(__BLST_RUST_BINDGEN__) +typedef struct {} blst_pairing; +#else +typedef struct blst_opaque blst_pairing; +#endif + +size_t blst_pairing_sizeof(void); +void blst_pairing_init(blst_pairing *new_ctx, bool hash_or_encode, + const byte *DST DEFNULL, size_t DST_len DEFNULL); +const byte *blst_pairing_get_dst(const blst_pairing *ctx); +void blst_pairing_commit(blst_pairing *ctx); +BLST_ERROR blst_pairing_aggregate_pk_in_g2(blst_pairing *ctx, + const blst_p2_affine *PK, + const blst_p1_affine *signature, + const byte *msg, size_t msg_len, + const byte *aug DEFNULL, + size_t aug_len DEFNULL); +BLST_ERROR blst_pairing_chk_n_aggr_pk_in_g2(blst_pairing *ctx, + const blst_p2_affine *PK, + bool pk_grpchk, + const blst_p1_affine *signature, + bool sig_grpchk, + const byte *msg, size_t msg_len, + const byte *aug DEFNULL, + size_t aug_len DEFNULL); +BLST_ERROR blst_pairing_mul_n_aggregate_pk_in_g2(blst_pairing *ctx, + const blst_p2_affine *PK, + const blst_p1_affine *sig, + const byte *scalar, + size_t nbits, + const byte *msg, + size_t msg_len, + const byte *aug DEFNULL, + size_t aug_len DEFNULL); +BLST_ERROR blst_pairing_chk_n_mul_n_aggr_pk_in_g2(blst_pairing *ctx, + const blst_p2_affine *PK, + bool pk_grpchk, + const blst_p1_affine *sig, + bool sig_grpchk, + const byte *scalar, + size_t nbits, + const byte *msg, + size_t msg_len, + const byte *aug DEFNULL, + size_t aug_len DEFNULL); +BLST_ERROR blst_pairing_aggregate_pk_in_g1(blst_pairing *ctx, + const blst_p1_affine *PK, + const blst_p2_affine *signature, + const byte *msg, size_t msg_len, + const byte *aug DEFNULL, + size_t aug_len DEFNULL); +BLST_ERROR blst_pairing_chk_n_aggr_pk_in_g1(blst_pairing *ctx, + const blst_p1_affine *PK, + bool pk_grpchk, + const blst_p2_affine *signature, + bool sig_grpchk, + const byte *msg, size_t msg_len, + const byte *aug DEFNULL, + size_t aug_len DEFNULL); +BLST_ERROR blst_pairing_mul_n_aggregate_pk_in_g1(blst_pairing *ctx, + const blst_p1_affine *PK, + const blst_p2_affine *sig, + const byte *scalar, + size_t nbits, + const byte *msg, + size_t msg_len, + const byte *aug DEFNULL, + size_t aug_len DEFNULL); +BLST_ERROR blst_pairing_chk_n_mul_n_aggr_pk_in_g1(blst_pairing *ctx, + const blst_p1_affine *PK, + bool pk_grpchk, + const blst_p2_affine *sig, + bool sig_grpchk, + const byte *scalar, + size_t nbits, + const byte *msg, + size_t msg_len, + const byte *aug DEFNULL, + size_t aug_len DEFNULL); +BLST_ERROR blst_pairing_merge(blst_pairing *ctx, const blst_pairing *ctx1); +bool blst_pairing_finalverify(const blst_pairing *ctx, + const blst_fp12 *gtsig DEFNULL); + + +/* + * Customarily applications aggregate signatures separately. + * In which case application would have to pass NULLs for |signature| + * to blst_pairing_aggregate calls and pass aggregated signature + * collected with these calls to blst_pairing_finalverify. Inputs are + * Zcash-compatible "straight-from-wire" byte vectors, compressed or + * not. + */ +BLST_ERROR blst_aggregate_in_g1(blst_p1 *out, const blst_p1 *in, + const byte *zwire); +BLST_ERROR blst_aggregate_in_g2(blst_p2 *out, const blst_p2 *in, + const byte *zwire); + +void blst_aggregated_in_g1(blst_fp12 *out, const blst_p1_affine *signature); +void blst_aggregated_in_g2(blst_fp12 *out, const blst_p2_affine *signature); + +/* + * "One-shot" CoreVerify entry points. + */ +BLST_ERROR blst_core_verify_pk_in_g1(const blst_p1_affine *pk, + const blst_p2_affine *signature, + bool hash_or_encode, + const byte *msg, size_t msg_len, + const byte *DST DEFNULL, + size_t DST_len DEFNULL, + const byte *aug DEFNULL, + size_t aug_len DEFNULL); +BLST_ERROR blst_core_verify_pk_in_g2(const blst_p2_affine *pk, + const blst_p1_affine *signature, + bool hash_or_encode, + const byte *msg, size_t msg_len, + const byte *DST DEFNULL, + size_t DST_len DEFNULL, + const byte *aug DEFNULL, + size_t aug_len DEFNULL); + +extern const blst_p1_affine BLS12_381_G1; +extern const blst_p1_affine BLS12_381_NEG_G1; +extern const blst_p2_affine BLS12_381_G2; +extern const blst_p2_affine BLS12_381_NEG_G2; + +#include "blst_aux.h" + +#ifdef __cplusplus +} +#elif defined(__blst_h_bool__) +# undef __blst_h_bool__ +# undef bool +#endif +#endif diff --git a/vendor/github.com/ethereum/c-kzg-4844/v2/bindings/go/blst_headers/blst_aux.h b/vendor/github.com/ethereum/c-kzg-4844/v2/bindings/go/blst_headers/blst_aux.h new file mode 100644 index 00000000000..3de0850e330 --- /dev/null +++ b/vendor/github.com/ethereum/c-kzg-4844/v2/bindings/go/blst_headers/blst_aux.h @@ -0,0 +1,117 @@ +/* + * Copyright Supranational LLC + * Licensed under the Apache License, Version 2.0, see LICENSE for details. + * SPDX-License-Identifier: Apache-2.0 + */ +#ifndef __BLST_AUX_H__ +#define __BLST_AUX_H__ +/* + * This file lists interfaces that might be promoted to blst.h or removed, + * depending on their proven/unproven worthiness. + */ + +void blst_fr_ct_bfly(blst_fr *x0, blst_fr *x1, const blst_fr *twiddle); +void blst_fr_gs_bfly(blst_fr *x0, blst_fr *x1, const blst_fr *twiddle); +void blst_fr_to(blst_fr *ret, const blst_fr *a); +void blst_fr_from(blst_fr *ret, const blst_fr *a); +#ifdef BLST_FR_PENTAROOT +void blst_fr_pentaroot(blst_fr *ret, const blst_fr *a); +void blst_fr_pentapow(blst_fr *ret, const blst_fr *a); +#endif + +void blst_fp_to(blst_fp *ret, const blst_fp *a); +void blst_fp_from(blst_fp *ret, const blst_fp *a); + +bool blst_fp_is_square(const blst_fp *a); +bool blst_fp2_is_square(const blst_fp2 *a); + +void blst_p1_from_jacobian(blst_p1 *out, const blst_p1 *in); +void blst_p2_from_jacobian(blst_p2 *out, const blst_p2 *in); + +/* + * Below functions produce both point and deserialized outcome of + * SkToPk and Sign. However, deserialized outputs are pre-decorated + * with sign and infinity bits. This means that you have to bring the + * output into compliance prior returning to application. If you want + * compressed point value, then do [equivalent of] + * + * byte temp[96]; + * blst_sk_to_pk2_in_g1(temp, out_pk, SK); + * temp[0] |= 0x80; + * memcpy(out, temp, 48); + * + * Otherwise do + * + * blst_sk_to_pk2_in_g1(out, out_pk, SK); + * out[0] &= ~0x20; + * + * Either |out| or |out_| can be NULL. + */ +void blst_sk_to_pk2_in_g1(byte out[96], blst_p1_affine *out_pk, + const blst_scalar *SK); +void blst_sign_pk2_in_g1(byte out[192], blst_p2_affine *out_sig, + const blst_p2 *hash, const blst_scalar *SK); +void blst_sk_to_pk2_in_g2(byte out[192], blst_p2_affine *out_pk, + const blst_scalar *SK); +void blst_sign_pk2_in_g2(byte out[96], blst_p1_affine *out_sig, + const blst_p1 *hash, const blst_scalar *SK); + +#ifdef __BLST_RUST_BINDGEN__ +typedef struct {} blst_uniq; +#else +typedef struct blst_opaque blst_uniq; +#endif + +size_t blst_uniq_sizeof(size_t n_nodes); +void blst_uniq_init(blst_uniq *tree); +bool blst_uniq_test(blst_uniq *tree, const byte *msg, size_t len); + +#ifdef expand_message_xmd +void expand_message_xmd(unsigned char *bytes, size_t len_in_bytes, + const unsigned char *aug, size_t aug_len, + const unsigned char *msg, size_t msg_len, + const unsigned char *DST, size_t DST_len); +#else +void blst_expand_message_xmd(byte *out, size_t out_len, + const byte *msg, size_t msg_len, + const byte *DST, size_t DST_len); +#endif + +void blst_p1_unchecked_mult(blst_p1 *out, const blst_p1 *p, const byte *scalar, + size_t nbits); +void blst_p2_unchecked_mult(blst_p2 *out, const blst_p2 *p, const byte *scalar, + size_t nbits); + +void blst_pairing_raw_aggregate(blst_pairing *ctx, const blst_p2_affine *q, + const blst_p1_affine *p); +blst_fp12 *blst_pairing_as_fp12(blst_pairing *ctx); +void blst_bendian_from_fp12(byte out[48*12], const blst_fp12 *a); + +void blst_keygen_v3(blst_scalar *out_SK, const byte *IKM, size_t IKM_len, + const byte *info DEFNULL, size_t info_len DEFNULL); +void blst_keygen_v4_5(blst_scalar *out_SK, const byte *IKM, size_t IKM_len, + const byte *salt, size_t salt_len, + const byte *info DEFNULL, size_t info_len DEFNULL); +void blst_keygen_v5(blst_scalar *out_SK, const byte *IKM, size_t IKM_len, + const byte *salt, size_t salt_len, + const byte *info DEFNULL, size_t info_len DEFNULL); +void blst_derive_master_eip2333(blst_scalar *out_SK, + const byte *IKM, size_t IKM_len); +void blst_derive_child_eip2333(blst_scalar *out_SK, const blst_scalar *SK, + uint32_t child_index); + +void blst_scalar_from_hexascii(blst_scalar *out, const byte *hex); +void blst_fr_from_hexascii(blst_fr *ret, const byte *hex); +void blst_fp_from_hexascii(blst_fp *ret, const byte *hex); + +size_t blst_p1_sizeof(void); +size_t blst_p1_affine_sizeof(void); +size_t blst_p2_sizeof(void); +size_t blst_p2_affine_sizeof(void); +size_t blst_fp12_sizeof(void); + +/* + * Single-shot SHA-256 hash function. + */ +void blst_sha256(byte out[32], const byte *msg, size_t msg_len); +#endif diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/contrib/lax_der_parsing.c b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/contrib/lax_der_parsing.c new file mode 100644 index 00000000000..bf562303edd --- /dev/null +++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/contrib/lax_der_parsing.c @@ -0,0 +1,148 @@ +/*********************************************************************** + * Copyright (c) 2015 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#include + +#include "lax_der_parsing.h" + +int ecdsa_signature_parse_der_lax(const secp256k1_context* ctx, secp256k1_ecdsa_signature* sig, const unsigned char *input, size_t inputlen) { + size_t rpos, rlen, spos, slen; + size_t pos = 0; + size_t lenbyte; + unsigned char tmpsig[64] = {0}; + int overflow = 0; + + /* Hack to initialize sig with a correctly-parsed but invalid signature. */ + secp256k1_ecdsa_signature_parse_compact(ctx, sig, tmpsig); + + /* Sequence tag byte */ + if (pos == inputlen || input[pos] != 0x30) { + return 0; + } + pos++; + + /* Sequence length bytes */ + if (pos == inputlen) { + return 0; + } + lenbyte = input[pos++]; + if (lenbyte & 0x80) { + lenbyte -= 0x80; + if (lenbyte > inputlen - pos) { + return 0; + } + pos += lenbyte; + } + + /* Integer tag byte for R */ + if (pos == inputlen || input[pos] != 0x02) { + return 0; + } + pos++; + + /* Integer length for R */ + if (pos == inputlen) { + return 0; + } + lenbyte = input[pos++]; + if (lenbyte & 0x80) { + lenbyte -= 0x80; + if (lenbyte > inputlen - pos) { + return 0; + } + while (lenbyte > 0 && input[pos] == 0) { + pos++; + lenbyte--; + } + if (lenbyte >= sizeof(size_t)) { + return 0; + } + rlen = 0; + while (lenbyte > 0) { + rlen = (rlen << 8) + input[pos]; + pos++; + lenbyte--; + } + } else { + rlen = lenbyte; + } + if (rlen > inputlen - pos) { + return 0; + } + rpos = pos; + pos += rlen; + + /* Integer tag byte for S */ + if (pos == inputlen || input[pos] != 0x02) { + return 0; + } + pos++; + + /* Integer length for S */ + if (pos == inputlen) { + return 0; + } + lenbyte = input[pos++]; + if (lenbyte & 0x80) { + lenbyte -= 0x80; + if (lenbyte > inputlen - pos) { + return 0; + } + while (lenbyte > 0 && input[pos] == 0) { + pos++; + lenbyte--; + } + if (lenbyte >= sizeof(size_t)) { + return 0; + } + slen = 0; + while (lenbyte > 0) { + slen = (slen << 8) + input[pos]; + pos++; + lenbyte--; + } + } else { + slen = lenbyte; + } + if (slen > inputlen - pos) { + return 0; + } + spos = pos; + + /* Ignore leading zeroes in R */ + while (rlen > 0 && input[rpos] == 0) { + rlen--; + rpos++; + } + /* Copy R value */ + if (rlen > 32) { + overflow = 1; + } else if (rlen) { + memcpy(tmpsig + 32 - rlen, input + rpos, rlen); + } + + /* Ignore leading zeroes in S */ + while (slen > 0 && input[spos] == 0) { + slen--; + spos++; + } + /* Copy S value */ + if (slen > 32) { + overflow = 1; + } else if (slen) { + memcpy(tmpsig + 64 - slen, input + spos, slen); + } + + if (!overflow) { + overflow = !secp256k1_ecdsa_signature_parse_compact(ctx, sig, tmpsig); + } + if (overflow) { + memset(tmpsig, 0, 64); + secp256k1_ecdsa_signature_parse_compact(ctx, sig, tmpsig); + } + return 1; +} + diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/contrib/lax_der_parsing.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/contrib/lax_der_parsing.h new file mode 100644 index 00000000000..37c8c691f2f --- /dev/null +++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/contrib/lax_der_parsing.h @@ -0,0 +1,97 @@ +/*********************************************************************** + * Copyright (c) 2015 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +/**** + * Please do not link this file directly. It is not part of the libsecp256k1 + * project and does not promise any stability in its API, functionality or + * presence. Projects which use this code should instead copy this header + * and its accompanying .c file directly into their codebase. + ****/ + +/* This file defines a function that parses DER with various errors and + * violations. This is not a part of the library itself, because the allowed + * violations are chosen arbitrarily and do not follow or establish any + * standard. + * + * In many places it matters that different implementations do not only accept + * the same set of valid signatures, but also reject the same set of signatures. + * The only means to accomplish that is by strictly obeying a standard, and not + * accepting anything else. + * + * Nonetheless, sometimes there is a need for compatibility with systems that + * use signatures which do not strictly obey DER. The snippet below shows how + * certain violations are easily supported. You may need to adapt it. + * + * Do not use this for new systems. Use well-defined DER or compact signatures + * instead if you have the choice (see secp256k1_ecdsa_signature_parse_der and + * secp256k1_ecdsa_signature_parse_compact). + * + * The supported violations are: + * - All numbers are parsed as nonnegative integers, even though X.609-0207 + * section 8.3.3 specifies that integers are always encoded as two's + * complement. + * - Integers can have length 0, even though section 8.3.1 says they can't. + * - Integers with overly long padding are accepted, violation section + * 8.3.2. + * - 127-byte long length descriptors are accepted, even though section + * 8.1.3.5.c says that they are not. + * - Trailing garbage data inside or after the signature is ignored. + * - The length descriptor of the sequence is ignored. + * + * Compared to for example OpenSSL, many violations are NOT supported: + * - Using overly long tag descriptors for the sequence or integers inside, + * violating section 8.1.2.2. + * - Encoding primitive integers as constructed values, violating section + * 8.3.1. + */ + +#ifndef SECP256K1_CONTRIB_LAX_DER_PARSING_H +#define SECP256K1_CONTRIB_LAX_DER_PARSING_H + +/* #include secp256k1.h only when it hasn't been included yet. + This enables this file to be #included directly in other project + files (such as tests.c) without the need to set an explicit -I flag, + which would be necessary to locate secp256k1.h. */ +#ifndef SECP256K1_H +#include +#endif + +#ifdef __cplusplus +extern "C" { +#endif + +/** Parse a signature in "lax DER" format + * + * Returns: 1 when the signature could be parsed, 0 otherwise. + * Args: ctx: a secp256k1 context object + * Out: sig: pointer to a signature object + * In: input: pointer to the signature to be parsed + * inputlen: the length of the array pointed to be input + * + * This function will accept any valid DER encoded signature, even if the + * encoded numbers are out of range. In addition, it will accept signatures + * which violate the DER spec in various ways. Its purpose is to allow + * validation of the Bitcoin blockchain, which includes non-DER signatures + * from before the network rules were updated to enforce DER. Note that + * the set of supported violations is a strict subset of what OpenSSL will + * accept. + * + * After the call, sig will always be initialized. If parsing failed or the + * encoded numbers are out of range, signature validation with it is + * guaranteed to fail for every message and public key. + */ +int ecdsa_signature_parse_der_lax( + const secp256k1_context* ctx, + secp256k1_ecdsa_signature* sig, + const unsigned char *input, + size_t inputlen +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3); + +#ifdef __cplusplus +} +#endif + +#endif /* SECP256K1_CONTRIB_LAX_DER_PARSING_H */ diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/contrib/lax_der_privatekey_parsing.c b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/contrib/lax_der_privatekey_parsing.c new file mode 100644 index 00000000000..a1b8200079e --- /dev/null +++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/contrib/lax_der_privatekey_parsing.c @@ -0,0 +1,112 @@ +/*********************************************************************** + * Copyright (c) 2014, 2015 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#include + +#include "lax_der_privatekey_parsing.h" + +int ec_privkey_import_der(const secp256k1_context* ctx, unsigned char *out32, const unsigned char *privkey, size_t privkeylen) { + const unsigned char *end = privkey + privkeylen; + int lenb = 0; + int len = 0; + memset(out32, 0, 32); + /* sequence header */ + if (end < privkey+1 || *privkey != 0x30) { + return 0; + } + privkey++; + /* sequence length constructor */ + if (end < privkey+1 || !(*privkey & 0x80)) { + return 0; + } + lenb = *privkey & ~0x80; privkey++; + if (lenb < 1 || lenb > 2) { + return 0; + } + if (end < privkey+lenb) { + return 0; + } + /* sequence length */ + len = privkey[lenb-1] | (lenb > 1 ? privkey[lenb-2] << 8 : 0); + privkey += lenb; + if (end < privkey+len) { + return 0; + } + /* sequence element 0: version number (=1) */ + if (end < privkey+3 || privkey[0] != 0x02 || privkey[1] != 0x01 || privkey[2] != 0x01) { + return 0; + } + privkey += 3; + /* sequence element 1: octet string, up to 32 bytes */ + if (end < privkey+2 || privkey[0] != 0x04 || privkey[1] > 0x20 || end < privkey+2+privkey[1]) { + return 0; + } + if (privkey[1]) memcpy(out32 + 32 - privkey[1], privkey + 2, privkey[1]); + if (!secp256k1_ec_seckey_verify(ctx, out32)) { + memset(out32, 0, 32); + return 0; + } + return 1; +} + +int ec_privkey_export_der(const secp256k1_context *ctx, unsigned char *privkey, size_t *privkeylen, const unsigned char *key32, int compressed) { + secp256k1_pubkey pubkey; + size_t pubkeylen = 0; + if (!secp256k1_ec_pubkey_create(ctx, &pubkey, key32)) { + *privkeylen = 0; + return 0; + } + if (compressed) { + static const unsigned char begin[] = { + 0x30,0x81,0xD3,0x02,0x01,0x01,0x04,0x20 + }; + static const unsigned char middle[] = { + 0xA0,0x81,0x85,0x30,0x81,0x82,0x02,0x01,0x01,0x30,0x2C,0x06,0x07,0x2A,0x86,0x48, + 0xCE,0x3D,0x01,0x01,0x02,0x21,0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF,0xFE,0xFF,0xFF,0xFC,0x2F,0x30,0x06,0x04,0x01,0x00,0x04,0x01,0x07,0x04, + 0x21,0x02,0x79,0xBE,0x66,0x7E,0xF9,0xDC,0xBB,0xAC,0x55,0xA0,0x62,0x95,0xCE,0x87, + 0x0B,0x07,0x02,0x9B,0xFC,0xDB,0x2D,0xCE,0x28,0xD9,0x59,0xF2,0x81,0x5B,0x16,0xF8, + 0x17,0x98,0x02,0x21,0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF,0xFF,0xFF,0xFE,0xBA,0xAE,0xDC,0xE6,0xAF,0x48,0xA0,0x3B,0xBF,0xD2,0x5E, + 0x8C,0xD0,0x36,0x41,0x41,0x02,0x01,0x01,0xA1,0x24,0x03,0x22,0x00 + }; + unsigned char *ptr = privkey; + memcpy(ptr, begin, sizeof(begin)); ptr += sizeof(begin); + memcpy(ptr, key32, 32); ptr += 32; + memcpy(ptr, middle, sizeof(middle)); ptr += sizeof(middle); + pubkeylen = 33; + secp256k1_ec_pubkey_serialize(ctx, ptr, &pubkeylen, &pubkey, SECP256K1_EC_COMPRESSED); + ptr += pubkeylen; + *privkeylen = ptr - privkey; + } else { + static const unsigned char begin[] = { + 0x30,0x82,0x01,0x13,0x02,0x01,0x01,0x04,0x20 + }; + static const unsigned char middle[] = { + 0xA0,0x81,0xA5,0x30,0x81,0xA2,0x02,0x01,0x01,0x30,0x2C,0x06,0x07,0x2A,0x86,0x48, + 0xCE,0x3D,0x01,0x01,0x02,0x21,0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF,0xFE,0xFF,0xFF,0xFC,0x2F,0x30,0x06,0x04,0x01,0x00,0x04,0x01,0x07,0x04, + 0x41,0x04,0x79,0xBE,0x66,0x7E,0xF9,0xDC,0xBB,0xAC,0x55,0xA0,0x62,0x95,0xCE,0x87, + 0x0B,0x07,0x02,0x9B,0xFC,0xDB,0x2D,0xCE,0x28,0xD9,0x59,0xF2,0x81,0x5B,0x16,0xF8, + 0x17,0x98,0x48,0x3A,0xDA,0x77,0x26,0xA3,0xC4,0x65,0x5D,0xA4,0xFB,0xFC,0x0E,0x11, + 0x08,0xA8,0xFD,0x17,0xB4,0x48,0xA6,0x85,0x54,0x19,0x9C,0x47,0xD0,0x8F,0xFB,0x10, + 0xD4,0xB8,0x02,0x21,0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF,0xFF,0xFF,0xFE,0xBA,0xAE,0xDC,0xE6,0xAF,0x48,0xA0,0x3B,0xBF,0xD2,0x5E, + 0x8C,0xD0,0x36,0x41,0x41,0x02,0x01,0x01,0xA1,0x44,0x03,0x42,0x00 + }; + unsigned char *ptr = privkey; + memcpy(ptr, begin, sizeof(begin)); ptr += sizeof(begin); + memcpy(ptr, key32, 32); ptr += 32; + memcpy(ptr, middle, sizeof(middle)); ptr += sizeof(middle); + pubkeylen = 65; + secp256k1_ec_pubkey_serialize(ctx, ptr, &pubkeylen, &pubkey, SECP256K1_EC_UNCOMPRESSED); + ptr += pubkeylen; + *privkeylen = ptr - privkey; + } + return 1; +} diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/contrib/lax_der_privatekey_parsing.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/contrib/lax_der_privatekey_parsing.h new file mode 100644 index 00000000000..3749e418fe3 --- /dev/null +++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/contrib/lax_der_privatekey_parsing.h @@ -0,0 +1,95 @@ +/*********************************************************************** + * Copyright (c) 2014, 2015 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +/**** + * Please do not link this file directly. It is not part of the libsecp256k1 + * project and does not promise any stability in its API, functionality or + * presence. Projects which use this code should instead copy this header + * and its accompanying .c file directly into their codebase. + ****/ + +/* This file contains code snippets that parse DER private keys with + * various errors and violations. This is not a part of the library + * itself, because the allowed violations are chosen arbitrarily and + * do not follow or establish any standard. + * + * It also contains code to serialize private keys in a compatible + * manner. + * + * These functions are meant for compatibility with applications + * that require BER encoded keys. When working with secp256k1-specific + * code, the simple 32-byte private keys normally used by the + * library are sufficient. + */ + +#ifndef SECP256K1_CONTRIB_BER_PRIVATEKEY_H +#define SECP256K1_CONTRIB_BER_PRIVATEKEY_H + +/* #include secp256k1.h only when it hasn't been included yet. + This enables this file to be #included directly in other project + files (such as tests.c) without the need to set an explicit -I flag, + which would be necessary to locate secp256k1.h. */ +#ifndef SECP256K1_H +#include +#endif + +#ifdef __cplusplus +extern "C" { +#endif + +/** Export a private key in DER format. + * + * Returns: 1 if the private key was valid. + * Args: ctx: pointer to a context object (not secp256k1_context_static). + * Out: privkey: pointer to an array for storing the private key in BER. + * Should have space for 279 bytes, and cannot be NULL. + * privkeylen: Pointer to an int where the length of the private key in + * privkey will be stored. + * In: seckey: pointer to a 32-byte secret key to export. + * compressed: 1 if the key should be exported in + * compressed format, 0 otherwise + * + * This function is purely meant for compatibility with applications that + * require BER encoded keys. When working with secp256k1-specific code, the + * simple 32-byte private keys are sufficient. + * + * Note that this function does not guarantee correct DER output. It is + * guaranteed to be parsable by secp256k1_ec_privkey_import_der + */ +SECP256K1_WARN_UNUSED_RESULT int ec_privkey_export_der( + const secp256k1_context* ctx, + unsigned char *privkey, + size_t *privkeylen, + const unsigned char *seckey, + int compressed +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4); + +/** Import a private key in DER format. + * Returns: 1 if a private key was extracted. + * Args: ctx: pointer to a context object (cannot be NULL). + * Out: seckey: pointer to a 32-byte array for storing the private key. + * (cannot be NULL). + * In: privkey: pointer to a private key in DER format (cannot be NULL). + * privkeylen: length of the DER private key pointed to be privkey. + * + * This function will accept more than just strict DER, and even allow some BER + * violations. The public key stored inside the DER-encoded private key is not + * verified for correctness, nor are the curve parameters. Use this function + * only if you know in advance it is supposed to contain a secp256k1 private + * key. + */ +SECP256K1_WARN_UNUSED_RESULT int ec_privkey_import_der( + const secp256k1_context* ctx, + unsigned char *seckey, + const unsigned char *privkey, + size_t privkeylen +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3); + +#ifdef __cplusplus +} +#endif + +#endif /* SECP256K1_CONTRIB_BER_PRIVATEKEY_H */ diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/examples/ecdh.c b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/examples/ecdh.c new file mode 100644 index 00000000000..67b8c2047ab --- /dev/null +++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/examples/ecdh.c @@ -0,0 +1,121 @@ +/************************************************************************* + * Written in 2020-2022 by Elichai Turkel * + * To the extent possible under law, the author(s) have dedicated all * + * copyright and related and neighboring rights to the software in this * + * file to the public domain worldwide. This software is distributed * + * without any warranty. For the CC0 Public Domain Dedication, see * + * EXAMPLES_COPYING or https://creativecommons.org/publicdomain/zero/1.0 * + *************************************************************************/ + +#include +#include +#include +#include + +#include +#include + +#include "examples_util.h" + +int main(void) { + unsigned char seckey1[32]; + unsigned char seckey2[32]; + unsigned char compressed_pubkey1[33]; + unsigned char compressed_pubkey2[33]; + unsigned char shared_secret1[32]; + unsigned char shared_secret2[32]; + unsigned char randomize[32]; + int return_val; + size_t len; + secp256k1_pubkey pubkey1; + secp256k1_pubkey pubkey2; + + /* Before we can call actual API functions, we need to create a "context". */ + secp256k1_context* ctx = secp256k1_context_create(SECP256K1_CONTEXT_NONE); + if (!fill_random(randomize, sizeof(randomize))) { + printf("Failed to generate randomness\n"); + return EXIT_FAILURE; + } + /* Randomizing the context is recommended to protect against side-channel + * leakage See `secp256k1_context_randomize` in secp256k1.h for more + * information about it. This should never fail. */ + return_val = secp256k1_context_randomize(ctx, randomize); + assert(return_val); + + /*** Key Generation ***/ + if (!fill_random(seckey1, sizeof(seckey1)) || !fill_random(seckey2, sizeof(seckey2))) { + printf("Failed to generate randomness\n"); + return EXIT_FAILURE; + } + /* If the secret key is zero or out of range (greater than secp256k1's + * order), we fail. Note that the probability of this occurring is negligible + * with a properly functioning random number generator. */ + if (!secp256k1_ec_seckey_verify(ctx, seckey1) || !secp256k1_ec_seckey_verify(ctx, seckey2)) { + printf("Generated secret key is invalid. This indicates an issue with the random number generator.\n"); + return EXIT_FAILURE; + } + + /* Public key creation using a valid context with a verified secret key should never fail */ + return_val = secp256k1_ec_pubkey_create(ctx, &pubkey1, seckey1); + assert(return_val); + return_val = secp256k1_ec_pubkey_create(ctx, &pubkey2, seckey2); + assert(return_val); + + /* Serialize pubkey1 in a compressed form (33 bytes), should always return 1 */ + len = sizeof(compressed_pubkey1); + return_val = secp256k1_ec_pubkey_serialize(ctx, compressed_pubkey1, &len, &pubkey1, SECP256K1_EC_COMPRESSED); + assert(return_val); + /* Should be the same size as the size of the output, because we passed a 33 byte array. */ + assert(len == sizeof(compressed_pubkey1)); + + /* Serialize pubkey2 in a compressed form (33 bytes) */ + len = sizeof(compressed_pubkey2); + return_val = secp256k1_ec_pubkey_serialize(ctx, compressed_pubkey2, &len, &pubkey2, SECP256K1_EC_COMPRESSED); + assert(return_val); + /* Should be the same size as the size of the output, because we passed a 33 byte array. */ + assert(len == sizeof(compressed_pubkey2)); + + /*** Creating the shared secret ***/ + + /* Perform ECDH with seckey1 and pubkey2. Should never fail with a verified + * seckey and valid pubkey */ + return_val = secp256k1_ecdh(ctx, shared_secret1, &pubkey2, seckey1, NULL, NULL); + assert(return_val); + + /* Perform ECDH with seckey2 and pubkey1. Should never fail with a verified + * seckey and valid pubkey */ + return_val = secp256k1_ecdh(ctx, shared_secret2, &pubkey1, seckey2, NULL, NULL); + assert(return_val); + + /* Both parties should end up with the same shared secret */ + return_val = memcmp(shared_secret1, shared_secret2, sizeof(shared_secret1)); + assert(return_val == 0); + + printf("Secret Key1: "); + print_hex(seckey1, sizeof(seckey1)); + printf("Compressed Pubkey1: "); + print_hex(compressed_pubkey1, sizeof(compressed_pubkey1)); + printf("\nSecret Key2: "); + print_hex(seckey2, sizeof(seckey2)); + printf("Compressed Pubkey2: "); + print_hex(compressed_pubkey2, sizeof(compressed_pubkey2)); + printf("\nShared Secret: "); + print_hex(shared_secret1, sizeof(shared_secret1)); + + /* This will clear everything from the context and free the memory */ + secp256k1_context_destroy(ctx); + + /* It's best practice to try to clear secrets from memory after using them. + * This is done because some bugs can allow an attacker to leak memory, for + * example through "out of bounds" array access (see Heartbleed), or the OS + * swapping them to disk. Hence, we overwrite the secret key buffer with zeros. + * + * Here we are preventing these writes from being optimized out, as any good compiler + * will remove any writes that aren't used. */ + secure_erase(seckey1, sizeof(seckey1)); + secure_erase(seckey2, sizeof(seckey2)); + secure_erase(shared_secret1, sizeof(shared_secret1)); + secure_erase(shared_secret2, sizeof(shared_secret2)); + + return EXIT_SUCCESS; +} diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/examples/ecdsa.c b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/examples/ecdsa.c new file mode 100644 index 00000000000..ae16c180dc9 --- /dev/null +++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/examples/ecdsa.c @@ -0,0 +1,138 @@ +/************************************************************************* + * Written in 2020-2022 by Elichai Turkel * + * To the extent possible under law, the author(s) have dedicated all * + * copyright and related and neighboring rights to the software in this * + * file to the public domain worldwide. This software is distributed * + * without any warranty. For the CC0 Public Domain Dedication, see * + * EXAMPLES_COPYING or https://creativecommons.org/publicdomain/zero/1.0 * + *************************************************************************/ + +#include +#include +#include +#include + +#include + +#include "examples_util.h" + +int main(void) { + /* Instead of signing the message directly, we must sign a 32-byte hash. + * Here the message is "Hello, world!" and the hash function was SHA-256. + * An actual implementation should just call SHA-256, but this example + * hardcodes the output to avoid depending on an additional library. + * See https://bitcoin.stackexchange.com/questions/81115/if-someone-wanted-to-pretend-to-be-satoshi-by-posting-a-fake-signature-to-defrau/81116#81116 */ + unsigned char msg_hash[32] = { + 0x31, 0x5F, 0x5B, 0xDB, 0x76, 0xD0, 0x78, 0xC4, + 0x3B, 0x8A, 0xC0, 0x06, 0x4E, 0x4A, 0x01, 0x64, + 0x61, 0x2B, 0x1F, 0xCE, 0x77, 0xC8, 0x69, 0x34, + 0x5B, 0xFC, 0x94, 0xC7, 0x58, 0x94, 0xED, 0xD3, + }; + unsigned char seckey[32]; + unsigned char randomize[32]; + unsigned char compressed_pubkey[33]; + unsigned char serialized_signature[64]; + size_t len; + int is_signature_valid, is_signature_valid2; + int return_val; + secp256k1_pubkey pubkey; + secp256k1_ecdsa_signature sig; + /* Before we can call actual API functions, we need to create a "context". */ + secp256k1_context* ctx = secp256k1_context_create(SECP256K1_CONTEXT_NONE); + if (!fill_random(randomize, sizeof(randomize))) { + printf("Failed to generate randomness\n"); + return EXIT_FAILURE; + } + /* Randomizing the context is recommended to protect against side-channel + * leakage See `secp256k1_context_randomize` in secp256k1.h for more + * information about it. This should never fail. */ + return_val = secp256k1_context_randomize(ctx, randomize); + assert(return_val); + + /*** Key Generation ***/ + if (!fill_random(seckey, sizeof(seckey))) { + printf("Failed to generate randomness\n"); + return EXIT_FAILURE; + } + /* If the secret key is zero or out of range (greater than secp256k1's + * order), we fail. Note that the probability of this occurring is negligible + * with a properly functioning random number generator. */ + if (!secp256k1_ec_seckey_verify(ctx, seckey)) { + printf("Generated secret key is invalid. This indicates an issue with the random number generator.\n"); + return EXIT_FAILURE; + } + + /* Public key creation using a valid context with a verified secret key should never fail */ + return_val = secp256k1_ec_pubkey_create(ctx, &pubkey, seckey); + assert(return_val); + + /* Serialize the pubkey in a compressed form(33 bytes). Should always return 1. */ + len = sizeof(compressed_pubkey); + return_val = secp256k1_ec_pubkey_serialize(ctx, compressed_pubkey, &len, &pubkey, SECP256K1_EC_COMPRESSED); + assert(return_val); + /* Should be the same size as the size of the output, because we passed a 33 byte array. */ + assert(len == sizeof(compressed_pubkey)); + + /*** Signing ***/ + + /* Generate an ECDSA signature `noncefp` and `ndata` allows you to pass a + * custom nonce function, passing `NULL` will use the RFC-6979 safe default. + * Signing with a valid context, verified secret key + * and the default nonce function should never fail. */ + return_val = secp256k1_ecdsa_sign(ctx, &sig, msg_hash, seckey, NULL, NULL); + assert(return_val); + + /* Serialize the signature in a compact form. Should always return 1 + * according to the documentation in secp256k1.h. */ + return_val = secp256k1_ecdsa_signature_serialize_compact(ctx, serialized_signature, &sig); + assert(return_val); + + + /*** Verification ***/ + + /* Deserialize the signature. This will return 0 if the signature can't be parsed correctly. */ + if (!secp256k1_ecdsa_signature_parse_compact(ctx, &sig, serialized_signature)) { + printf("Failed parsing the signature\n"); + return EXIT_FAILURE; + } + + /* Deserialize the public key. This will return 0 if the public key can't be parsed correctly. */ + if (!secp256k1_ec_pubkey_parse(ctx, &pubkey, compressed_pubkey, sizeof(compressed_pubkey))) { + printf("Failed parsing the public key\n"); + return EXIT_FAILURE; + } + + /* Verify a signature. This will return 1 if it's valid and 0 if it's not. */ + is_signature_valid = secp256k1_ecdsa_verify(ctx, &sig, msg_hash, &pubkey); + + printf("Is the signature valid? %s\n", is_signature_valid ? "true" : "false"); + printf("Secret Key: "); + print_hex(seckey, sizeof(seckey)); + printf("Public Key: "); + print_hex(compressed_pubkey, sizeof(compressed_pubkey)); + printf("Signature: "); + print_hex(serialized_signature, sizeof(serialized_signature)); + + /* This will clear everything from the context and free the memory */ + secp256k1_context_destroy(ctx); + + /* Bonus example: if all we need is signature verification (and no key + generation or signing), we don't need to use a context created via + secp256k1_context_create(). We can simply use the static (i.e., global) + context secp256k1_context_static. See its description in + include/secp256k1.h for details. */ + is_signature_valid2 = secp256k1_ecdsa_verify(secp256k1_context_static, + &sig, msg_hash, &pubkey); + assert(is_signature_valid2 == is_signature_valid); + + /* It's best practice to try to clear secrets from memory after using them. + * This is done because some bugs can allow an attacker to leak memory, for + * example through "out of bounds" array access (see Heartbleed), or the OS + * swapping them to disk. Hence, we overwrite the secret key buffer with zeros. + * + * Here we are preventing these writes from being optimized out, as any good compiler + * will remove any writes that aren't used. */ + secure_erase(seckey, sizeof(seckey)); + + return EXIT_SUCCESS; +} diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/examples/ellswift.c b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/examples/ellswift.c new file mode 100644 index 00000000000..d58e96b053d --- /dev/null +++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/examples/ellswift.c @@ -0,0 +1,122 @@ +/************************************************************************* + * Written in 2024 by Sebastian Falbesoner * + * To the extent possible under law, the author(s) have dedicated all * + * copyright and related and neighboring rights to the software in this * + * file to the public domain worldwide. This software is distributed * + * without any warranty. For the CC0 Public Domain Dedication, see * + * EXAMPLES_COPYING or https://creativecommons.org/publicdomain/zero/1.0 * + *************************************************************************/ + +/** This file demonstrates how to use the ElligatorSwift module to perform + * a key exchange according to BIP 324. Additionally, see the documentation + * in include/secp256k1_ellswift.h and doc/ellswift.md. + */ + +#include +#include +#include +#include + +#include +#include + +#include "examples_util.h" + +int main(void) { + secp256k1_context* ctx; + unsigned char randomize[32]; + unsigned char auxrand1[32]; + unsigned char auxrand2[32]; + unsigned char seckey1[32]; + unsigned char seckey2[32]; + unsigned char ellswift_pubkey1[64]; + unsigned char ellswift_pubkey2[64]; + unsigned char shared_secret1[32]; + unsigned char shared_secret2[32]; + int return_val; + + /* Create a secp256k1 context */ + ctx = secp256k1_context_create(SECP256K1_CONTEXT_NONE); + if (!fill_random(randomize, sizeof(randomize))) { + printf("Failed to generate randomness\n"); + return EXIT_FAILURE; + } + /* Randomizing the context is recommended to protect against side-channel + * leakage. See `secp256k1_context_randomize` in secp256k1.h for more + * information about it. This should never fail. */ + return_val = secp256k1_context_randomize(ctx, randomize); + assert(return_val); + + /*** Generate secret keys ***/ + if (!fill_random(seckey1, sizeof(seckey1)) || !fill_random(seckey2, sizeof(seckey2))) { + printf("Failed to generate randomness\n"); + return EXIT_FAILURE; + } + /* If the secret key is zero or out of range (greater than secp256k1's + * order), we fail. Note that the probability of this occurring is negligible + * with a properly functioning random number generator. */ + if (!secp256k1_ec_seckey_verify(ctx, seckey1) || !secp256k1_ec_seckey_verify(ctx, seckey2)) { + printf("Generated secret key is invalid. This indicates an issue with the random number generator.\n"); + return EXIT_FAILURE; + } + + /* Generate ElligatorSwift public keys. This should never fail with valid context and + verified secret keys. Note that providing additional randomness (fourth parameter) is + optional, but recommended. */ + if (!fill_random(auxrand1, sizeof(auxrand1)) || !fill_random(auxrand2, sizeof(auxrand2))) { + printf("Failed to generate randomness\n"); + return EXIT_FAILURE; + } + return_val = secp256k1_ellswift_create(ctx, ellswift_pubkey1, seckey1, auxrand1); + assert(return_val); + return_val = secp256k1_ellswift_create(ctx, ellswift_pubkey2, seckey2, auxrand2); + assert(return_val); + + /*** Create the shared secret on each side ***/ + + /* Perform x-only ECDH with seckey1 and ellswift_pubkey2. Should never fail + * with a verified seckey and valid pubkey. Note that both parties pass both + * EllSwift pubkeys in the same order; the pubkey of the calling party is + * determined by the "party" boolean (sixth parameter). */ + return_val = secp256k1_ellswift_xdh(ctx, shared_secret1, ellswift_pubkey1, ellswift_pubkey2, + seckey1, 0, secp256k1_ellswift_xdh_hash_function_bip324, NULL); + assert(return_val); + + /* Perform x-only ECDH with seckey2 and ellswift_pubkey1. Should never fail + * with a verified seckey and valid pubkey. */ + return_val = secp256k1_ellswift_xdh(ctx, shared_secret2, ellswift_pubkey1, ellswift_pubkey2, + seckey2, 1, secp256k1_ellswift_xdh_hash_function_bip324, NULL); + assert(return_val); + + /* Both parties should end up with the same shared secret */ + return_val = memcmp(shared_secret1, shared_secret2, sizeof(shared_secret1)); + assert(return_val == 0); + + printf( " Secret Key1: "); + print_hex(seckey1, sizeof(seckey1)); + printf( "EllSwift Pubkey1: "); + print_hex(ellswift_pubkey1, sizeof(ellswift_pubkey1)); + printf("\n Secret Key2: "); + print_hex(seckey2, sizeof(seckey2)); + printf( "EllSwift Pubkey2: "); + print_hex(ellswift_pubkey2, sizeof(ellswift_pubkey2)); + printf("\n Shared Secret: "); + print_hex(shared_secret1, sizeof(shared_secret1)); + + /* This will clear everything from the context and free the memory */ + secp256k1_context_destroy(ctx); + + /* It's best practice to try to clear secrets from memory after using them. + * This is done because some bugs can allow an attacker to leak memory, for + * example through "out of bounds" array access (see Heartbleed), or the OS + * swapping them to disk. Hence, we overwrite the secret key buffer with zeros. + * + * Here we are preventing these writes from being optimized out, as any good compiler + * will remove any writes that aren't used. */ + secure_erase(seckey1, sizeof(seckey1)); + secure_erase(seckey2, sizeof(seckey2)); + secure_erase(shared_secret1, sizeof(shared_secret1)); + secure_erase(shared_secret2, sizeof(shared_secret2)); + + return EXIT_SUCCESS; +} diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/examples/examples_util.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/examples/examples_util.h new file mode 100644 index 00000000000..3293b640321 --- /dev/null +++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/examples/examples_util.h @@ -0,0 +1,108 @@ +/************************************************************************* + * Copyright (c) 2020-2021 Elichai Turkel * + * Distributed under the CC0 software license, see the accompanying file * + * EXAMPLES_COPYING or https://creativecommons.org/publicdomain/zero/1.0 * + *************************************************************************/ + +/* + * This file is an attempt at collecting best practice methods for obtaining randomness with different operating systems. + * It may be out-of-date. Consult the documentation of the operating system before considering to use the methods below. + * + * Platform randomness sources: + * Linux -> `getrandom(2)`(`sys/random.h`), if not available `/dev/urandom` should be used. http://man7.org/linux/man-pages/man2/getrandom.2.html, https://linux.die.net/man/4/urandom + * macOS -> `getentropy(2)`(`sys/random.h`), if not available `/dev/urandom` should be used. https://www.unix.com/man-page/mojave/2/getentropy, https://opensource.apple.com/source/xnu/xnu-517.12.7/bsd/man/man4/random.4.auto.html + * FreeBSD -> `getrandom(2)`(`sys/random.h`), if not available `kern.arandom` should be used. https://www.freebsd.org/cgi/man.cgi?query=getrandom, https://www.freebsd.org/cgi/man.cgi?query=random&sektion=4 + * OpenBSD -> `getentropy(2)`(`unistd.h`), if not available `/dev/urandom` should be used. https://man.openbsd.org/getentropy, https://man.openbsd.org/urandom + * Windows -> `BCryptGenRandom`(`bcrypt.h`). https://docs.microsoft.com/en-us/windows/win32/api/bcrypt/nf-bcrypt-bcryptgenrandom + */ + +#if defined(_WIN32) +/* + * The defined WIN32_NO_STATUS macro disables return code definitions in + * windows.h, which avoids "macro redefinition" MSVC warnings in ntstatus.h. + */ +#define WIN32_NO_STATUS +#include +#undef WIN32_NO_STATUS +#include +#include +#elif defined(__linux__) || defined(__APPLE__) || defined(__FreeBSD__) +#include +#elif defined(__OpenBSD__) +#include +#else +#error "Couldn't identify the OS" +#endif + +#include +#include +#include + + +/* Returns 1 on success, and 0 on failure. */ +static int fill_random(unsigned char* data, size_t size) { +#if defined(_WIN32) + NTSTATUS res = BCryptGenRandom(NULL, data, size, BCRYPT_USE_SYSTEM_PREFERRED_RNG); + if (res != STATUS_SUCCESS || size > ULONG_MAX) { + return 0; + } else { + return 1; + } +#elif defined(__linux__) || defined(__FreeBSD__) + /* If `getrandom(2)` is not available you should fallback to /dev/urandom */ + ssize_t res = getrandom(data, size, 0); + if (res < 0 || (size_t)res != size ) { + return 0; + } else { + return 1; + } +#elif defined(__APPLE__) || defined(__OpenBSD__) + /* If `getentropy(2)` is not available you should fallback to either + * `SecRandomCopyBytes` or /dev/urandom */ + int res = getentropy(data, size); + if (res == 0) { + return 1; + } else { + return 0; + } +#endif + return 0; +} + +static void print_hex(unsigned char* data, size_t size) { + size_t i; + printf("0x"); + for (i = 0; i < size; i++) { + printf("%02x", data[i]); + } + printf("\n"); +} + +#if defined(_MSC_VER) +// For SecureZeroMemory +#include +#endif +/* Cleanses memory to prevent leaking sensitive info. Won't be optimized out. */ +static void secure_erase(void *ptr, size_t len) { +#if defined(_MSC_VER) + /* SecureZeroMemory is guaranteed not to be optimized out by MSVC. */ + SecureZeroMemory(ptr, len); +#elif defined(__GNUC__) + /* We use a memory barrier that scares the compiler away from optimizing out the memset. + * + * Quoting Adam Langley in commit ad1907fe73334d6c696c8539646c21b11178f20f + * in BoringSSL (ISC License): + * As best as we can tell, this is sufficient to break any optimisations that + * might try to eliminate "superfluous" memsets. + * This method used in memzero_explicit() the Linux kernel, too. Its advantage is that it is + * pretty efficient, because the compiler can still implement the memset() efficiently, + * just not remove it entirely. See "Dead Store Elimination (Still) Considered Harmful" by + * Yang et al. (USENIX Security 2017) for more background. + */ + memset(ptr, 0, len); + __asm__ __volatile__("" : : "r"(ptr) : "memory"); +#else + void *(*volatile const volatile_memset)(void *, int, size_t) = memset; + volatile_memset(ptr, 0, len); +#endif +} diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/examples/musig.c b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/examples/musig.c new file mode 100644 index 00000000000..bdb8fced0cf --- /dev/null +++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/examples/musig.c @@ -0,0 +1,261 @@ +/************************************************************************* + * To the extent possible under law, the author(s) have dedicated all * + * copyright and related and neighboring rights to the software in this * + * file to the public domain worldwide. This software is distributed * + * without any warranty. For the CC0 Public Domain Dedication, see * + * EXAMPLES_COPYING or https://creativecommons.org/publicdomain/zero/1.0 * + *************************************************************************/ + +/** This file demonstrates how to use the MuSig module to create a + * 3-of-3 multisignature. Additionally, see the documentation in + * include/secp256k1_musig.h and doc/musig.md. + */ + +#include +#include +#include +#include + +#include +#include +#include +#include + +#include "examples_util.h" + +struct signer_secrets { + secp256k1_keypair keypair; + secp256k1_musig_secnonce secnonce; +}; + +struct signer { + secp256k1_pubkey pubkey; + secp256k1_musig_pubnonce pubnonce; + secp256k1_musig_partial_sig partial_sig; +}; + + /* Number of public keys involved in creating the aggregate signature */ +#define N_SIGNERS 3 +/* Create a key pair, store it in signer_secrets->keypair and signer->pubkey */ +static int create_keypair(const secp256k1_context* ctx, struct signer_secrets *signer_secrets, struct signer *signer) { + unsigned char seckey[32]; + + if (!fill_random(seckey, sizeof(seckey))) { + printf("Failed to generate randomness\n"); + return 0; + } + /* Try to create a keypair with a valid context. This only fails if the + * secret key is zero or out of range (greater than secp256k1's order). Note + * that the probability of this occurring is negligible with a properly + * functioning random number generator. */ + if (!secp256k1_keypair_create(ctx, &signer_secrets->keypair, seckey)) { + return 0; + } + if (!secp256k1_keypair_pub(ctx, &signer->pubkey, &signer_secrets->keypair)) { + return 0; + } + + secure_erase(seckey, sizeof(seckey)); + return 1; +} + +/* Tweak the pubkey corresponding to the provided keyagg cache, update the cache + * and return the tweaked aggregate pk. */ +static int tweak(const secp256k1_context* ctx, secp256k1_xonly_pubkey *agg_pk, secp256k1_musig_keyagg_cache *cache) { + secp256k1_pubkey output_pk; + /* For BIP 32 tweaking the plain_tweak is set to a hash as defined in BIP + * 32. */ + unsigned char plain_tweak[32] = "this could be a BIP32 tweak...."; + /* For Taproot tweaking the xonly_tweak is set to the TapTweak hash as + * defined in BIP 341 */ + unsigned char xonly_tweak[32] = "this could be a Taproot tweak.."; + + + /* Plain tweaking which, for example, allows deriving multiple child + * public keys from a single aggregate key using BIP32 */ + if (!secp256k1_musig_pubkey_ec_tweak_add(ctx, NULL, cache, plain_tweak)) { + return 0; + } + /* Note that we did not provide an output_pk argument, because the + * resulting pk is also saved in the cache and so if one is just interested + * in signing, the output_pk argument is unnecessary. On the other hand, if + * one is not interested in signing, the same output_pk can be obtained by + * calling `secp256k1_musig_pubkey_get` right after key aggregation to get + * the full pubkey and then call `secp256k1_ec_pubkey_tweak_add`. */ + + /* Xonly tweaking which, for example, allows creating Taproot commitments */ + if (!secp256k1_musig_pubkey_xonly_tweak_add(ctx, &output_pk, cache, xonly_tweak)) { + return 0; + } + /* Note that if we wouldn't care about signing, we can arrive at the same + * output_pk by providing the untweaked public key to + * `secp256k1_xonly_pubkey_tweak_add` (after converting it to an xonly pubkey + * if necessary with `secp256k1_xonly_pubkey_from_pubkey`). */ + + /* Now we convert the output_pk to an xonly pubkey to allow to later verify + * the Schnorr signature against it. For this purpose we can ignore the + * `pk_parity` output argument; we would need it if we would have to open + * the Taproot commitment. */ + if (!secp256k1_xonly_pubkey_from_pubkey(ctx, agg_pk, NULL, &output_pk)) { + return 0; + } + return 1; +} + +/* Sign a message hash with the given key pairs and store the result in sig */ +static int sign(const secp256k1_context* ctx, struct signer_secrets *signer_secrets, struct signer *signer, const secp256k1_musig_keyagg_cache *cache, const unsigned char *msg32, unsigned char *sig64) { + int i; + const secp256k1_musig_pubnonce *pubnonces[N_SIGNERS]; + const secp256k1_musig_partial_sig *partial_sigs[N_SIGNERS]; + /* The same for all signers */ + secp256k1_musig_session session; + secp256k1_musig_aggnonce agg_pubnonce; + + for (i = 0; i < N_SIGNERS; i++) { + unsigned char seckey[32]; + unsigned char session_secrand[32]; + /* Create random session ID. It is absolutely necessary that the session ID + * is unique for every call of secp256k1_musig_nonce_gen. Otherwise + * it's trivial for an attacker to extract the secret key! */ + if (!fill_random(session_secrand, sizeof(session_secrand))) { + return 0; + } + if (!secp256k1_keypair_sec(ctx, seckey, &signer_secrets[i].keypair)) { + return 0; + } + /* Initialize session and create secret nonce for signing and public + * nonce to send to the other signers. */ + if (!secp256k1_musig_nonce_gen(ctx, &signer_secrets[i].secnonce, &signer[i].pubnonce, session_secrand, seckey, &signer[i].pubkey, msg32, NULL, NULL)) { + return 0; + } + pubnonces[i] = &signer[i].pubnonce; + + secure_erase(seckey, sizeof(seckey)); + } + + /* Communication round 1: Every signer sends their pubnonce to the + * coordinator. The coordinator runs secp256k1_musig_nonce_agg and sends + * agg_pubnonce to each signer */ + if (!secp256k1_musig_nonce_agg(ctx, &agg_pubnonce, pubnonces, N_SIGNERS)) { + return 0; + } + + /* Every signer creates a partial signature */ + for (i = 0; i < N_SIGNERS; i++) { + /* Initialize the signing session by processing the aggregate nonce */ + if (!secp256k1_musig_nonce_process(ctx, &session, &agg_pubnonce, msg32, cache)) { + return 0; + } + /* partial_sign will clear the secnonce by setting it to 0. That's because + * you must _never_ reuse the secnonce (or use the same session_secrand to + * create a secnonce). If you do, you effectively reuse the nonce and + * leak the secret key. */ + if (!secp256k1_musig_partial_sign(ctx, &signer[i].partial_sig, &signer_secrets[i].secnonce, &signer_secrets[i].keypair, cache, &session)) { + return 0; + } + partial_sigs[i] = &signer[i].partial_sig; + } + /* Communication round 2: Every signer sends their partial signature to the + * coordinator, who verifies the partial signatures and aggregates them. */ + for (i = 0; i < N_SIGNERS; i++) { + /* To check whether signing was successful, it suffices to either verify + * the aggregate signature with the aggregate public key using + * secp256k1_schnorrsig_verify, or verify all partial signatures of all + * signers individually. Verifying the aggregate signature is cheaper but + * verifying the individual partial signatures has the advantage that it + * can be used to determine which of the partial signatures are invalid + * (if any), i.e., which of the partial signatures cause the aggregate + * signature to be invalid and thus the protocol run to fail. It's also + * fine to first verify the aggregate sig, and only verify the individual + * sigs if it does not work. + */ + if (!secp256k1_musig_partial_sig_verify(ctx, &signer[i].partial_sig, &signer[i].pubnonce, &signer[i].pubkey, cache, &session)) { + return 0; + } + } + return secp256k1_musig_partial_sig_agg(ctx, sig64, &session, partial_sigs, N_SIGNERS); +} + +int main(void) { + secp256k1_context* ctx; + int i; + struct signer_secrets signer_secrets[N_SIGNERS]; + struct signer signers[N_SIGNERS]; + const secp256k1_pubkey *pubkeys_ptr[N_SIGNERS]; + secp256k1_xonly_pubkey agg_pk; + secp256k1_musig_keyagg_cache cache; + unsigned char msg[32] = "this_could_be_the_hash_of_a_msg"; + unsigned char sig[64]; + + /* Create a secp256k1 context */ + ctx = secp256k1_context_create(SECP256K1_CONTEXT_NONE); + printf("Creating key pairs......"); + fflush(stdout); + for (i = 0; i < N_SIGNERS; i++) { + if (!create_keypair(ctx, &signer_secrets[i], &signers[i])) { + printf("FAILED\n"); + return EXIT_FAILURE; + } + pubkeys_ptr[i] = &signers[i].pubkey; + } + printf("ok\n"); + + /* The aggregate public key produced by secp256k1_musig_pubkey_agg depends + * on the order of the provided public keys. If there is no canonical order + * of the signers, the individual public keys can optionally be sorted with + * secp256k1_ec_pubkey_sort to ensure that the aggregate public key is + * independent of the order of signers. */ + printf("Sorting public keys....."); + fflush(stdout); + if (!secp256k1_ec_pubkey_sort(ctx, pubkeys_ptr, N_SIGNERS)) { + printf("FAILED\n"); + return EXIT_FAILURE; + } + printf("ok\n"); + + printf("Combining public keys..."); + fflush(stdout); + /* If you just want to aggregate and not sign, you can call + * secp256k1_musig_pubkey_agg with the keyagg_cache argument set to NULL + * while providing a non-NULL agg_pk argument. */ + if (!secp256k1_musig_pubkey_agg(ctx, NULL, &cache, pubkeys_ptr, N_SIGNERS)) { + printf("FAILED\n"); + return EXIT_FAILURE; + } + printf("ok\n"); + printf("Tweaking................"); + fflush(stdout); + /* Optionally tweak the aggregate key */ + if (!tweak(ctx, &agg_pk, &cache)) { + printf("FAILED\n"); + return EXIT_FAILURE; + } + printf("ok\n"); + printf("Signing message........."); + fflush(stdout); + if (!sign(ctx, signer_secrets, signers, &cache, msg, sig)) { + printf("FAILED\n"); + return EXIT_FAILURE; + } + printf("ok\n"); + printf("Verifying signature....."); + fflush(stdout); + if (!secp256k1_schnorrsig_verify(ctx, sig, msg, 32, &agg_pk)) { + printf("FAILED\n"); + return EXIT_FAILURE; + } + printf("ok\n"); + + /* It's best practice to try to clear secrets from memory after using them. + * This is done because some bugs can allow an attacker to leak memory, for + * example through "out of bounds" array access (see Heartbleed), or the OS + * swapping them to disk. Hence, we overwrite secret key material with zeros. + * + * Here we are preventing these writes from being optimized out, as any good compiler + * will remove any writes that aren't used. */ + for (i = 0; i < N_SIGNERS; i++) { + secure_erase(&signer_secrets[i], sizeof(signer_secrets[i])); + } + secp256k1_context_destroy(ctx); + return EXIT_SUCCESS; +} diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/examples/schnorr.c b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/examples/schnorr.c new file mode 100644 index 00000000000..49baed24beb --- /dev/null +++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/examples/schnorr.c @@ -0,0 +1,154 @@ +/************************************************************************* + * Written in 2020-2022 by Elichai Turkel * + * To the extent possible under law, the author(s) have dedicated all * + * copyright and related and neighboring rights to the software in this * + * file to the public domain worldwide. This software is distributed * + * without any warranty. For the CC0 Public Domain Dedication, see * + * EXAMPLES_COPYING or https://creativecommons.org/publicdomain/zero/1.0 * + *************************************************************************/ + +#include +#include +#include +#include + +#include +#include +#include + +#include "examples_util.h" + +int main(void) { + unsigned char msg[] = {'H', 'e', 'l', 'l', 'o', ' ', 'W', 'o', 'r', 'l', 'd', '!'}; + unsigned char msg_hash[32]; + unsigned char tag[] = {'m', 'y', '_', 'f', 'a', 'n', 'c', 'y', '_', 'p', 'r', 'o', 't', 'o', 'c', 'o', 'l'}; + unsigned char seckey[32]; + unsigned char randomize[32]; + unsigned char auxiliary_rand[32]; + unsigned char serialized_pubkey[32]; + unsigned char signature[64]; + int is_signature_valid, is_signature_valid2; + int return_val; + secp256k1_xonly_pubkey pubkey; + secp256k1_keypair keypair; + /* Before we can call actual API functions, we need to create a "context". */ + secp256k1_context* ctx = secp256k1_context_create(SECP256K1_CONTEXT_NONE); + if (!fill_random(randomize, sizeof(randomize))) { + printf("Failed to generate randomness\n"); + return EXIT_FAILURE; + } + /* Randomizing the context is recommended to protect against side-channel + * leakage See `secp256k1_context_randomize` in secp256k1.h for more + * information about it. This should never fail. */ + return_val = secp256k1_context_randomize(ctx, randomize); + assert(return_val); + + /*** Key Generation ***/ + if (!fill_random(seckey, sizeof(seckey))) { + printf("Failed to generate randomness\n"); + return EXIT_FAILURE; + } + /* Try to create a keypair with a valid context. This only fails if the + * secret key is zero or out of range (greater than secp256k1's order). Note + * that the probability of this occurring is negligible with a properly + * functioning random number generator. */ + if (!secp256k1_keypair_create(ctx, &keypair, seckey)) { + printf("Generated secret key is invalid. This indicates an issue with the random number generator.\n"); + return EXIT_FAILURE; + } + + /* Extract the X-only public key from the keypair. We pass NULL for + * `pk_parity` as the parity isn't needed for signing or verification. + * `secp256k1_keypair_xonly_pub` supports returning the parity for + * other use cases such as tests or verifying Taproot tweaks. + * This should never fail with a valid context and public key. */ + return_val = secp256k1_keypair_xonly_pub(ctx, &pubkey, NULL, &keypair); + assert(return_val); + + /* Serialize the public key. Should always return 1 for a valid public key. */ + return_val = secp256k1_xonly_pubkey_serialize(ctx, serialized_pubkey, &pubkey); + assert(return_val); + + /*** Signing ***/ + + /* Instead of signing (possibly very long) messages directly, we sign a + * 32-byte hash of the message in this example. + * + * We use secp256k1_tagged_sha256 to create this hash. This function expects + * a context-specific "tag", which restricts the context in which the signed + * messages should be considered valid. For example, if protocol A mandates + * to use the tag "my_fancy_protocol" and protocol B mandates to use the tag + * "my_boring_protocol", then signed messages from protocol A will never be + * valid in protocol B (and vice versa), even if keys are reused across + * protocols. This implements "domain separation", which is considered good + * practice. It avoids attacks in which users are tricked into signing a + * message that has intended consequences in the intended context (e.g., + * protocol A) but would have unintended consequences if it were valid in + * some other context (e.g., protocol B). */ + return_val = secp256k1_tagged_sha256(ctx, msg_hash, tag, sizeof(tag), msg, sizeof(msg)); + assert(return_val); + + /* Generate 32 bytes of randomness to use with BIP-340 schnorr signing. */ + if (!fill_random(auxiliary_rand, sizeof(auxiliary_rand))) { + printf("Failed to generate randomness\n"); + return EXIT_FAILURE; + } + + /* Generate a Schnorr signature. + * + * We use the secp256k1_schnorrsig_sign32 function that provides a simple + * interface for signing 32-byte messages (which in our case is a hash of + * the actual message). BIP-340 recommends passing 32 bytes of randomness + * to the signing function to improve security against side-channel attacks. + * Signing with a valid context, a 32-byte message, a verified keypair, and + * any 32 bytes of auxiliary random data should never fail. */ + return_val = secp256k1_schnorrsig_sign32(ctx, signature, msg_hash, &keypair, auxiliary_rand); + assert(return_val); + + /*** Verification ***/ + + /* Deserialize the public key. This will return 0 if the public key can't + * be parsed correctly */ + if (!secp256k1_xonly_pubkey_parse(ctx, &pubkey, serialized_pubkey)) { + printf("Failed parsing the public key\n"); + return EXIT_FAILURE; + } + + /* Compute the tagged hash on the received messages using the same tag as the signer. */ + return_val = secp256k1_tagged_sha256(ctx, msg_hash, tag, sizeof(tag), msg, sizeof(msg)); + assert(return_val); + + /* Verify a signature. This will return 1 if it's valid and 0 if it's not. */ + is_signature_valid = secp256k1_schnorrsig_verify(ctx, signature, msg_hash, 32, &pubkey); + + + printf("Is the signature valid? %s\n", is_signature_valid ? "true" : "false"); + printf("Secret Key: "); + print_hex(seckey, sizeof(seckey)); + printf("Public Key: "); + print_hex(serialized_pubkey, sizeof(serialized_pubkey)); + printf("Signature: "); + print_hex(signature, sizeof(signature)); + + /* This will clear everything from the context and free the memory */ + secp256k1_context_destroy(ctx); + + /* Bonus example: if all we need is signature verification (and no key + generation or signing), we don't need to use a context created via + secp256k1_context_create(). We can simply use the static (i.e., global) + context secp256k1_context_static. See its description in + include/secp256k1.h for details. */ + is_signature_valid2 = secp256k1_schnorrsig_verify(secp256k1_context_static, + signature, msg_hash, 32, &pubkey); + assert(is_signature_valid2 == is_signature_valid); + + /* It's best practice to try to clear secrets from memory after using them. + * This is done because some bugs can allow an attacker to leak memory, for + * example through "out of bounds" array access (see Heartbleed), or the OS + * swapping them to disk. Hence, we overwrite the secret key buffer with zeros. + * + * Here we are preventing these writes from being optimized out, as any good compiler + * will remove any writes that aren't used. */ + secure_erase(seckey, sizeof(seckey)); + return EXIT_SUCCESS; +} diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/ecdh/bench_impl.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/ecdh/bench_impl.h new file mode 100644 index 00000000000..c23aaa94d17 --- /dev/null +++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/ecdh/bench_impl.h @@ -0,0 +1,57 @@ +/*********************************************************************** + * Copyright (c) 2015 Pieter Wuille, Andrew Poelstra * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_MODULE_ECDH_BENCH_H +#define SECP256K1_MODULE_ECDH_BENCH_H + +#include "../../../include/secp256k1_ecdh.h" + +typedef struct { + secp256k1_context *ctx; + secp256k1_pubkey point; + unsigned char scalar[32]; +} bench_ecdh_data; + +static void bench_ecdh_setup(void* arg) { + int i; + bench_ecdh_data *data = (bench_ecdh_data*)arg; + const unsigned char point[] = { + 0x03, + 0x54, 0x94, 0xc1, 0x5d, 0x32, 0x09, 0x97, 0x06, + 0xc2, 0x39, 0x5f, 0x94, 0x34, 0x87, 0x45, 0xfd, + 0x75, 0x7c, 0xe3, 0x0e, 0x4e, 0x8c, 0x90, 0xfb, + 0xa2, 0xba, 0xd1, 0x84, 0xf8, 0x83, 0xc6, 0x9f + }; + + for (i = 0; i < 32; i++) { + data->scalar[i] = i + 1; + } + CHECK(secp256k1_ec_pubkey_parse(data->ctx, &data->point, point, sizeof(point)) == 1); +} + +static void bench_ecdh(void* arg, int iters) { + int i; + unsigned char res[32]; + bench_ecdh_data *data = (bench_ecdh_data*)arg; + + for (i = 0; i < iters; i++) { + CHECK(secp256k1_ecdh(data->ctx, res, &data->point, data->scalar, NULL, NULL) == 1); + } +} + +static void run_ecdh_bench(int iters, int argc, char** argv) { + bench_ecdh_data data; + int d = argc == 1; + + /* create a context with no capabilities */ + data.ctx = secp256k1_context_create(SECP256K1_FLAGS_TYPE_CONTEXT); + + if (d || have_flag(argc, argv, "ecdh")) run_benchmark("ecdh", bench_ecdh, bench_ecdh_setup, NULL, &data, 10, iters); + + secp256k1_context_destroy(data.ctx); +} + +#endif /* SECP256K1_MODULE_ECDH_BENCH_H */ diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/ecdh/main_impl.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/ecdh/main_impl.h new file mode 100644 index 00000000000..842b5359e37 --- /dev/null +++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/ecdh/main_impl.h @@ -0,0 +1,74 @@ +/*********************************************************************** + * Copyright (c) 2015 Andrew Poelstra * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_MODULE_ECDH_MAIN_H +#define SECP256K1_MODULE_ECDH_MAIN_H + +#include "../../../include/secp256k1_ecdh.h" +#include "../../ecmult_const_impl.h" + +static int ecdh_hash_function_sha256(unsigned char *output, const unsigned char *x32, const unsigned char *y32, void *data) { + unsigned char version = (y32[31] & 0x01) | 0x02; + secp256k1_sha256 sha; + (void)data; + + secp256k1_sha256_initialize(&sha); + secp256k1_sha256_write(&sha, &version, 1); + secp256k1_sha256_write(&sha, x32, 32); + secp256k1_sha256_finalize(&sha, output); + secp256k1_sha256_clear(&sha); + + return 1; +} + +const secp256k1_ecdh_hash_function secp256k1_ecdh_hash_function_sha256 = ecdh_hash_function_sha256; +const secp256k1_ecdh_hash_function secp256k1_ecdh_hash_function_default = ecdh_hash_function_sha256; + +int secp256k1_ecdh(const secp256k1_context* ctx, unsigned char *output, const secp256k1_pubkey *point, const unsigned char *scalar, secp256k1_ecdh_hash_function hashfp, void *data) { + int ret = 0; + int overflow = 0; + secp256k1_gej res; + secp256k1_ge pt; + secp256k1_scalar s; + unsigned char x[32]; + unsigned char y[32]; + + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(output != NULL); + ARG_CHECK(point != NULL); + ARG_CHECK(scalar != NULL); + + if (hashfp == NULL) { + hashfp = secp256k1_ecdh_hash_function_default; + } + + secp256k1_pubkey_load(ctx, &pt, point); + secp256k1_scalar_set_b32(&s, scalar, &overflow); + + overflow |= secp256k1_scalar_is_zero(&s); + secp256k1_scalar_cmov(&s, &secp256k1_scalar_one, overflow); + + secp256k1_ecmult_const(&res, &pt, &s); + secp256k1_ge_set_gej(&pt, &res); + + /* Compute a hash of the point */ + secp256k1_fe_normalize(&pt.x); + secp256k1_fe_normalize(&pt.y); + secp256k1_fe_get_b32(x, &pt.x); + secp256k1_fe_get_b32(y, &pt.y); + + ret = hashfp(output, x, y, data); + + secp256k1_memclear(x, sizeof(x)); + secp256k1_memclear(y, sizeof(y)); + secp256k1_scalar_clear(&s); + secp256k1_ge_clear(&pt); + secp256k1_gej_clear(&res); + + return !!ret & !overflow; +} + +#endif /* SECP256K1_MODULE_ECDH_MAIN_H */ diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/ecdh/tests_impl.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/ecdh/tests_impl.h new file mode 100644 index 00000000000..3c3acdaf8c3 --- /dev/null +++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/ecdh/tests_impl.h @@ -0,0 +1,152 @@ +/*********************************************************************** + * Copyright (c) 2015 Andrew Poelstra * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_MODULE_ECDH_TESTS_H +#define SECP256K1_MODULE_ECDH_TESTS_H + +static int ecdh_hash_function_test_fail(unsigned char *output, const unsigned char *x, const unsigned char *y, void *data) { + (void)output; + (void)x; + (void)y; + (void)data; + return 0; +} + +static int ecdh_hash_function_custom(unsigned char *output, const unsigned char *x, const unsigned char *y, void *data) { + (void)data; + /* Save x and y as uncompressed public key */ + output[0] = 0x04; + memcpy(output + 1, x, 32); + memcpy(output + 33, y, 32); + return 1; +} + +static void test_ecdh_api(void) { + secp256k1_pubkey point; + unsigned char res[32]; + unsigned char s_one[32] = { 0 }; + s_one[31] = 1; + + CHECK(secp256k1_ec_pubkey_create(CTX, &point, s_one) == 1); + + /* Check all NULLs are detected */ + CHECK(secp256k1_ecdh(CTX, res, &point, s_one, NULL, NULL) == 1); + CHECK_ILLEGAL(CTX, secp256k1_ecdh(CTX, NULL, &point, s_one, NULL, NULL)); + CHECK_ILLEGAL(CTX, secp256k1_ecdh(CTX, res, NULL, s_one, NULL, NULL)); + CHECK_ILLEGAL(CTX, secp256k1_ecdh(CTX, res, &point, NULL, NULL, NULL)); + CHECK(secp256k1_ecdh(CTX, res, &point, s_one, NULL, NULL) == 1); +} + +static void test_ecdh_generator_basepoint(void) { + unsigned char s_one[32] = { 0 }; + secp256k1_pubkey point[2]; + int i; + + s_one[31] = 1; + /* Check against pubkey creation when the basepoint is the generator */ + for (i = 0; i < 2 * COUNT; ++i) { + secp256k1_sha256 sha; + unsigned char s_b32[32]; + unsigned char output_ecdh[65]; + unsigned char output_ser[32]; + unsigned char point_ser[65]; + size_t point_ser_len = sizeof(point_ser); + secp256k1_scalar s; + + testutil_random_scalar_order(&s); + secp256k1_scalar_get_b32(s_b32, &s); + + CHECK(secp256k1_ec_pubkey_create(CTX, &point[0], s_one) == 1); + CHECK(secp256k1_ec_pubkey_create(CTX, &point[1], s_b32) == 1); + + /* compute using ECDH function with custom hash function */ + CHECK(secp256k1_ecdh(CTX, output_ecdh, &point[0], s_b32, ecdh_hash_function_custom, NULL) == 1); + /* compute "explicitly" */ + CHECK(secp256k1_ec_pubkey_serialize(CTX, point_ser, &point_ser_len, &point[1], SECP256K1_EC_UNCOMPRESSED) == 1); + /* compare */ + CHECK(secp256k1_memcmp_var(output_ecdh, point_ser, 65) == 0); + + /* compute using ECDH function with default hash function */ + CHECK(secp256k1_ecdh(CTX, output_ecdh, &point[0], s_b32, NULL, NULL) == 1); + /* compute "explicitly" */ + CHECK(secp256k1_ec_pubkey_serialize(CTX, point_ser, &point_ser_len, &point[1], SECP256K1_EC_COMPRESSED) == 1); + secp256k1_sha256_initialize(&sha); + secp256k1_sha256_write(&sha, point_ser, point_ser_len); + secp256k1_sha256_finalize(&sha, output_ser); + /* compare */ + CHECK(secp256k1_memcmp_var(output_ecdh, output_ser, 32) == 0); + } +} + +static void test_bad_scalar(void) { + unsigned char s_zero[32] = { 0 }; + unsigned char s_overflow[32] = { + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, + 0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0, 0x3b, + 0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41, 0x41 + }; + unsigned char s_rand[32] = { 0 }; + unsigned char output[32]; + secp256k1_scalar rand; + secp256k1_pubkey point; + + /* Create random point */ + testutil_random_scalar_order(&rand); + secp256k1_scalar_get_b32(s_rand, &rand); + CHECK(secp256k1_ec_pubkey_create(CTX, &point, s_rand) == 1); + + /* Try to multiply it by bad values */ + CHECK(secp256k1_ecdh(CTX, output, &point, s_zero, NULL, NULL) == 0); + CHECK(secp256k1_ecdh(CTX, output, &point, s_overflow, NULL, NULL) == 0); + /* ...and a good one */ + s_overflow[31] -= 1; + CHECK(secp256k1_ecdh(CTX, output, &point, s_overflow, NULL, NULL) == 1); + + /* Hash function failure results in ecdh failure */ + CHECK(secp256k1_ecdh(CTX, output, &point, s_overflow, ecdh_hash_function_test_fail, NULL) == 0); +} + +/** Test that ECDH(sG, 1/s) == ECDH((1/s)G, s) == ECDH(G, 1) for a few random s. */ +static void test_result_basepoint(void) { + secp256k1_pubkey point; + secp256k1_scalar rand; + unsigned char s[32]; + unsigned char s_inv[32]; + unsigned char out[32]; + unsigned char out_inv[32]; + unsigned char out_base[32]; + int i; + + unsigned char s_one[32] = { 0 }; + s_one[31] = 1; + CHECK(secp256k1_ec_pubkey_create(CTX, &point, s_one) == 1); + CHECK(secp256k1_ecdh(CTX, out_base, &point, s_one, NULL, NULL) == 1); + + for (i = 0; i < 2 * COUNT; i++) { + testutil_random_scalar_order(&rand); + secp256k1_scalar_get_b32(s, &rand); + secp256k1_scalar_inverse(&rand, &rand); + secp256k1_scalar_get_b32(s_inv, &rand); + + CHECK(secp256k1_ec_pubkey_create(CTX, &point, s) == 1); + CHECK(secp256k1_ecdh(CTX, out, &point, s_inv, NULL, NULL) == 1); + CHECK(secp256k1_memcmp_var(out, out_base, 32) == 0); + + CHECK(secp256k1_ec_pubkey_create(CTX, &point, s_inv) == 1); + CHECK(secp256k1_ecdh(CTX, out_inv, &point, s, NULL, NULL) == 1); + CHECK(secp256k1_memcmp_var(out_inv, out_base, 32) == 0); + } +} + +static void run_ecdh_tests(void) { + test_ecdh_api(); + test_ecdh_generator_basepoint(); + test_bad_scalar(); + test_result_basepoint(); +} + +#endif /* SECP256K1_MODULE_ECDH_TESTS_H */ diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/ellswift/bench_impl.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/ellswift/bench_impl.h new file mode 100644 index 00000000000..b16a3a36870 --- /dev/null +++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/ellswift/bench_impl.h @@ -0,0 +1,106 @@ +/*********************************************************************** + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_MODULE_ELLSWIFT_BENCH_H +#define SECP256K1_MODULE_ELLSWIFT_BENCH_H + +#include "../../../include/secp256k1_ellswift.h" + +typedef struct { + secp256k1_context *ctx; + secp256k1_pubkey point[256]; + unsigned char rnd64[64]; +} bench_ellswift_data; + +static void bench_ellswift_setup(void *arg) { + int i; + bench_ellswift_data *data = (bench_ellswift_data*)arg; + static const unsigned char init[64] = { + 0x78, 0x1f, 0xb7, 0xd4, 0x67, 0x7f, 0x08, 0x68, + 0xdb, 0xe3, 0x1d, 0x7f, 0x1b, 0xb0, 0xf6, 0x9e, + 0x0a, 0x64, 0xca, 0x32, 0x9e, 0xc6, 0x20, 0x79, + 0x03, 0xf3, 0xd0, 0x46, 0x7a, 0x0f, 0xd2, 0x21, + 0xb0, 0x2c, 0x46, 0xd8, 0xba, 0xca, 0x26, 0x4f, + 0x8f, 0x8c, 0xd4, 0xdd, 0x2d, 0x04, 0xbe, 0x30, + 0x48, 0x51, 0x1e, 0xd4, 0x16, 0xfd, 0x42, 0x85, + 0x62, 0xc9, 0x02, 0xf9, 0x89, 0x84, 0xff, 0xdc + }; + memcpy(data->rnd64, init, 64); + for (i = 0; i < 256; ++i) { + int j; + CHECK(secp256k1_ellswift_decode(data->ctx, &data->point[i], data->rnd64)); + for (j = 0; j < 64; ++j) { + data->rnd64[j] += 1; + } + } + CHECK(secp256k1_ellswift_encode(data->ctx, data->rnd64, &data->point[255], init + 16)); +} + +static void bench_ellswift_encode(void *arg, int iters) { + int i; + bench_ellswift_data *data = (bench_ellswift_data*)arg; + + for (i = 0; i < iters; i++) { + CHECK(secp256k1_ellswift_encode(data->ctx, data->rnd64, &data->point[i & 255], data->rnd64 + 16)); + } +} + +static void bench_ellswift_create(void *arg, int iters) { + int i; + bench_ellswift_data *data = (bench_ellswift_data*)arg; + + for (i = 0; i < iters; i++) { + unsigned char buf[64]; + CHECK(secp256k1_ellswift_create(data->ctx, buf, data->rnd64, data->rnd64 + 32)); + memcpy(data->rnd64, buf, 64); + } +} + +static void bench_ellswift_decode(void *arg, int iters) { + int i; + secp256k1_pubkey out; + size_t len; + bench_ellswift_data *data = (bench_ellswift_data*)arg; + + for (i = 0; i < iters; i++) { + CHECK(secp256k1_ellswift_decode(data->ctx, &out, data->rnd64) == 1); + len = 33; + CHECK(secp256k1_ec_pubkey_serialize(data->ctx, data->rnd64 + (i % 32), &len, &out, SECP256K1_EC_COMPRESSED)); + } +} + +static void bench_ellswift_xdh(void *arg, int iters) { + int i; + bench_ellswift_data *data = (bench_ellswift_data*)arg; + + for (i = 0; i < iters; i++) { + int party = i & 1; + CHECK(secp256k1_ellswift_xdh(data->ctx, + data->rnd64 + (i % 33), + data->rnd64, + data->rnd64, + data->rnd64 + ((i + 16) % 33), + party, + secp256k1_ellswift_xdh_hash_function_bip324, + NULL) == 1); + } +} + +void run_ellswift_bench(int iters, int argc, char **argv) { + bench_ellswift_data data; + int d = argc == 1; + + /* create a context with signing capabilities */ + data.ctx = secp256k1_context_create(SECP256K1_CONTEXT_NONE); + + if (d || have_flag(argc, argv, "ellswift") || have_flag(argc, argv, "encode") || have_flag(argc, argv, "ellswift_encode")) run_benchmark("ellswift_encode", bench_ellswift_encode, bench_ellswift_setup, NULL, &data, 10, iters); + if (d || have_flag(argc, argv, "ellswift") || have_flag(argc, argv, "decode") || have_flag(argc, argv, "ellswift_decode")) run_benchmark("ellswift_decode", bench_ellswift_decode, bench_ellswift_setup, NULL, &data, 10, iters); + if (d || have_flag(argc, argv, "ellswift") || have_flag(argc, argv, "keygen") || have_flag(argc, argv, "ellswift_keygen")) run_benchmark("ellswift_keygen", bench_ellswift_create, bench_ellswift_setup, NULL, &data, 10, iters); + if (d || have_flag(argc, argv, "ellswift") || have_flag(argc, argv, "ecdh") || have_flag(argc, argv, "ellswift_ecdh")) run_benchmark("ellswift_ecdh", bench_ellswift_xdh, bench_ellswift_setup, NULL, &data, 10, iters); + + secp256k1_context_destroy(data.ctx); +} + +#endif diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/ellswift/main_impl.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/ellswift/main_impl.h new file mode 100644 index 00000000000..745a969139b --- /dev/null +++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/ellswift/main_impl.h @@ -0,0 +1,592 @@ +/*********************************************************************** + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_MODULE_ELLSWIFT_MAIN_H +#define SECP256K1_MODULE_ELLSWIFT_MAIN_H + +#include "../../../include/secp256k1.h" +#include "../../../include/secp256k1_ellswift.h" +#include "../../eckey.h" +#include "../../hash.h" + +/** c1 = (sqrt(-3)-1)/2 */ +static const secp256k1_fe secp256k1_ellswift_c1 = SECP256K1_FE_CONST(0x851695d4, 0x9a83f8ef, 0x919bb861, 0x53cbcb16, 0x630fb68a, 0xed0a766a, 0x3ec693d6, 0x8e6afa40); +/** c2 = (-sqrt(-3)-1)/2 = -(c1+1) */ +static const secp256k1_fe secp256k1_ellswift_c2 = SECP256K1_FE_CONST(0x7ae96a2b, 0x657c0710, 0x6e64479e, 0xac3434e9, 0x9cf04975, 0x12f58995, 0xc1396c28, 0x719501ee); +/** c3 = (-sqrt(-3)+1)/2 = -c1 = c2+1 */ +static const secp256k1_fe secp256k1_ellswift_c3 = SECP256K1_FE_CONST(0x7ae96a2b, 0x657c0710, 0x6e64479e, 0xac3434e9, 0x9cf04975, 0x12f58995, 0xc1396c28, 0x719501ef); +/** c4 = (sqrt(-3)+1)/2 = -c2 = c1+1 */ +static const secp256k1_fe secp256k1_ellswift_c4 = SECP256K1_FE_CONST(0x851695d4, 0x9a83f8ef, 0x919bb861, 0x53cbcb16, 0x630fb68a, 0xed0a766a, 0x3ec693d6, 0x8e6afa41); + +/** Decode ElligatorSwift encoding (u, t) to a fraction xn/xd representing a curve X coordinate. */ +static void secp256k1_ellswift_xswiftec_frac_var(secp256k1_fe *xn, secp256k1_fe *xd, const secp256k1_fe *u, const secp256k1_fe *t) { + /* The implemented algorithm is the following (all operations in GF(p)): + * + * - Let c0 = sqrt(-3) = 0xa2d2ba93507f1df233770c2a797962cc61f6d15da14ecd47d8d27ae1cd5f852. + * - If u = 0, set u = 1. + * - If t = 0, set t = 1. + * - If u^3+7+t^2 = 0, set t = 2*t. + * - Let X = (u^3+7-t^2)/(2*t). + * - Let Y = (X+t)/(c0*u). + * - If x3 = u+4*Y^2 is a valid x coordinate, return it. + * - If x2 = (-X/Y-u)/2 is a valid x coordinate, return it. + * - Return x1 = (X/Y-u)/2 (which is now guaranteed to be a valid x coordinate). + * + * Introducing s=t^2, g=u^3+7, and simplifying x1=-(x2+u) we get: + * + * - Let c0 = ... + * - If u = 0, set u = 1. + * - If t = 0, set t = 1. + * - Let s = t^2 + * - Let g = u^3+7 + * - If g+s = 0, set t = 2*t, s = 4*s + * - Let X = (g-s)/(2*t). + * - Let Y = (X+t)/(c0*u) = (g+s)/(2*c0*t*u). + * - If x3 = u+4*Y^2 is a valid x coordinate, return it. + * - If x2 = (-X/Y-u)/2 is a valid x coordinate, return it. + * - Return x1 = -(x2+u). + * + * Now substitute Y^2 = -(g+s)^2/(12*s*u^2) and X/Y = c0*u*(g-s)/(g+s). This + * means X and Y do not need to be evaluated explicitly anymore. + * + * - ... + * - If g+s = 0, set s = 4*s. + * - If x3 = u-(g+s)^2/(3*s*u^2) is a valid x coordinate, return it. + * - If x2 = (-c0*u*(g-s)/(g+s)-u)/2 is a valid x coordinate, return it. + * - Return x1 = -(x2+u). + * + * Simplifying x2 using 2 additional constants: + * + * - Let c1 = (c0-1)/2 = 0x851695d49a83f8ef919bb86153cbcb16630fb68aed0a766a3ec693d68e6afa40. + * - Let c2 = (-c0-1)/2 = 0x7ae96a2b657c07106e64479eac3434e99cf0497512f58995c1396c28719501ee. + * - ... + * - If x2 = u*(c1*s+c2*g)/(g+s) is a valid x coordinate, return it. + * - ... + * + * Writing x3 as a fraction: + * + * - ... + * - If x3 = (3*s*u^3-(g+s)^2)/(3*s*u^2) ... + * - ... + + * Overall, we get: + * + * - Let c1 = 0x851695d49a83f8ef919bb86153cbcb16630fb68aed0a766a3ec693d68e6afa40. + * - Let c2 = 0x7ae96a2b657c07106e64479eac3434e99cf0497512f58995c1396c28719501ee. + * - If u = 0, set u = 1. + * - If t = 0, set s = 1, else set s = t^2. + * - Let g = u^3+7. + * - If g+s = 0, set s = 4*s. + * - If x3 = (3*s*u^3-(g+s)^2)/(3*s*u^2) is a valid x coordinate, return it. + * - If x2 = u*(c1*s+c2*g)/(g+s) is a valid x coordinate, return it. + * - Return x1 = -(x2+u). + */ + secp256k1_fe u1, s, g, p, d, n, l; + u1 = *u; + if (EXPECT(secp256k1_fe_normalizes_to_zero_var(&u1), 0)) u1 = secp256k1_fe_one; + secp256k1_fe_sqr(&s, t); + if (EXPECT(secp256k1_fe_normalizes_to_zero_var(t), 0)) s = secp256k1_fe_one; + secp256k1_fe_sqr(&l, &u1); /* l = u^2 */ + secp256k1_fe_mul(&g, &l, &u1); /* g = u^3 */ + secp256k1_fe_add_int(&g, SECP256K1_B); /* g = u^3 + 7 */ + p = g; /* p = g */ + secp256k1_fe_add(&p, &s); /* p = g+s */ + if (EXPECT(secp256k1_fe_normalizes_to_zero_var(&p), 0)) { + secp256k1_fe_mul_int(&s, 4); + /* Recompute p = g+s */ + p = g; /* p = g */ + secp256k1_fe_add(&p, &s); /* p = g+s */ + } + secp256k1_fe_mul(&d, &s, &l); /* d = s*u^2 */ + secp256k1_fe_mul_int(&d, 3); /* d = 3*s*u^2 */ + secp256k1_fe_sqr(&l, &p); /* l = (g+s)^2 */ + secp256k1_fe_negate(&l, &l, 1); /* l = -(g+s)^2 */ + secp256k1_fe_mul(&n, &d, &u1); /* n = 3*s*u^3 */ + secp256k1_fe_add(&n, &l); /* n = 3*s*u^3-(g+s)^2 */ + if (secp256k1_ge_x_frac_on_curve_var(&n, &d)) { + /* Return x3 = n/d = (3*s*u^3-(g+s)^2)/(3*s*u^2) */ + *xn = n; + *xd = d; + return; + } + *xd = p; + secp256k1_fe_mul(&l, &secp256k1_ellswift_c1, &s); /* l = c1*s */ + secp256k1_fe_mul(&n, &secp256k1_ellswift_c2, &g); /* n = c2*g */ + secp256k1_fe_add(&n, &l); /* n = c1*s+c2*g */ + secp256k1_fe_mul(&n, &n, &u1); /* n = u*(c1*s+c2*g) */ + /* Possible optimization: in the invocation below, p^2 = (g+s)^2 is computed, + * which we already have computed above. This could be deduplicated. */ + if (secp256k1_ge_x_frac_on_curve_var(&n, &p)) { + /* Return x2 = n/p = u*(c1*s+c2*g)/(g+s) */ + *xn = n; + return; + } + secp256k1_fe_mul(&l, &p, &u1); /* l = u*(g+s) */ + secp256k1_fe_add(&n, &l); /* n = u*(c1*s+c2*g)+u*(g+s) */ + secp256k1_fe_negate(xn, &n, 2); /* n = -u*(c1*s+c2*g)-u*(g+s) */ + + VERIFY_CHECK(secp256k1_ge_x_frac_on_curve_var(xn, &p)); + /* Return x3 = n/p = -(u*(c1*s+c2*g)/(g+s)+u) */ +} + +/** Decode ElligatorSwift encoding (u, t) to X coordinate. */ +static void secp256k1_ellswift_xswiftec_var(secp256k1_fe *x, const secp256k1_fe *u, const secp256k1_fe *t) { + secp256k1_fe xn, xd; + secp256k1_ellswift_xswiftec_frac_var(&xn, &xd, u, t); + secp256k1_fe_inv_var(&xd, &xd); + secp256k1_fe_mul(x, &xn, &xd); +} + +/** Decode ElligatorSwift encoding (u, t) to point P. */ +static void secp256k1_ellswift_swiftec_var(secp256k1_ge *p, const secp256k1_fe *u, const secp256k1_fe *t) { + secp256k1_fe x; + secp256k1_ellswift_xswiftec_var(&x, u, t); + secp256k1_ge_set_xo_var(p, &x, secp256k1_fe_is_odd(t)); +} + +/* Try to complete an ElligatorSwift encoding (u, t) for X coordinate x, given u and x. + * + * There may be up to 8 distinct t values such that (u, t) decodes back to x, but also + * fewer, or none at all. Each such partial inverse can be accessed individually using a + * distinct input argument c (in range 0-7), and some or all of these may return failure. + * The following guarantees exist: + * - Given (x, u), no two distinct c values give the same successful result t. + * - Every successful result maps back to x through secp256k1_ellswift_xswiftec_var. + * - Given (x, u), all t values that map back to x can be reached by combining the + * successful results from this function over all c values, with the exception of: + * - this function cannot be called with u=0 + * - no result with t=0 will be returned + * - no result for which u^3 + t^2 + 7 = 0 will be returned. + * + * The rather unusual encoding of bits in c (a large "if" based on the middle bit, and then + * using the low and high bits to pick signs of square roots) is to match the paper's + * encoding more closely: c=0 through c=3 match branches 1..4 in the paper, while c=4 through + * c=7 are copies of those with an additional negation of sqrt(w). + */ +static int secp256k1_ellswift_xswiftec_inv_var(secp256k1_fe *t, const secp256k1_fe *x_in, const secp256k1_fe *u_in, int c) { + /* The implemented algorithm is this (all arithmetic, except involving c, is mod p): + * + * - If (c & 2) = 0: + * - If (-x-u) is a valid X coordinate, fail. + * - Let s=-(u^3+7)/(u^2+u*x+x^2). + * - If s is not square, fail. + * - Let v=x. + * - If (c & 2) = 2: + * - Let s=x-u. + * - If s is not square, fail. + * - Let r=sqrt(-s*(4*(u^3+7)+3*u^2*s)); fail if it doesn't exist. + * - If (c & 1) = 1 and r = 0, fail. + * - If s=0, fail. + * - Let v=(r/s-u)/2. + * - Let w=sqrt(s). + * - If (c & 5) = 0: return -w*(c3*u + v). + * - If (c & 5) = 1: return w*(c4*u + v). + * - If (c & 5) = 4: return w*(c3*u + v). + * - If (c & 5) = 5: return -w*(c4*u + v). + */ + secp256k1_fe x = *x_in, u = *u_in, g, v, s, m, r, q; + int ret; + + secp256k1_fe_normalize_weak(&x); + secp256k1_fe_normalize_weak(&u); + + VERIFY_CHECK(c >= 0 && c < 8); + VERIFY_CHECK(secp256k1_ge_x_on_curve_var(&x)); + + if (!(c & 2)) { + /* c is in {0, 1, 4, 5}. In this case we look for an inverse under the x1 (if c=0 or + * c=4) formula, or x2 (if c=1 or c=5) formula. */ + + /* If -u-x is a valid X coordinate, fail. This would yield an encoding that roundtrips + * back under the x3 formula instead (which has priority over x1 and x2, so the decoding + * would not match x). */ + m = x; /* m = x */ + secp256k1_fe_add(&m, &u); /* m = u+x */ + secp256k1_fe_negate(&m, &m, 2); /* m = -u-x */ + /* Test if (-u-x) is a valid X coordinate. If so, fail. */ + if (secp256k1_ge_x_on_curve_var(&m)) return 0; + + /* Let s = -(u^3 + 7)/(u^2 + u*x + x^2) [first part] */ + secp256k1_fe_sqr(&s, &m); /* s = (u+x)^2 */ + secp256k1_fe_negate(&s, &s, 1); /* s = -(u+x)^2 */ + secp256k1_fe_mul(&m, &u, &x); /* m = u*x */ + secp256k1_fe_add(&s, &m); /* s = -(u^2 + u*x + x^2) */ + + /* Note that at this point, s = 0 is impossible. If it were the case: + * s = -(u^2 + u*x + x^2) = 0 + * => u^2 + u*x + x^2 = 0 + * => (u + 2*x) * (u^2 + u*x + x^2) = 0 + * => 2*x^3 + 3*x^2*u + 3*x*u^2 + u^3 = 0 + * => (x + u)^3 + x^3 = 0 + * => x^3 = -(x + u)^3 + * => x^3 + B = (-u - x)^3 + B + * + * However, we know x^3 + B is square (because x is on the curve) and + * that (-u-x)^3 + B is not square (the secp256k1_ge_x_on_curve_var(&m) + * test above would have failed). This is a contradiction, and thus the + * assumption s=0 is false. */ + VERIFY_CHECK(!secp256k1_fe_normalizes_to_zero_var(&s)); + + /* If s is not square, fail. We have not fully computed s yet, but s is square iff + * -(u^3+7)*(u^2+u*x+x^2) is square (because a/b is square iff a*b is square and b is + * nonzero). */ + secp256k1_fe_sqr(&g, &u); /* g = u^2 */ + secp256k1_fe_mul(&g, &g, &u); /* g = u^3 */ + secp256k1_fe_add_int(&g, SECP256K1_B); /* g = u^3+7 */ + secp256k1_fe_mul(&m, &s, &g); /* m = -(u^3 + 7)*(u^2 + u*x + x^2) */ + if (!secp256k1_fe_is_square_var(&m)) return 0; + + /* Let s = -(u^3 + 7)/(u^2 + u*x + x^2) [second part] */ + secp256k1_fe_inv_var(&s, &s); /* s = -1/(u^2 + u*x + x^2) [no div by 0] */ + secp256k1_fe_mul(&s, &s, &g); /* s = -(u^3 + 7)/(u^2 + u*x + x^2) */ + + /* Let v = x. */ + v = x; + } else { + /* c is in {2, 3, 6, 7}. In this case we look for an inverse under the x3 formula. */ + + /* Let s = x-u. */ + secp256k1_fe_negate(&m, &u, 1); /* m = -u */ + s = m; /* s = -u */ + secp256k1_fe_add(&s, &x); /* s = x-u */ + + /* If s is not square, fail. */ + if (!secp256k1_fe_is_square_var(&s)) return 0; + + /* Let r = sqrt(-s*(4*(u^3+7)+3*u^2*s)); fail if it doesn't exist. */ + secp256k1_fe_sqr(&g, &u); /* g = u^2 */ + secp256k1_fe_mul(&q, &s, &g); /* q = s*u^2 */ + secp256k1_fe_mul_int(&q, 3); /* q = 3*s*u^2 */ + secp256k1_fe_mul(&g, &g, &u); /* g = u^3 */ + secp256k1_fe_mul_int(&g, 4); /* g = 4*u^3 */ + secp256k1_fe_add_int(&g, 4 * SECP256K1_B); /* g = 4*(u^3+7) */ + secp256k1_fe_add(&q, &g); /* q = 4*(u^3+7)+3*s*u^2 */ + secp256k1_fe_mul(&q, &q, &s); /* q = s*(4*(u^3+7)+3*u^2*s) */ + secp256k1_fe_negate(&q, &q, 1); /* q = -s*(4*(u^3+7)+3*u^2*s) */ + if (!secp256k1_fe_is_square_var(&q)) return 0; + ret = secp256k1_fe_sqrt(&r, &q); /* r = sqrt(-s*(4*(u^3+7)+3*u^2*s)) */ +#ifdef VERIFY + VERIFY_CHECK(ret); +#else + (void)ret; +#endif + + /* If (c & 1) = 1 and r = 0, fail. */ + if (EXPECT((c & 1) && secp256k1_fe_normalizes_to_zero_var(&r), 0)) return 0; + + /* If s = 0, fail. */ + if (EXPECT(secp256k1_fe_normalizes_to_zero_var(&s), 0)) return 0; + + /* Let v = (r/s-u)/2. */ + secp256k1_fe_inv_var(&v, &s); /* v = 1/s [no div by 0] */ + secp256k1_fe_mul(&v, &v, &r); /* v = r/s */ + secp256k1_fe_add(&v, &m); /* v = r/s-u */ + secp256k1_fe_half(&v); /* v = (r/s-u)/2 */ + } + + /* Let w = sqrt(s). */ + ret = secp256k1_fe_sqrt(&m, &s); /* m = sqrt(s) = w */ + VERIFY_CHECK(ret); + + /* Return logic. */ + if ((c & 5) == 0 || (c & 5) == 5) { + secp256k1_fe_negate(&m, &m, 1); /* m = -w */ + } + /* Now m = {-w if c&5=0 or c&5=5; w otherwise}. */ + secp256k1_fe_mul(&u, &u, c&1 ? &secp256k1_ellswift_c4 : &secp256k1_ellswift_c3); + /* u = {c4 if c&1=1; c3 otherwise}*u */ + secp256k1_fe_add(&u, &v); /* u = {c4 if c&1=1; c3 otherwise}*u + v */ + secp256k1_fe_mul(t, &m, &u); + return 1; +} + +/** Use SHA256 as a PRNG, returning SHA256(hasher || cnt). + * + * hasher is a SHA256 object to which an incrementing 4-byte counter is written to generate randomness. + * Writing 13 bytes (4 bytes for counter, plus 9 bytes for the SHA256 padding) cannot cross a + * 64-byte block size boundary (to make sure it only triggers a single SHA256 compression). */ +static void secp256k1_ellswift_prng(unsigned char* out32, const secp256k1_sha256 *hasher, uint32_t cnt) { + secp256k1_sha256 hash = *hasher; + unsigned char buf4[4]; +#ifdef VERIFY + size_t blocks = hash.bytes >> 6; +#endif + buf4[0] = cnt; + buf4[1] = cnt >> 8; + buf4[2] = cnt >> 16; + buf4[3] = cnt >> 24; + secp256k1_sha256_write(&hash, buf4, 4); + secp256k1_sha256_finalize(&hash, out32); + + /* Writing and finalizing together should trigger exactly one SHA256 compression. */ + VERIFY_CHECK(((hash.bytes) >> 6) == (blocks + 1)); +} + +/** Find an ElligatorSwift encoding (u, t) for X coordinate x, and random Y coordinate. + * + * u32 is the 32-byte big endian encoding of u; t is the output field element t that still + * needs encoding. + * + * hasher is a hasher in the secp256k1_ellswift_prng sense, with the same restrictions. */ +static void secp256k1_ellswift_xelligatorswift_var(unsigned char *u32, secp256k1_fe *t, const secp256k1_fe *x, const secp256k1_sha256 *hasher) { + /* Pool of 3-bit branch values. */ + unsigned char branch_hash[32]; + /* Number of 3-bit values in branch_hash left. */ + int branches_left = 0; + /* Field elements u and branch values are extracted from RNG based on hasher for consecutive + * values of cnt. cnt==0 is first used to populate a pool of 64 4-bit branch values. The 64 + * cnt values that follow are used to generate field elements u. cnt==65 (and multiples + * thereof) are used to repopulate the pool and start over, if that were ever necessary. + * On average, 4 iterations are needed. */ + uint32_t cnt = 0; + while (1) { + int branch; + secp256k1_fe u; + /* If the pool of branch values is empty, populate it. */ + if (branches_left == 0) { + secp256k1_ellswift_prng(branch_hash, hasher, cnt++); + branches_left = 64; + } + /* Take a 3-bit branch value from the branch pool (top bit is discarded). */ + --branches_left; + branch = (branch_hash[branches_left >> 1] >> ((branches_left & 1) << 2)) & 7; + /* Compute a new u value by hashing. */ + secp256k1_ellswift_prng(u32, hasher, cnt++); + /* overflow is not a problem (we prefer uniform u32 over uniform u). */ + secp256k1_fe_set_b32_mod(&u, u32); + /* Since u is the output of a hash, it should practically never be 0. We could apply the + * u=0 to u=1 correction here too to deal with that case still, but it's such a low + * probability event that we do not bother. */ + VERIFY_CHECK(!secp256k1_fe_normalizes_to_zero_var(&u)); + + /* Find a remainder t, and return it if found. */ + if (EXPECT(secp256k1_ellswift_xswiftec_inv_var(t, x, &u, branch), 0)) break; + } +} + +/** Find an ElligatorSwift encoding (u, t) for point P. + * + * This is similar secp256k1_ellswift_xelligatorswift_var, except it takes a full group element p + * as input, and returns an encoding that matches the provided Y coordinate rather than a random + * one. + */ +static void secp256k1_ellswift_elligatorswift_var(unsigned char *u32, secp256k1_fe *t, const secp256k1_ge *p, const secp256k1_sha256 *hasher) { + secp256k1_ellswift_xelligatorswift_var(u32, t, &p->x, hasher); + secp256k1_fe_normalize_var(t); + if (secp256k1_fe_is_odd(t) != secp256k1_fe_is_odd(&p->y)) { + secp256k1_fe_negate(t, t, 1); + secp256k1_fe_normalize_var(t); + } +} + +/** Set hash state to the BIP340 tagged hash midstate for "secp256k1_ellswift_encode". */ +static void secp256k1_ellswift_sha256_init_encode(secp256k1_sha256* hash) { + secp256k1_sha256_initialize(hash); + hash->s[0] = 0xd1a6524bul; + hash->s[1] = 0x028594b3ul; + hash->s[2] = 0x96e42f4eul; + hash->s[3] = 0x1037a177ul; + hash->s[4] = 0x1b8fcb8bul; + hash->s[5] = 0x56023885ul; + hash->s[6] = 0x2560ede1ul; + hash->s[7] = 0xd626b715ul; + + hash->bytes = 64; +} + +int secp256k1_ellswift_encode(const secp256k1_context *ctx, unsigned char *ell64, const secp256k1_pubkey *pubkey, const unsigned char *rnd32) { + secp256k1_ge p; + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(ell64 != NULL); + ARG_CHECK(pubkey != NULL); + ARG_CHECK(rnd32 != NULL); + + if (secp256k1_pubkey_load(ctx, &p, pubkey)) { + secp256k1_fe t; + unsigned char p64[64] = {0}; + size_t ser_size; + int ser_ret; + secp256k1_sha256 hash; + + /* Set up hasher state; the used RNG is H(pubkey || "\x00"*31 || rnd32 || cnt++), using + * BIP340 tagged hash with tag "secp256k1_ellswift_encode". */ + secp256k1_ellswift_sha256_init_encode(&hash); + ser_ret = secp256k1_eckey_pubkey_serialize(&p, p64, &ser_size, 1); +#ifdef VERIFY + VERIFY_CHECK(ser_ret && ser_size == 33); +#else + (void)ser_ret; +#endif + secp256k1_sha256_write(&hash, p64, sizeof(p64)); + secp256k1_sha256_write(&hash, rnd32, 32); + + /* Compute ElligatorSwift encoding and construct output. */ + secp256k1_ellswift_elligatorswift_var(ell64, &t, &p, &hash); /* puts u in ell64[0..32] */ + secp256k1_fe_get_b32(ell64 + 32, &t); /* puts t in ell64[32..64] */ + return 1; + } + /* Only reached in case the provided pubkey is invalid. */ + memset(ell64, 0, 64); + return 0; +} + +/** Set hash state to the BIP340 tagged hash midstate for "secp256k1_ellswift_create". */ +static void secp256k1_ellswift_sha256_init_create(secp256k1_sha256* hash) { + secp256k1_sha256_initialize(hash); + hash->s[0] = 0xd29e1bf5ul; + hash->s[1] = 0xf7025f42ul; + hash->s[2] = 0x9b024773ul; + hash->s[3] = 0x094cb7d5ul; + hash->s[4] = 0xe59ed789ul; + hash->s[5] = 0x03bc9786ul; + hash->s[6] = 0x68335b35ul; + hash->s[7] = 0x4e363b53ul; + + hash->bytes = 64; +} + +int secp256k1_ellswift_create(const secp256k1_context *ctx, unsigned char *ell64, const unsigned char *seckey32, const unsigned char *auxrnd32) { + secp256k1_ge p; + secp256k1_fe t; + secp256k1_sha256 hash; + secp256k1_scalar seckey_scalar; + int ret; + static const unsigned char zero32[32] = {0}; + + /* Sanity check inputs. */ + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(ell64 != NULL); + memset(ell64, 0, 64); + ARG_CHECK(secp256k1_ecmult_gen_context_is_built(&ctx->ecmult_gen_ctx)); + ARG_CHECK(seckey32 != NULL); + + /* Compute (affine) public key */ + ret = secp256k1_ec_pubkey_create_helper(&ctx->ecmult_gen_ctx, &seckey_scalar, &p, seckey32); + secp256k1_declassify(ctx, &p, sizeof(p)); /* not constant time in produced pubkey */ + secp256k1_fe_normalize_var(&p.x); + secp256k1_fe_normalize_var(&p.y); + + /* Set up hasher state. The used RNG is H(privkey || "\x00"*32 [|| auxrnd32] || cnt++), + * using BIP340 tagged hash with tag "secp256k1_ellswift_create". */ + secp256k1_ellswift_sha256_init_create(&hash); + secp256k1_sha256_write(&hash, seckey32, 32); + secp256k1_sha256_write(&hash, zero32, sizeof(zero32)); + secp256k1_declassify(ctx, &hash, sizeof(hash)); /* private key is hashed now */ + if (auxrnd32) secp256k1_sha256_write(&hash, auxrnd32, 32); + + /* Compute ElligatorSwift encoding and construct output. */ + secp256k1_ellswift_elligatorswift_var(ell64, &t, &p, &hash); /* puts u in ell64[0..32] */ + secp256k1_fe_get_b32(ell64 + 32, &t); /* puts t in ell64[32..64] */ + + secp256k1_memczero(ell64, 64, !ret); + secp256k1_scalar_clear(&seckey_scalar); + + return ret; +} + +int secp256k1_ellswift_decode(const secp256k1_context *ctx, secp256k1_pubkey *pubkey, const unsigned char *ell64) { + secp256k1_fe u, t; + secp256k1_ge p; + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(pubkey != NULL); + ARG_CHECK(ell64 != NULL); + + secp256k1_fe_set_b32_mod(&u, ell64); + secp256k1_fe_set_b32_mod(&t, ell64 + 32); + secp256k1_fe_normalize_var(&t); + secp256k1_ellswift_swiftec_var(&p, &u, &t); + secp256k1_pubkey_save(pubkey, &p); + return 1; +} + +static int ellswift_xdh_hash_function_prefix(unsigned char *output, const unsigned char *x32, const unsigned char *ell_a64, const unsigned char *ell_b64, void *data) { + secp256k1_sha256 sha; + + secp256k1_sha256_initialize(&sha); + secp256k1_sha256_write(&sha, data, 64); + secp256k1_sha256_write(&sha, ell_a64, 64); + secp256k1_sha256_write(&sha, ell_b64, 64); + secp256k1_sha256_write(&sha, x32, 32); + secp256k1_sha256_finalize(&sha, output); + secp256k1_sha256_clear(&sha); + + return 1; +} + +/** Set hash state to the BIP340 tagged hash midstate for "bip324_ellswift_xonly_ecdh". */ +static void secp256k1_ellswift_sha256_init_bip324(secp256k1_sha256* hash) { + secp256k1_sha256_initialize(hash); + hash->s[0] = 0x8c12d730ul; + hash->s[1] = 0x827bd392ul; + hash->s[2] = 0x9e4fb2eeul; + hash->s[3] = 0x207b373eul; + hash->s[4] = 0x2292bd7aul; + hash->s[5] = 0xaa5441bcul; + hash->s[6] = 0x15c3779ful; + hash->s[7] = 0xcfb52549ul; + + hash->bytes = 64; +} + +static int ellswift_xdh_hash_function_bip324(unsigned char* output, const unsigned char *x32, const unsigned char *ell_a64, const unsigned char *ell_b64, void *data) { + secp256k1_sha256 sha; + + (void)data; + + secp256k1_ellswift_sha256_init_bip324(&sha); + secp256k1_sha256_write(&sha, ell_a64, 64); + secp256k1_sha256_write(&sha, ell_b64, 64); + secp256k1_sha256_write(&sha, x32, 32); + secp256k1_sha256_finalize(&sha, output); + secp256k1_sha256_clear(&sha); + + return 1; +} + +const secp256k1_ellswift_xdh_hash_function secp256k1_ellswift_xdh_hash_function_prefix = ellswift_xdh_hash_function_prefix; +const secp256k1_ellswift_xdh_hash_function secp256k1_ellswift_xdh_hash_function_bip324 = ellswift_xdh_hash_function_bip324; + +int secp256k1_ellswift_xdh(const secp256k1_context *ctx, unsigned char *output, const unsigned char *ell_a64, const unsigned char *ell_b64, const unsigned char *seckey32, int party, secp256k1_ellswift_xdh_hash_function hashfp, void *data) { + int ret = 0; + int overflow; + secp256k1_scalar s; + secp256k1_fe xn, xd, px, u, t; + unsigned char sx[32]; + const unsigned char* theirs64; + + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(output != NULL); + ARG_CHECK(ell_a64 != NULL); + ARG_CHECK(ell_b64 != NULL); + ARG_CHECK(seckey32 != NULL); + ARG_CHECK(hashfp != NULL); + + /* Load remote public key (as fraction). */ + theirs64 = party ? ell_a64 : ell_b64; + secp256k1_fe_set_b32_mod(&u, theirs64); + secp256k1_fe_set_b32_mod(&t, theirs64 + 32); + secp256k1_ellswift_xswiftec_frac_var(&xn, &xd, &u, &t); + + /* Load private key (using one if invalid). */ + secp256k1_scalar_set_b32(&s, seckey32, &overflow); + overflow = secp256k1_scalar_is_zero(&s); + secp256k1_scalar_cmov(&s, &secp256k1_scalar_one, overflow); + + /* Compute shared X coordinate. */ + secp256k1_ecmult_const_xonly(&px, &xn, &xd, &s, 1); + secp256k1_fe_normalize(&px); + secp256k1_fe_get_b32(sx, &px); + + /* Invoke hasher */ + ret = hashfp(output, sx, ell_a64, ell_b64, data); + + secp256k1_memclear(sx, sizeof(sx)); + secp256k1_fe_clear(&px); + secp256k1_scalar_clear(&s); + + return !!ret & !overflow; +} + +#endif diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/ellswift/tests_exhaustive_impl.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/ellswift/tests_exhaustive_impl.h new file mode 100644 index 00000000000..839c24aee45 --- /dev/null +++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/ellswift/tests_exhaustive_impl.h @@ -0,0 +1,39 @@ +/*********************************************************************** + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_MODULE_ELLSWIFT_TESTS_EXHAUSTIVE_H +#define SECP256K1_MODULE_ELLSWIFT_TESTS_EXHAUSTIVE_H + +#include "../../../include/secp256k1_ellswift.h" +#include "main_impl.h" + +static void test_exhaustive_ellswift(const secp256k1_context *ctx, const secp256k1_ge *group) { + int i; + + /* Note that SwiftEC/ElligatorSwift are inherently curve operations, not + * group operations, and this test only checks the curve points which are in + * a tiny subgroup. In that sense it can't be really seen as exhaustive as + * it doesn't (and for computational reasons obviously cannot) test the + * entire domain ellswift operates under. */ + for (i = 1; i < EXHAUSTIVE_TEST_ORDER; i++) { + secp256k1_scalar scalar_i; + unsigned char sec32[32]; + unsigned char ell64[64]; + secp256k1_pubkey pub_decoded; + secp256k1_ge ge_decoded; + + /* Construct ellswift pubkey from exhaustive loop scalar i. */ + secp256k1_scalar_set_int(&scalar_i, i); + secp256k1_scalar_get_b32(sec32, &scalar_i); + CHECK(secp256k1_ellswift_create(ctx, ell64, sec32, NULL)); + + /* Decode ellswift pubkey and check that it matches the precomputed group element. */ + secp256k1_ellswift_decode(ctx, &pub_decoded, ell64); + secp256k1_pubkey_load(ctx, &ge_decoded, &pub_decoded); + CHECK(secp256k1_ge_eq_var(&ge_decoded, &group[i])); + } +} + +#endif diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/ellswift/tests_impl.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/ellswift/tests_impl.h new file mode 100644 index 00000000000..3c314c9b502 --- /dev/null +++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/ellswift/tests_impl.h @@ -0,0 +1,436 @@ +/*********************************************************************** + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_MODULE_ELLSWIFT_TESTS_H +#define SECP256K1_MODULE_ELLSWIFT_TESTS_H + +#include "../../../include/secp256k1_ellswift.h" + +struct ellswift_xswiftec_inv_test { + int enc_bitmap; + secp256k1_fe u; + secp256k1_fe x; + secp256k1_fe encs[8]; +}; + +struct ellswift_decode_test { + unsigned char enc[64]; + secp256k1_fe x; + int odd_y; +}; + +struct ellswift_xdh_test { + unsigned char priv_ours[32]; + unsigned char ellswift_ours[64]; + unsigned char ellswift_theirs[64]; + int initiating; + unsigned char shared_secret[32]; +}; + +/* Set of (point, encodings) test vectors, selected to maximize branch coverage, part of the BIP324 + * test vectors. Created using an independent implementation, and tested decoding against paper + * authors' code. */ +static const struct ellswift_xswiftec_inv_test ellswift_xswiftec_inv_tests[] = { + {0xcc, SECP256K1_FE_CONST(0x05ff6bda, 0xd900fc32, 0x61bc7fe3, 0x4e2fb0f5, 0x69f06e09, 0x1ae437d3, 0xa52e9da0, 0xcbfb9590), SECP256K1_FE_CONST(0x80cdf637, 0x74ec7022, 0xc89a5a85, 0x58e373a2, 0x79170285, 0xe0ab2741, 0x2dbce510, 0xbdfe23fc), {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0x45654798, 0xece071ba, 0x79286d04, 0xf7f3eb1c, 0x3f1d17dd, 0x883610f2, 0xad2efd82, 0xa287466b), SECP256K1_FE_CONST(0x0aeaa886, 0xf6b76c71, 0x58452418, 0xcbf5033a, 0xdc5747e9, 0xe9b5d3b2, 0x303db969, 0x36528557), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0xba9ab867, 0x131f8e45, 0x86d792fb, 0x080c14e3, 0xc0e2e822, 0x77c9ef0d, 0x52d1027c, 0x5d78b5c4), SECP256K1_FE_CONST(0xf5155779, 0x0948938e, 0xa7badbe7, 0x340afcc5, 0x23a8b816, 0x164a2c4d, 0xcfc24695, 0xc9ad76d8)}}, + {0x33, SECP256K1_FE_CONST(0x1737a85f, 0x4c8d146c, 0xec96e3ff, 0xdca76d99, 0x03dcf3bd, 0x53061868, 0xd478c78c, 0x63c2aa9e), SECP256K1_FE_CONST(0x39e48dd1, 0x50d2f429, 0xbe088dfd, 0x5b61882e, 0x7e840748, 0x3702ae9a, 0x5ab35927, 0xb15f85ea), {SECP256K1_FE_CONST(0x1be8cc0b, 0x04be0c68, 0x1d0c6a68, 0xf733f82c, 0x6c896e0c, 0x8a262fcd, 0x392918e3, 0x03a7abf4), SECP256K1_FE_CONST(0x605b5814, 0xbf9b8cb0, 0x66667c9e, 0x5480d22d, 0xc5b6c92f, 0x14b4af3e, 0xe0a9eb83, 0xb03685e3), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0xe41733f4, 0xfb41f397, 0xe2f39597, 0x08cc07d3, 0x937691f3, 0x75d9d032, 0xc6d6e71b, 0xfc58503b), SECP256K1_FE_CONST(0x9fa4a7eb, 0x4064734f, 0x99998361, 0xab7f2dd2, 0x3a4936d0, 0xeb4b50c1, 0x1f56147b, 0x4fc9764c), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0)}}, + {0x00, SECP256K1_FE_CONST(0x1aaa1cce, 0xbf9c7241, 0x91033df3, 0x66b36f69, 0x1c4d902c, 0x228033ff, 0x4516d122, 0xb2564f68), SECP256K1_FE_CONST(0xc7554125, 0x9d3ba98f, 0x207eaa30, 0xc69634d1, 0x87d0b6da, 0x594e719e, 0x420f4898, 0x638fc5b0), {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0)}}, + {0x33, SECP256K1_FE_CONST(0x2323a1d0, 0x79b0fd72, 0xfc8bb62e, 0xc34230a8, 0x15cb0596, 0xc2bfac99, 0x8bd6b842, 0x60f5dc26), SECP256K1_FE_CONST(0x239342df, 0xb675500a, 0x34a19631, 0x0b8d87d5, 0x4f49dcac, 0x9da50c17, 0x43ceab41, 0xa7b249ff), {SECP256K1_FE_CONST(0xf63580b8, 0xaa49c484, 0x6de56e39, 0xe1b3e73f, 0x171e881e, 0xba8c66f6, 0x14e67e5c, 0x975dfc07), SECP256K1_FE_CONST(0xb6307b33, 0x2e699f1c, 0xf77841d9, 0x0af25365, 0x404deb7f, 0xed5edb30, 0x90db49e6, 0x42a156b6), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0x09ca7f47, 0x55b63b7b, 0x921a91c6, 0x1e4c18c0, 0xe8e177e1, 0x45739909, 0xeb1981a2, 0x68a20028), SECP256K1_FE_CONST(0x49cf84cc, 0xd19660e3, 0x0887be26, 0xf50dac9a, 0xbfb21480, 0x12a124cf, 0x6f24b618, 0xbd5ea579), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0)}}, + {0x33, SECP256K1_FE_CONST(0x2dc90e64, 0x0cb646ae, 0x9164c0b5, 0xa9ef0169, 0xfebe34dc, 0x4437d6e4, 0x6acb0e27, 0xe219d1e8), SECP256K1_FE_CONST(0xd236f19b, 0xf349b951, 0x6e9b3f4a, 0x5610fe96, 0x0141cb23, 0xbbc8291b, 0x9534f1d7, 0x1de62a47), {SECP256K1_FE_CONST(0xe69df7d9, 0xc026c366, 0x00ebdf58, 0x80726758, 0x47c0c431, 0xc8eb7306, 0x82533e96, 0x4b6252c9), SECP256K1_FE_CONST(0x4f18bbdf, 0x7c2d6c5f, 0x818c1880, 0x2fa35cd0, 0x69eaa79f, 0xff74e4fc, 0x837c80d9, 0x3fece2f8), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0x19620826, 0x3fd93c99, 0xff1420a7, 0x7f8d98a7, 0xb83f3bce, 0x37148cf9, 0x7dacc168, 0xb49da966), SECP256K1_FE_CONST(0xb0e74420, 0x83d293a0, 0x7e73e77f, 0xd05ca32f, 0x96155860, 0x008b1b03, 0x7c837f25, 0xc0131937), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0)}}, + {0xcc, SECP256K1_FE_CONST(0x3edd7b39, 0x80e2f2f3, 0x4d1409a2, 0x07069f88, 0x1fda5f96, 0xf08027ac, 0x4465b63d, 0xc278d672), SECP256K1_FE_CONST(0x053a98de, 0x4a27b196, 0x1155822b, 0x3a3121f0, 0x3b2a1445, 0x8bd80eb4, 0xa560c4c7, 0xa85c149c), {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0xb3dae4b7, 0xdcf858e4, 0xc6968057, 0xcef2b156, 0x46543152, 0x6538199c, 0xf52dc1b2, 0xd62fda30), SECP256K1_FE_CONST(0x4aa77dd5, 0x5d6b6d3c, 0xfa10cc9d, 0x0fe42f79, 0x232e4575, 0x661049ae, 0x36779c1d, 0x0c666d88), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0x4c251b48, 0x2307a71b, 0x39697fa8, 0x310d4ea9, 0xb9abcead, 0x9ac7e663, 0x0ad23e4c, 0x29d021ff), SECP256K1_FE_CONST(0xb558822a, 0xa29492c3, 0x05ef3362, 0xf01bd086, 0xdcd1ba8a, 0x99efb651, 0xc98863e1, 0xf3998ea7)}}, + {0x00, SECP256K1_FE_CONST(0x4295737e, 0xfcb1da6f, 0xb1d96b9c, 0xa7dcd1e3, 0x20024b37, 0xa736c494, 0x8b625981, 0x73069f70), SECP256K1_FE_CONST(0xfa7ffe4f, 0x25f88362, 0x831c087a, 0xfe2e8a9b, 0x0713e2ca, 0xc1ddca6a, 0x383205a2, 0x66f14307), {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0)}}, + {0xff, SECP256K1_FE_CONST(0x587c1a0c, 0xee91939e, 0x7f784d23, 0xb963004a, 0x3bf44f5d, 0x4e32a008, 0x1995ba20, 0xb0fca59e), SECP256K1_FE_CONST(0x2ea98853, 0x0715e8d1, 0x0363907f, 0xf2512452, 0x4d471ba2, 0x454d5ce3, 0xbe3f0419, 0x4dfd3a3c), {SECP256K1_FE_CONST(0xcfd5a094, 0xaa0b9b88, 0x91b76c6a, 0xb9438f66, 0xaa1c095a, 0x65f9f701, 0x35e81712, 0x92245e74), SECP256K1_FE_CONST(0xa89057d7, 0xc6563f0d, 0x6efa19ae, 0x84412b8a, 0x7b47e791, 0xa191ecdf, 0xdf2af84f, 0xd97bc339), SECP256K1_FE_CONST(0x475d0ae9, 0xef46920d, 0xf07b3411, 0x7be5a081, 0x7de1023e, 0x3cc32689, 0xe9be145b, 0x406b0aef), SECP256K1_FE_CONST(0xa0759178, 0xad802324, 0x54f827ef, 0x05ea3e72, 0xad8d7541, 0x8e6d4cc1, 0xcd4f5306, 0xc5e7c453), SECP256K1_FE_CONST(0x302a5f6b, 0x55f46477, 0x6e489395, 0x46bc7099, 0x55e3f6a5, 0x9a0608fe, 0xca17e8ec, 0x6ddb9dbb), SECP256K1_FE_CONST(0x576fa828, 0x39a9c0f2, 0x9105e651, 0x7bbed475, 0x84b8186e, 0x5e6e1320, 0x20d507af, 0x268438f6), SECP256K1_FE_CONST(0xb8a2f516, 0x10b96df2, 0x0f84cbee, 0x841a5f7e, 0x821efdc1, 0xc33cd976, 0x1641eba3, 0xbf94f140), SECP256K1_FE_CONST(0x5f8a6e87, 0x527fdcdb, 0xab07d810, 0xfa15c18d, 0x52728abe, 0x7192b33e, 0x32b0acf8, 0x3a1837dc)}}, + {0xcc, SECP256K1_FE_CONST(0x5fa88b33, 0x65a635cb, 0xbcee003c, 0xce9ef51d, 0xd1a310de, 0x277e441a, 0xbccdb7be, 0x1e4ba249), SECP256K1_FE_CONST(0x79461ff6, 0x2bfcbcac, 0x4249ba84, 0xdd040f2c, 0xec3c63f7, 0x25204dc7, 0xf464c16b, 0xf0ff3170), {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0x6bb700e1, 0xf4d7e236, 0xe8d193ff, 0x4a76c1b3, 0xbcd4e2b2, 0x5acac3d5, 0x1c8dac65, 0x3fe909a0), SECP256K1_FE_CONST(0xf4c73410, 0x633da7f6, 0x3a4f1d55, 0xaec6dd32, 0xc4c6d89e, 0xe74075ed, 0xb5515ed9, 0x0da9e683), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0x9448ff1e, 0x0b281dc9, 0x172e6c00, 0xb5893e4c, 0x432b1d4d, 0xa5353c2a, 0xe3725399, 0xc016f28f), SECP256K1_FE_CONST(0x0b38cbef, 0x9cc25809, 0xc5b0e2aa, 0x513922cd, 0x3b392761, 0x18bf8a12, 0x4aaea125, 0xf25615ac)}}, + {0xcc, SECP256K1_FE_CONST(0x6fb31c75, 0x31f03130, 0xb42b155b, 0x952779ef, 0xbb46087d, 0xd9807d24, 0x1a48eac6, 0x3c3d96d6), SECP256K1_FE_CONST(0x56f81be7, 0x53e8d4ae, 0x4940ea6f, 0x46f6ec9f, 0xda66a6f9, 0x6cc95f50, 0x6cb2b574, 0x90e94260), {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0x59059774, 0x795bdb7a, 0x837fbe11, 0x40a5fa59, 0x984f48af, 0x8df95d57, 0xdd6d1c05, 0x437dcec1), SECP256K1_FE_CONST(0x22a644db, 0x79376ad4, 0xe7b3a009, 0xe58b3f13, 0x137c54fd, 0xf911122c, 0xc93667c4, 0x7077d784), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0xa6fa688b, 0x86a42485, 0x7c8041ee, 0xbf5a05a6, 0x67b0b750, 0x7206a2a8, 0x2292e3f9, 0xbc822d6e), SECP256K1_FE_CONST(0xdd59bb24, 0x86c8952b, 0x184c5ff6, 0x1a74c0ec, 0xec83ab02, 0x06eeedd3, 0x36c9983a, 0x8f8824ab)}}, + {0x00, SECP256K1_FE_CONST(0x704cd226, 0xe71cb682, 0x6a590e80, 0xdac90f2d, 0x2f5830f0, 0xfdf135a3, 0xeae3965b, 0xff25ff12), SECP256K1_FE_CONST(0x138e0afa, 0x68936ee6, 0x70bd2b8d, 0xb53aedbb, 0x7bea2a85, 0x97388b24, 0xd0518edd, 0x22ad66ec), {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0)}}, + {0x33, SECP256K1_FE_CONST(0x725e9147, 0x92cb8c89, 0x49e7e116, 0x8b7cdd8a, 0x8094c91c, 0x6ec2202c, 0xcd53a6a1, 0x8771edeb), SECP256K1_FE_CONST(0x8da16eb8, 0x6d347376, 0xb6181ee9, 0x74832275, 0x7f6b36e3, 0x913ddfd3, 0x32ac595d, 0x788e0e44), {SECP256K1_FE_CONST(0xdd357786, 0xb9f68733, 0x30391aa5, 0x62580965, 0x4e43116e, 0x82a5a5d8, 0x2ffd1d66, 0x24101fc4), SECP256K1_FE_CONST(0xa0b7efca, 0x01814594, 0xc59c9aae, 0x8e497001, 0x86ca5d95, 0xe88bcc80, 0x399044d9, 0xc2d8613d), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0x22ca8879, 0x460978cc, 0xcfc6e55a, 0x9da7f69a, 0xb1bcee91, 0x7d5a5a27, 0xd002e298, 0xdbefdc6b), SECP256K1_FE_CONST(0x5f481035, 0xfe7eba6b, 0x3a636551, 0x71b68ffe, 0x7935a26a, 0x1774337f, 0xc66fbb25, 0x3d279af2), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0)}}, + {0x00, SECP256K1_FE_CONST(0x78fe6b71, 0x7f2ea4a3, 0x2708d79c, 0x151bf503, 0xa5312a18, 0xc0963437, 0xe865cc6e, 0xd3f6ae97), SECP256K1_FE_CONST(0x8701948e, 0x80d15b5c, 0xd8f72863, 0xeae40afc, 0x5aced5e7, 0x3f69cbc8, 0x179a3390, 0x2c094d98), {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0)}}, + {0x44, SECP256K1_FE_CONST(0x7c37bb9c, 0x5061dc07, 0x413f11ac, 0xd5a34006, 0xe64c5c45, 0x7fdb9a43, 0x8f217255, 0xa961f50d), SECP256K1_FE_CONST(0x5c1a76b4, 0x4568eb59, 0xd6789a74, 0x42d9ed7c, 0xdc6226b7, 0x752b4ff8, 0xeaf8e1a9, 0x5736e507), {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0xb94d30cd, 0x7dbff60b, 0x64620c17, 0xca0fafaa, 0x40b3d1f5, 0x2d077a60, 0xa2e0cafd, 0x145086c2), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0x46b2cf32, 0x824009f4, 0x9b9df3e8, 0x35f05055, 0xbf4c2e0a, 0xd2f8859f, 0x5d1f3501, 0xebaf756d), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0)}}, + {0x00, SECP256K1_FE_CONST(0x82388888, 0x967f82a6, 0xb444438a, 0x7d44838e, 0x13c0d478, 0xb9ca060d, 0xa95a41fb, 0x94303de6), SECP256K1_FE_CONST(0x29e96541, 0x70628fec, 0x8b497289, 0x8b113cf9, 0x8807f460, 0x9274f4f3, 0x140d0674, 0x157c90a0), {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0)}}, + {0x33, SECP256K1_FE_CONST(0x91298f57, 0x70af7a27, 0xf0a47188, 0xd24c3b7b, 0xf98ab299, 0x0d84b0b8, 0x98507e3c, 0x561d6472), SECP256K1_FE_CONST(0x144f4ccb, 0xd9a74698, 0xa88cbf6f, 0xd00ad886, 0xd339d29e, 0xa19448f2, 0xc572cac0, 0xa07d5562), {SECP256K1_FE_CONST(0xe6a0ffa3, 0x807f09da, 0xdbe71e0f, 0x4be4725f, 0x2832e76c, 0xad8dc1d9, 0x43ce8393, 0x75eff248), SECP256K1_FE_CONST(0x837b8e68, 0xd4917544, 0x764ad090, 0x3cb11f86, 0x15d2823c, 0xefbb06d8, 0x9049dbab, 0xc69befda), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0x195f005c, 0x7f80f625, 0x2418e1f0, 0xb41b8da0, 0xd7cd1893, 0x52723e26, 0xbc317c6b, 0x8a1009e7), SECP256K1_FE_CONST(0x7c847197, 0x2b6e8abb, 0x89b52f6f, 0xc34ee079, 0xea2d7dc3, 0x1044f927, 0x6fb62453, 0x39640c55), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0)}}, + {0x00, SECP256K1_FE_CONST(0xb682f3d0, 0x3bbb5dee, 0x4f54b5eb, 0xfba931b4, 0xf52f6a19, 0x1e5c2f48, 0x3c73c66e, 0x9ace97e1), SECP256K1_FE_CONST(0x904717bf, 0x0bc0cb78, 0x73fcdc38, 0xaa97f19e, 0x3a626309, 0x72acff92, 0xb24cc6dd, 0xa197cb96), {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0)}}, + {0x77, SECP256K1_FE_CONST(0xc17ec69e, 0x665f0fb0, 0xdbab48d9, 0xc2f94d12, 0xec8a9d7e, 0xacb58084, 0x83309180, 0x1eb0b80b), SECP256K1_FE_CONST(0x147756e6, 0x6d96e31c, 0x426d3cc8, 0x5ed0c4cf, 0xbef6341d, 0xd8b28558, 0x5aa574ea, 0x0204b55e), {SECP256K1_FE_CONST(0x6f4aea43, 0x1a0043bd, 0xd03134d6, 0xd9159119, 0xce034b88, 0xc32e50e8, 0xe36c4ee4, 0x5eac7ae9), SECP256K1_FE_CONST(0xfd5be16d, 0x4ffa2690, 0x126c67c3, 0xef7cb9d2, 0x9b74d397, 0xc78b06b3, 0x605fda34, 0xdc9696a6), SECP256K1_FE_CONST(0x5e9c6079, 0x2a2f000e, 0x45c6250f, 0x296f875e, 0x174efc0e, 0x9703e628, 0x706103a9, 0xdd2d82c7), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0x90b515bc, 0xe5ffbc42, 0x2fcecb29, 0x26ea6ee6, 0x31fcb477, 0x3cd1af17, 0x1c93b11a, 0xa1538146), SECP256K1_FE_CONST(0x02a41e92, 0xb005d96f, 0xed93983c, 0x1083462d, 0x648b2c68, 0x3874f94c, 0x9fa025ca, 0x23696589), SECP256K1_FE_CONST(0xa1639f86, 0xd5d0fff1, 0xba39daf0, 0xd69078a1, 0xe8b103f1, 0x68fc19d7, 0x8f9efc55, 0x22d27968), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0)}}, + {0xcc, SECP256K1_FE_CONST(0xc25172fc, 0x3f29b6fc, 0x4a1155b8, 0x57523315, 0x5486b274, 0x64b74b8b, 0x260b499a, 0x3f53cb14), SECP256K1_FE_CONST(0x1ea9cbdb, 0x35cf6e03, 0x29aa31b0, 0xbb0a702a, 0x65123ed0, 0x08655a93, 0xb7dcd528, 0x0e52e1ab), {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0x7422edc7, 0x843136af, 0x0053bb88, 0x54448a82, 0x99994f9d, 0xdcefd3a9, 0xa92d4546, 0x2c59298a), SECP256K1_FE_CONST(0x78c7774a, 0x266f8b97, 0xea23d05d, 0x064f033c, 0x77319f92, 0x3f6b78bc, 0xe4e20bf0, 0x5fa5398d), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0x8bdd1238, 0x7bcec950, 0xffac4477, 0xabbb757d, 0x6666b062, 0x23102c56, 0x56d2bab8, 0xd3a6d2a5), SECP256K1_FE_CONST(0x873888b5, 0xd9907468, 0x15dc2fa2, 0xf9b0fcc3, 0x88ce606d, 0xc0948743, 0x1b1df40e, 0xa05ac2a2)}}, + {0x00, SECP256K1_FE_CONST(0xcab6626f, 0x832a4b12, 0x80ba7add, 0x2fc5322f, 0xf011caed, 0xedf7ff4d, 0xb6735d50, 0x26dc0367), SECP256K1_FE_CONST(0x2b2bef08, 0x52c6f7c9, 0x5d72ac99, 0xa23802b8, 0x75029cd5, 0x73b248d1, 0xf1b3fc80, 0x33788eb6), {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0)}}, + {0x33, SECP256K1_FE_CONST(0xd8621b4f, 0xfc85b9ed, 0x56e99d8d, 0xd1dd24ae, 0xdcecb147, 0x63b861a1, 0x7112dc77, 0x1a104fd2), SECP256K1_FE_CONST(0x812cabe9, 0x72a22aa6, 0x7c7da0c9, 0x4d8a9362, 0x96eb9949, 0xd70c37cb, 0x2b248757, 0x4cb3ce58), {SECP256K1_FE_CONST(0xfbc5febc, 0x6fdbc9ae, 0x3eb88a93, 0xb982196e, 0x8b6275a6, 0xd5a73c17, 0x387e000c, 0x711bd0e3), SECP256K1_FE_CONST(0x8724c96b, 0xd4e5527f, 0x2dd195a5, 0x1c468d2d, 0x211ba2fa, 0xc7cbe0b4, 0xb3434253, 0x409fb42d), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0x043a0143, 0x90243651, 0xc147756c, 0x467de691, 0x749d8a59, 0x2a58c3e8, 0xc781fff2, 0x8ee42b4c), SECP256K1_FE_CONST(0x78db3694, 0x2b1aad80, 0xd22e6a5a, 0xe3b972d2, 0xdee45d05, 0x38341f4b, 0x4cbcbdab, 0xbf604802), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0)}}, + {0x00, SECP256K1_FE_CONST(0xda463164, 0xc6f4bf71, 0x29ee5f0e, 0xc00f65a6, 0x75a8adf1, 0xbd931b39, 0xb64806af, 0xdcda9a22), SECP256K1_FE_CONST(0x25b9ce9b, 0x390b408e, 0xd611a0f1, 0x3ff09a59, 0x8a57520e, 0x426ce4c6, 0x49b7f94f, 0x2325620d), {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0)}}, + {0xcc, SECP256K1_FE_CONST(0xdafc971e, 0x4a3a7b6d, 0xcfb42a08, 0xd9692d82, 0xad9e7838, 0x523fcbda, 0x1d4827e1, 0x4481ae2d), SECP256K1_FE_CONST(0x250368e1, 0xb5c58492, 0x304bd5f7, 0x2696d27d, 0x526187c7, 0xadc03425, 0xe2b7d81d, 0xbb7e4e02), {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0x370c28f1, 0xbe665efa, 0xcde6aa43, 0x6bf86fe2, 0x1e6e314c, 0x1e53dd04, 0x0e6c73a4, 0x6b4c8c49), SECP256K1_FE_CONST(0xcd8acee9, 0x8ffe5653, 0x1a84d7eb, 0x3e48fa40, 0x34206ce8, 0x25ace907, 0xd0edf0ea, 0xeb5e9ca2), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0xc8f3d70e, 0x4199a105, 0x321955bc, 0x9407901d, 0xe191ceb3, 0xe1ac22fb, 0xf1938c5a, 0x94b36fe6), SECP256K1_FE_CONST(0x32753116, 0x7001a9ac, 0xe57b2814, 0xc1b705bf, 0xcbdf9317, 0xda5316f8, 0x2f120f14, 0x14a15f8d)}}, + {0x44, SECP256K1_FE_CONST(0xe0294c8b, 0xc1a36b41, 0x66ee92bf, 0xa70a5c34, 0x976fa982, 0x9405efea, 0x8f9cd54d, 0xcb29b99e), SECP256K1_FE_CONST(0xae9690d1, 0x3b8d20a0, 0xfbbf37be, 0xd8474f67, 0xa04e142f, 0x56efd787, 0x70a76b35, 0x9165d8a1), {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0xdcd45d93, 0x5613916a, 0xf167b029, 0x058ba3a7, 0x00d37150, 0xb9df3472, 0x8cb05412, 0xc16d4182), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0x232ba26c, 0xa9ec6e95, 0x0e984fd6, 0xfa745c58, 0xff2c8eaf, 0x4620cb8d, 0x734fabec, 0x3e92baad), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0)}}, + {0x00, SECP256K1_FE_CONST(0xe148441c, 0xd7b92b8b, 0x0e4fa3bd, 0x68712cfd, 0x0d709ad1, 0x98cace61, 0x1493c10e, 0x97f5394e), SECP256K1_FE_CONST(0x164a6397, 0x94d74c53, 0xafc4d329, 0x4e79cdb3, 0xcd25f99f, 0x6df45c00, 0x0f758aba, 0x54d699c0), {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0)}}, + {0xff, SECP256K1_FE_CONST(0xe4b00ec9, 0x7aadcca9, 0x7644d3b0, 0xc8a931b1, 0x4ce7bcf7, 0xbc877954, 0x6d6e35aa, 0x5937381c), SECP256K1_FE_CONST(0x94e9588d, 0x41647b3f, 0xcc772dc8, 0xd83c67ce, 0x3be00353, 0x8517c834, 0x103d2cd4, 0x9d62ef4d), {SECP256K1_FE_CONST(0xc88d25f4, 0x1407376b, 0xb2c03a7f, 0xffeb3ec7, 0x811cc434, 0x91a0c3aa, 0xc0378cdc, 0x78357bee), SECP256K1_FE_CONST(0x51c02636, 0xce00c234, 0x5ecd89ad, 0xb6089fe4, 0xd5e18ac9, 0x24e3145e, 0x6669501c, 0xd37a00d4), SECP256K1_FE_CONST(0x205b3512, 0xdb40521c, 0xb200952e, 0x67b46f67, 0xe09e7839, 0xe0de4400, 0x4138329e, 0xbd9138c5), SECP256K1_FE_CONST(0x58aab390, 0xab6fb55c, 0x1d1b8089, 0x7a207ce9, 0x4a78fa5b, 0x4aa61a33, 0x398bcae9, 0xadb20d3e), SECP256K1_FE_CONST(0x3772da0b, 0xebf8c894, 0x4d3fc580, 0x0014c138, 0x7ee33bcb, 0x6e5f3c55, 0x3fc87322, 0x87ca8041), SECP256K1_FE_CONST(0xae3fd9c9, 0x31ff3dcb, 0xa1327652, 0x49f7601b, 0x2a1e7536, 0xdb1ceba1, 0x9996afe2, 0x2c85fb5b), SECP256K1_FE_CONST(0xdfa4caed, 0x24bfade3, 0x4dff6ad1, 0x984b9098, 0x1f6187c6, 0x1f21bbff, 0xbec7cd60, 0x426ec36a), SECP256K1_FE_CONST(0xa7554c6f, 0x54904aa3, 0xe2e47f76, 0x85df8316, 0xb58705a4, 0xb559e5cc, 0xc6743515, 0x524deef1)}}, + {0x00, SECP256K1_FE_CONST(0xe5bbb9ef, 0x360d0a50, 0x1618f006, 0x7d36dceb, 0x75f5be9a, 0x620232aa, 0x9fd5139d, 0x0863fde5), SECP256K1_FE_CONST(0xe5bbb9ef, 0x360d0a50, 0x1618f006, 0x7d36dceb, 0x75f5be9a, 0x620232aa, 0x9fd5139d, 0x0863fde5), {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0)}}, + {0xff, SECP256K1_FE_CONST(0xe6bcb5c3, 0xd63467d4, 0x90bfa54f, 0xbbc6092a, 0x7248c25e, 0x11b248dc, 0x2964a6e1, 0x5edb1457), SECP256K1_FE_CONST(0x19434a3c, 0x29cb982b, 0x6f405ab0, 0x4439f6d5, 0x8db73da1, 0xee4db723, 0xd69b591d, 0xa124e7d8), {SECP256K1_FE_CONST(0x67119877, 0x832ab8f4, 0x59a82165, 0x6d8261f5, 0x44a553b8, 0x9ae4f25c, 0x52a97134, 0xb70f3426), SECP256K1_FE_CONST(0xffee02f5, 0xe649c07f, 0x0560eff1, 0x867ec7b3, 0x2d0e595e, 0x9b1c0ea6, 0xe2a4fc70, 0xc97cd71f), SECP256K1_FE_CONST(0xb5e0c189, 0xeb5b4bac, 0xd025b744, 0x4d74178b, 0xe8d5246c, 0xfa4a9a20, 0x7964a057, 0xee969992), SECP256K1_FE_CONST(0x5746e459, 0x1bf7f4c3, 0x044609ea, 0x372e9086, 0x03975d27, 0x9fdef834, 0x9f0b08d3, 0x2f07619d), SECP256K1_FE_CONST(0x98ee6788, 0x7cd5470b, 0xa657de9a, 0x927d9e0a, 0xbb5aac47, 0x651b0da3, 0xad568eca, 0x48f0c809), SECP256K1_FE_CONST(0x0011fd0a, 0x19b63f80, 0xfa9f100e, 0x7981384c, 0xd2f1a6a1, 0x64e3f159, 0x1d5b038e, 0x36832510), SECP256K1_FE_CONST(0x4a1f3e76, 0x14a4b453, 0x2fda48bb, 0xb28be874, 0x172adb93, 0x05b565df, 0x869b5fa7, 0x1169629d), SECP256K1_FE_CONST(0xa8b91ba6, 0xe4080b3c, 0xfbb9f615, 0xc8d16f79, 0xfc68a2d8, 0x602107cb, 0x60f4f72b, 0xd0f89a92)}}, + {0x33, SECP256K1_FE_CONST(0xf28fba64, 0xaf766845, 0xeb2f4302, 0x456e2b9f, 0x8d80affe, 0x57e7aae4, 0x2738d7cd, 0xdb1c2ce6), SECP256K1_FE_CONST(0xf28fba64, 0xaf766845, 0xeb2f4302, 0x456e2b9f, 0x8d80affe, 0x57e7aae4, 0x2738d7cd, 0xdb1c2ce6), {SECP256K1_FE_CONST(0x4f867ad8, 0xbb3d8404, 0x09d26b67, 0x307e6210, 0x0153273f, 0x72fa4b74, 0x84becfa1, 0x4ebe7408), SECP256K1_FE_CONST(0x5bbc4f59, 0xe452cc5f, 0x22a99144, 0xb10ce898, 0x9a89a995, 0xec3cea1c, 0x91ae10e8, 0xf721bb5d), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0xb0798527, 0x44c27bfb, 0xf62d9498, 0xcf819def, 0xfeacd8c0, 0x8d05b48b, 0x7b41305d, 0xb1418827), SECP256K1_FE_CONST(0xa443b0a6, 0x1bad33a0, 0xdd566ebb, 0x4ef31767, 0x6576566a, 0x13c315e3, 0x6e51ef16, 0x08de40d2), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0)}}, + {0xcc, SECP256K1_FE_CONST(0xf455605b, 0xc85bf48e, 0x3a908c31, 0x023faf98, 0x381504c6, 0xc6d3aeb9, 0xede55f8d, 0xd528924d), SECP256K1_FE_CONST(0xd31fbcd5, 0xcdb798f6, 0xc00db669, 0x2f8fe896, 0x7fa9c79d, 0xd10958f4, 0xa194f013, 0x74905e99), {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0x0c00c571, 0x5b56fe63, 0x2d814ad8, 0xa77f8e66, 0x628ea47a, 0x6116834f, 0x8c1218f3, 0xa03cbd50), SECP256K1_FE_CONST(0xdf88e44f, 0xac84fa52, 0xdf4d59f4, 0x8819f18f, 0x6a8cd415, 0x1d162afa, 0xf773166f, 0x57c7ff46), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0xf3ff3a8e, 0xa4a9019c, 0xd27eb527, 0x58807199, 0x9d715b85, 0x9ee97cb0, 0x73ede70b, 0x5fc33edf), SECP256K1_FE_CONST(0x20771bb0, 0x537b05ad, 0x20b2a60b, 0x77e60e70, 0x95732bea, 0xe2e9d505, 0x088ce98f, 0xa837fce9)}}, + {0xff, SECP256K1_FE_CONST(0xf58cd4d9, 0x830bad32, 0x2699035e, 0x8246007d, 0x4be27e19, 0xb6f53621, 0x317b4f30, 0x9b3daa9d), SECP256K1_FE_CONST(0x78ec2b3d, 0xc0948de5, 0x60148bbc, 0x7c6dc963, 0x3ad5df70, 0xa5a5750c, 0xbed72180, 0x4f082a3b), {SECP256K1_FE_CONST(0x6c4c580b, 0x76c75940, 0x43569f9d, 0xae16dc28, 0x01c16a1f, 0xbe128608, 0x81b75f8e, 0xf929bce5), SECP256K1_FE_CONST(0x94231355, 0xe7385c5f, 0x25ca436a, 0xa6419147, 0x1aea4393, 0xd6e86ab7, 0xa35fe2af, 0xacaefd0d), SECP256K1_FE_CONST(0xdff2a195, 0x1ada6db5, 0x74df8340, 0x48149da3, 0x397a75b8, 0x29abf58c, 0x7e69db1b, 0x41ac0989), SECP256K1_FE_CONST(0xa52b66d3, 0xc9070355, 0x48028bf8, 0x04711bf4, 0x22aba95f, 0x1a666fc8, 0x6f4648e0, 0x5f29caae), SECP256K1_FE_CONST(0x93b3a7f4, 0x8938a6bf, 0xbca96062, 0x51e923d7, 0xfe3e95e0, 0x41ed79f7, 0x7e48a070, 0x06d63f4a), SECP256K1_FE_CONST(0x6bdcecaa, 0x18c7a3a0, 0xda35bc95, 0x59be6eb8, 0xe515bc6c, 0x29179548, 0x5ca01d4f, 0x5350ff22), SECP256K1_FE_CONST(0x200d5e6a, 0xe525924a, 0x8b207cbf, 0xb7eb625c, 0xc6858a47, 0xd6540a73, 0x819624e3, 0xbe53f2a6), SECP256K1_FE_CONST(0x5ad4992c, 0x36f8fcaa, 0xb7fd7407, 0xfb8ee40b, 0xdd5456a0, 0xe5999037, 0x90b9b71e, 0xa0d63181)}}, + {0x00, SECP256K1_FE_CONST(0xfd7d912a, 0x40f182a3, 0x588800d6, 0x9ebfb504, 0x8766da20, 0x6fd7ebc8, 0xd2436c81, 0xcbef6421), SECP256K1_FE_CONST(0x8d37c862, 0x054debe7, 0x31694536, 0xff46b273, 0xec122b35, 0xa9bf1445, 0xac3c4ff9, 0xf262c952), {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0)}}, +}; + +/* Set of (encoding, xcoord) test vectors, selected to maximize branch coverage, part of the BIP324 + * test vectors. Created using an independent implementation, and tested decoding against the paper + * authors' code. */ +static const struct ellswift_decode_test ellswift_decode_tests[] = { + {{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}, SECP256K1_FE_CONST(0xedd1fd3e, 0x327ce90c, 0xc7a35426, 0x14289aee, 0x9682003e, 0x9cf7dcc9, 0xcf2ca974, 0x3be5aa0c), 0}, + {{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, 0xd3, 0x47, 0x5b, 0xf7, 0x65, 0x5b, 0x0f, 0xb2, 0xd8, 0x52, 0x92, 0x10, 0x35, 0xb2, 0xef, 0x60, 0x7f, 0x49, 0x06, 0x9b, 0x97, 0x45, 0x4e, 0x67, 0x95, 0x25, 0x10, 0x62, 0x74, 0x17, 0x71}, SECP256K1_FE_CONST(0xb5da00b7, 0x3cd65605, 0x20e7c364, 0x086e7cd2, 0x3a34bf60, 0xd0e707be, 0x9fc34d4c, 0xd5fdfa2c), 1}, + {{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x82, 0x27, 0x7c, 0x4a, 0x71, 0xf9, 0xd2, 0x2e, 0x66, 0xec, 0xe5, 0x23, 0xf8, 0xfa, 0x08, 0x74, 0x1a, 0x7c, 0x09, 0x12, 0xc6, 0x6a, 0x69, 0xce, 0x68, 0x51, 0x4b, 0xfd, 0x35, 0x15, 0xb4, 0x9f}, SECP256K1_FE_CONST(0xf482f2e2, 0x41753ad0, 0xfb89150d, 0x8491dc1e, 0x34ff0b8a, 0xcfbb442c, 0xfe999e2e, 0x5e6fd1d2), 1}, + {{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x84, 0x21, 0xcc, 0x93, 0x0e, 0x77, 0xc9, 0xf5, 0x14, 0xb6, 0x91, 0x5c, 0x3d, 0xbe, 0x2a, 0x94, 0xc6, 0xd8, 0xf6, 0x90, 0xb5, 0xb7, 0x39, 0x86, 0x4b, 0xa6, 0x78, 0x9f, 0xb8, 0xa5, 0x5d, 0xd0}, SECP256K1_FE_CONST(0x9f59c402, 0x75f5085a, 0x006f05da, 0xe77eb98c, 0x6fd0db1a, 0xb4a72ac4, 0x7eae90a4, 0xfc9e57e0), 0}, + {{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xbd, 0xe7, 0x0d, 0xf5, 0x19, 0x39, 0xb9, 0x4c, 0x9c, 0x24, 0x97, 0x9f, 0xa7, 0xdd, 0x04, 0xeb, 0xd9, 0xb3, 0x57, 0x2d, 0xa7, 0x80, 0x22, 0x90, 0x43, 0x8a, 0xf2, 0xa6, 0x81, 0x89, 0x54, 0x41}, SECP256K1_FE_CONST(0xaaaaaaaa, 0xaaaaaaaa, 0xaaaaaaaa, 0xaaaaaaaa, 0xaaaaaaaa, 0xaaaaaaaa, 0xaaaaaaa9, 0xfffffd6b), 1}, + {{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xd1, 0x9c, 0x18, 0x2d, 0x27, 0x59, 0xcd, 0x99, 0x82, 0x42, 0x28, 0xd9, 0x47, 0x99, 0xf8, 0xc6, 0x55, 0x7c, 0x38, 0xa1, 0xc0, 0xd6, 0x77, 0x9b, 0x9d, 0x4b, 0x72, 0x9c, 0x6f, 0x1c, 0xcc, 0x42}, SECP256K1_FE_CONST(0x70720db7, 0xe238d041, 0x21f5b1af, 0xd8cc5ad9, 0xd18944c6, 0xbdc94881, 0xf502b7a3, 0xaf3aecff), 0}, + {{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2f}, SECP256K1_FE_CONST(0xedd1fd3e, 0x327ce90c, 0xc7a35426, 0x14289aee, 0x9682003e, 0x9cf7dcc9, 0xcf2ca974, 0x3be5aa0c), 0}, + {{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x26, 0x64, 0xbb, 0xd5}, SECP256K1_FE_CONST(0x50873db3, 0x1badcc71, 0x890e4f67, 0x753a6575, 0x7f97aaa7, 0xdd5f1e82, 0xb753ace3, 0x2219064b), 0}, + {{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x70, 0x28, 0xde, 0x7d}, SECP256K1_FE_CONST(0x1eea9cc5, 0x9cfcf2fa, 0x151ac6c2, 0x74eea411, 0x0feb4f7b, 0x68c59657, 0x32e9992e, 0x976ef68e), 0}, + {{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xcb, 0xcf, 0xb7, 0xe7}, SECP256K1_FE_CONST(0x12303941, 0xaedc2088, 0x80735b1f, 0x1795c8e5, 0x5be520ea, 0x93e10335, 0x7b5d2adb, 0x7ed59b8e), 0}, + {{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xf3, 0x11, 0x3a, 0xd9}, SECP256K1_FE_CONST(0x7eed6b70, 0xe7b0767c, 0x7d7feac0, 0x4e57aa2a, 0x12fef5e0, 0xf48f878f, 0xcbb88b3b, 0x6b5e0783), 0}, + {{0x0a, 0x2d, 0x2b, 0xa9, 0x35, 0x07, 0xf1, 0xdf, 0x23, 0x37, 0x70, 0xc2, 0xa7, 0x97, 0x96, 0x2c, 0xc6, 0x1f, 0x6d, 0x15, 0xda, 0x14, 0xec, 0xd4, 0x7d, 0x8d, 0x27, 0xae, 0x1c, 0xd5, 0xf8, 0x53, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}, SECP256K1_FE_CONST(0x532167c1, 0x1200b08c, 0x0e84a354, 0xe74dcc40, 0xf8b25f4f, 0xe686e308, 0x69526366, 0x278a0688), 0}, + {{0x0a, 0x2d, 0x2b, 0xa9, 0x35, 0x07, 0xf1, 0xdf, 0x23, 0x37, 0x70, 0xc2, 0xa7, 0x97, 0x96, 0x2c, 0xc6, 0x1f, 0x6d, 0x15, 0xda, 0x14, 0xec, 0xd4, 0x7d, 0x8d, 0x27, 0xae, 0x1c, 0xd5, 0xf8, 0x53, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2f}, SECP256K1_FE_CONST(0x532167c1, 0x1200b08c, 0x0e84a354, 0xe74dcc40, 0xf8b25f4f, 0xe686e308, 0x69526366, 0x278a0688), 0}, + {{0x0f, 0xfd, 0xe9, 0xca, 0x81, 0xd7, 0x51, 0xe9, 0xcd, 0xaf, 0xfc, 0x1a, 0x50, 0x77, 0x92, 0x45, 0x32, 0x0b, 0x28, 0x99, 0x6d, 0xba, 0xf3, 0x2f, 0x82, 0x2f, 0x20, 0x11, 0x7c, 0x22, 0xfb, 0xd6, 0xc7, 0x4d, 0x99, 0xef, 0xce, 0xaa, 0x55, 0x0f, 0x1a, 0xd1, 0xc0, 0xf4, 0x3f, 0x46, 0xe7, 0xff, 0x1e, 0xe3, 0xbd, 0x01, 0x62, 0xb7, 0xbf, 0x55, 0xf2, 0x96, 0x5d, 0xa9, 0xc3, 0x45, 0x06, 0x46}, SECP256K1_FE_CONST(0x74e880b3, 0xffd18fe3, 0xcddf7902, 0x522551dd, 0xf97fa4a3, 0x5a3cfda8, 0x197f9470, 0x81a57b8f), 0}, + {{0x0f, 0xfd, 0xe9, 0xca, 0x81, 0xd7, 0x51, 0xe9, 0xcd, 0xaf, 0xfc, 0x1a, 0x50, 0x77, 0x92, 0x45, 0x32, 0x0b, 0x28, 0x99, 0x6d, 0xba, 0xf3, 0x2f, 0x82, 0x2f, 0x20, 0x11, 0x7c, 0x22, 0xfb, 0xd6, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x15, 0x6c, 0xa8, 0x96}, SECP256K1_FE_CONST(0x377b643f, 0xce2271f6, 0x4e5c8101, 0x566107c1, 0xbe498074, 0x50917838, 0x04f65478, 0x1ac9217c), 1}, + {{0x12, 0x36, 0x58, 0x44, 0x4f, 0x32, 0xbe, 0x8f, 0x02, 0xea, 0x20, 0x34, 0xaf, 0xa7, 0xef, 0x4b, 0xbe, 0x8a, 0xdc, 0x91, 0x8c, 0xeb, 0x49, 0xb1, 0x27, 0x73, 0xb6, 0x25, 0xf4, 0x90, 0xb3, 0x68, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x8d, 0xc5, 0xfe, 0x11}, SECP256K1_FE_CONST(0xed16d65c, 0xf3a9538f, 0xcb2c139f, 0x1ecbc143, 0xee148271, 0x20cbc265, 0x9e667256, 0x800b8142), 0}, + {{0x14, 0x6f, 0x92, 0x46, 0x4d, 0x15, 0xd3, 0x6e, 0x35, 0x38, 0x2b, 0xd3, 0xca, 0x5b, 0x0f, 0x97, 0x6c, 0x95, 0xcb, 0x08, 0xac, 0xdc, 0xf2, 0xd5, 0xb3, 0x57, 0x06, 0x17, 0x99, 0x08, 0x39, 0xd7, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x31, 0x45, 0xe9, 0x3b}, SECP256K1_FE_CONST(0x0d5cd840, 0x427f941f, 0x65193079, 0xab8e2e83, 0x024ef2ee, 0x7ca558d8, 0x8879ffd8, 0x79fb6657), 0}, + {{0x15, 0xfd, 0xf5, 0xcf, 0x09, 0xc9, 0x07, 0x59, 0xad, 0xd2, 0x27, 0x2d, 0x57, 0x4d, 0x2b, 0xb5, 0xfe, 0x14, 0x29, 0xf9, 0xf3, 0xc1, 0x4c, 0x65, 0xe3, 0x19, 0x4b, 0xf6, 0x1b, 0x82, 0xaa, 0x73, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x04, 0xcf, 0xd9, 0x06}, SECP256K1_FE_CONST(0x16d0e439, 0x46aec93f, 0x62d57eb8, 0xcde68951, 0xaf136cf4, 0xb307938d, 0xd1447411, 0xe07bffe1), 1}, + {{0x1f, 0x67, 0xed, 0xf7, 0x79, 0xa8, 0xa6, 0x49, 0xd6, 0xde, 0xf6, 0x00, 0x35, 0xf2, 0xfa, 0x22, 0xd0, 0x22, 0xdd, 0x35, 0x90, 0x79, 0xa1, 0xa1, 0x44, 0x07, 0x3d, 0x84, 0xf1, 0x9b, 0x92, 0xd5, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}, SECP256K1_FE_CONST(0x025661f9, 0xaba9d15c, 0x3118456b, 0xbe980e3e, 0x1b8ba2e0, 0x47c737a4, 0xeb48a040, 0xbb566f6c), 0}, + {{0x1f, 0x67, 0xed, 0xf7, 0x79, 0xa8, 0xa6, 0x49, 0xd6, 0xde, 0xf6, 0x00, 0x35, 0xf2, 0xfa, 0x22, 0xd0, 0x22, 0xdd, 0x35, 0x90, 0x79, 0xa1, 0xa1, 0x44, 0x07, 0x3d, 0x84, 0xf1, 0x9b, 0x92, 0xd5, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2f}, SECP256K1_FE_CONST(0x025661f9, 0xaba9d15c, 0x3118456b, 0xbe980e3e, 0x1b8ba2e0, 0x47c737a4, 0xeb48a040, 0xbb566f6c), 0}, + {{0x1f, 0xe1, 0xe5, 0xef, 0x3f, 0xce, 0xb5, 0xc1, 0x35, 0xab, 0x77, 0x41, 0x33, 0x3c, 0xe5, 0xa6, 0xe8, 0x0d, 0x68, 0x16, 0x76, 0x53, 0xf6, 0xb2, 0xb2, 0x4b, 0xcb, 0xcf, 0xaa, 0xaf, 0xf5, 0x07, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2f}, SECP256K1_FE_CONST(0x98bec3b2, 0xa351fa96, 0xcfd191c1, 0x77835193, 0x1b9e9ba9, 0xad1149f6, 0xd9eadca8, 0x0981b801), 0}, + {{0x40, 0x56, 0xa3, 0x4a, 0x21, 0x0e, 0xec, 0x78, 0x92, 0xe8, 0x82, 0x06, 0x75, 0xc8, 0x60, 0x09, 0x9f, 0x85, 0x7b, 0x26, 0xaa, 0xd8, 0x54, 0x70, 0xee, 0x6d, 0x3c, 0xf1, 0x30, 0x4a, 0x9d, 0xcf, 0x37, 0x5e, 0x70, 0x37, 0x42, 0x71, 0xf2, 0x0b, 0x13, 0xc9, 0x98, 0x6e, 0xd7, 0xd3, 0xc1, 0x77, 0x99, 0x69, 0x8c, 0xfc, 0x43, 0x5d, 0xbe, 0xd3, 0xa9, 0xf3, 0x4b, 0x38, 0xc8, 0x23, 0xc2, 0xb4}, SECP256K1_FE_CONST(0x868aac20, 0x03b29dbc, 0xad1a3e80, 0x3855e078, 0xa89d1654, 0x3ac64392, 0xd1224172, 0x98cec76e), 0}, + {{0x41, 0x97, 0xec, 0x37, 0x23, 0xc6, 0x54, 0xcf, 0xdd, 0x32, 0xab, 0x07, 0x55, 0x06, 0x64, 0x8b, 0x2f, 0xf5, 0x07, 0x03, 0x62, 0xd0, 0x1a, 0x4f, 0xff, 0x14, 0xb3, 0x36, 0xb7, 0x8f, 0x96, 0x3f, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xb3, 0xab, 0x1e, 0x95}, SECP256K1_FE_CONST(0xba5a6314, 0x502a8952, 0xb8f456e0, 0x85928105, 0xf665377a, 0x8ce27726, 0xa5b0eb7e, 0xc1ac0286), 0}, + {{0x47, 0xeb, 0x3e, 0x20, 0x8f, 0xed, 0xcd, 0xf8, 0x23, 0x4c, 0x94, 0x21, 0xe9, 0xcd, 0x9a, 0x7a, 0xe8, 0x73, 0xbf, 0xbd, 0xbc, 0x39, 0x37, 0x23, 0xd1, 0xba, 0x1e, 0x1e, 0x6a, 0x8e, 0x6b, 0x24, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7c, 0xd1, 0x2c, 0xb1}, SECP256K1_FE_CONST(0xd192d520, 0x07e541c9, 0x807006ed, 0x0468df77, 0xfd214af0, 0xa795fe11, 0x9359666f, 0xdcf08f7c), 0}, + {{0x5e, 0xb9, 0x69, 0x6a, 0x23, 0x36, 0xfe, 0x2c, 0x3c, 0x66, 0x6b, 0x02, 0xc7, 0x55, 0xdb, 0x4c, 0x0c, 0xfd, 0x62, 0x82, 0x5c, 0x7b, 0x58, 0x9a, 0x7b, 0x7b, 0xb4, 0x42, 0xe1, 0x41, 0xc1, 0xd6, 0x93, 0x41, 0x3f, 0x00, 0x52, 0xd4, 0x9e, 0x64, 0xab, 0xec, 0x6d, 0x58, 0x31, 0xd6, 0x6c, 0x43, 0x61, 0x28, 0x30, 0xa1, 0x7d, 0xf1, 0xfe, 0x43, 0x83, 0xdb, 0x89, 0x64, 0x68, 0x10, 0x02, 0x21}, SECP256K1_FE_CONST(0xef6e1da6, 0xd6c7627e, 0x80f7a723, 0x4cb08a02, 0x2c1ee1cf, 0x29e4d0f9, 0x642ae924, 0xcef9eb38), 1}, + {{0x7b, 0xf9, 0x6b, 0x7b, 0x6d, 0xa1, 0x5d, 0x34, 0x76, 0xa2, 0xb1, 0x95, 0x93, 0x4b, 0x69, 0x0a, 0x3a, 0x3d, 0xe3, 0xe8, 0xab, 0x84, 0x74, 0x85, 0x68, 0x63, 0xb0, 0xde, 0x3a, 0xf9, 0x0b, 0x0e, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}, SECP256K1_FE_CONST(0x50851dfc, 0x9f418c31, 0x4a437295, 0xb24feeea, 0x27af3d0c, 0xd2308348, 0xfda6e21c, 0x463e46ff), 0}, + {{0x7b, 0xf9, 0x6b, 0x7b, 0x6d, 0xa1, 0x5d, 0x34, 0x76, 0xa2, 0xb1, 0x95, 0x93, 0x4b, 0x69, 0x0a, 0x3a, 0x3d, 0xe3, 0xe8, 0xab, 0x84, 0x74, 0x85, 0x68, 0x63, 0xb0, 0xde, 0x3a, 0xf9, 0x0b, 0x0e, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2f}, SECP256K1_FE_CONST(0x50851dfc, 0x9f418c31, 0x4a437295, 0xb24feeea, 0x27af3d0c, 0xd2308348, 0xfda6e21c, 0x463e46ff), 0}, + {{0x85, 0x1b, 0x1c, 0xa9, 0x45, 0x49, 0x37, 0x1c, 0x4f, 0x1f, 0x71, 0x87, 0x32, 0x1d, 0x39, 0xbf, 0x51, 0xc6, 0xb7, 0xfb, 0x61, 0xf7, 0xcb, 0xf0, 0x27, 0xc9, 0xda, 0x62, 0x02, 0x1b, 0x7a, 0x65, 0xfc, 0x54, 0xc9, 0x68, 0x37, 0xfb, 0x22, 0xb3, 0x62, 0xed, 0xa6, 0x3e, 0xc5, 0x2e, 0xc8, 0x3d, 0x81, 0xbe, 0xdd, 0x16, 0x0c, 0x11, 0xb2, 0x2d, 0x96, 0x5d, 0x9f, 0x4a, 0x6d, 0x64, 0xd2, 0x51}, SECP256K1_FE_CONST(0x3e731051, 0xe12d3323, 0x7eb324f2, 0xaa5b16bb, 0x868eb49a, 0x1aa1fadc, 0x19b6e876, 0x1b5a5f7b), 1}, + {{0x94, 0x3c, 0x2f, 0x77, 0x51, 0x08, 0xb7, 0x37, 0xfe, 0x65, 0xa9, 0x53, 0x1e, 0x19, 0xf2, 0xfc, 0x2a, 0x19, 0x7f, 0x56, 0x03, 0xe3, 0xa2, 0x88, 0x1d, 0x1d, 0x83, 0xe4, 0x00, 0x8f, 0x91, 0x25, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}, SECP256K1_FE_CONST(0x311c61f0, 0xab2f32b7, 0xb1f0223f, 0xa72f0a78, 0x752b8146, 0xe46107f8, 0x876dd9c4, 0xf92b2942), 0}, + {{0x94, 0x3c, 0x2f, 0x77, 0x51, 0x08, 0xb7, 0x37, 0xfe, 0x65, 0xa9, 0x53, 0x1e, 0x19, 0xf2, 0xfc, 0x2a, 0x19, 0x7f, 0x56, 0x03, 0xe3, 0xa2, 0x88, 0x1d, 0x1d, 0x83, 0xe4, 0x00, 0x8f, 0x91, 0x25, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2f}, SECP256K1_FE_CONST(0x311c61f0, 0xab2f32b7, 0xb1f0223f, 0xa72f0a78, 0x752b8146, 0xe46107f8, 0x876dd9c4, 0xf92b2942), 0}, + {{0xa0, 0xf1, 0x84, 0x92, 0x18, 0x3e, 0x61, 0xe8, 0x06, 0x3e, 0x57, 0x36, 0x06, 0x59, 0x14, 0x21, 0xb0, 0x6b, 0xc3, 0x51, 0x36, 0x31, 0x57, 0x8a, 0x73, 0xa3, 0x9c, 0x1c, 0x33, 0x06, 0x23, 0x9f, 0x2f, 0x32, 0x90, 0x4f, 0x0d, 0x2a, 0x33, 0xec, 0xca, 0x8a, 0x54, 0x51, 0x70, 0x5b, 0xb5, 0x37, 0xd3, 0xbf, 0x44, 0xe0, 0x71, 0x22, 0x60, 0x25, 0xcd, 0xbf, 0xd2, 0x49, 0xfe, 0x0f, 0x7a, 0xd6}, SECP256K1_FE_CONST(0x97a09cf1, 0xa2eae7c4, 0x94df3c6f, 0x8a9445bf, 0xb8c09d60, 0x832f9b0b, 0x9d5eabe2, 0x5fbd14b9), 0}, + {{0xa1, 0xed, 0x0a, 0x0b, 0xd7, 0x9d, 0x8a, 0x23, 0xcf, 0xe4, 0xec, 0x5f, 0xef, 0x5b, 0xa5, 0xcc, 0xcf, 0xd8, 0x44, 0xe4, 0xff, 0x5c, 0xb4, 0xb0, 0xf2, 0xe7, 0x16, 0x27, 0x34, 0x1f, 0x1c, 0x5b, 0x17, 0xc4, 0x99, 0x24, 0x9e, 0x0a, 0xc0, 0x8d, 0x5d, 0x11, 0xea, 0x1c, 0x2c, 0x8c, 0xa7, 0x00, 0x16, 0x16, 0x55, 0x9a, 0x79, 0x94, 0xea, 0xde, 0xc9, 0xca, 0x10, 0xfb, 0x4b, 0x85, 0x16, 0xdc}, SECP256K1_FE_CONST(0x65a89640, 0x744192cd, 0xac64b2d2, 0x1ddf989c, 0xdac75007, 0x25b645be, 0xf8e2200a, 0xe39691f2), 0}, + {{0xba, 0x94, 0x59, 0x4a, 0x43, 0x27, 0x21, 0xaa, 0x35, 0x80, 0xb8, 0x4c, 0x16, 0x1d, 0x0d, 0x13, 0x4b, 0xc3, 0x54, 0xb6, 0x90, 0x40, 0x4d, 0x7c, 0xd4, 0xec, 0x57, 0xc1, 0x6d, 0x3f, 0xbe, 0x98, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xea, 0x50, 0x7d, 0xd7}, SECP256K1_FE_CONST(0x5e0d7656, 0x4aae92cb, 0x347e01a6, 0x2afd389a, 0x9aa401c7, 0x6c8dd227, 0x543dc9cd, 0x0efe685a), 0}, + {{0xbc, 0xaf, 0x72, 0x19, 0xf2, 0xf6, 0xfb, 0xf5, 0x5f, 0xe5, 0xe0, 0x62, 0xdc, 0xe0, 0xe4, 0x8c, 0x18, 0xf6, 0x81, 0x03, 0xf1, 0x0b, 0x81, 0x98, 0xe9, 0x74, 0xc1, 0x84, 0x75, 0x0e, 0x1b, 0xe3, 0x93, 0x20, 0x16, 0xcb, 0xf6, 0x9c, 0x44, 0x71, 0xbd, 0x1f, 0x65, 0x6c, 0x6a, 0x10, 0x7f, 0x19, 0x73, 0xde, 0x4a, 0xf7, 0x08, 0x6d, 0xb8, 0x97, 0x27, 0x70, 0x60, 0xe2, 0x56, 0x77, 0xf1, 0x9a}, SECP256K1_FE_CONST(0x2d97f96c, 0xac882dfe, 0x73dc44db, 0x6ce0f1d3, 0x1d624135, 0x8dd5d74e, 0xb3d3b500, 0x03d24c2b), 0}, + {{0xbc, 0xaf, 0x72, 0x19, 0xf2, 0xf6, 0xfb, 0xf5, 0x5f, 0xe5, 0xe0, 0x62, 0xdc, 0xe0, 0xe4, 0x8c, 0x18, 0xf6, 0x81, 0x03, 0xf1, 0x0b, 0x81, 0x98, 0xe9, 0x74, 0xc1, 0x84, 0x75, 0x0e, 0x1b, 0xe3, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x65, 0x07, 0xd0, 0x9a}, SECP256K1_FE_CONST(0xe7008afe, 0x6e8cbd50, 0x55df120b, 0xd748757c, 0x686dadb4, 0x1cce75e4, 0xaddcc5e0, 0x2ec02b44), 1}, + {{0xc5, 0x98, 0x1b, 0xae, 0x27, 0xfd, 0x84, 0x40, 0x1c, 0x72, 0xa1, 0x55, 0xe5, 0x70, 0x7f, 0xbb, 0x81, 0x1b, 0x2b, 0x62, 0x06, 0x45, 0xd1, 0x02, 0x8e, 0xa2, 0x70, 0xcb, 0xe0, 0xee, 0x22, 0x5d, 0x4b, 0x62, 0xaa, 0x4d, 0xca, 0x65, 0x06, 0xc1, 0xac, 0xdb, 0xec, 0xc0, 0x55, 0x25, 0x69, 0xb4, 0xb2, 0x14, 0x36, 0xa5, 0x69, 0x2e, 0x25, 0xd9, 0x0d, 0x3b, 0xc2, 0xeb, 0x7c, 0xe2, 0x40, 0x78}, SECP256K1_FE_CONST(0x948b40e7, 0x181713bc, 0x018ec170, 0x2d3d054d, 0x15746c59, 0xa7020730, 0xdd13ecf9, 0x85a010d7), 0}, + {{0xc8, 0x94, 0xce, 0x48, 0xbf, 0xec, 0x43, 0x30, 0x14, 0xb9, 0x31, 0xa6, 0xad, 0x42, 0x26, 0xd7, 0xdb, 0xd8, 0xea, 0xa7, 0xb6, 0xe3, 0xfa, 0xa8, 0xd0, 0xef, 0x94, 0x05, 0x2b, 0xcf, 0x8c, 0xff, 0x33, 0x6e, 0xeb, 0x39, 0x19, 0xe2, 0xb4, 0xef, 0xb7, 0x46, 0xc7, 0xf7, 0x1b, 0xbc, 0xa7, 0xe9, 0x38, 0x32, 0x30, 0xfb, 0xbc, 0x48, 0xff, 0xaf, 0xe7, 0x7e, 0x8b, 0xcc, 0x69, 0x54, 0x24, 0x71}, SECP256K1_FE_CONST(0xf1c91acd, 0xc2525330, 0xf9b53158, 0x434a4d43, 0xa1c547cf, 0xf29f1550, 0x6f5da4eb, 0x4fe8fa5a), 1}, + {{0xcb, 0xb0, 0xde, 0xab, 0x12, 0x57, 0x54, 0xf1, 0xfd, 0xb2, 0x03, 0x8b, 0x04, 0x34, 0xed, 0x9c, 0xb3, 0xfb, 0x53, 0xab, 0x73, 0x53, 0x91, 0x12, 0x99, 0x94, 0xa5, 0x35, 0xd9, 0x25, 0xf6, 0x73, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}, SECP256K1_FE_CONST(0x872d81ed, 0x8831d999, 0x8b67cb71, 0x05243edb, 0xf86c10ed, 0xfebb786c, 0x110b02d0, 0x7b2e67cd), 0}, + {{0xd9, 0x17, 0xb7, 0x86, 0xda, 0xc3, 0x56, 0x70, 0xc3, 0x30, 0xc9, 0xc5, 0xae, 0x59, 0x71, 0xdf, 0xb4, 0x95, 0xc8, 0xae, 0x52, 0x3e, 0xd9, 0x7e, 0xe2, 0x42, 0x01, 0x17, 0xb1, 0x71, 0xf4, 0x1e, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x20, 0x01, 0xf6, 0xf6}, SECP256K1_FE_CONST(0xe45b71e1, 0x10b831f2, 0xbdad8651, 0x994526e5, 0x8393fde4, 0x328b1ec0, 0x4d598971, 0x42584691), 1}, + {{0xe2, 0x8b, 0xd8, 0xf5, 0x92, 0x9b, 0x46, 0x7e, 0xb7, 0x0e, 0x04, 0x33, 0x23, 0x74, 0xff, 0xb7, 0xe7, 0x18, 0x02, 0x18, 0xad, 0x16, 0xea, 0xa4, 0x6b, 0x71, 0x61, 0xaa, 0x67, 0x9e, 0xb4, 0x26, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}, SECP256K1_FE_CONST(0x66b8c980, 0xa75c72e5, 0x98d383a3, 0x5a62879f, 0x844242ad, 0x1e73ff12, 0xedaa59f4, 0xe58632b5), 0}, + {{0xe2, 0x8b, 0xd8, 0xf5, 0x92, 0x9b, 0x46, 0x7e, 0xb7, 0x0e, 0x04, 0x33, 0x23, 0x74, 0xff, 0xb7, 0xe7, 0x18, 0x02, 0x18, 0xad, 0x16, 0xea, 0xa4, 0x6b, 0x71, 0x61, 0xaa, 0x67, 0x9e, 0xb4, 0x26, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2f}, SECP256K1_FE_CONST(0x66b8c980, 0xa75c72e5, 0x98d383a3, 0x5a62879f, 0x844242ad, 0x1e73ff12, 0xedaa59f4, 0xe58632b5), 0}, + {{0xe7, 0xee, 0x58, 0x14, 0xc1, 0x70, 0x6b, 0xf8, 0xa8, 0x93, 0x96, 0xa9, 0xb0, 0x32, 0xbc, 0x01, 0x4c, 0x2c, 0xac, 0x9c, 0x12, 0x11, 0x27, 0xdb, 0xf6, 0xc9, 0x92, 0x78, 0xf8, 0xbb, 0x53, 0xd1, 0xdf, 0xd0, 0x4d, 0xbc, 0xda, 0x8e, 0x35, 0x24, 0x66, 0xb6, 0xfc, 0xd5, 0xf2, 0xde, 0xa3, 0xe1, 0x7d, 0x5e, 0x13, 0x31, 0x15, 0x88, 0x6e, 0xda, 0x20, 0xdb, 0x8a, 0x12, 0xb5, 0x4d, 0xe7, 0x1b}, SECP256K1_FE_CONST(0xe842c6e3, 0x529b2342, 0x70a5e977, 0x44edc34a, 0x04d7ba94, 0xe44b6d25, 0x23c9cf01, 0x95730a50), 1}, + {{0xf2, 0x92, 0xe4, 0x68, 0x25, 0xf9, 0x22, 0x5a, 0xd2, 0x3d, 0xc0, 0x57, 0xc1, 0xd9, 0x1c, 0x4f, 0x57, 0xfc, 0xb1, 0x38, 0x6f, 0x29, 0xef, 0x10, 0x48, 0x1c, 0xb1, 0xd2, 0x25, 0x18, 0x59, 0x3f, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x70, 0x11, 0xc9, 0x89}, SECP256K1_FE_CONST(0x3cea2c53, 0xb8b01701, 0x66ac7da6, 0x7194694a, 0xdacc84d5, 0x6389225e, 0x330134da, 0xb85a4d55), 0}, + {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2f, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}, SECP256K1_FE_CONST(0xedd1fd3e, 0x327ce90c, 0xc7a35426, 0x14289aee, 0x9682003e, 0x9cf7dcc9, 0xcf2ca974, 0x3be5aa0c), 0}, + {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2f, 0x01, 0xd3, 0x47, 0x5b, 0xf7, 0x65, 0x5b, 0x0f, 0xb2, 0xd8, 0x52, 0x92, 0x10, 0x35, 0xb2, 0xef, 0x60, 0x7f, 0x49, 0x06, 0x9b, 0x97, 0x45, 0x4e, 0x67, 0x95, 0x25, 0x10, 0x62, 0x74, 0x17, 0x71}, SECP256K1_FE_CONST(0xb5da00b7, 0x3cd65605, 0x20e7c364, 0x086e7cd2, 0x3a34bf60, 0xd0e707be, 0x9fc34d4c, 0xd5fdfa2c), 1}, + {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2f, 0x42, 0x18, 0xf2, 0x0a, 0xe6, 0xc6, 0x46, 0xb3, 0x63, 0xdb, 0x68, 0x60, 0x58, 0x22, 0xfb, 0x14, 0x26, 0x4c, 0xa8, 0xd2, 0x58, 0x7f, 0xdd, 0x6f, 0xbc, 0x75, 0x0d, 0x58, 0x7e, 0x76, 0xa7, 0xee}, SECP256K1_FE_CONST(0xaaaaaaaa, 0xaaaaaaaa, 0xaaaaaaaa, 0xaaaaaaaa, 0xaaaaaaaa, 0xaaaaaaaa, 0xaaaaaaa9, 0xfffffd6b), 0}, + {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2f, 0x82, 0x27, 0x7c, 0x4a, 0x71, 0xf9, 0xd2, 0x2e, 0x66, 0xec, 0xe5, 0x23, 0xf8, 0xfa, 0x08, 0x74, 0x1a, 0x7c, 0x09, 0x12, 0xc6, 0x6a, 0x69, 0xce, 0x68, 0x51, 0x4b, 0xfd, 0x35, 0x15, 0xb4, 0x9f}, SECP256K1_FE_CONST(0xf482f2e2, 0x41753ad0, 0xfb89150d, 0x8491dc1e, 0x34ff0b8a, 0xcfbb442c, 0xfe999e2e, 0x5e6fd1d2), 1}, + {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2f, 0x84, 0x21, 0xcc, 0x93, 0x0e, 0x77, 0xc9, 0xf5, 0x14, 0xb6, 0x91, 0x5c, 0x3d, 0xbe, 0x2a, 0x94, 0xc6, 0xd8, 0xf6, 0x90, 0xb5, 0xb7, 0x39, 0x86, 0x4b, 0xa6, 0x78, 0x9f, 0xb8, 0xa5, 0x5d, 0xd0}, SECP256K1_FE_CONST(0x9f59c402, 0x75f5085a, 0x006f05da, 0xe77eb98c, 0x6fd0db1a, 0xb4a72ac4, 0x7eae90a4, 0xfc9e57e0), 0}, + {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2f, 0xd1, 0x9c, 0x18, 0x2d, 0x27, 0x59, 0xcd, 0x99, 0x82, 0x42, 0x28, 0xd9, 0x47, 0x99, 0xf8, 0xc6, 0x55, 0x7c, 0x38, 0xa1, 0xc0, 0xd6, 0x77, 0x9b, 0x9d, 0x4b, 0x72, 0x9c, 0x6f, 0x1c, 0xcc, 0x42}, SECP256K1_FE_CONST(0x70720db7, 0xe238d041, 0x21f5b1af, 0xd8cc5ad9, 0xd18944c6, 0xbdc94881, 0xf502b7a3, 0xaf3aecff), 0}, + {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2f, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2f}, SECP256K1_FE_CONST(0xedd1fd3e, 0x327ce90c, 0xc7a35426, 0x14289aee, 0x9682003e, 0x9cf7dcc9, 0xcf2ca974, 0x3be5aa0c), 0}, + {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2f, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x26, 0x64, 0xbb, 0xd5}, SECP256K1_FE_CONST(0x50873db3, 0x1badcc71, 0x890e4f67, 0x753a6575, 0x7f97aaa7, 0xdd5f1e82, 0xb753ace3, 0x2219064b), 0}, + {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2f, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x70, 0x28, 0xde, 0x7d}, SECP256K1_FE_CONST(0x1eea9cc5, 0x9cfcf2fa, 0x151ac6c2, 0x74eea411, 0x0feb4f7b, 0x68c59657, 0x32e9992e, 0x976ef68e), 0}, + {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2f, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xcb, 0xcf, 0xb7, 0xe7}, SECP256K1_FE_CONST(0x12303941, 0xaedc2088, 0x80735b1f, 0x1795c8e5, 0x5be520ea, 0x93e10335, 0x7b5d2adb, 0x7ed59b8e), 0}, + {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2f, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xf3, 0x11, 0x3a, 0xd9}, SECP256K1_FE_CONST(0x7eed6b70, 0xe7b0767c, 0x7d7feac0, 0x4e57aa2a, 0x12fef5e0, 0xf48f878f, 0xcbb88b3b, 0x6b5e0783), 0}, + {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x13, 0xce, 0xa4, 0xa7, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}, SECP256K1_FE_CONST(0x64998443, 0x5b62b4a2, 0x5d40c613, 0x3e8d9ab8, 0xc53d4b05, 0x9ee8a154, 0xa3be0fcf, 0x4e892edb), 0}, + {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x13, 0xce, 0xa4, 0xa7, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2f}, SECP256K1_FE_CONST(0x64998443, 0x5b62b4a2, 0x5d40c613, 0x3e8d9ab8, 0xc53d4b05, 0x9ee8a154, 0xa3be0fcf, 0x4e892edb), 0}, + {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x15, 0x02, 0x8c, 0x59, 0x00, 0x63, 0xf6, 0x4d, 0x5a, 0x7f, 0x1c, 0x14, 0x91, 0x5c, 0xd6, 0x1e, 0xac, 0x88, 0x6a, 0xb2, 0x95, 0xbe, 0xbd, 0x91, 0x99, 0x25, 0x04, 0xcf, 0x77, 0xed, 0xb0, 0x28, 0xbd, 0xd6, 0x26, 0x7f}, SECP256K1_FE_CONST(0x3fde5713, 0xf8282eea, 0xd7d39d42, 0x01f44a7c, 0x85a5ac8a, 0x0681f35e, 0x54085c6b, 0x69543374), 1}, + {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x27, 0x15, 0xde, 0x86, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}, SECP256K1_FE_CONST(0x3524f77f, 0xa3a6eb43, 0x89c3cb5d, 0x27f1f914, 0x62086429, 0xcd6c0cb0, 0xdf43ea8f, 0x1e7b3fb4), 0}, + {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x27, 0x15, 0xde, 0x86, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2f}, SECP256K1_FE_CONST(0x3524f77f, 0xa3a6eb43, 0x89c3cb5d, 0x27f1f914, 0x62086429, 0xcd6c0cb0, 0xdf43ea8f, 0x1e7b3fb4), 0}, + {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x2c, 0x2c, 0x57, 0x09, 0xe7, 0x15, 0x6c, 0x41, 0x77, 0x17, 0xf2, 0xfe, 0xab, 0x14, 0x71, 0x41, 0xec, 0x3d, 0xa1, 0x9f, 0xb7, 0x59, 0x57, 0x5c, 0xc6, 0xe3, 0x7b, 0x2e, 0xa5, 0xac, 0x93, 0x09, 0xf2, 0x6f, 0x0f, 0x66}, SECP256K1_FE_CONST(0xd2469ab3, 0xe04acbb2, 0x1c65a180, 0x9f39caaf, 0xe7a77c13, 0xd10f9dd3, 0x8f391c01, 0xdc499c52), 0}, + {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x3a, 0x08, 0xcc, 0x1e, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xf7, 0x60, 0xe9, 0xf0}, SECP256K1_FE_CONST(0x38e2a5ce, 0x6a93e795, 0xe16d2c39, 0x8bc99f03, 0x69202ce2, 0x1e8f09d5, 0x6777b40f, 0xc512bccc), 1}, + {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x3e, 0x91, 0x25, 0x7d, 0x93, 0x20, 0x16, 0xcb, 0xf6, 0x9c, 0x44, 0x71, 0xbd, 0x1f, 0x65, 0x6c, 0x6a, 0x10, 0x7f, 0x19, 0x73, 0xde, 0x4a, 0xf7, 0x08, 0x6d, 0xb8, 0x97, 0x27, 0x70, 0x60, 0xe2, 0x56, 0x77, 0xf1, 0x9a}, SECP256K1_FE_CONST(0x864b3dc9, 0x02c37670, 0x9c10a93a, 0xd4bbe29f, 0xce0012f3, 0xdc8672c6, 0x286bba28, 0xd7d6d6fc), 0}, + {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x79, 0x5d, 0x6c, 0x1c, 0x32, 0x2c, 0xad, 0xf5, 0x99, 0xdb, 0xb8, 0x64, 0x81, 0x52, 0x2b, 0x3c, 0xc5, 0x5f, 0x15, 0xa6, 0x79, 0x32, 0xdb, 0x2a, 0xfa, 0x01, 0x11, 0xd9, 0xed, 0x69, 0x81, 0xbc, 0xd1, 0x24, 0xbf, 0x44}, SECP256K1_FE_CONST(0x766dfe4a, 0x700d9bee, 0x288b903a, 0xd58870e3, 0xd4fe2f0e, 0xf780bcac, 0x5c823f32, 0x0d9a9bef), 0}, + {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x8e, 0x42, 0x6f, 0x03, 0x92, 0x38, 0x90, 0x78, 0xc1, 0x2b, 0x1a, 0x89, 0xe9, 0x54, 0x2f, 0x05, 0x93, 0xbc, 0x96, 0xb6, 0xbf, 0xde, 0x82, 0x24, 0xf8, 0x65, 0x4e, 0xf5, 0xd5, 0xcd, 0xa9, 0x35, 0xa3, 0x58, 0x21, 0x94}, SECP256K1_FE_CONST(0xfaec7bc1, 0x987b6323, 0x3fbc5f95, 0x6edbf37d, 0x54404e74, 0x61c58ab8, 0x631bc68e, 0x451a0478), 0}, + {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x91, 0x19, 0x21, 0x39, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x45, 0xf0, 0xf1, 0xeb}, SECP256K1_FE_CONST(0xec29a50b, 0xae138dbf, 0x7d8e2482, 0x5006bb5f, 0xc1a2cc12, 0x43ba335b, 0xc6116fb9, 0xe498ec1f), 0}, + {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x98, 0xeb, 0x9a, 0xb7, 0x6e, 0x84, 0x49, 0x9c, 0x48, 0x3b, 0x3b, 0xf0, 0x62, 0x14, 0xab, 0xfe, 0x06, 0x5d, 0xdd, 0xf4, 0x3b, 0x86, 0x01, 0xde, 0x59, 0x6d, 0x63, 0xb9, 0xe4, 0x5a, 0x16, 0x6a, 0x58, 0x05, 0x41, 0xfe}, SECP256K1_FE_CONST(0x1e0ff2de, 0xe9b09b13, 0x6292a9e9, 0x10f0d6ac, 0x3e552a64, 0x4bba39e6, 0x4e9dd3e3, 0xbbd3d4d4), 0}, + {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x9b, 0x77, 0xb7, 0xf2, 0xc7, 0x4d, 0x99, 0xef, 0xce, 0xaa, 0x55, 0x0f, 0x1a, 0xd1, 0xc0, 0xf4, 0x3f, 0x46, 0xe7, 0xff, 0x1e, 0xe3, 0xbd, 0x01, 0x62, 0xb7, 0xbf, 0x55, 0xf2, 0x96, 0x5d, 0xa9, 0xc3, 0x45, 0x06, 0x46}, SECP256K1_FE_CONST(0x8b7dd5c3, 0xedba9ee9, 0x7b70eff4, 0x38f22dca, 0x9849c825, 0x4a2f3345, 0xa0a572ff, 0xeaae0928), 0}, + {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x9b, 0x77, 0xb7, 0xf2, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x15, 0x6c, 0xa8, 0x96}, SECP256K1_FE_CONST(0x0881950c, 0x8f51d6b9, 0xa6387465, 0xd5f12609, 0xef1bb254, 0x12a08a74, 0xcb2dfb20, 0x0c74bfbf), 1}, + {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xa2, 0xf5, 0xcd, 0x83, 0x88, 0x16, 0xc1, 0x6c, 0x4f, 0xe8, 0xa1, 0x66, 0x1d, 0x60, 0x6f, 0xdb, 0x13, 0xcf, 0x9a, 0xf0, 0x4b, 0x97, 0x9a, 0x2e, 0x15, 0x9a, 0x09, 0x40, 0x9e, 0xbc, 0x86, 0x45, 0xd5, 0x8f, 0xde, 0x02}, SECP256K1_FE_CONST(0x2f083207, 0xb9fd9b55, 0x0063c31c, 0xd62b8746, 0xbd543bdc, 0x5bbf10e3, 0xa35563e9, 0x27f440c8), 0}, + {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xb1, 0x3f, 0x75, 0xc0, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}, SECP256K1_FE_CONST(0x4f51e0be, 0x078e0cdd, 0xab274215, 0x6adba7e7, 0xa148e731, 0x57072fd6, 0x18cd6094, 0x2b146bd0), 0}, + {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xb1, 0x3f, 0x75, 0xc0, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2f}, SECP256K1_FE_CONST(0x4f51e0be, 0x078e0cdd, 0xab274215, 0x6adba7e7, 0xa148e731, 0x57072fd6, 0x18cd6094, 0x2b146bd0), 0}, + {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xe7, 0xbc, 0x1f, 0x8d, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}, SECP256K1_FE_CONST(0x16c2ccb5, 0x4352ff4b, 0xd794f6ef, 0xd613c721, 0x97ab7082, 0xda5b563b, 0xdf9cb3ed, 0xaafe74c2), 0}, + {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xe7, 0xbc, 0x1f, 0x8d, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2f}, SECP256K1_FE_CONST(0x16c2ccb5, 0x4352ff4b, 0xd794f6ef, 0xd613c721, 0x97ab7082, 0xda5b563b, 0xdf9cb3ed, 0xaafe74c2), 0}, + {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xef, 0x64, 0xd1, 0x62, 0x75, 0x05, 0x46, 0xce, 0x42, 0xb0, 0x43, 0x13, 0x61, 0xe5, 0x2d, 0x4f, 0x52, 0x42, 0xd8, 0xf2, 0x4f, 0x33, 0xe6, 0xb1, 0xf9, 0x9b, 0x59, 0x16, 0x47, 0xcb, 0xc8, 0x08, 0xf4, 0x62, 0xaf, 0x51}, SECP256K1_FE_CONST(0xd41244d1, 0x1ca4f652, 0x40687759, 0xf95ca9ef, 0xbab767ed, 0xedb38fd1, 0x8c36e18c, 0xd3b6f6a9), 1}, + {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xf0, 0xe5, 0xbe, 0x52, 0x37, 0x2d, 0xd6, 0xe8, 0x94, 0xb2, 0xa3, 0x26, 0xfc, 0x36, 0x05, 0xa6, 0xe8, 0xf3, 0xc6, 0x9c, 0x71, 0x0b, 0xf2, 0x7d, 0x63, 0x0d, 0xfe, 0x20, 0x04, 0x98, 0x8b, 0x78, 0xeb, 0x6e, 0xab, 0x36}, SECP256K1_FE_CONST(0x64bf84dd, 0x5e03670f, 0xdb24c0f5, 0xd3c2c365, 0x736f51db, 0x6c92d950, 0x10716ad2, 0xd36134c8), 0}, + {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xfb, 0xb9, 0x82, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xf6, 0xd6, 0xdb, 0x1f}, SECP256K1_FE_CONST(0x1c92ccdf, 0xcf4ac550, 0xc28db57c, 0xff0c8515, 0xcb26936c, 0x786584a7, 0x0114008d, 0x6c33a34b), 0}, +}; + +/* Set of expected ellswift_xdh BIP324 shared secrets, given private key, encodings, initiating, + * taken from the BIP324 test vectors. Created using an independent implementation, and tested + * against the paper authors' decoding code. */ +static const struct ellswift_xdh_test ellswift_xdh_tests_bip324[] = { + {{0x61, 0x06, 0x2e, 0xa5, 0x07, 0x1d, 0x80, 0x0b, 0xbf, 0xd5, 0x9e, 0x2e, 0x8b, 0x53, 0xd4, 0x7d, 0x19, 0x4b, 0x09, 0x5a, 0xe5, 0xa4, 0xdf, 0x04, 0x93, 0x6b, 0x49, 0x77, 0x2e, 0xf0, 0xd4, 0xd7}, {0xec, 0x0a, 0xdf, 0xf2, 0x57, 0xbb, 0xfe, 0x50, 0x0c, 0x18, 0x8c, 0x80, 0xb4, 0xfd, 0xd6, 0x40, 0xf6, 0xb4, 0x5a, 0x48, 0x2b, 0xbc, 0x15, 0xfc, 0x7c, 0xef, 0x59, 0x31, 0xde, 0xff, 0x0a, 0xa1, 0x86, 0xf6, 0xeb, 0x9b, 0xba, 0x7b, 0x85, 0xdc, 0x4d, 0xcc, 0x28, 0xb2, 0x87, 0x22, 0xde, 0x1e, 0x3d, 0x91, 0x08, 0xb9, 0x85, 0xe2, 0x96, 0x70, 0x45, 0x66, 0x8f, 0x66, 0x09, 0x8e, 0x47, 0x5b}, {0xa4, 0xa9, 0x4d, 0xfc, 0xe6, 0x9b, 0x4a, 0x2a, 0x0a, 0x09, 0x93, 0x13, 0xd1, 0x0f, 0x9f, 0x7e, 0x7d, 0x64, 0x9d, 0x60, 0x50, 0x1c, 0x9e, 0x1d, 0x27, 0x4c, 0x30, 0x0e, 0x0d, 0x89, 0xaa, 0xfa, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x8f, 0xaf, 0x88, 0xd5}, 1, {0xc6, 0x99, 0x2a, 0x11, 0x7f, 0x5e, 0xdb, 0xea, 0x70, 0xc3, 0xf5, 0x11, 0xd3, 0x2d, 0x26, 0xb9, 0x79, 0x8b, 0xe4, 0xb8, 0x1a, 0x62, 0xea, 0xee, 0x1a, 0x5a, 0xca, 0xa8, 0x45, 0x9a, 0x35, 0x92}}, + {{0x1f, 0x9c, 0x58, 0x1b, 0x35, 0x23, 0x18, 0x38, 0xf0, 0xf1, 0x7c, 0xf0, 0xc9, 0x79, 0x83, 0x5b, 0xac, 0xcb, 0x7f, 0x3a, 0xbb, 0xbb, 0x96, 0xff, 0xcc, 0x31, 0x8a, 0xb7, 0x1e, 0x6e, 0x12, 0x6f}, {0xa1, 0x85, 0x5e, 0x10, 0xe9, 0x4e, 0x00, 0xba, 0xa2, 0x30, 0x41, 0xd9, 0x16, 0xe2, 0x59, 0xf7, 0x04, 0x4e, 0x49, 0x1d, 0xa6, 0x17, 0x12, 0x69, 0x69, 0x47, 0x63, 0xf0, 0x18, 0xc7, 0xe6, 0x36, 0x93, 0xd2, 0x95, 0x75, 0xdc, 0xb4, 0x64, 0xac, 0x81, 0x6b, 0xaa, 0x1b, 0xe3, 0x53, 0xba, 0x12, 0xe3, 0x87, 0x6c, 0xba, 0x76, 0x28, 0xbd, 0x0b, 0xd8, 0xe7, 0x55, 0xe7, 0x21, 0xeb, 0x01, 0x40}, {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2f, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}, 0, {0xa0, 0x13, 0x8f, 0x56, 0x4f, 0x74, 0xd0, 0xad, 0x70, 0xbc, 0x33, 0x7d, 0xac, 0xc9, 0xd0, 0xbf, 0x1d, 0x23, 0x49, 0x36, 0x4c, 0xaf, 0x11, 0x88, 0xa1, 0xe6, 0xe8, 0xdd, 0xb3, 0xb7, 0xb1, 0x84}}, + {{0x02, 0x86, 0xc4, 0x1c, 0xd3, 0x09, 0x13, 0xdb, 0x0f, 0xdf, 0xf7, 0xa6, 0x4e, 0xbd, 0xa5, 0xc8, 0xe3, 0xe7, 0xce, 0xf1, 0x0f, 0x2a, 0xeb, 0xc0, 0x0a, 0x76, 0x50, 0x44, 0x3c, 0xf4, 0xc6, 0x0d}, {0xd1, 0xee, 0x8a, 0x93, 0xa0, 0x11, 0x30, 0xcb, 0xf2, 0x99, 0x24, 0x9a, 0x25, 0x8f, 0x94, 0xfe, 0xb5, 0xf4, 0x69, 0xe7, 0xd0, 0xf2, 0xf2, 0x8f, 0x69, 0xee, 0x5e, 0x9a, 0xa8, 0xf9, 0xb5, 0x4a, 0x60, 0xf2, 0xc3, 0xff, 0x2d, 0x02, 0x36, 0x34, 0xec, 0x7f, 0x41, 0x27, 0xa9, 0x6c, 0xc1, 0x16, 0x62, 0xe4, 0x02, 0x89, 0x4c, 0xf1, 0xf6, 0x94, 0xfb, 0x9a, 0x7e, 0xaa, 0x5f, 0x1d, 0x92, 0x44}, {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x22, 0xd5, 0xe4, 0x41, 0x52, 0x4d, 0x57, 0x1a, 0x52, 0xb3, 0xde, 0xf1, 0x26, 0x18, 0x9d, 0x3f, 0x41, 0x68, 0x90, 0xa9, 0x9d, 0x4d, 0xa6, 0xed, 0xe2, 0xb0, 0xcd, 0xe1, 0x76, 0x0c, 0xe2, 0xc3, 0xf9, 0x84, 0x57, 0xae}, 1, {0x25, 0x0b, 0x93, 0x57, 0x0d, 0x41, 0x11, 0x49, 0x10, 0x5a, 0xb8, 0xcb, 0x0b, 0xc5, 0x07, 0x99, 0x14, 0x90, 0x63, 0x06, 0x36, 0x8c, 0x23, 0xe9, 0xd7, 0x7c, 0x2a, 0x33, 0x26, 0x5b, 0x99, 0x4c}}, + {{0x6c, 0x77, 0x43, 0x2d, 0x1f, 0xda, 0x31, 0xe9, 0xf9, 0x42, 0xf8, 0xaf, 0x44, 0x60, 0x7e, 0x10, 0xf3, 0xad, 0x38, 0xa6, 0x5f, 0x8a, 0x4b, 0xdd, 0xae, 0x82, 0x3e, 0x5e, 0xff, 0x90, 0xdc, 0x38}, {0xd2, 0x68, 0x50, 0x70, 0xc1, 0xe6, 0x37, 0x6e, 0x63, 0x3e, 0x82, 0x52, 0x96, 0x63, 0x4f, 0xd4, 0x61, 0xfa, 0x9e, 0x5b, 0xdf, 0x21, 0x09, 0xbc, 0xeb, 0xd7, 0x35, 0xe5, 0xa9, 0x1f, 0x3e, 0x58, 0x7c, 0x5c, 0xb7, 0x82, 0xab, 0xb7, 0x97, 0xfb, 0xf6, 0xbb, 0x50, 0x74, 0xfd, 0x15, 0x42, 0xa4, 0x74, 0xf2, 0xa4, 0x5b, 0x67, 0x37, 0x63, 0xec, 0x2d, 0xb7, 0xfb, 0x99, 0xb7, 0x37, 0xbb, 0xb9}, {0x56, 0xbd, 0x0c, 0x06, 0xf1, 0x03, 0x52, 0xc3, 0xa1, 0xa9, 0xf4, 0xb4, 0xc9, 0x2f, 0x6f, 0xa2, 0xb2, 0x6d, 0xf1, 0x24, 0xb5, 0x78, 0x78, 0x35, 0x3c, 0x1f, 0xc6, 0x91, 0xc5, 0x1a, 0xbe, 0xa7, 0x7c, 0x88, 0x17, 0xda, 0xee, 0xb9, 0xfa, 0x54, 0x6b, 0x77, 0xc8, 0xda, 0xf7, 0x9d, 0x89, 0xb2, 0x2b, 0x0e, 0x1b, 0x87, 0x57, 0x4e, 0xce, 0x42, 0x37, 0x1f, 0x00, 0x23, 0x7a, 0xa9, 0xd8, 0x3a}, 0, {0x19, 0x18, 0xb7, 0x41, 0xef, 0x5f, 0x9d, 0x1d, 0x76, 0x70, 0xb0, 0x50, 0xc1, 0x52, 0xb4, 0xa4, 0xea, 0xd2, 0xc3, 0x1b, 0xe9, 0xae, 0xcb, 0x06, 0x81, 0xc0, 0xcd, 0x43, 0x24, 0x15, 0x08, 0x53}}, + {{0xa6, 0xec, 0x25, 0x12, 0x7c, 0xa1, 0xaa, 0x4c, 0xf1, 0x6b, 0x20, 0x08, 0x4b, 0xa1, 0xe6, 0x51, 0x6b, 0xaa, 0xe4, 0xd3, 0x24, 0x22, 0x28, 0x8e, 0x9b, 0x36, 0xd8, 0xbd, 0xdd, 0x2d, 0xe3, 0x5a}, {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x05, 0x3d, 0x7e, 0xcc, 0xa5, 0x3e, 0x33, 0xe1, 0x85, 0xa8, 0xb9, 0xbe, 0x4e, 0x76, 0x99, 0xa9, 0x7c, 0x6f, 0xf4, 0xc7, 0x95, 0x52, 0x2e, 0x59, 0x18, 0xab, 0x7c, 0xd6, 0xb6, 0x88, 0x4f, 0x67, 0xe6, 0x83, 0xf3, 0xdc}, {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xa7, 0x73, 0x0b, 0xe3, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}, 1, {0xdd, 0x21, 0x0a, 0xa6, 0x62, 0x9f, 0x20, 0xbb, 0x32, 0x8e, 0x5d, 0x89, 0xda, 0xa6, 0xeb, 0x2a, 0xc3, 0xd1, 0xc6, 0x58, 0xa7, 0x25, 0x53, 0x6f, 0xf1, 0x54, 0xf3, 0x1b, 0x53, 0x6c, 0x23, 0xb2}}, + {{0x0a, 0xf9, 0x52, 0x65, 0x9e, 0xd7, 0x6f, 0x80, 0xf5, 0x85, 0x96, 0x6b, 0x95, 0xab, 0x6e, 0x6f, 0xd6, 0x86, 0x54, 0x67, 0x28, 0x27, 0x87, 0x86, 0x84, 0xc8, 0xb5, 0x47, 0xb1, 0xb9, 0x4f, 0x5a}, {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xc8, 0x10, 0x17, 0xfd, 0x92, 0xfd, 0x31, 0x63, 0x7c, 0x26, 0xc9, 0x06, 0xb4, 0x20, 0x92, 0xe1, 0x1c, 0xc0, 0xd3, 0xaf, 0xae, 0x8d, 0x90, 0x19, 0xd2, 0x57, 0x8a, 0xf2, 0x27, 0x35, 0xce, 0x7b, 0xc4, 0x69, 0xc7, 0x2d}, {0x96, 0x52, 0xd7, 0x8b, 0xae, 0xfc, 0x02, 0x8c, 0xd3, 0x7a, 0x6a, 0x92, 0x62, 0x5b, 0x8b, 0x8f, 0x85, 0xfd, 0xe1, 0xe4, 0xc9, 0x44, 0xad, 0x3f, 0x20, 0xe1, 0x98, 0xbe, 0xf8, 0xc0, 0x2f, 0x19, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xf2, 0xe9, 0x18, 0x70}, 0, {0x35, 0x68, 0xf2, 0xae, 0xa2, 0xe1, 0x4e, 0xf4, 0xee, 0x4a, 0x3c, 0x2a, 0x8b, 0x8d, 0x31, 0xbc, 0x5e, 0x31, 0x87, 0xba, 0x86, 0xdb, 0x10, 0x73, 0x9b, 0x4f, 0xf8, 0xec, 0x92, 0xff, 0x66, 0x55}}, + {{0xf9, 0x0e, 0x08, 0x0c, 0x64, 0xb0, 0x58, 0x24, 0xc5, 0xa2, 0x4b, 0x25, 0x01, 0xd5, 0xae, 0xaf, 0x08, 0xaf, 0x38, 0x72, 0xee, 0x86, 0x0a, 0xa8, 0x0b, 0xdc, 0xd4, 0x30, 0xf7, 0xb6, 0x34, 0x94}, {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x11, 0x51, 0x73, 0x76, 0x5d, 0xc2, 0x02, 0xcf, 0x02, 0x9a, 0xd3, 0xf1, 0x54, 0x79, 0x73, 0x5d, 0x57, 0x69, 0x7a, 0xf1, 0x2b, 0x01, 0x31, 0xdd, 0x21, 0x43, 0x0d, 0x57, 0x72, 0xe4, 0xef, 0x11, 0x47, 0x4d, 0x58, 0xb9}, {0x12, 0xa5, 0x0f, 0x3f, 0xaf, 0xea, 0x7c, 0x1e, 0xea, 0xda, 0x4c, 0xf8, 0xd3, 0x37, 0x77, 0x70, 0x4b, 0x77, 0x36, 0x14, 0x53, 0xaf, 0xc8, 0x3b, 0xda, 0x91, 0xee, 0xf3, 0x49, 0xae, 0x04, 0x4d, 0x20, 0x12, 0x6c, 0x62, 0x00, 0x54, 0x7e, 0xa5, 0xa6, 0x91, 0x17, 0x76, 0xc0, 0x5d, 0xee, 0x2a, 0x7f, 0x1a, 0x9b, 0xa7, 0xdf, 0xba, 0xbb, 0xbd, 0x27, 0x3c, 0x3e, 0xf2, 0x9e, 0xf4, 0x6e, 0x46}, 1, {0xe2, 0x54, 0x61, 0xfb, 0x0e, 0x4c, 0x16, 0x2e, 0x18, 0x12, 0x3e, 0xcd, 0xe8, 0x83, 0x42, 0xd5, 0x4d, 0x44, 0x96, 0x31, 0xe9, 0xb7, 0x5a, 0x26, 0x6f, 0xd9, 0x26, 0x0c, 0x2b, 0xb2, 0xf4, 0x1d}}, +}; + +/** This is a hasher for ellswift_xdh which just returns the shared X coordinate. + * + * This is generally a bad idea as it means changes to the encoding of the + * exchanged public keys do not affect the shared secret. However, it's used here + * in tests to be able to verify the X coordinate through other means. + */ +static int ellswift_xdh_hash_x32(unsigned char *output, const unsigned char *x32, const unsigned char *ell_a64, const unsigned char *ell_b64, void *data) { + (void)ell_a64; + (void)ell_b64; + (void)data; + memcpy(output, x32, 32); + return 1; +} + +void run_ellswift_tests(void) { + int i = 0; + /* Test vectors. */ + for (i = 0; (unsigned)i < sizeof(ellswift_xswiftec_inv_tests) / sizeof(ellswift_xswiftec_inv_tests[0]); ++i) { + const struct ellswift_xswiftec_inv_test *testcase = &ellswift_xswiftec_inv_tests[i]; + int c; + for (c = 0; c < 8; ++c) { + secp256k1_fe t; + int ret = secp256k1_ellswift_xswiftec_inv_var(&t, &testcase->x, &testcase->u, c); + CHECK(ret == ((testcase->enc_bitmap >> c) & 1)); + if (ret) { + secp256k1_fe x2; + CHECK(fe_equal(&t, &testcase->encs[c])); + secp256k1_ellswift_xswiftec_var(&x2, &testcase->u, &testcase->encs[c]); + CHECK(fe_equal(&testcase->x, &x2)); + } + } + } + for (i = 0; (unsigned)i < sizeof(ellswift_decode_tests) / sizeof(ellswift_decode_tests[0]); ++i) { + const struct ellswift_decode_test *testcase = &ellswift_decode_tests[i]; + secp256k1_pubkey pubkey; + secp256k1_ge ge; + int ret; + ret = secp256k1_ellswift_decode(CTX, &pubkey, testcase->enc); + CHECK(ret); + ret = secp256k1_pubkey_load(CTX, &ge, &pubkey); + CHECK(ret); + CHECK(fe_equal(&testcase->x, &ge.x)); + CHECK(secp256k1_fe_is_odd(&ge.y) == testcase->odd_y); + } + for (i = 0; (unsigned)i < sizeof(ellswift_xdh_tests_bip324) / sizeof(ellswift_xdh_tests_bip324[0]); ++i) { + const struct ellswift_xdh_test *test = &ellswift_xdh_tests_bip324[i]; + unsigned char shared_secret[32]; + int ret; + int party = !test->initiating; + const unsigned char* ell_a64 = party ? test->ellswift_theirs : test->ellswift_ours; + const unsigned char* ell_b64 = party ? test->ellswift_ours : test->ellswift_theirs; + ret = secp256k1_ellswift_xdh(CTX, shared_secret, + ell_a64, ell_b64, + test->priv_ours, + party, + secp256k1_ellswift_xdh_hash_function_bip324, + NULL); + CHECK(ret); + CHECK(secp256k1_memcmp_var(shared_secret, test->shared_secret, 32) == 0); + } + /* Verify that secp256k1_ellswift_encode + decode roundtrips. */ + for (i = 0; i < 1000 * COUNT; i++) { + unsigned char rnd32[32]; + unsigned char ell64[64]; + secp256k1_ge g, g2; + secp256k1_pubkey pubkey, pubkey2; + /* Generate random public key and random randomizer. */ + testutil_random_ge_test(&g); + secp256k1_pubkey_save(&pubkey, &g); + testrand256(rnd32); + /* Convert the public key to ElligatorSwift and back. */ + secp256k1_ellswift_encode(CTX, ell64, &pubkey, rnd32); + secp256k1_ellswift_decode(CTX, &pubkey2, ell64); + secp256k1_pubkey_load(CTX, &g2, &pubkey2); + /* Compare with original. */ + CHECK(secp256k1_ge_eq_var(&g, &g2)); + } + /* Verify the behavior of secp256k1_ellswift_create */ + for (i = 0; i < 400 * COUNT; i++) { + unsigned char auxrnd32[32], sec32[32]; + secp256k1_scalar sec; + secp256k1_gej res; + secp256k1_ge dec; + secp256k1_pubkey pub; + unsigned char ell64[64]; + int ret; + /* Generate random secret key and random randomizer. */ + if (i & 1) testrand256_test(auxrnd32); + testutil_random_scalar_order_test(&sec); + secp256k1_scalar_get_b32(sec32, &sec); + /* Construct ElligatorSwift-encoded public keys for that key. */ + ret = secp256k1_ellswift_create(CTX, ell64, sec32, (i & 1) ? auxrnd32 : NULL); + CHECK(ret); + /* Decode it, and compare with traditionally-computed public key. */ + secp256k1_ellswift_decode(CTX, &pub, ell64); + secp256k1_pubkey_load(CTX, &dec, &pub); + secp256k1_ecmult(&res, NULL, &secp256k1_scalar_zero, &sec); + CHECK(secp256k1_gej_eq_ge_var(&res, &dec)); + } + /* Verify that secp256k1_ellswift_xdh computes the right shared X coordinate. */ + for (i = 0; i < 800 * COUNT; i++) { + unsigned char ell64[64], sec32[32], share32[32]; + secp256k1_scalar sec; + secp256k1_ge dec, res; + secp256k1_fe share_x; + secp256k1_gej decj, resj; + secp256k1_pubkey pub; + int ret; + /* Generate random secret key. */ + testutil_random_scalar_order_test(&sec); + secp256k1_scalar_get_b32(sec32, &sec); + /* Generate random ElligatorSwift encoding for the remote key and decode it. */ + testrand256_test(ell64); + testrand256_test(ell64 + 32); + secp256k1_ellswift_decode(CTX, &pub, ell64); + secp256k1_pubkey_load(CTX, &dec, &pub); + secp256k1_gej_set_ge(&decj, &dec); + /* Compute the X coordinate of seckey*pubkey using ellswift_xdh. Note that we + * pass ell64 as claimed (but incorrect) encoding for sec32 here; this works + * because the "hasher" function we use here ignores the ell64 arguments. */ + ret = secp256k1_ellswift_xdh(CTX, share32, ell64, ell64, sec32, i & 1, &ellswift_xdh_hash_x32, NULL); + CHECK(ret); + (void)secp256k1_fe_set_b32_limit(&share_x, share32); /* no overflow is possible */ + SECP256K1_FE_VERIFY(&share_x); + /* Compute seckey*pubkey directly. */ + secp256k1_ecmult(&resj, &decj, &sec, NULL); + secp256k1_ge_set_gej(&res, &resj); + /* Compare. */ + CHECK(fe_equal(&res.x, &share_x)); + } + /* Verify the joint behavior of secp256k1_ellswift_xdh */ + for (i = 0; i < 200 * COUNT; i++) { + unsigned char auxrnd32a[32], auxrnd32b[32], auxrnd32a_bad[32], auxrnd32b_bad[32]; + unsigned char sec32a[32], sec32b[32], sec32a_bad[32], sec32b_bad[32]; + secp256k1_scalar seca, secb; + unsigned char ell64a[64], ell64b[64], ell64a_bad[64], ell64b_bad[64]; + unsigned char share32a[32], share32b[32], share32_bad[32]; + unsigned char prefix64[64]; + secp256k1_ellswift_xdh_hash_function hash_function; + void* data; + int ret; + + /* Pick hasher to use. */ + if ((i % 3) == 0) { + hash_function = ellswift_xdh_hash_x32; + data = NULL; + } else if ((i % 3) == 1) { + hash_function = secp256k1_ellswift_xdh_hash_function_bip324; + data = NULL; + } else { + hash_function = secp256k1_ellswift_xdh_hash_function_prefix; + testrand256_test(prefix64); + testrand256_test(prefix64 + 32); + data = prefix64; + } + + /* Generate random secret keys and random randomizers. */ + testrand256_test(auxrnd32a); + testrand256_test(auxrnd32b); + testutil_random_scalar_order_test(&seca); + /* Draw secb uniformly at random to make sure that the secret keys + * differ */ + testutil_random_scalar_order(&secb); + secp256k1_scalar_get_b32(sec32a, &seca); + secp256k1_scalar_get_b32(sec32b, &secb); + + /* Construct ElligatorSwift-encoded public keys for those keys. */ + /* For A: */ + ret = secp256k1_ellswift_create(CTX, ell64a, sec32a, auxrnd32a); + CHECK(ret); + /* For B: */ + ret = secp256k1_ellswift_create(CTX, ell64b, sec32b, auxrnd32b); + CHECK(ret); + + /* Compute the shared secret both ways and compare with each other. */ + /* For A: */ + ret = secp256k1_ellswift_xdh(CTX, share32a, ell64a, ell64b, sec32a, 0, hash_function, data); + CHECK(ret); + /* For B: */ + ret = secp256k1_ellswift_xdh(CTX, share32b, ell64a, ell64b, sec32b, 1, hash_function, data); + CHECK(ret); + /* And compare: */ + CHECK(secp256k1_memcmp_var(share32a, share32b, 32) == 0); + + /* Verify that the shared secret doesn't match if other side's public key is incorrect. */ + /* For A (using a bad public key for B): */ + memcpy(ell64b_bad, ell64b, sizeof(ell64a_bad)); + testrand_flip(ell64b_bad, sizeof(ell64b_bad)); + ret = secp256k1_ellswift_xdh(CTX, share32_bad, ell64a, ell64b_bad, sec32a, 0, hash_function, data); + CHECK(ret); /* Mismatching encodings don't get detected by secp256k1_ellswift_xdh. */ + CHECK(secp256k1_memcmp_var(share32_bad, share32a, 32) != 0); + /* For B (using a bad public key for A): */ + memcpy(ell64a_bad, ell64a, sizeof(ell64a_bad)); + testrand_flip(ell64a_bad, sizeof(ell64a_bad)); + ret = secp256k1_ellswift_xdh(CTX, share32_bad, ell64a_bad, ell64b, sec32b, 1, hash_function, data); + CHECK(ret); + CHECK(secp256k1_memcmp_var(share32_bad, share32b, 32) != 0); + + /* Verify that the shared secret doesn't match if the private key is incorrect. */ + /* For A: */ + memcpy(sec32a_bad, sec32a, sizeof(sec32a_bad)); + testrand_flip(sec32a_bad, sizeof(sec32a_bad)); + ret = secp256k1_ellswift_xdh(CTX, share32_bad, ell64a, ell64b, sec32a_bad, 0, hash_function, data); + CHECK(!ret || secp256k1_memcmp_var(share32_bad, share32a, 32) != 0); + /* For B: */ + memcpy(sec32b_bad, sec32b, sizeof(sec32b_bad)); + testrand_flip(sec32b_bad, sizeof(sec32b_bad)); + ret = secp256k1_ellswift_xdh(CTX, share32_bad, ell64a, ell64b, sec32b_bad, 1, hash_function, data); + CHECK(!ret || secp256k1_memcmp_var(share32_bad, share32b, 32) != 0); + + if (hash_function != ellswift_xdh_hash_x32) { + /* Verify that the shared secret doesn't match when a different encoding of the same public key is used. */ + /* For A (changing B's public key): */ + memcpy(auxrnd32b_bad, auxrnd32b, sizeof(auxrnd32b_bad)); + testrand_flip(auxrnd32b_bad, sizeof(auxrnd32b_bad)); + ret = secp256k1_ellswift_create(CTX, ell64b_bad, sec32b, auxrnd32b_bad); + CHECK(ret); + ret = secp256k1_ellswift_xdh(CTX, share32_bad, ell64a, ell64b_bad, sec32a, 0, hash_function, data); + CHECK(ret); + CHECK(secp256k1_memcmp_var(share32_bad, share32a, 32) != 0); + /* For B (changing A's public key): */ + memcpy(auxrnd32a_bad, auxrnd32a, sizeof(auxrnd32a_bad)); + testrand_flip(auxrnd32a_bad, sizeof(auxrnd32a_bad)); + ret = secp256k1_ellswift_create(CTX, ell64a_bad, sec32a, auxrnd32a_bad); + CHECK(ret); + ret = secp256k1_ellswift_xdh(CTX, share32_bad, ell64a_bad, ell64b, sec32b, 1, hash_function, data); + CHECK(ret); + CHECK(secp256k1_memcmp_var(share32_bad, share32b, 32) != 0); + + /* Verify that swapping sides changes the shared secret. */ + /* For A (claiming to be B): */ + ret = secp256k1_ellswift_xdh(CTX, share32_bad, ell64a, ell64b, sec32a, 1, hash_function, data); + CHECK(ret); + CHECK(secp256k1_memcmp_var(share32_bad, share32a, 32) != 0); + /* For B (claiming to be A): */ + ret = secp256k1_ellswift_xdh(CTX, share32_bad, ell64a, ell64b, sec32b, 0, hash_function, data); + CHECK(ret); + CHECK(secp256k1_memcmp_var(share32_bad, share32b, 32) != 0); + } + } + + /* Test hash initializers. */ + { + secp256k1_sha256 sha, sha_optimized; + static const unsigned char encode_tag[] = {'s', 'e', 'c', 'p', '2', '5', '6', 'k', '1', '_', 'e', 'l', 'l', 's', 'w', 'i', 'f', 't', '_', 'e', 'n', 'c', 'o', 'd', 'e'}; + static const unsigned char create_tag[] = {'s', 'e', 'c', 'p', '2', '5', '6', 'k', '1', '_', 'e', 'l', 'l', 's', 'w', 'i', 'f', 't', '_', 'c', 'r', 'e', 'a', 't', 'e'}; + static const unsigned char bip324_tag[] = {'b', 'i', 'p', '3', '2', '4', '_', 'e', 'l', 'l', 's', 'w', 'i', 'f', 't', '_', 'x', 'o', 'n', 'l', 'y', '_', 'e', 'c', 'd', 'h'}; + + /* Check that hash initialized by + * secp256k1_ellswift_sha256_init_encode has the expected + * state. */ + secp256k1_sha256_initialize_tagged(&sha, encode_tag, sizeof(encode_tag)); + secp256k1_ellswift_sha256_init_encode(&sha_optimized); + test_sha256_eq(&sha, &sha_optimized); + + /* Check that hash initialized by + * secp256k1_ellswift_sha256_init_create has the expected + * state. */ + secp256k1_sha256_initialize_tagged(&sha, create_tag, sizeof(create_tag)); + secp256k1_ellswift_sha256_init_create(&sha_optimized); + test_sha256_eq(&sha, &sha_optimized); + + /* Check that hash initialized by + * secp256k1_ellswift_sha256_init_bip324 has the expected + * state. */ + secp256k1_sha256_initialize_tagged(&sha, bip324_tag, sizeof(bip324_tag)); + secp256k1_ellswift_sha256_init_bip324(&sha_optimized); + test_sha256_eq(&sha, &sha_optimized); + } +} + +#endif diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/extrakeys/main_impl.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/extrakeys/main_impl.h new file mode 100644 index 00000000000..0c7e266777c --- /dev/null +++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/extrakeys/main_impl.h @@ -0,0 +1,285 @@ +/*********************************************************************** + * Copyright (c) 2020 Jonas Nick * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_MODULE_EXTRAKEYS_MAIN_H +#define SECP256K1_MODULE_EXTRAKEYS_MAIN_H + +#include "../../../include/secp256k1.h" +#include "../../../include/secp256k1_extrakeys.h" +#include "../../util.h" + +static SECP256K1_INLINE int secp256k1_xonly_pubkey_load(const secp256k1_context* ctx, secp256k1_ge *ge, const secp256k1_xonly_pubkey *pubkey) { + return secp256k1_pubkey_load(ctx, ge, (const secp256k1_pubkey *) pubkey); +} + +static SECP256K1_INLINE void secp256k1_xonly_pubkey_save(secp256k1_xonly_pubkey *pubkey, secp256k1_ge *ge) { + secp256k1_pubkey_save((secp256k1_pubkey *) pubkey, ge); +} + +int secp256k1_xonly_pubkey_parse(const secp256k1_context* ctx, secp256k1_xonly_pubkey *pubkey, const unsigned char *input32) { + secp256k1_ge pk; + secp256k1_fe x; + + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(pubkey != NULL); + memset(pubkey, 0, sizeof(*pubkey)); + ARG_CHECK(input32 != NULL); + + if (!secp256k1_fe_set_b32_limit(&x, input32)) { + return 0; + } + if (!secp256k1_ge_set_xo_var(&pk, &x, 0)) { + return 0; + } + if (!secp256k1_ge_is_in_correct_subgroup(&pk)) { + return 0; + } + secp256k1_xonly_pubkey_save(pubkey, &pk); + return 1; +} + +int secp256k1_xonly_pubkey_serialize(const secp256k1_context* ctx, unsigned char *output32, const secp256k1_xonly_pubkey *pubkey) { + secp256k1_ge pk; + + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(output32 != NULL); + memset(output32, 0, 32); + ARG_CHECK(pubkey != NULL); + + if (!secp256k1_xonly_pubkey_load(ctx, &pk, pubkey)) { + return 0; + } + secp256k1_fe_get_b32(output32, &pk.x); + return 1; +} + +int secp256k1_xonly_pubkey_cmp(const secp256k1_context* ctx, const secp256k1_xonly_pubkey* pk0, const secp256k1_xonly_pubkey* pk1) { + unsigned char out[2][32]; + const secp256k1_xonly_pubkey* pk[2]; + int i; + + VERIFY_CHECK(ctx != NULL); + pk[0] = pk0; pk[1] = pk1; + for (i = 0; i < 2; i++) { + /* If the public key is NULL or invalid, xonly_pubkey_serialize will + * call the illegal_callback and return 0. In that case we will + * serialize the key as all zeros which is less than any valid public + * key. This results in consistent comparisons even if NULL or invalid + * pubkeys are involved and prevents edge cases such as sorting + * algorithms that use this function and do not terminate as a + * result. */ + if (!secp256k1_xonly_pubkey_serialize(ctx, out[i], pk[i])) { + /* Note that xonly_pubkey_serialize should already set the output to + * zero in that case, but it's not guaranteed by the API, we can't + * test it and writing a VERIFY_CHECK is more complex than + * explicitly memsetting (again). */ + memset(out[i], 0, sizeof(out[i])); + } + } + return secp256k1_memcmp_var(out[0], out[1], sizeof(out[1])); +} + +/** Keeps a group element as is if it has an even Y and otherwise negates it. + * y_parity is set to 0 in the former case and to 1 in the latter case. + * Requires that the coordinates of r are normalized. */ +static int secp256k1_extrakeys_ge_even_y(secp256k1_ge *r) { + int y_parity = 0; + VERIFY_CHECK(!secp256k1_ge_is_infinity(r)); + + if (secp256k1_fe_is_odd(&r->y)) { + secp256k1_fe_negate(&r->y, &r->y, 1); + y_parity = 1; + } + return y_parity; +} + +int secp256k1_xonly_pubkey_from_pubkey(const secp256k1_context* ctx, secp256k1_xonly_pubkey *xonly_pubkey, int *pk_parity, const secp256k1_pubkey *pubkey) { + secp256k1_ge pk; + int tmp; + + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(xonly_pubkey != NULL); + ARG_CHECK(pubkey != NULL); + + if (!secp256k1_pubkey_load(ctx, &pk, pubkey)) { + return 0; + } + tmp = secp256k1_extrakeys_ge_even_y(&pk); + if (pk_parity != NULL) { + *pk_parity = tmp; + } + secp256k1_xonly_pubkey_save(xonly_pubkey, &pk); + return 1; +} + +int secp256k1_xonly_pubkey_tweak_add(const secp256k1_context* ctx, secp256k1_pubkey *output_pubkey, const secp256k1_xonly_pubkey *internal_pubkey, const unsigned char *tweak32) { + secp256k1_ge pk; + + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(output_pubkey != NULL); + memset(output_pubkey, 0, sizeof(*output_pubkey)); + ARG_CHECK(internal_pubkey != NULL); + ARG_CHECK(tweak32 != NULL); + + if (!secp256k1_xonly_pubkey_load(ctx, &pk, internal_pubkey) + || !secp256k1_ec_pubkey_tweak_add_helper(&pk, tweak32)) { + return 0; + } + secp256k1_pubkey_save(output_pubkey, &pk); + return 1; +} + +int secp256k1_xonly_pubkey_tweak_add_check(const secp256k1_context* ctx, const unsigned char *tweaked_pubkey32, int tweaked_pk_parity, const secp256k1_xonly_pubkey *internal_pubkey, const unsigned char *tweak32) { + secp256k1_ge pk; + unsigned char pk_expected32[32]; + + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(internal_pubkey != NULL); + ARG_CHECK(tweaked_pubkey32 != NULL); + ARG_CHECK(tweak32 != NULL); + + if (!secp256k1_xonly_pubkey_load(ctx, &pk, internal_pubkey) + || !secp256k1_ec_pubkey_tweak_add_helper(&pk, tweak32)) { + return 0; + } + secp256k1_fe_normalize_var(&pk.x); + secp256k1_fe_normalize_var(&pk.y); + secp256k1_fe_get_b32(pk_expected32, &pk.x); + + return secp256k1_memcmp_var(&pk_expected32, tweaked_pubkey32, 32) == 0 + && secp256k1_fe_is_odd(&pk.y) == tweaked_pk_parity; +} + +static void secp256k1_keypair_save(secp256k1_keypair *keypair, const secp256k1_scalar *sk, secp256k1_ge *pk) { + secp256k1_scalar_get_b32(&keypair->data[0], sk); + secp256k1_pubkey_save((secp256k1_pubkey *)&keypair->data[32], pk); +} + + +static int secp256k1_keypair_seckey_load(const secp256k1_context* ctx, secp256k1_scalar *sk, const secp256k1_keypair *keypair) { + int ret; + + ret = secp256k1_scalar_set_b32_seckey(sk, &keypair->data[0]); + /* We can declassify ret here because sk is only zero if a keypair function + * failed (which zeroes the keypair) and its return value is ignored. */ + secp256k1_declassify(ctx, &ret, sizeof(ret)); + ARG_CHECK(ret); + return ret; +} + +/* Load a keypair into pk and sk (if non-NULL). This function declassifies pk + * and ARG_CHECKs that the keypair is not invalid. It always initializes sk and + * pk with dummy values. */ +static int secp256k1_keypair_load(const secp256k1_context* ctx, secp256k1_scalar *sk, secp256k1_ge *pk, const secp256k1_keypair *keypair) { + int ret; + const secp256k1_pubkey *pubkey = (const secp256k1_pubkey *)&keypair->data[32]; + + /* Need to declassify the pubkey because pubkey_load ARG_CHECKs if it's + * invalid. */ + secp256k1_declassify(ctx, pubkey, sizeof(*pubkey)); + ret = secp256k1_pubkey_load(ctx, pk, pubkey); + if (sk != NULL) { + ret = ret && secp256k1_keypair_seckey_load(ctx, sk, keypair); + } + if (!ret) { + *pk = secp256k1_ge_const_g; + if (sk != NULL) { + *sk = secp256k1_scalar_one; + } + } + return ret; +} + +int secp256k1_keypair_create(const secp256k1_context* ctx, secp256k1_keypair *keypair, const unsigned char *seckey32) { + secp256k1_scalar sk; + secp256k1_ge pk; + int ret = 0; + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(keypair != NULL); + memset(keypair, 0, sizeof(*keypair)); + ARG_CHECK(secp256k1_ecmult_gen_context_is_built(&ctx->ecmult_gen_ctx)); + ARG_CHECK(seckey32 != NULL); + + ret = secp256k1_ec_pubkey_create_helper(&ctx->ecmult_gen_ctx, &sk, &pk, seckey32); + secp256k1_keypair_save(keypair, &sk, &pk); + secp256k1_memczero(keypair, sizeof(*keypair), !ret); + + secp256k1_scalar_clear(&sk); + return ret; +} + +int secp256k1_keypair_sec(const secp256k1_context* ctx, unsigned char *seckey, const secp256k1_keypair *keypair) { + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(seckey != NULL); + memset(seckey, 0, 32); + ARG_CHECK(keypair != NULL); + + memcpy(seckey, &keypair->data[0], 32); + return 1; +} + +int secp256k1_keypair_pub(const secp256k1_context* ctx, secp256k1_pubkey *pubkey, const secp256k1_keypair *keypair) { + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(pubkey != NULL); + memset(pubkey, 0, sizeof(*pubkey)); + ARG_CHECK(keypair != NULL); + + memcpy(pubkey->data, &keypair->data[32], sizeof(*pubkey)); + return 1; +} + +int secp256k1_keypair_xonly_pub(const secp256k1_context* ctx, secp256k1_xonly_pubkey *pubkey, int *pk_parity, const secp256k1_keypair *keypair) { + secp256k1_ge pk; + int tmp; + + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(pubkey != NULL); + memset(pubkey, 0, sizeof(*pubkey)); + ARG_CHECK(keypair != NULL); + + if (!secp256k1_keypair_load(ctx, NULL, &pk, keypair)) { + return 0; + } + tmp = secp256k1_extrakeys_ge_even_y(&pk); + if (pk_parity != NULL) { + *pk_parity = tmp; + } + secp256k1_xonly_pubkey_save(pubkey, &pk); + + return 1; +} + +int secp256k1_keypair_xonly_tweak_add(const secp256k1_context* ctx, secp256k1_keypair *keypair, const unsigned char *tweak32) { + secp256k1_ge pk; + secp256k1_scalar sk; + int y_parity; + int ret; + + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(keypair != NULL); + ARG_CHECK(tweak32 != NULL); + + ret = secp256k1_keypair_load(ctx, &sk, &pk, keypair); + memset(keypair, 0, sizeof(*keypair)); + + y_parity = secp256k1_extrakeys_ge_even_y(&pk); + if (y_parity == 1) { + secp256k1_scalar_negate(&sk, &sk); + } + + ret &= secp256k1_ec_seckey_tweak_add_helper(&sk, tweak32); + ret &= secp256k1_ec_pubkey_tweak_add_helper(&pk, tweak32); + + secp256k1_declassify(ctx, &ret, sizeof(ret)); + if (ret) { + secp256k1_keypair_save(keypair, &sk, &pk); + } + + secp256k1_scalar_clear(&sk); + return ret; +} + +#endif diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/extrakeys/tests_exhaustive_impl.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/extrakeys/tests_exhaustive_impl.h new file mode 100644 index 00000000000..645bae2d470 --- /dev/null +++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/extrakeys/tests_exhaustive_impl.h @@ -0,0 +1,68 @@ +/*********************************************************************** + * Copyright (c) 2020 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_MODULE_EXTRAKEYS_TESTS_EXHAUSTIVE_H +#define SECP256K1_MODULE_EXTRAKEYS_TESTS_EXHAUSTIVE_H + +#include "../../../include/secp256k1_extrakeys.h" +#include "main_impl.h" + +static void test_exhaustive_extrakeys(const secp256k1_context *ctx, const secp256k1_ge* group) { + secp256k1_keypair keypair[EXHAUSTIVE_TEST_ORDER - 1]; + secp256k1_pubkey pubkey[EXHAUSTIVE_TEST_ORDER - 1]; + secp256k1_xonly_pubkey xonly_pubkey[EXHAUSTIVE_TEST_ORDER - 1]; + int parities[EXHAUSTIVE_TEST_ORDER - 1]; + unsigned char xonly_pubkey_bytes[EXHAUSTIVE_TEST_ORDER - 1][32]; + int i; + + for (i = 1; i < EXHAUSTIVE_TEST_ORDER; i++) { + secp256k1_fe fe; + secp256k1_scalar scalar_i; + unsigned char buf[33]; + int parity; + + secp256k1_scalar_set_int(&scalar_i, i); + secp256k1_scalar_get_b32(buf, &scalar_i); + + /* Construct pubkey and keypair. */ + CHECK(secp256k1_keypair_create(ctx, &keypair[i - 1], buf)); + CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey[i - 1], buf)); + + /* Construct serialized xonly_pubkey from keypair. */ + CHECK(secp256k1_keypair_xonly_pub(ctx, &xonly_pubkey[i - 1], &parities[i - 1], &keypair[i - 1])); + CHECK(secp256k1_xonly_pubkey_serialize(ctx, xonly_pubkey_bytes[i - 1], &xonly_pubkey[i - 1])); + + /* Parse the xonly_pubkey back and verify it matches the previously serialized value. */ + CHECK(secp256k1_xonly_pubkey_parse(ctx, &xonly_pubkey[i - 1], xonly_pubkey_bytes[i - 1])); + CHECK(secp256k1_xonly_pubkey_serialize(ctx, buf, &xonly_pubkey[i - 1])); + CHECK(secp256k1_memcmp_var(xonly_pubkey_bytes[i - 1], buf, 32) == 0); + + /* Construct the xonly_pubkey from the pubkey, and verify it matches the same. */ + CHECK(secp256k1_xonly_pubkey_from_pubkey(ctx, &xonly_pubkey[i - 1], &parity, &pubkey[i - 1])); + CHECK(parity == parities[i - 1]); + CHECK(secp256k1_xonly_pubkey_serialize(ctx, buf, &xonly_pubkey[i - 1])); + CHECK(secp256k1_memcmp_var(xonly_pubkey_bytes[i - 1], buf, 32) == 0); + + /* Compare the xonly_pubkey bytes against the precomputed group. */ + secp256k1_fe_set_b32_mod(&fe, xonly_pubkey_bytes[i - 1]); + CHECK(secp256k1_fe_equal(&fe, &group[i].x)); + + /* Check the parity against the precomputed group. */ + fe = group[i].y; + secp256k1_fe_normalize_var(&fe); + CHECK(secp256k1_fe_is_odd(&fe) == parities[i - 1]); + + /* Verify that the higher half is identical to the lower half mirrored. */ + if (i > EXHAUSTIVE_TEST_ORDER / 2) { + CHECK(secp256k1_memcmp_var(xonly_pubkey_bytes[i - 1], xonly_pubkey_bytes[EXHAUSTIVE_TEST_ORDER - i - 1], 32) == 0); + CHECK(parities[i - 1] == 1 - parities[EXHAUSTIVE_TEST_ORDER - i - 1]); + } + } + + /* TODO: keypair/xonly_pubkey tweak tests */ +} + +#endif diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/extrakeys/tests_impl.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/extrakeys/tests_impl.h new file mode 100644 index 00000000000..ab4ef4a74b5 --- /dev/null +++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/extrakeys/tests_impl.h @@ -0,0 +1,483 @@ +/*********************************************************************** + * Copyright (c) 2020 Jonas Nick * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_MODULE_EXTRAKEYS_TESTS_H +#define SECP256K1_MODULE_EXTRAKEYS_TESTS_H + +#include "../../../include/secp256k1_extrakeys.h" + +static void test_xonly_pubkey(void) { + secp256k1_pubkey pk; + secp256k1_xonly_pubkey xonly_pk, xonly_pk_tmp; + secp256k1_ge pk1; + secp256k1_ge pk2; + secp256k1_fe y; + unsigned char sk[32]; + unsigned char xy_sk[32]; + unsigned char buf32[32]; + unsigned char ones32[32]; + unsigned char zeros64[64] = { 0 }; + int pk_parity; + int i; + + testrand256(sk); + memset(ones32, 0xFF, 32); + testrand256(xy_sk); + CHECK(secp256k1_ec_pubkey_create(CTX, &pk, sk) == 1); + CHECK(secp256k1_xonly_pubkey_from_pubkey(CTX, &xonly_pk, &pk_parity, &pk) == 1); + + /* Test xonly_pubkey_from_pubkey */ + CHECK(secp256k1_xonly_pubkey_from_pubkey(CTX, &xonly_pk, &pk_parity, &pk) == 1); + CHECK_ILLEGAL(CTX, secp256k1_xonly_pubkey_from_pubkey(CTX, NULL, &pk_parity, &pk)); + CHECK(secp256k1_xonly_pubkey_from_pubkey(CTX, &xonly_pk, NULL, &pk) == 1); + CHECK_ILLEGAL(CTX, secp256k1_xonly_pubkey_from_pubkey(CTX, &xonly_pk, &pk_parity, NULL)); + memset(&pk, 0, sizeof(pk)); + CHECK_ILLEGAL(CTX, secp256k1_xonly_pubkey_from_pubkey(CTX, &xonly_pk, &pk_parity, &pk)); + + /* Choose a secret key such that the resulting pubkey and xonly_pubkey match. */ + memset(sk, 0, sizeof(sk)); + sk[0] = 1; + CHECK(secp256k1_ec_pubkey_create(CTX, &pk, sk) == 1); + CHECK(secp256k1_xonly_pubkey_from_pubkey(CTX, &xonly_pk, &pk_parity, &pk) == 1); + CHECK(secp256k1_memcmp_var(&pk, &xonly_pk, sizeof(pk)) == 0); + CHECK(pk_parity == 0); + + /* Choose a secret key such that pubkey and xonly_pubkey are each others + * negation. */ + sk[0] = 2; + CHECK(secp256k1_ec_pubkey_create(CTX, &pk, sk) == 1); + CHECK(secp256k1_xonly_pubkey_from_pubkey(CTX, &xonly_pk, &pk_parity, &pk) == 1); + CHECK(secp256k1_memcmp_var(&xonly_pk, &pk, sizeof(xonly_pk)) != 0); + CHECK(pk_parity == 1); + secp256k1_pubkey_load(CTX, &pk1, &pk); + secp256k1_pubkey_load(CTX, &pk2, (secp256k1_pubkey *) &xonly_pk); + CHECK(secp256k1_fe_equal(&pk1.x, &pk2.x) == 1); + secp256k1_fe_negate(&y, &pk2.y, 1); + CHECK(secp256k1_fe_equal(&pk1.y, &y) == 1); + + /* Test xonly_pubkey_serialize and xonly_pubkey_parse */ + CHECK_ILLEGAL(CTX, secp256k1_xonly_pubkey_serialize(CTX, NULL, &xonly_pk)); + CHECK_ILLEGAL(CTX, secp256k1_xonly_pubkey_serialize(CTX, buf32, NULL)); + CHECK(secp256k1_memcmp_var(buf32, zeros64, 32) == 0); + { + /* A pubkey filled with 0s will fail to serialize due to pubkey_load + * special casing. */ + secp256k1_xonly_pubkey pk_tmp; + memset(&pk_tmp, 0, sizeof(pk_tmp)); + /* pubkey_load calls illegal callback */ + CHECK_ILLEGAL(CTX, secp256k1_xonly_pubkey_serialize(CTX, buf32, &pk_tmp)); + } + + CHECK(secp256k1_xonly_pubkey_serialize(CTX, buf32, &xonly_pk) == 1); + CHECK_ILLEGAL(CTX, secp256k1_xonly_pubkey_parse(CTX, NULL, buf32)); + CHECK_ILLEGAL(CTX, secp256k1_xonly_pubkey_parse(CTX, &xonly_pk, NULL)); + + /* Serialization and parse roundtrip */ + CHECK(secp256k1_xonly_pubkey_from_pubkey(CTX, &xonly_pk, NULL, &pk) == 1); + CHECK(secp256k1_xonly_pubkey_serialize(CTX, buf32, &xonly_pk) == 1); + CHECK(secp256k1_xonly_pubkey_parse(CTX, &xonly_pk_tmp, buf32) == 1); + CHECK(secp256k1_memcmp_var(&xonly_pk, &xonly_pk_tmp, sizeof(xonly_pk)) == 0); + + /* Test parsing invalid field elements */ + memset(&xonly_pk, 1, sizeof(xonly_pk)); + /* Overflowing field element */ + CHECK(secp256k1_xonly_pubkey_parse(CTX, &xonly_pk, ones32) == 0); + CHECK(secp256k1_memcmp_var(&xonly_pk, zeros64, sizeof(xonly_pk)) == 0); + memset(&xonly_pk, 1, sizeof(xonly_pk)); + /* There's no point with x-coordinate 0 on secp256k1 */ + CHECK(secp256k1_xonly_pubkey_parse(CTX, &xonly_pk, zeros64) == 0); + CHECK(secp256k1_memcmp_var(&xonly_pk, zeros64, sizeof(xonly_pk)) == 0); + /* If a random 32-byte string can not be parsed with ec_pubkey_parse + * (because interpreted as X coordinate it does not correspond to a point on + * the curve) then xonly_pubkey_parse should fail as well. */ + for (i = 0; i < COUNT; i++) { + unsigned char rand33[33]; + testrand256(&rand33[1]); + rand33[0] = SECP256K1_TAG_PUBKEY_EVEN; + if (!secp256k1_ec_pubkey_parse(CTX, &pk, rand33, 33)) { + memset(&xonly_pk, 1, sizeof(xonly_pk)); + CHECK(secp256k1_xonly_pubkey_parse(CTX, &xonly_pk, &rand33[1]) == 0); + CHECK(secp256k1_memcmp_var(&xonly_pk, zeros64, sizeof(xonly_pk)) == 0); + } else { + CHECK(secp256k1_xonly_pubkey_parse(CTX, &xonly_pk, &rand33[1]) == 1); + } + } +} + +static void test_xonly_pubkey_comparison(void) { + unsigned char pk1_ser[32] = { + 0x58, 0x84, 0xb3, 0xa2, 0x4b, 0x97, 0x37, 0x88, 0x92, 0x38, 0xa6, 0x26, 0x62, 0x52, 0x35, 0x11, + 0xd0, 0x9a, 0xa1, 0x1b, 0x80, 0x0b, 0x5e, 0x93, 0x80, 0x26, 0x11, 0xef, 0x67, 0x4b, 0xd9, 0x23 + }; + const unsigned char pk2_ser[32] = { + 0xde, 0x36, 0x0e, 0x87, 0x59, 0x8f, 0x3c, 0x01, 0x36, 0x2a, 0x2a, 0xb8, 0xc6, 0xf4, 0x5e, 0x4d, + 0xb2, 0xc2, 0xd5, 0x03, 0xa7, 0xf9, 0xf1, 0x4f, 0xa8, 0xfa, 0x95, 0xa8, 0xe9, 0x69, 0x76, 0x1c + }; + secp256k1_xonly_pubkey pk1; + secp256k1_xonly_pubkey pk2; + + CHECK(secp256k1_xonly_pubkey_parse(CTX, &pk1, pk1_ser) == 1); + CHECK(secp256k1_xonly_pubkey_parse(CTX, &pk2, pk2_ser) == 1); + + CHECK_ILLEGAL_VOID(CTX, CHECK(secp256k1_xonly_pubkey_cmp(CTX, NULL, &pk2) < 0)); + CHECK_ILLEGAL_VOID(CTX, CHECK(secp256k1_xonly_pubkey_cmp(CTX, &pk1, NULL) > 0)); + CHECK(secp256k1_xonly_pubkey_cmp(CTX, &pk1, &pk2) < 0); + CHECK(secp256k1_xonly_pubkey_cmp(CTX, &pk2, &pk1) > 0); + CHECK(secp256k1_xonly_pubkey_cmp(CTX, &pk1, &pk1) == 0); + CHECK(secp256k1_xonly_pubkey_cmp(CTX, &pk2, &pk2) == 0); + memset(&pk1, 0, sizeof(pk1)); /* illegal pubkey */ + CHECK_ILLEGAL_VOID(CTX, CHECK(secp256k1_xonly_pubkey_cmp(CTX, &pk1, &pk2) < 0)); + { + int32_t ecount = 0; + secp256k1_context_set_illegal_callback(CTX, counting_callback_fn, &ecount); + CHECK(secp256k1_xonly_pubkey_cmp(CTX, &pk1, &pk1) == 0); + CHECK(ecount == 2); + secp256k1_context_set_illegal_callback(CTX, NULL, NULL); + } + CHECK_ILLEGAL_VOID(CTX, CHECK(secp256k1_xonly_pubkey_cmp(CTX, &pk2, &pk1) > 0)); +} + +static void test_xonly_pubkey_tweak(void) { + unsigned char zeros64[64] = { 0 }; + unsigned char overflows[32]; + unsigned char sk[32]; + secp256k1_pubkey internal_pk; + secp256k1_xonly_pubkey internal_xonly_pk; + secp256k1_pubkey output_pk; + int pk_parity; + unsigned char tweak[32]; + int i; + + memset(overflows, 0xff, sizeof(overflows)); + testrand256(tweak); + testrand256(sk); + CHECK(secp256k1_ec_pubkey_create(CTX, &internal_pk, sk) == 1); + CHECK(secp256k1_xonly_pubkey_from_pubkey(CTX, &internal_xonly_pk, &pk_parity, &internal_pk) == 1); + + CHECK(secp256k1_xonly_pubkey_tweak_add(CTX, &output_pk, &internal_xonly_pk, tweak) == 1); + CHECK(secp256k1_xonly_pubkey_tweak_add(CTX, &output_pk, &internal_xonly_pk, tweak) == 1); + CHECK(secp256k1_xonly_pubkey_tweak_add(CTX, &output_pk, &internal_xonly_pk, tweak) == 1); + CHECK_ILLEGAL(CTX, secp256k1_xonly_pubkey_tweak_add(CTX, NULL, &internal_xonly_pk, tweak)); + CHECK_ILLEGAL(CTX, secp256k1_xonly_pubkey_tweak_add(CTX, &output_pk, NULL, tweak)); + /* NULL internal_xonly_pk zeroes the output_pk */ + CHECK(secp256k1_memcmp_var(&output_pk, zeros64, sizeof(output_pk)) == 0); + CHECK_ILLEGAL(CTX, secp256k1_xonly_pubkey_tweak_add(CTX, &output_pk, &internal_xonly_pk, NULL)); + /* NULL tweak zeroes the output_pk */ + CHECK(secp256k1_memcmp_var(&output_pk, zeros64, sizeof(output_pk)) == 0); + + /* Invalid tweak zeroes the output_pk */ + CHECK(secp256k1_xonly_pubkey_tweak_add(CTX, &output_pk, &internal_xonly_pk, overflows) == 0); + CHECK(secp256k1_memcmp_var(&output_pk, zeros64, sizeof(output_pk)) == 0); + + /* A zero tweak is fine */ + CHECK(secp256k1_xonly_pubkey_tweak_add(CTX, &output_pk, &internal_xonly_pk, zeros64) == 1); + + /* Fails if the resulting key was infinity */ + for (i = 0; i < COUNT; i++) { + secp256k1_scalar scalar_tweak; + /* Because sk may be negated before adding, we need to try with tweak = + * sk as well as tweak = -sk. */ + secp256k1_scalar_set_b32(&scalar_tweak, sk, NULL); + secp256k1_scalar_negate(&scalar_tweak, &scalar_tweak); + secp256k1_scalar_get_b32(tweak, &scalar_tweak); + CHECK((secp256k1_xonly_pubkey_tweak_add(CTX, &output_pk, &internal_xonly_pk, sk) == 0) + || (secp256k1_xonly_pubkey_tweak_add(CTX, &output_pk, &internal_xonly_pk, tweak) == 0)); + CHECK(secp256k1_memcmp_var(&output_pk, zeros64, sizeof(output_pk)) == 0); + } + + /* Invalid pk with a valid tweak */ + memset(&internal_xonly_pk, 0, sizeof(internal_xonly_pk)); + testrand256(tweak); + CHECK_ILLEGAL(CTX, secp256k1_xonly_pubkey_tweak_add(CTX, &output_pk, &internal_xonly_pk, tweak)); + CHECK(secp256k1_memcmp_var(&output_pk, zeros64, sizeof(output_pk)) == 0); +} + +static void test_xonly_pubkey_tweak_check(void) { + unsigned char zeros64[64] = { 0 }; + unsigned char overflows[32]; + unsigned char sk[32]; + secp256k1_pubkey internal_pk; + secp256k1_xonly_pubkey internal_xonly_pk; + secp256k1_pubkey output_pk; + secp256k1_xonly_pubkey output_xonly_pk; + unsigned char output_pk32[32]; + unsigned char buf32[32]; + int pk_parity; + unsigned char tweak[32]; + + memset(overflows, 0xff, sizeof(overflows)); + testrand256(tweak); + testrand256(sk); + CHECK(secp256k1_ec_pubkey_create(CTX, &internal_pk, sk) == 1); + CHECK(secp256k1_xonly_pubkey_from_pubkey(CTX, &internal_xonly_pk, &pk_parity, &internal_pk) == 1); + + CHECK(secp256k1_xonly_pubkey_tweak_add(CTX, &output_pk, &internal_xonly_pk, tweak) == 1); + CHECK(secp256k1_xonly_pubkey_from_pubkey(CTX, &output_xonly_pk, &pk_parity, &output_pk) == 1); + CHECK(secp256k1_xonly_pubkey_serialize(CTX, buf32, &output_xonly_pk) == 1); + CHECK(secp256k1_xonly_pubkey_tweak_add_check(CTX, buf32, pk_parity, &internal_xonly_pk, tweak) == 1); + CHECK(secp256k1_xonly_pubkey_tweak_add_check(CTX, buf32, pk_parity, &internal_xonly_pk, tweak) == 1); + CHECK(secp256k1_xonly_pubkey_tweak_add_check(CTX, buf32, pk_parity, &internal_xonly_pk, tweak) == 1); + CHECK_ILLEGAL(CTX, secp256k1_xonly_pubkey_tweak_add_check(CTX, NULL, pk_parity, &internal_xonly_pk, tweak)); + /* invalid pk_parity value */ + CHECK(secp256k1_xonly_pubkey_tweak_add_check(CTX, buf32, 2, &internal_xonly_pk, tweak) == 0); + CHECK_ILLEGAL(CTX, secp256k1_xonly_pubkey_tweak_add_check(CTX, buf32, pk_parity, NULL, tweak)); + CHECK_ILLEGAL(CTX, secp256k1_xonly_pubkey_tweak_add_check(CTX, buf32, pk_parity, &internal_xonly_pk, NULL)); + + memset(tweak, 1, sizeof(tweak)); + CHECK(secp256k1_xonly_pubkey_from_pubkey(CTX, &internal_xonly_pk, NULL, &internal_pk) == 1); + CHECK(secp256k1_xonly_pubkey_tweak_add(CTX, &output_pk, &internal_xonly_pk, tweak) == 1); + CHECK(secp256k1_xonly_pubkey_from_pubkey(CTX, &output_xonly_pk, &pk_parity, &output_pk) == 1); + CHECK(secp256k1_xonly_pubkey_serialize(CTX, output_pk32, &output_xonly_pk) == 1); + CHECK(secp256k1_xonly_pubkey_tweak_add_check(CTX, output_pk32, pk_parity, &internal_xonly_pk, tweak) == 1); + + /* Wrong pk_parity */ + CHECK(secp256k1_xonly_pubkey_tweak_add_check(CTX, output_pk32, !pk_parity, &internal_xonly_pk, tweak) == 0); + /* Wrong public key */ + CHECK(secp256k1_xonly_pubkey_serialize(CTX, buf32, &internal_xonly_pk) == 1); + CHECK(secp256k1_xonly_pubkey_tweak_add_check(CTX, buf32, pk_parity, &internal_xonly_pk, tweak) == 0); + + /* Overflowing tweak not allowed */ + CHECK(secp256k1_xonly_pubkey_tweak_add_check(CTX, output_pk32, pk_parity, &internal_xonly_pk, overflows) == 0); + CHECK(secp256k1_xonly_pubkey_tweak_add(CTX, &output_pk, &internal_xonly_pk, overflows) == 0); + CHECK(secp256k1_memcmp_var(&output_pk, zeros64, sizeof(output_pk)) == 0); +} + +/* Starts with an initial pubkey and recursively creates N_PUBKEYS - 1 + * additional pubkeys by calling tweak_add. Then verifies every tweak starting + * from the last pubkey. */ +#define N_PUBKEYS 32 +static void test_xonly_pubkey_tweak_recursive(void) { + unsigned char sk[32]; + secp256k1_pubkey pk[N_PUBKEYS]; + unsigned char pk_serialized[32]; + unsigned char tweak[N_PUBKEYS - 1][32]; + int i; + + testrand256(sk); + CHECK(secp256k1_ec_pubkey_create(CTX, &pk[0], sk) == 1); + /* Add tweaks */ + for (i = 0; i < N_PUBKEYS - 1; i++) { + secp256k1_xonly_pubkey xonly_pk; + memset(tweak[i], i + 1, sizeof(tweak[i])); + CHECK(secp256k1_xonly_pubkey_from_pubkey(CTX, &xonly_pk, NULL, &pk[i]) == 1); + CHECK(secp256k1_xonly_pubkey_tweak_add(CTX, &pk[i + 1], &xonly_pk, tweak[i]) == 1); + } + + /* Verify tweaks */ + for (i = N_PUBKEYS - 1; i > 0; i--) { + secp256k1_xonly_pubkey xonly_pk; + int pk_parity; + CHECK(secp256k1_xonly_pubkey_from_pubkey(CTX, &xonly_pk, &pk_parity, &pk[i]) == 1); + CHECK(secp256k1_xonly_pubkey_serialize(CTX, pk_serialized, &xonly_pk) == 1); + CHECK(secp256k1_xonly_pubkey_from_pubkey(CTX, &xonly_pk, NULL, &pk[i - 1]) == 1); + CHECK(secp256k1_xonly_pubkey_tweak_add_check(CTX, pk_serialized, pk_parity, &xonly_pk, tweak[i - 1]) == 1); + } +} +#undef N_PUBKEYS + +static void test_keypair(void) { + unsigned char sk[32]; + unsigned char sk_tmp[32]; + unsigned char zeros96[96] = { 0 }; + unsigned char overflows[32]; + secp256k1_keypair keypair; + secp256k1_pubkey pk, pk_tmp; + secp256k1_xonly_pubkey xonly_pk, xonly_pk_tmp; + int pk_parity, pk_parity_tmp; + + CHECK(sizeof(zeros96) == sizeof(keypair)); + memset(overflows, 0xFF, sizeof(overflows)); + + /* Test keypair_create */ + testrand256(sk); + CHECK(secp256k1_keypair_create(CTX, &keypair, sk) == 1); + CHECK(secp256k1_memcmp_var(zeros96, &keypair, sizeof(keypair)) != 0); + CHECK(secp256k1_keypair_create(CTX, &keypair, sk) == 1); + CHECK(secp256k1_memcmp_var(zeros96, &keypair, sizeof(keypair)) != 0); + CHECK_ILLEGAL(CTX, secp256k1_keypair_create(CTX, NULL, sk)); + CHECK_ILLEGAL(CTX, secp256k1_keypair_create(CTX, &keypair, NULL)); + CHECK(secp256k1_memcmp_var(zeros96, &keypair, sizeof(keypair)) == 0); + CHECK(secp256k1_keypair_create(CTX, &keypair, sk) == 1); + CHECK_ILLEGAL(STATIC_CTX, secp256k1_keypair_create(STATIC_CTX, &keypair, sk)); + CHECK(secp256k1_memcmp_var(zeros96, &keypair, sizeof(keypair)) == 0); + + /* Invalid secret key */ + CHECK(secp256k1_keypair_create(CTX, &keypair, zeros96) == 0); + CHECK(secp256k1_memcmp_var(zeros96, &keypair, sizeof(keypair)) == 0); + CHECK(secp256k1_keypair_create(CTX, &keypair, overflows) == 0); + CHECK(secp256k1_memcmp_var(zeros96, &keypair, sizeof(keypair)) == 0); + + /* Test keypair_pub */ + testrand256(sk); + CHECK(secp256k1_keypair_create(CTX, &keypair, sk) == 1); + CHECK(secp256k1_keypair_pub(CTX, &pk, &keypair) == 1); + CHECK_ILLEGAL(CTX, secp256k1_keypair_pub(CTX, NULL, &keypair)); + CHECK_ILLEGAL(CTX, secp256k1_keypair_pub(CTX, &pk, NULL)); + CHECK(secp256k1_memcmp_var(zeros96, &pk, sizeof(pk)) == 0); + + /* Using an invalid keypair is fine for keypair_pub */ + memset(&keypair, 0, sizeof(keypair)); + CHECK(secp256k1_keypair_pub(CTX, &pk, &keypair) == 1); + CHECK(secp256k1_memcmp_var(zeros96, &pk, sizeof(pk)) == 0); + + /* keypair holds the same pubkey as pubkey_create */ + CHECK(secp256k1_ec_pubkey_create(CTX, &pk, sk) == 1); + CHECK(secp256k1_keypair_create(CTX, &keypair, sk) == 1); + CHECK(secp256k1_keypair_pub(CTX, &pk_tmp, &keypair) == 1); + CHECK(secp256k1_memcmp_var(&pk, &pk_tmp, sizeof(pk)) == 0); + + /** Test keypair_xonly_pub **/ + testrand256(sk); + CHECK(secp256k1_keypair_create(CTX, &keypair, sk) == 1); + CHECK(secp256k1_keypair_xonly_pub(CTX, &xonly_pk, &pk_parity, &keypair) == 1); + CHECK_ILLEGAL(CTX, secp256k1_keypair_xonly_pub(CTX, NULL, &pk_parity, &keypair)); + CHECK(secp256k1_keypair_xonly_pub(CTX, &xonly_pk, NULL, &keypair) == 1); + CHECK_ILLEGAL(CTX, secp256k1_keypair_xonly_pub(CTX, &xonly_pk, &pk_parity, NULL)); + CHECK(secp256k1_memcmp_var(zeros96, &xonly_pk, sizeof(xonly_pk)) == 0); + /* Using an invalid keypair will set the xonly_pk to 0 (first reset + * xonly_pk). */ + CHECK(secp256k1_keypair_xonly_pub(CTX, &xonly_pk, &pk_parity, &keypair) == 1); + memset(&keypair, 0, sizeof(keypair)); + CHECK_ILLEGAL(CTX, secp256k1_keypair_xonly_pub(CTX, &xonly_pk, &pk_parity, &keypair)); + CHECK(secp256k1_memcmp_var(zeros96, &xonly_pk, sizeof(xonly_pk)) == 0); + + /** keypair holds the same xonly pubkey as pubkey_create **/ + CHECK(secp256k1_ec_pubkey_create(CTX, &pk, sk) == 1); + CHECK(secp256k1_xonly_pubkey_from_pubkey(CTX, &xonly_pk, &pk_parity, &pk) == 1); + CHECK(secp256k1_keypair_create(CTX, &keypair, sk) == 1); + CHECK(secp256k1_keypair_xonly_pub(CTX, &xonly_pk_tmp, &pk_parity_tmp, &keypair) == 1); + CHECK(secp256k1_memcmp_var(&xonly_pk, &xonly_pk_tmp, sizeof(pk)) == 0); + CHECK(pk_parity == pk_parity_tmp); + + /* Test keypair_seckey */ + testrand256(sk); + CHECK(secp256k1_keypair_create(CTX, &keypair, sk) == 1); + CHECK(secp256k1_keypair_sec(CTX, sk_tmp, &keypair) == 1); + CHECK_ILLEGAL(CTX, secp256k1_keypair_sec(CTX, NULL, &keypair)); + CHECK_ILLEGAL(CTX, secp256k1_keypair_sec(CTX, sk_tmp, NULL)); + CHECK(secp256k1_memcmp_var(zeros96, sk_tmp, sizeof(sk_tmp)) == 0); + + /* keypair returns the same seckey it got */ + CHECK(secp256k1_keypair_create(CTX, &keypair, sk) == 1); + CHECK(secp256k1_keypair_sec(CTX, sk_tmp, &keypair) == 1); + CHECK(secp256k1_memcmp_var(sk, sk_tmp, sizeof(sk_tmp)) == 0); + + + /* Using an invalid keypair is fine for keypair_seckey */ + memset(&keypair, 0, sizeof(keypair)); + CHECK(secp256k1_keypair_sec(CTX, sk_tmp, &keypair) == 1); + CHECK(secp256k1_memcmp_var(zeros96, sk_tmp, sizeof(sk_tmp)) == 0); +} + +static void test_keypair_add(void) { + unsigned char sk[32]; + secp256k1_keypair keypair; + unsigned char overflows[32]; + unsigned char zeros96[96] = { 0 }; + unsigned char tweak[32]; + int i; + + CHECK(sizeof(zeros96) == sizeof(keypair)); + testrand256(sk); + testrand256(tweak); + memset(overflows, 0xFF, 32); + CHECK(secp256k1_keypair_create(CTX, &keypair, sk) == 1); + + CHECK(secp256k1_keypair_xonly_tweak_add(CTX, &keypair, tweak) == 1); + CHECK(secp256k1_keypair_xonly_tweak_add(CTX, &keypair, tweak) == 1); + CHECK(secp256k1_keypair_xonly_tweak_add(CTX, &keypair, tweak) == 1); + CHECK_ILLEGAL(CTX, secp256k1_keypair_xonly_tweak_add(CTX, NULL, tweak)); + CHECK_ILLEGAL(CTX, secp256k1_keypair_xonly_tweak_add(CTX, &keypair, NULL)); + /* This does not set the keypair to zeroes */ + CHECK(secp256k1_memcmp_var(&keypair, zeros96, sizeof(keypair)) != 0); + + /* Invalid tweak zeroes the keypair */ + CHECK(secp256k1_keypair_create(CTX, &keypair, sk) == 1); + CHECK(secp256k1_keypair_xonly_tweak_add(CTX, &keypair, overflows) == 0); + CHECK(secp256k1_memcmp_var(&keypair, zeros96, sizeof(keypair)) == 0); + + /* A zero tweak is fine */ + CHECK(secp256k1_keypair_create(CTX, &keypair, sk) == 1); + CHECK(secp256k1_keypair_xonly_tweak_add(CTX, &keypair, zeros96) == 1); + + /* Fails if the resulting keypair was (sk=0, pk=infinity) */ + for (i = 0; i < COUNT; i++) { + secp256k1_scalar scalar_tweak; + secp256k1_keypair keypair_tmp; + testrand256(sk); + CHECK(secp256k1_keypair_create(CTX, &keypair, sk) == 1); + memcpy(&keypair_tmp, &keypair, sizeof(keypair)); + /* Because sk may be negated before adding, we need to try with tweak = + * sk as well as tweak = -sk. */ + secp256k1_scalar_set_b32(&scalar_tweak, sk, NULL); + secp256k1_scalar_negate(&scalar_tweak, &scalar_tweak); + secp256k1_scalar_get_b32(tweak, &scalar_tweak); + CHECK((secp256k1_keypair_xonly_tweak_add(CTX, &keypair, sk) == 0) + || (secp256k1_keypair_xonly_tweak_add(CTX, &keypair_tmp, tweak) == 0)); + CHECK(secp256k1_memcmp_var(&keypair, zeros96, sizeof(keypair)) == 0 + || secp256k1_memcmp_var(&keypair_tmp, zeros96, sizeof(keypair_tmp)) == 0); + } + + /* Invalid keypair with a valid tweak */ + memset(&keypair, 0, sizeof(keypair)); + testrand256(tweak); + CHECK_ILLEGAL(CTX, secp256k1_keypair_xonly_tweak_add(CTX, &keypair, tweak)); + CHECK(secp256k1_memcmp_var(&keypair, zeros96, sizeof(keypair)) == 0); + /* Only seckey part of keypair invalid */ + CHECK(secp256k1_keypair_create(CTX, &keypair, sk) == 1); + memset(&keypair, 0, 32); + CHECK_ILLEGAL(CTX, secp256k1_keypair_xonly_tweak_add(CTX, &keypair, tweak)); + /* Only pubkey part of keypair invalid */ + CHECK(secp256k1_keypair_create(CTX, &keypair, sk) == 1); + memset(&keypair.data[32], 0, 64); + CHECK_ILLEGAL(CTX, secp256k1_keypair_xonly_tweak_add(CTX, &keypair, tweak)); + + /* Check that the keypair_tweak_add implementation is correct */ + CHECK(secp256k1_keypair_create(CTX, &keypair, sk) == 1); + for (i = 0; i < COUNT; i++) { + secp256k1_xonly_pubkey internal_pk; + secp256k1_xonly_pubkey output_pk; + secp256k1_pubkey output_pk_xy; + secp256k1_pubkey output_pk_expected; + unsigned char pk32[32]; + unsigned char sk32[32]; + int pk_parity; + + testrand256(tweak); + CHECK(secp256k1_keypair_xonly_pub(CTX, &internal_pk, NULL, &keypair) == 1); + CHECK(secp256k1_keypair_xonly_tweak_add(CTX, &keypair, tweak) == 1); + CHECK(secp256k1_keypair_xonly_pub(CTX, &output_pk, &pk_parity, &keypair) == 1); + + /* Check that it passes xonly_pubkey_tweak_add_check */ + CHECK(secp256k1_xonly_pubkey_serialize(CTX, pk32, &output_pk) == 1); + CHECK(secp256k1_xonly_pubkey_tweak_add_check(CTX, pk32, pk_parity, &internal_pk, tweak) == 1); + + /* Check that the resulting pubkey matches xonly_pubkey_tweak_add */ + CHECK(secp256k1_keypair_pub(CTX, &output_pk_xy, &keypair) == 1); + CHECK(secp256k1_xonly_pubkey_tweak_add(CTX, &output_pk_expected, &internal_pk, tweak) == 1); + CHECK(secp256k1_memcmp_var(&output_pk_xy, &output_pk_expected, sizeof(output_pk_xy)) == 0); + + /* Check that the secret key in the keypair is tweaked correctly */ + CHECK(secp256k1_keypair_sec(CTX, sk32, &keypair) == 1); + CHECK(secp256k1_ec_pubkey_create(CTX, &output_pk_expected, sk32) == 1); + CHECK(secp256k1_memcmp_var(&output_pk_xy, &output_pk_expected, sizeof(output_pk_xy)) == 0); + } +} + +static void run_extrakeys_tests(void) { + /* xonly key test cases */ + test_xonly_pubkey(); + test_xonly_pubkey_tweak(); + test_xonly_pubkey_tweak_check(); + test_xonly_pubkey_tweak_recursive(); + test_xonly_pubkey_comparison(); + + /* keypair tests */ + test_keypair(); + test_keypair_add(); +} + +#endif diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/musig/keyagg.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/musig/keyagg.h new file mode 100644 index 00000000000..a0b37252f8a --- /dev/null +++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/musig/keyagg.h @@ -0,0 +1,32 @@ +/*********************************************************************** + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_MODULE_MUSIG_KEYAGG_H +#define SECP256K1_MODULE_MUSIG_KEYAGG_H + +#include "../../../include/secp256k1.h" +#include "../../../include/secp256k1_musig.h" + +#include "../../group.h" +#include "../../scalar.h" + +typedef struct { + secp256k1_ge pk; + /* If there is no "second" public key, second_pk is set to the point at + * infinity */ + secp256k1_ge second_pk; + unsigned char pks_hash[32]; + /* tweak is identical to value tacc[v] in the specification. */ + secp256k1_scalar tweak; + /* parity_acc corresponds to (1 - gacc[v])/2 in the spec. So if gacc[v] is + * -1, parity_acc is 1. Otherwise, parity_acc is 0. */ + int parity_acc; +} secp256k1_keyagg_cache_internal; + +static int secp256k1_keyagg_cache_load(const secp256k1_context* ctx, secp256k1_keyagg_cache_internal *cache_i, const secp256k1_musig_keyagg_cache *cache); + +static void secp256k1_musig_keyaggcoef(secp256k1_scalar *r, const secp256k1_keyagg_cache_internal *cache_i, secp256k1_ge *pk); + +#endif diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/musig/keyagg_impl.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/musig/keyagg_impl.h new file mode 100644 index 00000000000..0db4fce8596 --- /dev/null +++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/musig/keyagg_impl.h @@ -0,0 +1,291 @@ +/*********************************************************************** + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_MODULE_MUSIG_KEYAGG_IMPL_H +#define SECP256K1_MODULE_MUSIG_KEYAGG_IMPL_H + +#include + +#include "keyagg.h" +#include "../../eckey.h" +#include "../../ecmult.h" +#include "../../field.h" +#include "../../group.h" +#include "../../hash.h" +#include "../../util.h" + +static const unsigned char secp256k1_musig_keyagg_cache_magic[4] = { 0xf4, 0xad, 0xbb, 0xdf }; + +/* A keyagg cache consists of + * - 4 byte magic set during initialization to allow detecting an uninitialized + * object. + * - 64 byte aggregate (and potentially tweaked) public key + * - 64 byte "second" public key (set to the point at infinity if not present) + * - 32 byte hash of all public keys + * - 1 byte the parity of the internal key (if tweaked, otherwise 0) + * - 32 byte tweak + */ +/* Requires that cache_i->pk is not infinity. */ +static void secp256k1_keyagg_cache_save(secp256k1_musig_keyagg_cache *cache, const secp256k1_keyagg_cache_internal *cache_i) { + unsigned char *ptr = cache->data; + memcpy(ptr, secp256k1_musig_keyagg_cache_magic, 4); + ptr += 4; + secp256k1_ge_to_bytes(ptr, &cache_i->pk); + ptr += 64; + secp256k1_ge_to_bytes_ext(ptr, &cache_i->second_pk); + ptr += 64; + memcpy(ptr, cache_i->pks_hash, 32); + ptr += 32; + *ptr = cache_i->parity_acc; + ptr += 1; + secp256k1_scalar_get_b32(ptr, &cache_i->tweak); +} + +static int secp256k1_keyagg_cache_load(const secp256k1_context* ctx, secp256k1_keyagg_cache_internal *cache_i, const secp256k1_musig_keyagg_cache *cache) { + const unsigned char *ptr = cache->data; + ARG_CHECK(secp256k1_memcmp_var(ptr, secp256k1_musig_keyagg_cache_magic, 4) == 0); + ptr += 4; + secp256k1_ge_from_bytes(&cache_i->pk, ptr); + ptr += 64; + secp256k1_ge_from_bytes_ext(&cache_i->second_pk, ptr); + ptr += 64; + memcpy(cache_i->pks_hash, ptr, 32); + ptr += 32; + cache_i->parity_acc = *ptr & 1; + ptr += 1; + secp256k1_scalar_set_b32(&cache_i->tweak, ptr, NULL); + return 1; +} + +/* Initializes SHA256 with fixed midstate. This midstate was computed by applying + * SHA256 to SHA256("KeyAgg list")||SHA256("KeyAgg list"). */ +static void secp256k1_musig_keyagglist_sha256(secp256k1_sha256 *sha) { + secp256k1_sha256_initialize(sha); + + sha->s[0] = 0xb399d5e0ul; + sha->s[1] = 0xc8fff302ul; + sha->s[2] = 0x6badac71ul; + sha->s[3] = 0x07c5b7f1ul; + sha->s[4] = 0x9701e2eful; + sha->s[5] = 0x2a72ecf8ul; + sha->s[6] = 0x201a4c7bul; + sha->s[7] = 0xab148a38ul; + sha->bytes = 64; +} + +/* Computes pks_hash = tagged_hash(pk[0], ..., pk[np-1]) */ +static int secp256k1_musig_compute_pks_hash(const secp256k1_context *ctx, unsigned char *pks_hash, const secp256k1_pubkey * const* pks, size_t np) { + secp256k1_sha256 sha; + size_t i; + + secp256k1_musig_keyagglist_sha256(&sha); + for (i = 0; i < np; i++) { + unsigned char ser[33]; + size_t ser_len = sizeof(ser); + if (!secp256k1_ec_pubkey_serialize(ctx, ser, &ser_len, pks[i], SECP256K1_EC_COMPRESSED)) { + return 0; + } + VERIFY_CHECK(ser_len == sizeof(ser)); + secp256k1_sha256_write(&sha, ser, sizeof(ser)); + } + secp256k1_sha256_finalize(&sha, pks_hash); + return 1; +} + +/* Initializes SHA256 with fixed midstate. This midstate was computed by applying + * SHA256 to SHA256("KeyAgg coefficient")||SHA256("KeyAgg coefficient"). */ +static void secp256k1_musig_keyaggcoef_sha256(secp256k1_sha256 *sha) { + secp256k1_sha256_initialize(sha); + + sha->s[0] = 0x6ef02c5aul; + sha->s[1] = 0x06a480deul; + sha->s[2] = 0x1f298665ul; + sha->s[3] = 0x1d1134f2ul; + sha->s[4] = 0x56a0b063ul; + sha->s[5] = 0x52da4147ul; + sha->s[6] = 0xf280d9d4ul; + sha->s[7] = 0x4484be15ul; + sha->bytes = 64; +} + +/* Compute KeyAgg coefficient which is constant 1 for the second pubkey and + * otherwise tagged_hash(pks_hash, pk) where pks_hash is the hash of public keys. + * second_pk is the point at infinity in case there is no second_pk. Assumes + * that pk is not the point at infinity and that the Y-coordinates of pk and + * second_pk are normalized. */ +static void secp256k1_musig_keyaggcoef_internal(secp256k1_scalar *r, const unsigned char *pks_hash, secp256k1_ge *pk, const secp256k1_ge *second_pk) { + VERIFY_CHECK(!secp256k1_ge_is_infinity(pk)); + + if (!secp256k1_ge_is_infinity(second_pk) + && secp256k1_ge_eq_var(pk, second_pk)) { + secp256k1_scalar_set_int(r, 1); + } else { + secp256k1_sha256 sha; + unsigned char buf[33]; + size_t buflen = sizeof(buf); + int ret; + secp256k1_musig_keyaggcoef_sha256(&sha); + secp256k1_sha256_write(&sha, pks_hash, 32); + ret = secp256k1_eckey_pubkey_serialize(pk, buf, &buflen, 1); +#ifdef VERIFY + /* Serialization does not fail since the pk is not the point at infinity + * (according to this function's precondition). */ + VERIFY_CHECK(ret && buflen == sizeof(buf)); +#else + (void) ret; +#endif + secp256k1_sha256_write(&sha, buf, sizeof(buf)); + secp256k1_sha256_finalize(&sha, buf); + secp256k1_scalar_set_b32(r, buf, NULL); + } +} + +/* Assumes that pk is not the point at infinity and that the Y-coordinates of pk + * and cache_i->second_pk are normalized. */ +static void secp256k1_musig_keyaggcoef(secp256k1_scalar *r, const secp256k1_keyagg_cache_internal *cache_i, secp256k1_ge *pk) { + secp256k1_musig_keyaggcoef_internal(r, cache_i->pks_hash, pk, &cache_i->second_pk); +} + +typedef struct { + const secp256k1_context *ctx; + /* pks_hash is the hash of the public keys */ + unsigned char pks_hash[32]; + const secp256k1_pubkey * const* pks; + secp256k1_ge second_pk; +} secp256k1_musig_pubkey_agg_ecmult_data; + +/* Callback for batch EC multiplication to compute keyaggcoef_0*P0 + keyaggcoef_1*P1 + ... */ +static int secp256k1_musig_pubkey_agg_callback(secp256k1_scalar *sc, secp256k1_ge *pt, size_t idx, void *data) { + secp256k1_musig_pubkey_agg_ecmult_data *ctx = (secp256k1_musig_pubkey_agg_ecmult_data *) data; + int ret; + ret = secp256k1_pubkey_load(ctx->ctx, pt, ctx->pks[idx]); +#ifdef VERIFY + /* pubkey_load can't fail because the same pks have already been loaded in + * `musig_compute_pks_hash` (and we test this). */ + VERIFY_CHECK(ret); +#else + (void) ret; +#endif + secp256k1_musig_keyaggcoef_internal(sc, ctx->pks_hash, pt, &ctx->second_pk); + return 1; +} + +int secp256k1_musig_pubkey_agg(const secp256k1_context* ctx, secp256k1_xonly_pubkey *agg_pk, secp256k1_musig_keyagg_cache *keyagg_cache, const secp256k1_pubkey * const* pubkeys, size_t n_pubkeys) { + secp256k1_musig_pubkey_agg_ecmult_data ecmult_data; + secp256k1_gej pkj; + secp256k1_ge pkp; + size_t i; + + VERIFY_CHECK(ctx != NULL); + if (agg_pk != NULL) { + memset(agg_pk, 0, sizeof(*agg_pk)); + } + ARG_CHECK(pubkeys != NULL); + ARG_CHECK(n_pubkeys > 0); + + ecmult_data.ctx = ctx; + ecmult_data.pks = pubkeys; + + secp256k1_ge_set_infinity(&ecmult_data.second_pk); + for (i = 1; i < n_pubkeys; i++) { + if (secp256k1_memcmp_var(pubkeys[0], pubkeys[i], sizeof(*pubkeys[0])) != 0) { + secp256k1_ge pk; + if (!secp256k1_pubkey_load(ctx, &pk, pubkeys[i])) { + return 0; + } + ecmult_data.second_pk = pk; + break; + } + } + + if (!secp256k1_musig_compute_pks_hash(ctx, ecmult_data.pks_hash, pubkeys, n_pubkeys)) { + return 0; + } + /* TODO: actually use optimized ecmult_multi algorithms by providing a + * scratch space */ + if (!secp256k1_ecmult_multi_var(&ctx->error_callback, NULL, &pkj, NULL, secp256k1_musig_pubkey_agg_callback, (void *) &ecmult_data, n_pubkeys)) { + /* In order to reach this line with the current implementation of + * ecmult_multi_var one would need to provide a callback that can + * fail. */ + return 0; + } + secp256k1_ge_set_gej(&pkp, &pkj); + secp256k1_fe_normalize_var(&pkp.y); + /* The resulting public key is infinity with negligible probability */ + VERIFY_CHECK(!secp256k1_ge_is_infinity(&pkp)); + if (keyagg_cache != NULL) { + secp256k1_keyagg_cache_internal cache_i = { 0 }; + cache_i.pk = pkp; + cache_i.second_pk = ecmult_data.second_pk; + memcpy(cache_i.pks_hash, ecmult_data.pks_hash, sizeof(cache_i.pks_hash)); + secp256k1_keyagg_cache_save(keyagg_cache, &cache_i); + } + + if (agg_pk != NULL) { + secp256k1_extrakeys_ge_even_y(&pkp); + secp256k1_xonly_pubkey_save(agg_pk, &pkp); + } + return 1; +} + +int secp256k1_musig_pubkey_get(const secp256k1_context* ctx, secp256k1_pubkey *agg_pk, const secp256k1_musig_keyagg_cache *keyagg_cache) { + secp256k1_keyagg_cache_internal cache_i; + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(agg_pk != NULL); + memset(agg_pk, 0, sizeof(*agg_pk)); + ARG_CHECK(keyagg_cache != NULL); + + if (!secp256k1_keyagg_cache_load(ctx, &cache_i, keyagg_cache)) { + return 0; + } + secp256k1_pubkey_save(agg_pk, &cache_i.pk); + return 1; +} + +static int secp256k1_musig_pubkey_tweak_add_internal(const secp256k1_context* ctx, secp256k1_pubkey *output_pubkey, secp256k1_musig_keyagg_cache *keyagg_cache, const unsigned char *tweak32, int xonly) { + secp256k1_keyagg_cache_internal cache_i; + int overflow = 0; + secp256k1_scalar tweak; + + VERIFY_CHECK(ctx != NULL); + if (output_pubkey != NULL) { + memset(output_pubkey, 0, sizeof(*output_pubkey)); + } + ARG_CHECK(keyagg_cache != NULL); + ARG_CHECK(tweak32 != NULL); + + if (!secp256k1_keyagg_cache_load(ctx, &cache_i, keyagg_cache)) { + return 0; + } + secp256k1_scalar_set_b32(&tweak, tweak32, &overflow); + if (overflow) { + return 0; + } + if (xonly && secp256k1_extrakeys_ge_even_y(&cache_i.pk)) { + cache_i.parity_acc ^= 1; + secp256k1_scalar_negate(&cache_i.tweak, &cache_i.tweak); + } + secp256k1_scalar_add(&cache_i.tweak, &cache_i.tweak, &tweak); + if (!secp256k1_eckey_pubkey_tweak_add(&cache_i.pk, &tweak)) { + return 0; + } + /* eckey_pubkey_tweak_add fails if cache_i.pk is infinity */ + VERIFY_CHECK(!secp256k1_ge_is_infinity(&cache_i.pk)); + secp256k1_keyagg_cache_save(keyagg_cache, &cache_i); + if (output_pubkey != NULL) { + secp256k1_pubkey_save(output_pubkey, &cache_i.pk); + } + return 1; +} + +int secp256k1_musig_pubkey_ec_tweak_add(const secp256k1_context* ctx, secp256k1_pubkey *output_pubkey, secp256k1_musig_keyagg_cache *keyagg_cache, const unsigned char *tweak32) { + return secp256k1_musig_pubkey_tweak_add_internal(ctx, output_pubkey, keyagg_cache, tweak32, 0); +} + +int secp256k1_musig_pubkey_xonly_tweak_add(const secp256k1_context* ctx, secp256k1_pubkey *output_pubkey, secp256k1_musig_keyagg_cache *keyagg_cache, const unsigned char *tweak32) { + return secp256k1_musig_pubkey_tweak_add_internal(ctx, output_pubkey, keyagg_cache, tweak32, 1); +} + +#endif diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/musig/main_impl.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/musig/main_impl.h new file mode 100644 index 00000000000..a1311e41912 --- /dev/null +++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/musig/main_impl.h @@ -0,0 +1,12 @@ +/********************************************************************** + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#ifndef SECP256K1_MODULE_MUSIG_MAIN_H +#define SECP256K1_MODULE_MUSIG_MAIN_H + +#include "keyagg_impl.h" +#include "session_impl.h" + +#endif diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/musig/session.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/musig/session.h new file mode 100644 index 00000000000..d6d76bc6c11 --- /dev/null +++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/musig/session.h @@ -0,0 +1,24 @@ +/*********************************************************************** + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_MODULE_MUSIG_SESSION_H +#define SECP256K1_MODULE_MUSIG_SESSION_H + +#include "../../../include/secp256k1.h" +#include "../../../include/secp256k1_musig.h" + +#include "../../scalar.h" + +typedef struct { + int fin_nonce_parity; + unsigned char fin_nonce[32]; + secp256k1_scalar noncecoef; + secp256k1_scalar challenge; + secp256k1_scalar s_part; +} secp256k1_musig_session_internal; + +static int secp256k1_musig_session_load(const secp256k1_context* ctx, secp256k1_musig_session_internal *session_i, const secp256k1_musig_session *session); + +#endif diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/musig/session_impl.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/musig/session_impl.h new file mode 100644 index 00000000000..dde38085827 --- /dev/null +++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/musig/session_impl.h @@ -0,0 +1,816 @@ +/*********************************************************************** + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_MODULE_MUSIG_SESSION_IMPL_H +#define SECP256K1_MODULE_MUSIG_SESSION_IMPL_H + +#include + +#include "../../../include/secp256k1.h" +#include "../../../include/secp256k1_extrakeys.h" +#include "../../../include/secp256k1_musig.h" + +#include "keyagg.h" +#include "session.h" +#include "../../eckey.h" +#include "../../hash.h" +#include "../../scalar.h" +#include "../../util.h" + +/* Outputs 33 zero bytes if the given group element is the point at infinity and + * otherwise outputs the compressed serialization */ +static void secp256k1_musig_ge_serialize_ext(unsigned char *out33, secp256k1_ge* ge) { + if (secp256k1_ge_is_infinity(ge)) { + memset(out33, 0, 33); + } else { + int ret; + size_t size = 33; + ret = secp256k1_eckey_pubkey_serialize(ge, out33, &size, 1); +#ifdef VERIFY + /* Serialize must succeed because the point is not at infinity */ + VERIFY_CHECK(ret && size == 33); +#else + (void) ret; +#endif + } +} + +/* Outputs the point at infinity if the given byte array is all zero, otherwise + * attempts to parse compressed point serialization. */ +static int secp256k1_musig_ge_parse_ext(secp256k1_ge* ge, const unsigned char *in33) { + unsigned char zeros[33] = { 0 }; + + if (secp256k1_memcmp_var(in33, zeros, sizeof(zeros)) == 0) { + secp256k1_ge_set_infinity(ge); + return 1; + } + if (!secp256k1_eckey_pubkey_parse(ge, in33, 33)) { + return 0; + } + return secp256k1_ge_is_in_correct_subgroup(ge); +} + +static const unsigned char secp256k1_musig_secnonce_magic[4] = { 0x22, 0x0e, 0xdc, 0xf1 }; + +static void secp256k1_musig_secnonce_save(secp256k1_musig_secnonce *secnonce, const secp256k1_scalar *k, const secp256k1_ge *pk) { + memcpy(&secnonce->data[0], secp256k1_musig_secnonce_magic, 4); + secp256k1_scalar_get_b32(&secnonce->data[4], &k[0]); + secp256k1_scalar_get_b32(&secnonce->data[36], &k[1]); + secp256k1_ge_to_bytes(&secnonce->data[68], pk); +} + +static int secp256k1_musig_secnonce_load(const secp256k1_context* ctx, secp256k1_scalar *k, secp256k1_ge *pk, const secp256k1_musig_secnonce *secnonce) { + int is_zero; + ARG_CHECK(secp256k1_memcmp_var(&secnonce->data[0], secp256k1_musig_secnonce_magic, 4) == 0); + /* We make very sure that the nonce isn't invalidated by checking the values + * in addition to the magic. */ + is_zero = secp256k1_is_zero_array(&secnonce->data[4], 2 * 32); + secp256k1_declassify(ctx, &is_zero, sizeof(is_zero)); + ARG_CHECK(!is_zero); + + secp256k1_scalar_set_b32(&k[0], &secnonce->data[4], NULL); + secp256k1_scalar_set_b32(&k[1], &secnonce->data[36], NULL); + secp256k1_ge_from_bytes(pk, &secnonce->data[68]); + return 1; +} + +/* If flag is true, invalidate the secnonce; otherwise leave it. Constant-time. */ +static void secp256k1_musig_secnonce_invalidate(const secp256k1_context* ctx, secp256k1_musig_secnonce *secnonce, int flag) { + secp256k1_memczero(secnonce->data, sizeof(secnonce->data), flag); + /* The flag argument is usually classified. So, the line above makes the + * magic and public key classified. However, we need both to be + * declassified. Note that we don't declassify the entire object, because if + * flag is 0, then k[0] and k[1] have not been zeroed. */ + secp256k1_declassify(ctx, secnonce->data, sizeof(secp256k1_musig_secnonce_magic)); + secp256k1_declassify(ctx, &secnonce->data[68], 64); +} + +static const unsigned char secp256k1_musig_pubnonce_magic[4] = { 0xf5, 0x7a, 0x3d, 0xa0 }; + +/* Saves two group elements into a pubnonce. Requires that none of the provided + * group elements is infinity. */ +static void secp256k1_musig_pubnonce_save(secp256k1_musig_pubnonce* nonce, const secp256k1_ge* ges) { + int i; + memcpy(&nonce->data[0], secp256k1_musig_pubnonce_magic, 4); + for (i = 0; i < 2; i++) { + secp256k1_ge_to_bytes(nonce->data + 4+64*i, &ges[i]); + } +} + +/* Loads two group elements from a pubnonce. Returns 1 unless the nonce wasn't + * properly initialized */ +static int secp256k1_musig_pubnonce_load(const secp256k1_context* ctx, secp256k1_ge* ges, const secp256k1_musig_pubnonce* nonce) { + int i; + + ARG_CHECK(secp256k1_memcmp_var(&nonce->data[0], secp256k1_musig_pubnonce_magic, 4) == 0); + for (i = 0; i < 2; i++) { + secp256k1_ge_from_bytes(&ges[i], nonce->data + 4 + 64*i); + } + return 1; +} + +static const unsigned char secp256k1_musig_aggnonce_magic[4] = { 0xa8, 0xb7, 0xe4, 0x67 }; + +static void secp256k1_musig_aggnonce_save(secp256k1_musig_aggnonce* nonce, const secp256k1_ge* ges) { + int i; + memcpy(&nonce->data[0], secp256k1_musig_aggnonce_magic, 4); + for (i = 0; i < 2; i++) { + secp256k1_ge_to_bytes_ext(&nonce->data[4 + 64*i], &ges[i]); + } +} + +static int secp256k1_musig_aggnonce_load(const secp256k1_context* ctx, secp256k1_ge* ges, const secp256k1_musig_aggnonce* nonce) { + int i; + + ARG_CHECK(secp256k1_memcmp_var(&nonce->data[0], secp256k1_musig_aggnonce_magic, 4) == 0); + for (i = 0; i < 2; i++) { + secp256k1_ge_from_bytes_ext(&ges[i], &nonce->data[4 + 64*i]); + } + return 1; +} + +static const unsigned char secp256k1_musig_session_cache_magic[4] = { 0x9d, 0xed, 0xe9, 0x17 }; + +/* A session consists of + * - 4 byte session cache magic + * - 1 byte the parity of the final nonce + * - 32 byte serialized x-only final nonce + * - 32 byte nonce coefficient b + * - 32 byte signature challenge hash e + * - 32 byte scalar s that is added to the partial signatures of the signers + */ +static void secp256k1_musig_session_save(secp256k1_musig_session *session, const secp256k1_musig_session_internal *session_i) { + unsigned char *ptr = session->data; + + memcpy(ptr, secp256k1_musig_session_cache_magic, 4); + ptr += 4; + *ptr = session_i->fin_nonce_parity; + ptr += 1; + memcpy(ptr, session_i->fin_nonce, 32); + ptr += 32; + secp256k1_scalar_get_b32(ptr, &session_i->noncecoef); + ptr += 32; + secp256k1_scalar_get_b32(ptr, &session_i->challenge); + ptr += 32; + secp256k1_scalar_get_b32(ptr, &session_i->s_part); +} + +static int secp256k1_musig_session_load(const secp256k1_context* ctx, secp256k1_musig_session_internal *session_i, const secp256k1_musig_session *session) { + const unsigned char *ptr = session->data; + + ARG_CHECK(secp256k1_memcmp_var(ptr, secp256k1_musig_session_cache_magic, 4) == 0); + ptr += 4; + session_i->fin_nonce_parity = *ptr; + ptr += 1; + memcpy(session_i->fin_nonce, ptr, 32); + ptr += 32; + secp256k1_scalar_set_b32(&session_i->noncecoef, ptr, NULL); + ptr += 32; + secp256k1_scalar_set_b32(&session_i->challenge, ptr, NULL); + ptr += 32; + secp256k1_scalar_set_b32(&session_i->s_part, ptr, NULL); + return 1; +} + +static const unsigned char secp256k1_musig_partial_sig_magic[4] = { 0xeb, 0xfb, 0x1a, 0x32 }; + +static void secp256k1_musig_partial_sig_save(secp256k1_musig_partial_sig* sig, secp256k1_scalar *s) { + memcpy(&sig->data[0], secp256k1_musig_partial_sig_magic, 4); + secp256k1_scalar_get_b32(&sig->data[4], s); +} + +static int secp256k1_musig_partial_sig_load(const secp256k1_context* ctx, secp256k1_scalar *s, const secp256k1_musig_partial_sig* sig) { + int overflow; + + ARG_CHECK(secp256k1_memcmp_var(&sig->data[0], secp256k1_musig_partial_sig_magic, 4) == 0); + secp256k1_scalar_set_b32(s, &sig->data[4], &overflow); + /* Parsed signatures can not overflow */ + VERIFY_CHECK(!overflow); + return 1; +} + +int secp256k1_musig_pubnonce_parse(const secp256k1_context* ctx, secp256k1_musig_pubnonce* nonce, const unsigned char *in66) { + secp256k1_ge ges[2]; + int i; + + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(nonce != NULL); + ARG_CHECK(in66 != NULL); + + for (i = 0; i < 2; i++) { + if (!secp256k1_eckey_pubkey_parse(&ges[i], &in66[33*i], 33)) { + return 0; + } + if (!secp256k1_ge_is_in_correct_subgroup(&ges[i])) { + return 0; + } + } + secp256k1_musig_pubnonce_save(nonce, ges); + return 1; +} + +int secp256k1_musig_pubnonce_serialize(const secp256k1_context* ctx, unsigned char *out66, const secp256k1_musig_pubnonce* nonce) { + secp256k1_ge ges[2]; + int i; + + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(out66 != NULL); + memset(out66, 0, 66); + ARG_CHECK(nonce != NULL); + + if (!secp256k1_musig_pubnonce_load(ctx, ges, nonce)) { + return 0; + } + for (i = 0; i < 2; i++) { + int ret; + size_t size = 33; + ret = secp256k1_eckey_pubkey_serialize(&ges[i], &out66[33*i], &size, 1); +#ifdef VERIFY + /* serialize must succeed because the point was just loaded */ + VERIFY_CHECK(ret && size == 33); +#else + (void) ret; +#endif + } + return 1; +} + +int secp256k1_musig_aggnonce_parse(const secp256k1_context* ctx, secp256k1_musig_aggnonce* nonce, const unsigned char *in66) { + secp256k1_ge ges[2]; + int i; + + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(nonce != NULL); + ARG_CHECK(in66 != NULL); + + for (i = 0; i < 2; i++) { + if (!secp256k1_musig_ge_parse_ext(&ges[i], &in66[33*i])) { + return 0; + } + } + secp256k1_musig_aggnonce_save(nonce, ges); + return 1; +} + +int secp256k1_musig_aggnonce_serialize(const secp256k1_context* ctx, unsigned char *out66, const secp256k1_musig_aggnonce* nonce) { + secp256k1_ge ges[2]; + int i; + + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(out66 != NULL); + memset(out66, 0, 66); + ARG_CHECK(nonce != NULL); + + if (!secp256k1_musig_aggnonce_load(ctx, ges, nonce)) { + return 0; + } + for (i = 0; i < 2; i++) { + secp256k1_musig_ge_serialize_ext(&out66[33*i], &ges[i]); + } + return 1; +} + +int secp256k1_musig_partial_sig_parse(const secp256k1_context* ctx, secp256k1_musig_partial_sig* sig, const unsigned char *in32) { + secp256k1_scalar tmp; + int overflow; + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(sig != NULL); + ARG_CHECK(in32 != NULL); + + /* Ensure that using the signature will fail if parsing fails (and the user + * doesn't check the return value). */ + memset(sig, 0, sizeof(*sig)); + + secp256k1_scalar_set_b32(&tmp, in32, &overflow); + if (overflow) { + return 0; + } + secp256k1_musig_partial_sig_save(sig, &tmp); + return 1; +} + +int secp256k1_musig_partial_sig_serialize(const secp256k1_context* ctx, unsigned char *out32, const secp256k1_musig_partial_sig* sig) { + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(out32 != NULL); + ARG_CHECK(sig != NULL); + ARG_CHECK(secp256k1_memcmp_var(&sig->data[0], secp256k1_musig_partial_sig_magic, 4) == 0); + + memcpy(out32, &sig->data[4], 32); + return 1; +} + +/* Write optional inputs into the hash */ +static void secp256k1_nonce_function_musig_helper(secp256k1_sha256 *sha, unsigned int prefix_size, const unsigned char *data, unsigned char len) { + unsigned char zero[7] = { 0 }; + /* The spec requires length prefixes to be between 1 and 8 bytes + * (inclusive) */ + VERIFY_CHECK(prefix_size >= 1 && prefix_size <= 8); + /* Since the length of all input data fits in a byte, we can always pad the + * length prefix with prefix_size - 1 zero bytes. */ + secp256k1_sha256_write(sha, zero, prefix_size - 1); + if (data != NULL) { + secp256k1_sha256_write(sha, &len, 1); + secp256k1_sha256_write(sha, data, len); + } else { + len = 0; + secp256k1_sha256_write(sha, &len, 1); + } +} + +/* Initializes SHA256 with fixed midstate. This midstate was computed by applying + * SHA256 to SHA256("MuSig/aux")||SHA256("MuSig/aux"). */ +static void secp256k1_nonce_function_musig_sha256_tagged_aux(secp256k1_sha256 *sha) { + secp256k1_sha256_initialize(sha); + sha->s[0] = 0xa19e884bul; + sha->s[1] = 0xf463fe7eul; + sha->s[2] = 0x2f18f9a2ul; + sha->s[3] = 0xbeb0f9fful; + sha->s[4] = 0x0f37e8b0ul; + sha->s[5] = 0x06ebd26ful; + sha->s[6] = 0xe3b243d2ul; + sha->s[7] = 0x522fb150ul; + sha->bytes = 64; +} + +/* Initializes SHA256 with fixed midstate. This midstate was computed by applying + * SHA256 to SHA256("MuSig/nonce")||SHA256("MuSig/nonce"). */ +static void secp256k1_nonce_function_musig_sha256_tagged(secp256k1_sha256 *sha) { + secp256k1_sha256_initialize(sha); + sha->s[0] = 0x07101b64ul; + sha->s[1] = 0x18003414ul; + sha->s[2] = 0x0391bc43ul; + sha->s[3] = 0x0e6258eeul; + sha->s[4] = 0x29d26b72ul; + sha->s[5] = 0x8343937eul; + sha->s[6] = 0xb7a0a4fbul; + sha->s[7] = 0xff568a30ul; + sha->bytes = 64; +} + +static void secp256k1_nonce_function_musig(secp256k1_scalar *k, const unsigned char *session_secrand, const unsigned char *msg32, const unsigned char *seckey32, const unsigned char *pk33, const unsigned char *agg_pk32, const unsigned char *extra_input32) { + secp256k1_sha256 sha; + unsigned char rand[32]; + unsigned char i; + unsigned char msg_present; + + if (seckey32 != NULL) { + secp256k1_nonce_function_musig_sha256_tagged_aux(&sha); + secp256k1_sha256_write(&sha, session_secrand, 32); + secp256k1_sha256_finalize(&sha, rand); + for (i = 0; i < 32; i++) { + rand[i] ^= seckey32[i]; + } + } else { + memcpy(rand, session_secrand, sizeof(rand)); + } + + secp256k1_nonce_function_musig_sha256_tagged(&sha); + secp256k1_sha256_write(&sha, rand, sizeof(rand)); + secp256k1_nonce_function_musig_helper(&sha, 1, pk33, 33); + secp256k1_nonce_function_musig_helper(&sha, 1, agg_pk32, 32); + msg_present = msg32 != NULL; + secp256k1_sha256_write(&sha, &msg_present, 1); + if (msg_present) { + secp256k1_nonce_function_musig_helper(&sha, 8, msg32, 32); + } + secp256k1_nonce_function_musig_helper(&sha, 4, extra_input32, 32); + + for (i = 0; i < 2; i++) { + unsigned char buf[32]; + secp256k1_sha256 sha_tmp = sha; + secp256k1_sha256_write(&sha_tmp, &i, 1); + secp256k1_sha256_finalize(&sha_tmp, buf); + secp256k1_scalar_set_b32(&k[i], buf, NULL); + + /* Attempt to erase secret data */ + secp256k1_memclear(buf, sizeof(buf)); + secp256k1_sha256_clear(&sha_tmp); + } + secp256k1_memclear(rand, sizeof(rand)); + secp256k1_sha256_clear(&sha); +} + +static int secp256k1_musig_nonce_gen_internal(const secp256k1_context* ctx, secp256k1_musig_secnonce *secnonce, secp256k1_musig_pubnonce *pubnonce, const unsigned char *input_nonce, const unsigned char *seckey, const secp256k1_pubkey *pubkey, const unsigned char *msg32, const secp256k1_musig_keyagg_cache *keyagg_cache, const unsigned char *extra_input32) { + secp256k1_scalar k[2]; + secp256k1_ge nonce_pts[2]; + int i; + unsigned char pk_ser[33]; + size_t pk_ser_len = sizeof(pk_ser); + unsigned char aggpk_ser[32]; + unsigned char *aggpk_ser_ptr = NULL; + secp256k1_ge pk; + int pk_serialize_success; + int ret = 1; + + ARG_CHECK(pubnonce != NULL); + memset(pubnonce, 0, sizeof(*pubnonce)); + ARG_CHECK(pubkey != NULL); + ARG_CHECK(secp256k1_ecmult_gen_context_is_built(&ctx->ecmult_gen_ctx)); + + /* Check that the seckey is valid to be able to sign for it later. */ + if (seckey != NULL) { + secp256k1_scalar sk; + ret &= secp256k1_scalar_set_b32_seckey(&sk, seckey); + secp256k1_scalar_clear(&sk); + } + + if (keyagg_cache != NULL) { + secp256k1_keyagg_cache_internal cache_i; + if (!secp256k1_keyagg_cache_load(ctx, &cache_i, keyagg_cache)) { + return 0; + } + /* The loaded point cache_i.pk can not be the point at infinity. */ + secp256k1_fe_get_b32(aggpk_ser, &cache_i.pk.x); + aggpk_ser_ptr = aggpk_ser; + } + if (!secp256k1_pubkey_load(ctx, &pk, pubkey)) { + return 0; + } + pk_serialize_success = secp256k1_eckey_pubkey_serialize(&pk, pk_ser, &pk_ser_len, 1); + +#ifdef VERIFY + /* A pubkey cannot be the point at infinity */ + VERIFY_CHECK(pk_serialize_success); + VERIFY_CHECK(pk_ser_len == sizeof(pk_ser)); +#else + (void) pk_serialize_success; +#endif + + secp256k1_nonce_function_musig(k, input_nonce, msg32, seckey, pk_ser, aggpk_ser_ptr, extra_input32); + VERIFY_CHECK(!secp256k1_scalar_is_zero(&k[0])); + VERIFY_CHECK(!secp256k1_scalar_is_zero(&k[1])); + secp256k1_musig_secnonce_save(secnonce, k, &pk); + secp256k1_musig_secnonce_invalidate(ctx, secnonce, !ret); + + for (i = 0; i < 2; i++) { + secp256k1_gej nonce_ptj; + secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &nonce_ptj, &k[i]); + secp256k1_ge_set_gej(&nonce_pts[i], &nonce_ptj); + secp256k1_declassify(ctx, &nonce_pts[i], sizeof(nonce_pts[i])); + secp256k1_scalar_clear(&k[i]); + secp256k1_gej_clear(&nonce_ptj); + } + /* None of the nonce_pts will be infinity because k != 0 with overwhelming + * probability */ + secp256k1_musig_pubnonce_save(pubnonce, nonce_pts); + return ret; +} + +int secp256k1_musig_nonce_gen(const secp256k1_context* ctx, secp256k1_musig_secnonce *secnonce, secp256k1_musig_pubnonce *pubnonce, unsigned char *session_secrand32, const unsigned char *seckey, const secp256k1_pubkey *pubkey, const unsigned char *msg32, const secp256k1_musig_keyagg_cache *keyagg_cache, const unsigned char *extra_input32) { + int ret = 1; + + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(secnonce != NULL); + memset(secnonce, 0, sizeof(*secnonce)); + ARG_CHECK(session_secrand32 != NULL); + + /* Check in constant time that the session_secrand32 is not 0 as a + * defense-in-depth measure that may protect against a faulty RNG. */ + ret &= !secp256k1_is_zero_array(session_secrand32, 32); + + /* We can declassify because branching on ret is only relevant when this + * function called with an invalid session_secrand32 argument */ + secp256k1_declassify(ctx, &ret, sizeof(ret)); + if (ret == 0) { + secp256k1_musig_secnonce_invalidate(ctx, secnonce, 1); + return 0; + } + + ret &= secp256k1_musig_nonce_gen_internal(ctx, secnonce, pubnonce, session_secrand32, seckey, pubkey, msg32, keyagg_cache, extra_input32); + + /* Set the session_secrand32 buffer to zero to prevent the caller from using + * nonce_gen multiple times with the same buffer. */ + secp256k1_memczero(session_secrand32, 32, ret); + return ret; +} + +int secp256k1_musig_nonce_gen_counter(const secp256k1_context* ctx, secp256k1_musig_secnonce *secnonce, secp256k1_musig_pubnonce *pubnonce, uint64_t nonrepeating_cnt, const secp256k1_keypair *keypair, const unsigned char *msg32, const secp256k1_musig_keyagg_cache *keyagg_cache, const unsigned char *extra_input32) { + unsigned char buf[32] = { 0 }; + unsigned char seckey[32]; + secp256k1_pubkey pubkey; + int ret; + + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(secnonce != NULL); + memset(secnonce, 0, sizeof(*secnonce)); + ARG_CHECK(keypair != NULL); + + secp256k1_write_be64(buf, nonrepeating_cnt); + /* keypair_sec and keypair_pub do not fail if the arguments are not NULL */ + ret = secp256k1_keypair_sec(ctx, seckey, keypair); + VERIFY_CHECK(ret); + ret = secp256k1_keypair_pub(ctx, &pubkey, keypair); + VERIFY_CHECK(ret); +#ifndef VERIFY + (void) ret; +#endif + + if (!secp256k1_musig_nonce_gen_internal(ctx, secnonce, pubnonce, buf, seckey, &pubkey, msg32, keyagg_cache, extra_input32)) { + return 0; + } + secp256k1_memclear(seckey, sizeof(seckey)); + return 1; +} + +static int secp256k1_musig_sum_pubnonces(const secp256k1_context* ctx, secp256k1_gej *summed_pubnonces, const secp256k1_musig_pubnonce * const* pubnonces, size_t n_pubnonces) { + size_t i; + int j; + + secp256k1_gej_set_infinity(&summed_pubnonces[0]); + secp256k1_gej_set_infinity(&summed_pubnonces[1]); + + for (i = 0; i < n_pubnonces; i++) { + secp256k1_ge nonce_pts[2]; + if (!secp256k1_musig_pubnonce_load(ctx, nonce_pts, pubnonces[i])) { + return 0; + } + for (j = 0; j < 2; j++) { + secp256k1_gej_add_ge_var(&summed_pubnonces[j], &summed_pubnonces[j], &nonce_pts[j], NULL); + } + } + return 1; +} + +int secp256k1_musig_nonce_agg(const secp256k1_context* ctx, secp256k1_musig_aggnonce *aggnonce, const secp256k1_musig_pubnonce * const* pubnonces, size_t n_pubnonces) { + secp256k1_gej aggnonce_ptsj[2]; + secp256k1_ge aggnonce_pts[2]; + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(aggnonce != NULL); + ARG_CHECK(pubnonces != NULL); + ARG_CHECK(n_pubnonces > 0); + + if (!secp256k1_musig_sum_pubnonces(ctx, aggnonce_ptsj, pubnonces, n_pubnonces)) { + return 0; + } + secp256k1_ge_set_all_gej_var(aggnonce_pts, aggnonce_ptsj, 2); + secp256k1_musig_aggnonce_save(aggnonce, aggnonce_pts); + return 1; +} + +/* Initializes SHA256 with fixed midstate. This midstate was computed by applying + * SHA256 to SHA256("MuSig/noncecoef")||SHA256("MuSig/noncecoef"). */ +static void secp256k1_musig_compute_noncehash_sha256_tagged(secp256k1_sha256 *sha) { + secp256k1_sha256_initialize(sha); + sha->s[0] = 0x2c7d5a45ul; + sha->s[1] = 0x06bf7e53ul; + sha->s[2] = 0x89be68a6ul; + sha->s[3] = 0x971254c0ul; + sha->s[4] = 0x60ac12d2ul; + sha->s[5] = 0x72846dcdul; + sha->s[6] = 0x6c81212ful; + sha->s[7] = 0xde7a2500ul; + sha->bytes = 64; +} + +/* tagged_hash(aggnonce[0], aggnonce[1], agg_pk, msg) */ +static void secp256k1_musig_compute_noncehash(unsigned char *noncehash, secp256k1_ge *aggnonce, const unsigned char *agg_pk32, const unsigned char *msg) { + unsigned char buf[33]; + secp256k1_sha256 sha; + int i; + + secp256k1_musig_compute_noncehash_sha256_tagged(&sha); + for (i = 0; i < 2; i++) { + secp256k1_musig_ge_serialize_ext(buf, &aggnonce[i]); + secp256k1_sha256_write(&sha, buf, sizeof(buf)); + } + secp256k1_sha256_write(&sha, agg_pk32, 32); + secp256k1_sha256_write(&sha, msg, 32); + secp256k1_sha256_finalize(&sha, noncehash); +} + +/* out_nonce = nonce_pts[0] + b*nonce_pts[1] */ +static void secp256k1_effective_nonce(secp256k1_gej *out_nonce, const secp256k1_ge *nonce_pts, const secp256k1_scalar *b) { + secp256k1_gej tmp; + + secp256k1_gej_set_ge(&tmp, &nonce_pts[1]); + secp256k1_ecmult(out_nonce, &tmp, b, NULL); + secp256k1_gej_add_ge_var(out_nonce, out_nonce, &nonce_pts[0], NULL); +} + +static void secp256k1_musig_nonce_process_internal(int *fin_nonce_parity, unsigned char *fin_nonce, secp256k1_scalar *b, secp256k1_ge *aggnonce_pts, const unsigned char *agg_pk32, const unsigned char *msg) { + unsigned char noncehash[32]; + secp256k1_ge fin_nonce_pt; + secp256k1_gej fin_nonce_ptj; + + secp256k1_musig_compute_noncehash(noncehash, aggnonce_pts, agg_pk32, msg); + secp256k1_scalar_set_b32(b, noncehash, NULL); + /* fin_nonce = aggnonce_pts[0] + b*aggnonce_pts[1] */ + secp256k1_effective_nonce(&fin_nonce_ptj, aggnonce_pts, b); + secp256k1_ge_set_gej(&fin_nonce_pt, &fin_nonce_ptj); + if (secp256k1_ge_is_infinity(&fin_nonce_pt)) { + fin_nonce_pt = secp256k1_ge_const_g; + } + /* fin_nonce_pt is not the point at infinity */ + secp256k1_fe_normalize_var(&fin_nonce_pt.x); + secp256k1_fe_get_b32(fin_nonce, &fin_nonce_pt.x); + secp256k1_fe_normalize_var(&fin_nonce_pt.y); + *fin_nonce_parity = secp256k1_fe_is_odd(&fin_nonce_pt.y); +} + +int secp256k1_musig_nonce_process(const secp256k1_context* ctx, secp256k1_musig_session *session, const secp256k1_musig_aggnonce *aggnonce, const unsigned char *msg32, const secp256k1_musig_keyagg_cache *keyagg_cache) { + secp256k1_keyagg_cache_internal cache_i; + secp256k1_ge aggnonce_pts[2]; + unsigned char fin_nonce[32]; + secp256k1_musig_session_internal session_i; + unsigned char agg_pk32[32]; + + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(session != NULL); + ARG_CHECK(aggnonce != NULL); + ARG_CHECK(msg32 != NULL); + ARG_CHECK(keyagg_cache != NULL); + + if (!secp256k1_keyagg_cache_load(ctx, &cache_i, keyagg_cache)) { + return 0; + } + secp256k1_fe_get_b32(agg_pk32, &cache_i.pk.x); + + if (!secp256k1_musig_aggnonce_load(ctx, aggnonce_pts, aggnonce)) { + return 0; + } + + secp256k1_musig_nonce_process_internal(&session_i.fin_nonce_parity, fin_nonce, &session_i.noncecoef, aggnonce_pts, agg_pk32, msg32); + secp256k1_schnorrsig_challenge(&session_i.challenge, fin_nonce, msg32, 32, agg_pk32); + + /* If there is a tweak then set `challenge` times `tweak` to the `s`-part.*/ + secp256k1_scalar_set_int(&session_i.s_part, 0); + if (!secp256k1_scalar_is_zero(&cache_i.tweak)) { + secp256k1_scalar e_tmp; + secp256k1_scalar_mul(&e_tmp, &session_i.challenge, &cache_i.tweak); + if (secp256k1_fe_is_odd(&cache_i.pk.y)) { + secp256k1_scalar_negate(&e_tmp, &e_tmp); + } + session_i.s_part = e_tmp; + } + memcpy(session_i.fin_nonce, fin_nonce, sizeof(session_i.fin_nonce)); + secp256k1_musig_session_save(session, &session_i); + return 1; +} + +static void secp256k1_musig_partial_sign_clear(secp256k1_scalar *sk, secp256k1_scalar *k) { + secp256k1_scalar_clear(sk); + secp256k1_scalar_clear(&k[0]); + secp256k1_scalar_clear(&k[1]); +} + +int secp256k1_musig_partial_sign(const secp256k1_context* ctx, secp256k1_musig_partial_sig *partial_sig, secp256k1_musig_secnonce *secnonce, const secp256k1_keypair *keypair, const secp256k1_musig_keyagg_cache *keyagg_cache, const secp256k1_musig_session *session) { + secp256k1_scalar sk; + secp256k1_ge pk, keypair_pk; + secp256k1_scalar k[2]; + secp256k1_scalar mu, s; + secp256k1_keyagg_cache_internal cache_i; + secp256k1_musig_session_internal session_i; + int ret; + + VERIFY_CHECK(ctx != NULL); + + ARG_CHECK(secnonce != NULL); + /* Fails if the magic doesn't match */ + ret = secp256k1_musig_secnonce_load(ctx, k, &pk, secnonce); + /* Set nonce to zero to avoid nonce reuse. This will cause subsequent calls + * of this function to fail */ + memset(secnonce, 0, sizeof(*secnonce)); + if (!ret) { + secp256k1_musig_partial_sign_clear(&sk, k); + return 0; + } + + ARG_CHECK(partial_sig != NULL); + ARG_CHECK(keypair != NULL); + ARG_CHECK(keyagg_cache != NULL); + ARG_CHECK(session != NULL); + + if (!secp256k1_keypair_load(ctx, &sk, &keypair_pk, keypair)) { + secp256k1_musig_partial_sign_clear(&sk, k); + return 0; + } + ARG_CHECK(secp256k1_fe_equal(&pk.x, &keypair_pk.x) + && secp256k1_fe_equal(&pk.y, &keypair_pk.y)); + if (!secp256k1_keyagg_cache_load(ctx, &cache_i, keyagg_cache)) { + secp256k1_musig_partial_sign_clear(&sk, k); + return 0; + } + + /* Negate sk if secp256k1_fe_is_odd(&cache_i.pk.y)) XOR cache_i.parity_acc. + * This corresponds to the line "Let d = gâ‹…gaccâ‹…d' mod n" in the + * specification. */ + if ((secp256k1_fe_is_odd(&cache_i.pk.y) + != cache_i.parity_acc)) { + secp256k1_scalar_negate(&sk, &sk); + } + + /* Multiply KeyAgg coefficient */ + secp256k1_musig_keyaggcoef(&mu, &cache_i, &pk); + secp256k1_scalar_mul(&sk, &sk, &mu); + + if (!secp256k1_musig_session_load(ctx, &session_i, session)) { + secp256k1_musig_partial_sign_clear(&sk, k); + return 0; + } + + if (session_i.fin_nonce_parity) { + secp256k1_scalar_negate(&k[0], &k[0]); + secp256k1_scalar_negate(&k[1], &k[1]); + } + + /* Sign */ + secp256k1_scalar_mul(&s, &session_i.challenge, &sk); + secp256k1_scalar_mul(&k[1], &session_i.noncecoef, &k[1]); + secp256k1_scalar_add(&k[0], &k[0], &k[1]); + secp256k1_scalar_add(&s, &s, &k[0]); + secp256k1_musig_partial_sig_save(partial_sig, &s); + secp256k1_musig_partial_sign_clear(&sk, k); + return 1; +} + +int secp256k1_musig_partial_sig_verify(const secp256k1_context* ctx, const secp256k1_musig_partial_sig *partial_sig, const secp256k1_musig_pubnonce *pubnonce, const secp256k1_pubkey *pubkey, const secp256k1_musig_keyagg_cache *keyagg_cache, const secp256k1_musig_session *session) { + secp256k1_keyagg_cache_internal cache_i; + secp256k1_musig_session_internal session_i; + secp256k1_scalar mu, e, s; + secp256k1_gej pkj; + secp256k1_ge nonce_pts[2]; + secp256k1_gej rj; + secp256k1_gej tmp; + secp256k1_ge pkp; + + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(partial_sig != NULL); + ARG_CHECK(pubnonce != NULL); + ARG_CHECK(pubkey != NULL); + ARG_CHECK(keyagg_cache != NULL); + ARG_CHECK(session != NULL); + + if (!secp256k1_musig_session_load(ctx, &session_i, session)) { + return 0; + } + + if (!secp256k1_musig_pubnonce_load(ctx, nonce_pts, pubnonce)) { + return 0; + } + /* Compute "effective" nonce rj = nonce_pts[0] + b*nonce_pts[1] */ + /* TODO: use multiexp to compute -s*G + e*mu*pubkey + nonce_pts[0] + b*nonce_pts[1] */ + secp256k1_effective_nonce(&rj, nonce_pts, &session_i.noncecoef); + + if (!secp256k1_pubkey_load(ctx, &pkp, pubkey)) { + return 0; + } + if (!secp256k1_keyagg_cache_load(ctx, &cache_i, keyagg_cache)) { + return 0; + } + /* Multiplying the challenge by the KeyAgg coefficient is equivalent + * to multiplying the signer's public key by the coefficient, except + * much easier to do. */ + secp256k1_musig_keyaggcoef(&mu, &cache_i, &pkp); + secp256k1_scalar_mul(&e, &session_i.challenge, &mu); + + /* Negate e if secp256k1_fe_is_odd(&cache_i.pk.y)) XOR cache_i.parity_acc. + * This corresponds to the line "Let g' = gâ‹…gacc mod n" and the multiplication "g'â‹…e" + * in the specification. */ + if (secp256k1_fe_is_odd(&cache_i.pk.y) + != cache_i.parity_acc) { + secp256k1_scalar_negate(&e, &e); + } + + if (!secp256k1_musig_partial_sig_load(ctx, &s, partial_sig)) { + return 0; + } + /* Compute -s*G + e*pkj + rj (e already includes the keyagg coefficient mu) */ + secp256k1_scalar_negate(&s, &s); + secp256k1_gej_set_ge(&pkj, &pkp); + secp256k1_ecmult(&tmp, &pkj, &e, &s); + if (session_i.fin_nonce_parity) { + secp256k1_gej_neg(&rj, &rj); + } + secp256k1_gej_add_var(&tmp, &tmp, &rj, NULL); + + return secp256k1_gej_is_infinity(&tmp); +} + +int secp256k1_musig_partial_sig_agg(const secp256k1_context* ctx, unsigned char *sig64, const secp256k1_musig_session *session, const secp256k1_musig_partial_sig * const* partial_sigs, size_t n_sigs) { + size_t i; + secp256k1_musig_session_internal session_i; + + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(sig64 != NULL); + ARG_CHECK(session != NULL); + ARG_CHECK(partial_sigs != NULL); + ARG_CHECK(n_sigs > 0); + + if (!secp256k1_musig_session_load(ctx, &session_i, session)) { + return 0; + } + for (i = 0; i < n_sigs; i++) { + secp256k1_scalar term; + if (!secp256k1_musig_partial_sig_load(ctx, &term, partial_sigs[i])) { + return 0; + } + secp256k1_scalar_add(&session_i.s_part, &session_i.s_part, &term); + } + secp256k1_scalar_get_b32(&sig64[32], &session_i.s_part); + memcpy(&sig64[0], session_i.fin_nonce, 32); + return 1; +} + +#endif diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/musig/tests_impl.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/musig/tests_impl.h new file mode 100644 index 00000000000..ce6ae1784d1 --- /dev/null +++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/musig/tests_impl.h @@ -0,0 +1,1143 @@ +/*********************************************************************** + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_MODULE_MUSIG_TESTS_IMPL_H +#define SECP256K1_MODULE_MUSIG_TESTS_IMPL_H + +#include +#include + +#include "../../../include/secp256k1.h" +#include "../../../include/secp256k1_extrakeys.h" +#include "../../../include/secp256k1_musig.h" + +#include "session.h" +#include "keyagg.h" +#include "../../scalar.h" +#include "../../field.h" +#include "../../group.h" +#include "../../hash.h" +#include "../../util.h" + +#include "vectors.h" + +static int create_keypair_and_pk(secp256k1_keypair *keypair, secp256k1_pubkey *pk, const unsigned char *sk) { + int ret; + secp256k1_keypair keypair_tmp; + ret = secp256k1_keypair_create(CTX, &keypair_tmp, sk); + ret &= secp256k1_keypair_pub(CTX, pk, &keypair_tmp); + if (keypair != NULL) { + *keypair = keypair_tmp; + } + return ret; +} + +/* Just a simple (non-tweaked) 2-of-2 MuSig aggregate, sign, verify + * test. */ +static void musig_simple_test(void) { + unsigned char sk[2][32]; + secp256k1_keypair keypair[2]; + secp256k1_musig_pubnonce pubnonce[2]; + const secp256k1_musig_pubnonce *pubnonce_ptr[2]; + secp256k1_musig_aggnonce aggnonce; + unsigned char msg[32]; + secp256k1_xonly_pubkey agg_pk; + secp256k1_musig_keyagg_cache keyagg_cache; + unsigned char session_secrand[2][32]; + secp256k1_musig_secnonce secnonce[2]; + secp256k1_pubkey pk[2]; + const secp256k1_pubkey *pk_ptr[2]; + secp256k1_musig_partial_sig partial_sig[2]; + const secp256k1_musig_partial_sig *partial_sig_ptr[2]; + unsigned char final_sig[64]; + secp256k1_musig_session session; + int i; + + testrand256(msg); + for (i = 0; i < 2; i++) { + testrand256(sk[i]); + pk_ptr[i] = &pk[i]; + pubnonce_ptr[i] = &pubnonce[i]; + partial_sig_ptr[i] = &partial_sig[i]; + + CHECK(create_keypair_and_pk(&keypair[i], &pk[i], sk[i])); + if (i == 0) { + testrand256(session_secrand[i]); + CHECK(secp256k1_musig_nonce_gen(CTX, &secnonce[i], &pubnonce[i], session_secrand[i], sk[i], &pk[i], NULL, NULL, NULL) == 1); + } else { + uint64_t nonrepeating_cnt = 0; + CHECK(secp256k1_musig_nonce_gen_counter(CTX, &secnonce[i], &pubnonce[i], nonrepeating_cnt, &keypair[i], NULL, NULL, NULL) == 1); + } + } + + CHECK(secp256k1_musig_pubkey_agg(CTX, &agg_pk, &keyagg_cache, pk_ptr, 2) == 1); + CHECK(secp256k1_musig_nonce_agg(CTX, &aggnonce, pubnonce_ptr, 2) == 1); + CHECK(secp256k1_musig_nonce_process(CTX, &session, &aggnonce, msg, &keyagg_cache) == 1); + + for (i = 0; i < 2; i++) { + CHECK(secp256k1_musig_partial_sign(CTX, &partial_sig[i], &secnonce[i], &keypair[i], &keyagg_cache, &session) == 1); + CHECK(secp256k1_musig_partial_sig_verify(CTX, &partial_sig[i], &pubnonce[i], &pk[i], &keyagg_cache, &session) == 1); + } + + CHECK(secp256k1_musig_partial_sig_agg(CTX, final_sig, &session, partial_sig_ptr, 2) == 1); + CHECK(secp256k1_schnorrsig_verify(CTX, final_sig, msg, sizeof(msg), &agg_pk) == 1); +} + +/* Generate two pubnonces such that both group elements of their sum (calculated + * with secp256k1_musig_sum_pubnonces) are infinity. */ +static void pubnonce_summing_to_inf(secp256k1_musig_pubnonce *pubnonce) { + secp256k1_ge ge[2]; + int i; + secp256k1_gej summed_pubnonces[2]; + const secp256k1_musig_pubnonce *pubnonce_ptr[2]; + + testutil_random_ge_test(&ge[0]); + testutil_random_ge_test(&ge[1]); + + for (i = 0; i < 2; i++) { + secp256k1_musig_pubnonce_save(&pubnonce[i], ge); + pubnonce_ptr[i] = &pubnonce[i]; + secp256k1_ge_neg(&ge[0], &ge[0]); + secp256k1_ge_neg(&ge[1], &ge[1]); + } + + secp256k1_musig_sum_pubnonces(CTX, summed_pubnonces, pubnonce_ptr, 2); + CHECK(secp256k1_gej_is_infinity(&summed_pubnonces[0])); + CHECK(secp256k1_gej_is_infinity(&summed_pubnonces[1])); +} + +int memcmp_and_randomize(unsigned char *value, const unsigned char *expected, size_t len) { + int ret; + size_t i; + ret = secp256k1_memcmp_var(value, expected, len); + for (i = 0; i < len; i++) { + value[i] = testrand_bits(8); + } + return ret; +} + +static void musig_api_tests(void) { + secp256k1_musig_partial_sig partial_sig[2]; + const secp256k1_musig_partial_sig *partial_sig_ptr[2]; + secp256k1_musig_partial_sig invalid_partial_sig; + const secp256k1_musig_partial_sig *invalid_partial_sig_ptr[2]; + unsigned char pre_sig[64]; + unsigned char buf[32]; + unsigned char sk[2][32]; + secp256k1_keypair keypair[2]; + secp256k1_keypair invalid_keypair; + unsigned char max64[64]; + unsigned char zeros132[132] = { 0 }; + unsigned char session_secrand[2][32]; + unsigned char nonrepeating_cnt = 0; + secp256k1_musig_secnonce secnonce[2]; + secp256k1_musig_secnonce secnonce_tmp; + secp256k1_musig_secnonce invalid_secnonce; + secp256k1_musig_pubnonce pubnonce[2]; + const secp256k1_musig_pubnonce *pubnonce_ptr[2]; + unsigned char pubnonce_ser[66]; + secp256k1_musig_pubnonce inf_pubnonce[2]; + const secp256k1_musig_pubnonce *inf_pubnonce_ptr[2]; + secp256k1_musig_pubnonce invalid_pubnonce; + const secp256k1_musig_pubnonce *invalid_pubnonce_ptr[1]; + secp256k1_musig_aggnonce aggnonce; + unsigned char aggnonce_ser[66]; + unsigned char msg[32]; + secp256k1_xonly_pubkey agg_pk; + secp256k1_pubkey full_agg_pk; + secp256k1_musig_keyagg_cache keyagg_cache; + secp256k1_musig_keyagg_cache invalid_keyagg_cache; + secp256k1_musig_session session; + secp256k1_musig_session invalid_session; + secp256k1_pubkey pk[2]; + const secp256k1_pubkey *pk_ptr[2]; + secp256k1_pubkey invalid_pk; + const secp256k1_pubkey *invalid_pk_ptr2[2]; + const secp256k1_pubkey *invalid_pk_ptr3[3]; + unsigned char tweak[32]; + int i; + + /** setup **/ + memset(max64, 0xff, sizeof(max64)); + memset(&invalid_keypair, 0, sizeof(invalid_keypair)); + memset(&invalid_pk, 0, sizeof(invalid_pk)); + memset(&invalid_secnonce, 0, sizeof(invalid_secnonce)); + memset(&invalid_partial_sig, 0, sizeof(invalid_partial_sig)); + pubnonce_summing_to_inf(inf_pubnonce); + /* Simulate structs being uninitialized by setting it to 0s. We don't want + * to produce undefined behavior by actually providing uninitialized + * structs. */ + memset(&invalid_keyagg_cache, 0, sizeof(invalid_keyagg_cache)); + memset(&invalid_pk, 0, sizeof(invalid_pk)); + memset(&invalid_pubnonce, 0, sizeof(invalid_pubnonce)); + memset(&invalid_session, 0, sizeof(invalid_session)); + + testrand256(msg); + testrand256(tweak); + for (i = 0; i < 2; i++) { + pk_ptr[i] = &pk[i]; + invalid_pk_ptr2[i] = &invalid_pk; + invalid_pk_ptr3[i] = &pk[i]; + pubnonce_ptr[i] = &pubnonce[i]; + inf_pubnonce_ptr[i] = &inf_pubnonce[i]; + partial_sig_ptr[i] = &partial_sig[i]; + invalid_partial_sig_ptr[i] = &partial_sig[i]; + testrand256(session_secrand[i]); + testrand256(sk[i]); + CHECK(create_keypair_and_pk(&keypair[i], &pk[i], sk[i])); + } + invalid_pubnonce_ptr[0] = &invalid_pubnonce; + invalid_partial_sig_ptr[0] = &invalid_partial_sig; + /* invalid_pk_ptr3 has two valid, one invalid pk, which is important to test + * musig_pubkey_agg */ + invalid_pk_ptr3[2] = &invalid_pk; + + /** main test body **/ + + /** Key aggregation **/ + CHECK(secp256k1_musig_pubkey_agg(CTX, &agg_pk, &keyagg_cache, pk_ptr, 2) == 1); + CHECK(secp256k1_musig_pubkey_agg(CTX, NULL, &keyagg_cache, pk_ptr, 2) == 1); + CHECK(secp256k1_musig_pubkey_agg(CTX, &agg_pk, NULL, pk_ptr, 2) == 1); + CHECK_ILLEGAL(CTX, secp256k1_musig_pubkey_agg(CTX, &agg_pk, &keyagg_cache, NULL, 2)); + CHECK(memcmp_and_randomize(agg_pk.data, zeros132, sizeof(agg_pk.data)) == 0); + CHECK_ILLEGAL(CTX, secp256k1_musig_pubkey_agg(CTX, &agg_pk, &keyagg_cache, invalid_pk_ptr2, 2)); + CHECK(memcmp_and_randomize(agg_pk.data, zeros132, sizeof(agg_pk.data)) == 0); + CHECK_ILLEGAL(CTX, secp256k1_musig_pubkey_agg(CTX, &agg_pk, &keyagg_cache, invalid_pk_ptr3, 3)); + CHECK(memcmp_and_randomize(agg_pk.data, zeros132, sizeof(agg_pk.data)) == 0); + CHECK_ILLEGAL(CTX, secp256k1_musig_pubkey_agg(CTX, &agg_pk, &keyagg_cache, pk_ptr, 0)); + CHECK(memcmp_and_randomize(agg_pk.data, zeros132, sizeof(agg_pk.data)) == 0); + CHECK_ILLEGAL(CTX, secp256k1_musig_pubkey_agg(CTX, &agg_pk, &keyagg_cache, NULL, 0)); + CHECK(memcmp_and_randomize(agg_pk.data, zeros132, sizeof(agg_pk.data)) == 0); + + CHECK(secp256k1_musig_pubkey_agg(CTX, &agg_pk, &keyagg_cache, pk_ptr, 2) == 1); + + /* pubkey_get */ + CHECK(secp256k1_musig_pubkey_get(CTX, &full_agg_pk, &keyagg_cache) == 1); + CHECK_ILLEGAL(CTX, secp256k1_musig_pubkey_get(CTX, NULL, &keyagg_cache)); + CHECK_ILLEGAL(CTX, secp256k1_musig_pubkey_get(CTX, &full_agg_pk, NULL)); + CHECK(secp256k1_memcmp_var(&full_agg_pk, zeros132, sizeof(full_agg_pk)) == 0); + + /** Tweaking **/ + { + int (*tweak_func[2]) (const secp256k1_context* ctx, secp256k1_pubkey *output_pubkey, secp256k1_musig_keyagg_cache *keyagg_cache, const unsigned char *tweak32); + tweak_func[0] = secp256k1_musig_pubkey_ec_tweak_add; + tweak_func[1] = secp256k1_musig_pubkey_xonly_tweak_add; + for (i = 0; i < 2; i++) { + secp256k1_pubkey tmp_output_pk; + secp256k1_musig_keyagg_cache tmp_keyagg_cache = keyagg_cache; + CHECK((*tweak_func[i])(CTX, &tmp_output_pk, &tmp_keyagg_cache, tweak) == 1); + /* Reset keyagg_cache */ + tmp_keyagg_cache = keyagg_cache; + CHECK((*tweak_func[i])(CTX, NULL, &tmp_keyagg_cache, tweak) == 1); + tmp_keyagg_cache = keyagg_cache; + CHECK_ILLEGAL(CTX, (*tweak_func[i])(CTX, &tmp_output_pk, NULL, tweak)); + CHECK(memcmp_and_randomize(tmp_output_pk.data, zeros132, sizeof(tmp_output_pk.data)) == 0); + tmp_keyagg_cache = keyagg_cache; + CHECK_ILLEGAL(CTX, (*tweak_func[i])(CTX, &tmp_output_pk, &tmp_keyagg_cache, NULL)); + CHECK(memcmp_and_randomize(tmp_output_pk.data, zeros132, sizeof(tmp_output_pk.data)) == 0); + tmp_keyagg_cache = keyagg_cache; + CHECK((*tweak_func[i])(CTX, &tmp_output_pk, &tmp_keyagg_cache, max64) == 0); + CHECK(memcmp_and_randomize(tmp_output_pk.data, zeros132, sizeof(tmp_output_pk.data)) == 0); + tmp_keyagg_cache = keyagg_cache; + /* Uninitialized keyagg_cache */ + CHECK_ILLEGAL(CTX, (*tweak_func[i])(CTX, &tmp_output_pk, &invalid_keyagg_cache, tweak)); + CHECK(memcmp_and_randomize(tmp_output_pk.data, zeros132, sizeof(tmp_output_pk.data)) == 0); + } + } + + /** Session creation with nonce_gen **/ + CHECK(secp256k1_musig_nonce_gen(CTX, &secnonce[0], &pubnonce[0], session_secrand[0], sk[0], &pk[0], msg, &keyagg_cache, max64) == 1); + /* nonce_gen, if successful, sets session_secrand to the zero array, which + * makes subsequent nonce_gen calls with the same session_secrand fail. So + * check that session_secrand is indeed the zero array and fill it with + * random values again. */ + CHECK(memcmp_and_randomize(session_secrand[0], zeros132, sizeof(session_secrand[0])) == 0); + + CHECK_ILLEGAL(STATIC_CTX, secp256k1_musig_nonce_gen(STATIC_CTX, &secnonce[0], &pubnonce[0], session_secrand[0], sk[0], &pk[0], msg, &keyagg_cache, max64)); + CHECK(memcmp_and_randomize(secnonce[0].data, zeros132, sizeof(secnonce[0].data)) == 0); + + CHECK_ILLEGAL(CTX, secp256k1_musig_nonce_gen(CTX, NULL, &pubnonce[0], session_secrand[0], sk[0], &pk[0], msg, &keyagg_cache, max64)); + + CHECK_ILLEGAL(CTX, secp256k1_musig_nonce_gen(CTX, &secnonce[0], NULL, session_secrand[0], sk[0], &pk[0], msg, &keyagg_cache, max64)); + CHECK(memcmp_and_randomize(secnonce[0].data, zeros132, sizeof(secnonce[0].data)) == 0); + + CHECK_ILLEGAL(CTX, secp256k1_musig_nonce_gen(CTX, &secnonce[0], &pubnonce[0], NULL, sk[0], &pk[0], msg, &keyagg_cache, max64)); + CHECK(memcmp_and_randomize(secnonce[0].data, zeros132, sizeof(secnonce[0].data)) == 0); + + /* session_secrand = 0 is disallowed because it indicates a faulty RNG */ + memcpy(&session_secrand[0], zeros132, sizeof(session_secrand[0])); + CHECK(secp256k1_musig_nonce_gen(CTX, &secnonce[0], &pubnonce[0], zeros132, sk[0], &pk[0], msg, &keyagg_cache, max64) == 0); + CHECK(memcmp_and_randomize(session_secrand[0], zeros132, sizeof(session_secrand[0])) == 0); + CHECK(memcmp_and_randomize(secnonce[0].data, zeros132, sizeof(secnonce[0].data)) == 0); + + CHECK(secp256k1_musig_nonce_gen(CTX, &secnonce[0], &pubnonce[0], session_secrand[0], NULL, &pk[0], msg, &keyagg_cache, max64) == 1); + CHECK(memcmp_and_randomize(session_secrand[0], zeros132, sizeof(session_secrand[0])) == 0); + + /* invalid seckey */ + CHECK(secp256k1_musig_nonce_gen(CTX, &secnonce[0], &pubnonce[0], session_secrand[0], max64, &pk[0], msg, &keyagg_cache, max64) == 0); + CHECK(memcmp_and_randomize(secnonce[0].data, zeros132, sizeof(secnonce[0].data)) == 0); + + CHECK_ILLEGAL(CTX, secp256k1_musig_nonce_gen(CTX, &secnonce[0], &pubnonce[0], session_secrand[0], sk[0], NULL, msg, &keyagg_cache, max64)); + CHECK(memcmp_and_randomize(secnonce[0].data, zeros132, sizeof(secnonce[0].data)) == 0); + + CHECK_ILLEGAL(CTX, secp256k1_musig_nonce_gen(CTX, &secnonce[0], &pubnonce[0], session_secrand[0], sk[0], &invalid_pk, msg, &keyagg_cache, max64)); + CHECK(memcmp_and_randomize(secnonce[0].data, zeros132, sizeof(secnonce[0].data)) == 0); + + CHECK(secp256k1_musig_nonce_gen(CTX, &secnonce[0], &pubnonce[0], session_secrand[0], sk[0], &pk[0], NULL, &keyagg_cache, max64) == 1); + CHECK(memcmp_and_randomize(session_secrand[0], zeros132, sizeof(session_secrand[0])) == 0); + + CHECK(secp256k1_musig_nonce_gen(CTX, &secnonce[0], &pubnonce[0], session_secrand[0], sk[0], &pk[0], msg, NULL, max64) == 1); + CHECK(memcmp_and_randomize(session_secrand[0], zeros132, sizeof(session_secrand[0])) == 0); + + CHECK_ILLEGAL(CTX, secp256k1_musig_nonce_gen(CTX, &secnonce[0], &pubnonce[0], session_secrand[0], sk[0], &pk[0], msg, &invalid_keyagg_cache, max64)); + CHECK(memcmp_and_randomize(secnonce[0].data, zeros132, sizeof(secnonce[0].data)) == 0); + + CHECK(secp256k1_musig_nonce_gen(CTX, &secnonce[0], &pubnonce[0], session_secrand[0], sk[0], &pk[0], msg, &keyagg_cache, NULL) == 1); + CHECK(memcmp_and_randomize(session_secrand[0], zeros132, sizeof(session_secrand[0])) == 0); + + /* Every in-argument except session_secrand and pubkey can be NULL */ + CHECK(secp256k1_musig_nonce_gen(CTX, &secnonce[0], &pubnonce[0], session_secrand[0], NULL, &pk[0], NULL, NULL, NULL) == 1); + CHECK(secp256k1_musig_nonce_gen(CTX, &secnonce[1], &pubnonce[1], session_secrand[1], sk[1], &pk[1], NULL, NULL, NULL) == 1); + + /** Session creation with nonce_gen_counter **/ + CHECK(secp256k1_musig_nonce_gen_counter(CTX, &secnonce[0], &pubnonce[0], nonrepeating_cnt, &keypair[0], msg, &keyagg_cache, max64) == 1); + CHECK_ILLEGAL(STATIC_CTX, secp256k1_musig_nonce_gen_counter(STATIC_CTX, &secnonce[0], &pubnonce[0], nonrepeating_cnt, &keypair[0], msg, &keyagg_cache, max64)); + CHECK(memcmp_and_randomize(secnonce[0].data, zeros132, sizeof(secnonce[0].data)) == 0); + CHECK_ILLEGAL(CTX, secp256k1_musig_nonce_gen_counter(CTX, NULL, &pubnonce[0], nonrepeating_cnt, &keypair[0], msg, &keyagg_cache, max64)); + CHECK_ILLEGAL(CTX, secp256k1_musig_nonce_gen_counter(CTX, &secnonce[0], NULL, nonrepeating_cnt, &keypair[0], msg, &keyagg_cache, max64)); + CHECK(memcmp_and_randomize(secnonce[0].data, zeros132, sizeof(secnonce[0].data)) == 0); + /* using nonce_gen_counter requires keypair */ + CHECK_ILLEGAL(CTX, secp256k1_musig_nonce_gen_counter(CTX, &secnonce[0], &pubnonce[0], nonrepeating_cnt, NULL, msg, &keyagg_cache, max64)); + CHECK(memcmp_and_randomize(secnonce[0].data, zeros132, sizeof(secnonce[0].data)) == 0); + /* invalid keypair */ + CHECK_ILLEGAL(CTX, secp256k1_musig_nonce_gen_counter(CTX, &secnonce[0], &pubnonce[0], nonrepeating_cnt, &invalid_keypair, msg, &keyagg_cache, max64)); + CHECK(memcmp_and_randomize(secnonce[0].data, zeros132, sizeof(secnonce[0].data)) == 0); + CHECK(secp256k1_musig_nonce_gen_counter(CTX, &secnonce[0], &pubnonce[0], nonrepeating_cnt, &keypair[0], NULL, &keyagg_cache, max64) == 1); + CHECK(secp256k1_musig_nonce_gen_counter(CTX, &secnonce[0], &pubnonce[0], nonrepeating_cnt, &keypair[0], msg, NULL, max64) == 1); + CHECK_ILLEGAL(CTX, secp256k1_musig_nonce_gen_counter(CTX, &secnonce[0], &pubnonce[0], nonrepeating_cnt, &keypair[0], msg, &invalid_keyagg_cache, max64)); + CHECK(memcmp_and_randomize(secnonce[0].data, zeros132, sizeof(secnonce[0].data)) == 0); + CHECK(secp256k1_musig_nonce_gen_counter(CTX, &secnonce[0], &pubnonce[0], nonrepeating_cnt,&keypair[0], msg, &keyagg_cache, NULL) == 1); + + /* Every in-argument except nonrepeating_cnt and keypair can be NULL */ + CHECK(secp256k1_musig_nonce_gen_counter(CTX, &secnonce[0], &pubnonce[0], nonrepeating_cnt, &keypair[0], NULL, NULL, NULL) == 1); + CHECK(secp256k1_musig_nonce_gen_counter(CTX, &secnonce[1], &pubnonce[1], nonrepeating_cnt, &keypair[1], NULL, NULL, NULL) == 1); + + + /** Serialize and parse public nonces **/ + CHECK_ILLEGAL(CTX, secp256k1_musig_pubnonce_serialize(CTX, NULL, &pubnonce[0])); + CHECK_ILLEGAL(CTX, secp256k1_musig_pubnonce_serialize(CTX, pubnonce_ser, NULL)); + CHECK(memcmp_and_randomize(pubnonce_ser, zeros132, sizeof(pubnonce_ser)) == 0); + CHECK_ILLEGAL(CTX, secp256k1_musig_pubnonce_serialize(CTX, pubnonce_ser, &invalid_pubnonce)); + CHECK(memcmp_and_randomize(pubnonce_ser, zeros132, sizeof(pubnonce_ser)) == 0); + CHECK(secp256k1_musig_pubnonce_serialize(CTX, pubnonce_ser, &pubnonce[0]) == 1); + + CHECK(secp256k1_musig_pubnonce_parse(CTX, &pubnonce[0], pubnonce_ser) == 1); + CHECK_ILLEGAL(CTX, secp256k1_musig_pubnonce_parse(CTX, NULL, pubnonce_ser)); + CHECK_ILLEGAL(CTX, secp256k1_musig_pubnonce_parse(CTX, &pubnonce[0], NULL)); + CHECK(secp256k1_musig_pubnonce_parse(CTX, &pubnonce[0], zeros132) == 0); + CHECK(secp256k1_musig_pubnonce_parse(CTX, &pubnonce[0], pubnonce_ser) == 1); + + { + /* Check that serialize and parse results in the same value */ + secp256k1_musig_pubnonce tmp; + CHECK(secp256k1_musig_pubnonce_serialize(CTX, pubnonce_ser, &pubnonce[0]) == 1); + CHECK(secp256k1_musig_pubnonce_parse(CTX, &tmp, pubnonce_ser) == 1); + CHECK(secp256k1_memcmp_var(&tmp, &pubnonce[0], sizeof(tmp)) == 0); + } + + /** Receive nonces and aggregate **/ + CHECK(secp256k1_musig_nonce_agg(CTX, &aggnonce, pubnonce_ptr, 2) == 1); + CHECK_ILLEGAL(CTX, secp256k1_musig_nonce_agg(CTX, NULL, pubnonce_ptr, 2)); + CHECK_ILLEGAL(CTX, secp256k1_musig_nonce_agg(CTX, &aggnonce, NULL, 2)); + CHECK_ILLEGAL(CTX, secp256k1_musig_nonce_agg(CTX, &aggnonce, pubnonce_ptr, 0)); + CHECK_ILLEGAL(CTX, secp256k1_musig_nonce_agg(CTX, &aggnonce, invalid_pubnonce_ptr, 1)); + CHECK(secp256k1_musig_nonce_agg(CTX, &aggnonce, inf_pubnonce_ptr, 2) == 1); + { + /* Check that the aggnonce encodes two points at infinity */ + secp256k1_ge aggnonce_pt[2]; + secp256k1_musig_aggnonce_load(CTX, aggnonce_pt, &aggnonce); + for (i = 0; i < 2; i++) { + secp256k1_ge_is_infinity(&aggnonce_pt[i]); + } + } + CHECK(secp256k1_musig_nonce_agg(CTX, &aggnonce, pubnonce_ptr, 2) == 1); + + /** Serialize and parse aggregate nonces **/ + CHECK(secp256k1_musig_aggnonce_serialize(CTX, aggnonce_ser, &aggnonce) == 1); + CHECK_ILLEGAL(CTX, secp256k1_musig_aggnonce_serialize(CTX, NULL, &aggnonce)); + CHECK_ILLEGAL(CTX, secp256k1_musig_aggnonce_serialize(CTX, aggnonce_ser, NULL)); + CHECK(memcmp_and_randomize(aggnonce_ser, zeros132, sizeof(aggnonce_ser)) == 0); + CHECK_ILLEGAL(CTX, secp256k1_musig_aggnonce_serialize(CTX, aggnonce_ser, (secp256k1_musig_aggnonce*) &invalid_pubnonce)); + CHECK(memcmp_and_randomize(aggnonce_ser, zeros132, sizeof(aggnonce_ser)) == 0); + CHECK(secp256k1_musig_aggnonce_serialize(CTX, aggnonce_ser, &aggnonce) == 1); + + CHECK(secp256k1_musig_aggnonce_parse(CTX, &aggnonce, aggnonce_ser) == 1); + CHECK_ILLEGAL(CTX, secp256k1_musig_aggnonce_parse(CTX, NULL, aggnonce_ser)); + CHECK_ILLEGAL(CTX, secp256k1_musig_aggnonce_parse(CTX, &aggnonce, NULL)); + CHECK(secp256k1_musig_aggnonce_parse(CTX, &aggnonce, zeros132) == 1); + CHECK(secp256k1_musig_aggnonce_parse(CTX, &aggnonce, aggnonce_ser) == 1); + + { + /* Check that serialize and parse results in the same value */ + secp256k1_musig_aggnonce tmp; + CHECK(secp256k1_musig_aggnonce_serialize(CTX, aggnonce_ser, &aggnonce) == 1); + CHECK(secp256k1_musig_aggnonce_parse(CTX, &tmp, aggnonce_ser) == 1); + CHECK(secp256k1_memcmp_var(&tmp, &aggnonce, sizeof(tmp)) == 0); + } + + /** Process nonces **/ + CHECK(secp256k1_musig_nonce_process(CTX, &session, &aggnonce, msg, &keyagg_cache) == 1); + CHECK_ILLEGAL(CTX, secp256k1_musig_nonce_process(CTX, NULL, &aggnonce, msg, &keyagg_cache)); + CHECK_ILLEGAL(CTX, secp256k1_musig_nonce_process(CTX, &session, NULL, msg, &keyagg_cache)); + CHECK_ILLEGAL(CTX, secp256k1_musig_nonce_process(CTX, &session, (secp256k1_musig_aggnonce*) &invalid_pubnonce, msg, &keyagg_cache)); + CHECK_ILLEGAL(CTX, secp256k1_musig_nonce_process(CTX, &session, &aggnonce, NULL, &keyagg_cache)); + CHECK_ILLEGAL(CTX, secp256k1_musig_nonce_process(CTX, &session, &aggnonce, msg, NULL)); + CHECK_ILLEGAL(CTX, secp256k1_musig_nonce_process(CTX, &session, &aggnonce, msg, &invalid_keyagg_cache)); + + CHECK(secp256k1_musig_nonce_process(CTX, &session, &aggnonce, msg, &keyagg_cache) == 1); + + memcpy(&secnonce_tmp, &secnonce[0], sizeof(secnonce_tmp)); + CHECK(secp256k1_musig_partial_sign(CTX, &partial_sig[0], &secnonce_tmp, &keypair[0], &keyagg_cache, &session) == 1); + /* The secnonce is set to 0 and subsequent signing attempts fail */ + CHECK(secp256k1_memcmp_var(&secnonce_tmp, zeros132, sizeof(secnonce_tmp)) == 0); + CHECK_ILLEGAL(CTX, secp256k1_musig_partial_sign(CTX, &partial_sig[0], &secnonce_tmp, &keypair[0], &keyagg_cache, &session)); + memcpy(&secnonce_tmp, &secnonce[0], sizeof(secnonce_tmp)); + CHECK_ILLEGAL(CTX, secp256k1_musig_partial_sign(CTX, NULL, &secnonce_tmp, &keypair[0], &keyagg_cache, &session)); + memcpy(&secnonce_tmp, &secnonce[0], sizeof(secnonce_tmp)); + CHECK_ILLEGAL(CTX, secp256k1_musig_partial_sign(CTX, &partial_sig[0], NULL, &keypair[0], &keyagg_cache, &session)); + CHECK_ILLEGAL(CTX, secp256k1_musig_partial_sign(CTX, &partial_sig[0], &invalid_secnonce, &keypair[0], &keyagg_cache, &session)); + CHECK_ILLEGAL(CTX, secp256k1_musig_partial_sign(CTX, &partial_sig[0], &secnonce_tmp, NULL, &keyagg_cache, &session)); + memcpy(&secnonce_tmp, &secnonce[0], sizeof(secnonce_tmp)); + CHECK_ILLEGAL(CTX, secp256k1_musig_partial_sign(CTX, &partial_sig[0], &secnonce_tmp, &invalid_keypair, &keyagg_cache, &session)); + memcpy(&secnonce_tmp, &secnonce[0], sizeof(secnonce_tmp)); + { + unsigned char sk_tmp[32]; + secp256k1_keypair keypair_tmp; + testrand256(sk_tmp); + CHECK(secp256k1_keypair_create(CTX, &keypair_tmp, sk_tmp)); + CHECK_ILLEGAL(CTX, secp256k1_musig_partial_sign(CTX, &partial_sig[0], &secnonce_tmp, &keypair_tmp, &keyagg_cache, &session)); + memcpy(&secnonce_tmp, &secnonce[0], sizeof(secnonce_tmp)); + } + CHECK_ILLEGAL(CTX, secp256k1_musig_partial_sign(CTX, &partial_sig[0], &secnonce_tmp, &keypair[0], NULL, &session)); + memcpy(&secnonce_tmp, &secnonce[0], sizeof(secnonce_tmp)); + CHECK_ILLEGAL(CTX, secp256k1_musig_partial_sign(CTX, &partial_sig[0], &secnonce_tmp, &keypair[0], &invalid_keyagg_cache, &session)); + memcpy(&secnonce_tmp, &secnonce[0], sizeof(secnonce_tmp)); + CHECK_ILLEGAL(CTX, secp256k1_musig_partial_sign(CTX, &partial_sig[0], &secnonce_tmp, &keypair[0], &keyagg_cache, NULL)); + memcpy(&secnonce_tmp, &secnonce[0], sizeof(secnonce_tmp)); + CHECK_ILLEGAL(CTX, secp256k1_musig_partial_sign(CTX, &partial_sig[0], &secnonce_tmp, &keypair[0], &keyagg_cache, &invalid_session)); + memcpy(&secnonce_tmp, &secnonce[0], sizeof(secnonce_tmp)); + + CHECK(secp256k1_musig_partial_sign(CTX, &partial_sig[0], &secnonce[0], &keypair[0], &keyagg_cache, &session) == 1); + CHECK(secp256k1_musig_partial_sign(CTX, &partial_sig[1], &secnonce[1], &keypair[1], &keyagg_cache, &session) == 1); + + CHECK(secp256k1_musig_partial_sig_serialize(CTX, buf, &partial_sig[0]) == 1); + CHECK_ILLEGAL(CTX, secp256k1_musig_partial_sig_serialize(CTX, NULL, &partial_sig[0])); + CHECK_ILLEGAL(CTX, secp256k1_musig_partial_sig_serialize(CTX, buf, NULL)); + CHECK_ILLEGAL(CTX, secp256k1_musig_partial_sig_serialize(CTX, buf, &invalid_partial_sig)); + CHECK(secp256k1_musig_partial_sig_parse(CTX, &partial_sig[0], buf) == 1); + CHECK_ILLEGAL(CTX, secp256k1_musig_partial_sig_parse(CTX, NULL, buf)); + { + /* Check that parsing failure results in an invalid sig */ + secp256k1_musig_partial_sig tmp; + CHECK(secp256k1_musig_partial_sig_parse(CTX, &tmp, max64) == 0); + CHECK(secp256k1_memcmp_var(&tmp, zeros132, sizeof(partial_sig[0])) == 0); + } + CHECK_ILLEGAL(CTX, secp256k1_musig_partial_sig_parse(CTX, &partial_sig[0], NULL)); + + { + /* Check that serialize and parse results in the same value */ + secp256k1_musig_partial_sig tmp; + CHECK(secp256k1_musig_partial_sig_serialize(CTX, buf, &partial_sig[0]) == 1); + CHECK(secp256k1_musig_partial_sig_parse(CTX, &tmp, buf) == 1); + CHECK(secp256k1_memcmp_var(&tmp, &partial_sig[0], sizeof(tmp)) == 0); + } + + /** Partial signature verification */ + CHECK(secp256k1_musig_partial_sig_verify(CTX, &partial_sig[0], &pubnonce[0], &pk[0], &keyagg_cache, &session) == 1); + CHECK(secp256k1_musig_partial_sig_verify(CTX, &partial_sig[1], &pubnonce[0], &pk[0], &keyagg_cache, &session) == 0); + CHECK_ILLEGAL(CTX, secp256k1_musig_partial_sig_verify(CTX, NULL, &pubnonce[0], &pk[0], &keyagg_cache, &session)); + CHECK_ILLEGAL(CTX, secp256k1_musig_partial_sig_verify(CTX, &invalid_partial_sig, &pubnonce[0], &pk[0], &keyagg_cache, &session)); + CHECK_ILLEGAL(CTX, secp256k1_musig_partial_sig_verify(CTX, &partial_sig[0], NULL, &pk[0], &keyagg_cache, &session)); + CHECK_ILLEGAL(CTX, secp256k1_musig_partial_sig_verify(CTX, &partial_sig[0], &invalid_pubnonce, &pk[0], &keyagg_cache, &session)); + CHECK_ILLEGAL(CTX, secp256k1_musig_partial_sig_verify(CTX, &partial_sig[0], &pubnonce[0], NULL, &keyagg_cache, &session)); + CHECK_ILLEGAL(CTX, secp256k1_musig_partial_sig_verify(CTX, &partial_sig[0], &pubnonce[0], &invalid_pk, &keyagg_cache, &session)); + CHECK_ILLEGAL(CTX, secp256k1_musig_partial_sig_verify(CTX, &partial_sig[0], &pubnonce[0], &pk[0], NULL, &session)); + CHECK_ILLEGAL(CTX, secp256k1_musig_partial_sig_verify(CTX, &partial_sig[0], &pubnonce[0], &pk[0], &invalid_keyagg_cache, &session)); + CHECK_ILLEGAL(CTX, secp256k1_musig_partial_sig_verify(CTX, &partial_sig[0], &pubnonce[0], &pk[0], &keyagg_cache, NULL)); + CHECK_ILLEGAL(CTX, secp256k1_musig_partial_sig_verify(CTX, &partial_sig[0], &pubnonce[0], &pk[0], &keyagg_cache, &invalid_session)); + + CHECK(secp256k1_musig_partial_sig_verify(CTX, &partial_sig[0], &pubnonce[0], &pk[0], &keyagg_cache, &session) == 1); + CHECK(secp256k1_musig_partial_sig_verify(CTX, &partial_sig[1], &pubnonce[1], &pk[1], &keyagg_cache, &session) == 1); + + /** Signature aggregation and verification */ + CHECK(secp256k1_musig_partial_sig_agg(CTX, pre_sig, &session, partial_sig_ptr, 2) == 1); + CHECK_ILLEGAL(CTX, secp256k1_musig_partial_sig_agg(CTX, NULL, &session, partial_sig_ptr, 2)); + CHECK_ILLEGAL(CTX, secp256k1_musig_partial_sig_agg(CTX, pre_sig, NULL, partial_sig_ptr, 2)); + CHECK_ILLEGAL(CTX, secp256k1_musig_partial_sig_agg(CTX, pre_sig, &invalid_session, partial_sig_ptr, 2)); + CHECK_ILLEGAL(CTX, secp256k1_musig_partial_sig_agg(CTX, pre_sig, &session, NULL, 2)); + CHECK_ILLEGAL(CTX, secp256k1_musig_partial_sig_agg(CTX, pre_sig, &session, invalid_partial_sig_ptr, 2)); + CHECK_ILLEGAL(CTX, secp256k1_musig_partial_sig_agg(CTX, pre_sig, &session, partial_sig_ptr, 0)); + CHECK(secp256k1_musig_partial_sig_agg(CTX, pre_sig, &session, partial_sig_ptr, 1) == 1); + CHECK(secp256k1_musig_partial_sig_agg(CTX, pre_sig, &session, partial_sig_ptr, 2) == 1); +} + +static void musig_nonce_bitflip(unsigned char **args, size_t n_flip, size_t n_bytes) { + secp256k1_scalar k1[2], k2[2]; + + secp256k1_nonce_function_musig(k1, args[0], args[1], args[2], args[3], args[4], args[5]); + testrand_flip(args[n_flip], n_bytes); + secp256k1_nonce_function_musig(k2, args[0], args[1], args[2], args[3], args[4], args[5]); + CHECK(secp256k1_scalar_eq(&k1[0], &k2[0]) == 0); + CHECK(secp256k1_scalar_eq(&k1[1], &k2[1]) == 0); +} + +static void musig_nonce_test(void) { + unsigned char *args[6]; + unsigned char session_secrand[32]; + unsigned char sk[32]; + unsigned char pk[33]; + unsigned char msg[32]; + unsigned char agg_pk[32]; + unsigned char extra_input[32]; + int i, j; + secp256k1_scalar k[6][2]; + + testrand_bytes_test(session_secrand, sizeof(session_secrand)); + testrand_bytes_test(sk, sizeof(sk)); + testrand_bytes_test(pk, sizeof(pk)); + testrand_bytes_test(msg, sizeof(msg)); + testrand_bytes_test(agg_pk, sizeof(agg_pk)); + testrand_bytes_test(extra_input, sizeof(extra_input)); + + /* Check that a bitflip in an argument results in different nonces. */ + args[0] = session_secrand; + args[1] = msg; + args[2] = sk; + args[3] = pk; + args[4] = agg_pk; + args[5] = extra_input; + for (i = 0; i < COUNT; i++) { + musig_nonce_bitflip(args, 0, sizeof(session_secrand)); + musig_nonce_bitflip(args, 1, sizeof(msg)); + musig_nonce_bitflip(args, 2, sizeof(sk)); + musig_nonce_bitflip(args, 3, sizeof(pk)); + musig_nonce_bitflip(args, 4, sizeof(agg_pk)); + musig_nonce_bitflip(args, 5, sizeof(extra_input)); + } + /* Check that if any argument is NULL, a different nonce is produced than if + * any other argument is NULL. */ + memcpy(msg, session_secrand, sizeof(msg)); + memcpy(sk, session_secrand, sizeof(sk)); + memcpy(pk, session_secrand, sizeof(session_secrand)); + memcpy(agg_pk, session_secrand, sizeof(agg_pk)); + memcpy(extra_input, session_secrand, sizeof(extra_input)); + secp256k1_nonce_function_musig(k[0], args[0], args[1], args[2], args[3], args[4], args[5]); + secp256k1_nonce_function_musig(k[1], args[0], NULL, args[2], args[3], args[4], args[5]); + secp256k1_nonce_function_musig(k[2], args[0], args[1], NULL, args[3], args[4], args[5]); + secp256k1_nonce_function_musig(k[3], args[0], args[1], args[2], NULL, args[4], args[5]); + secp256k1_nonce_function_musig(k[4], args[0], args[1], args[2], args[3], NULL, args[5]); + secp256k1_nonce_function_musig(k[5], args[0], args[1], args[2], args[3], args[4], NULL); + for (i = 0; i < 6; i++) { + CHECK(!secp256k1_scalar_eq(&k[i][0], &k[i][1])); + for (j = i+1; j < 6; j++) { + CHECK(!secp256k1_scalar_eq(&k[i][0], &k[j][0])); + CHECK(!secp256k1_scalar_eq(&k[i][1], &k[j][1])); + } + } +} + +static void sha256_tag_test_internal(secp256k1_sha256 *sha_tagged, unsigned char *tag, size_t taglen) { + secp256k1_sha256 sha; + secp256k1_sha256_initialize_tagged(&sha, tag, taglen); + test_sha256_eq(&sha, sha_tagged); +} + +/* Checks that the initialized tagged hashes have the expected + * state. */ +static void sha256_tag_test(void) { + secp256k1_sha256 sha; + { + char tag[] = "KeyAgg list"; + secp256k1_musig_keyagglist_sha256(&sha); + sha256_tag_test_internal(&sha, (unsigned char*)tag, sizeof(tag) - 1); + } + { + char tag[] = "KeyAgg coefficient"; + secp256k1_musig_keyaggcoef_sha256(&sha); + sha256_tag_test_internal(&sha, (unsigned char*)tag, sizeof(tag) - 1); + } + { + unsigned char tag[] = "MuSig/aux"; + secp256k1_nonce_function_musig_sha256_tagged_aux(&sha); + sha256_tag_test_internal(&sha, (unsigned char*)tag, sizeof(tag) - 1); + } + { + unsigned char tag[] = "MuSig/nonce"; + secp256k1_nonce_function_musig_sha256_tagged(&sha); + sha256_tag_test_internal(&sha, (unsigned char*)tag, sizeof(tag) - 1); + } + { + unsigned char tag[] = "MuSig/noncecoef"; + secp256k1_musig_compute_noncehash_sha256_tagged(&sha); + sha256_tag_test_internal(&sha, (unsigned char*)tag, sizeof(tag) - 1); + } +} + +/* Attempts to create a signature for the aggregate public key using given secret + * keys and keyagg_cache. */ +static void musig_tweak_test_helper(const secp256k1_xonly_pubkey* agg_pk, const unsigned char *sk0, const unsigned char *sk1, secp256k1_musig_keyagg_cache *keyagg_cache) { + secp256k1_pubkey pk[2]; + unsigned char session_secrand[2][32]; + unsigned char msg[32]; + secp256k1_musig_secnonce secnonce[2]; + secp256k1_musig_pubnonce pubnonce[2]; + const secp256k1_musig_pubnonce *pubnonce_ptr[2]; + secp256k1_musig_aggnonce aggnonce; + secp256k1_keypair keypair[2]; + secp256k1_musig_session session; + secp256k1_musig_partial_sig partial_sig[2]; + const secp256k1_musig_partial_sig *partial_sig_ptr[2]; + unsigned char final_sig[64]; + int i; + + for (i = 0; i < 2; i++) { + pubnonce_ptr[i] = &pubnonce[i]; + partial_sig_ptr[i] = &partial_sig[i]; + + testrand256(session_secrand[i]); + } + CHECK(create_keypair_and_pk(&keypair[0], &pk[0], sk0) == 1); + CHECK(create_keypair_and_pk(&keypair[1], &pk[1], sk1) == 1); + testrand256(msg); + + CHECK(secp256k1_musig_nonce_gen(CTX, &secnonce[0], &pubnonce[0], session_secrand[0], sk0, &pk[0], NULL, NULL, NULL) == 1); + CHECK(secp256k1_musig_nonce_gen(CTX, &secnonce[1], &pubnonce[1], session_secrand[1], sk1, &pk[1], NULL, NULL, NULL) == 1); + + CHECK(secp256k1_musig_nonce_agg(CTX, &aggnonce, pubnonce_ptr, 2) == 1); + CHECK(secp256k1_musig_nonce_process(CTX, &session, &aggnonce, msg, keyagg_cache) == 1); + + CHECK(secp256k1_musig_partial_sign(CTX, &partial_sig[0], &secnonce[0], &keypair[0], keyagg_cache, &session) == 1); + CHECK(secp256k1_musig_partial_sign(CTX, &partial_sig[1], &secnonce[1], &keypair[1], keyagg_cache, &session) == 1); + + CHECK(secp256k1_musig_partial_sig_verify(CTX, &partial_sig[0], &pubnonce[0], &pk[0], keyagg_cache, &session) == 1); + CHECK(secp256k1_musig_partial_sig_verify(CTX, &partial_sig[1], &pubnonce[1], &pk[1], keyagg_cache, &session) == 1); + + CHECK(secp256k1_musig_partial_sig_agg(CTX, final_sig, &session, partial_sig_ptr, 2) == 1); + CHECK(secp256k1_schnorrsig_verify(CTX, final_sig, msg, sizeof(msg), agg_pk) == 1); +} + +/* Create aggregate public key P[0], tweak multiple times (using xonly and + * plain tweaking) and test signing. */ +static void musig_tweak_test(void) { + unsigned char sk[2][32]; + secp256k1_pubkey pk[2]; + const secp256k1_pubkey *pk_ptr[2]; + secp256k1_musig_keyagg_cache keyagg_cache; + enum { N_TWEAKS = 8 }; + secp256k1_pubkey P[N_TWEAKS + 1]; + secp256k1_xonly_pubkey P_xonly[N_TWEAKS + 1]; + int i; + + /* Key Setup */ + for (i = 0; i < 2; i++) { + pk_ptr[i] = &pk[i]; + testrand256(sk[i]); + CHECK(create_keypair_and_pk(NULL, &pk[i], sk[i]) == 1); + } + /* Compute P0 = keyagg(pk0, pk1) and test signing for it */ + CHECK(secp256k1_musig_pubkey_agg(CTX, &P_xonly[0], &keyagg_cache, pk_ptr, 2) == 1); + musig_tweak_test_helper(&P_xonly[0], sk[0], sk[1], &keyagg_cache); + CHECK(secp256k1_musig_pubkey_get(CTX, &P[0], &keyagg_cache)); + + /* Compute Pi = f(Pj) + tweaki*G where where j = i-1 and try signing for + * that key. If xonly is set to true, the function f normalizes the input + * point to have an even X-coordinate ("xonly-tweaking"). + * Otherwise, the function f is the identity function. */ + for (i = 1; i <= N_TWEAKS; i++) { + unsigned char tweak[32]; + int P_parity; + int xonly = testrand_bits(1); + + testrand256(tweak); + if (xonly) { + CHECK(secp256k1_musig_pubkey_xonly_tweak_add(CTX, &P[i], &keyagg_cache, tweak) == 1); + } else { + CHECK(secp256k1_musig_pubkey_ec_tweak_add(CTX, &P[i], &keyagg_cache, tweak) == 1); + } + CHECK(secp256k1_xonly_pubkey_from_pubkey(CTX, &P_xonly[i], &P_parity, &P[i])); + /* Check that musig_pubkey_tweak_add produces same result as + * xonly_pubkey_tweak_add or ec_pubkey_tweak_add. */ + if (xonly) { + unsigned char P_serialized[32]; + CHECK(secp256k1_xonly_pubkey_serialize(CTX, P_serialized, &P_xonly[i])); + CHECK(secp256k1_xonly_pubkey_tweak_add_check(CTX, P_serialized, P_parity, &P_xonly[i-1], tweak) == 1); + } else { + secp256k1_pubkey tmp_key = P[i-1]; + CHECK(secp256k1_ec_pubkey_tweak_add(CTX, &tmp_key, tweak)); + CHECK(secp256k1_memcmp_var(&tmp_key, &P[i], sizeof(tmp_key)) == 0); + } + /* Test signing for P[i] */ + musig_tweak_test_helper(&P_xonly[i], sk[0], sk[1], &keyagg_cache); + } +} + +int musig_vectors_keyagg_and_tweak(enum MUSIG_ERROR *error, + secp256k1_musig_keyagg_cache *keyagg_cache, + unsigned char *agg_pk_ser, + const unsigned char pubkeys33[][33], + const unsigned char tweaks32[][32], + size_t key_indices_len, + const size_t *key_indices, + size_t tweak_indices_len, + const size_t *tweak_indices, + const int *is_xonly) { + secp256k1_pubkey pubkeys[MUSIG_VECTORS_MAX_PUBKEYS]; + const secp256k1_pubkey *pk_ptr[MUSIG_VECTORS_MAX_PUBKEYS]; + int i; + secp256k1_pubkey agg_pk; + secp256k1_xonly_pubkey agg_pk_xonly; + + for (i = 0; i < (int)key_indices_len; i++) { + if (!secp256k1_ec_pubkey_parse(CTX, &pubkeys[i], pubkeys33[key_indices[i]], 33)) { + *error = MUSIG_PUBKEY; + return 0; + } + pk_ptr[i] = &pubkeys[i]; + } + if (!secp256k1_musig_pubkey_agg(CTX, NULL, keyagg_cache, pk_ptr, key_indices_len)) { + *error = MUSIG_OTHER; + return 0; + } + + for (i = 0; i < (int)tweak_indices_len; i++) { + if (is_xonly[i]) { + if (!secp256k1_musig_pubkey_xonly_tweak_add(CTX, NULL, keyagg_cache, tweaks32[tweak_indices[i]])) { + *error = MUSIG_TWEAK; + return 0; + } + } else { + if (!secp256k1_musig_pubkey_ec_tweak_add(CTX, NULL, keyagg_cache, tweaks32[tweak_indices[i]])) { + *error = MUSIG_TWEAK; + return 0; + } + } + } + if (!secp256k1_musig_pubkey_get(CTX, &agg_pk, keyagg_cache)) { + *error = MUSIG_OTHER; + return 0; + } + + if (!secp256k1_xonly_pubkey_from_pubkey(CTX, &agg_pk_xonly, NULL, &agg_pk)) { + *error = MUSIG_OTHER; + return 0; + } + + if (agg_pk_ser != NULL) { + if (!secp256k1_xonly_pubkey_serialize(CTX, agg_pk_ser, &agg_pk_xonly)) { + *error = MUSIG_OTHER; + return 0; + } + } + + return 1; +} + +static void musig_test_vectors_keyagg(void) { + size_t i; + const struct musig_key_agg_vector *vector = &musig_key_agg_vector; + + for (i = 0; i < sizeof(vector->valid_case)/sizeof(vector->valid_case[0]); i++) { + const struct musig_key_agg_valid_test_case *c = &vector->valid_case[i]; + enum MUSIG_ERROR error; + secp256k1_musig_keyagg_cache keyagg_cache; + unsigned char agg_pk[32]; + + CHECK(musig_vectors_keyagg_and_tweak(&error, &keyagg_cache, agg_pk, vector->pubkeys, vector->tweaks, c->key_indices_len, c->key_indices, 0, NULL, NULL)); + CHECK(secp256k1_memcmp_var(agg_pk, c->expected, sizeof(agg_pk)) == 0); + } + + for (i = 0; i < sizeof(vector->error_case)/sizeof(vector->error_case[0]); i++) { + const struct musig_key_agg_error_test_case *c = &vector->error_case[i]; + enum MUSIG_ERROR error; + secp256k1_musig_keyagg_cache keyagg_cache; + + CHECK(!musig_vectors_keyagg_and_tweak(&error, &keyagg_cache, NULL, vector->pubkeys, vector->tweaks, c->key_indices_len, c->key_indices, c->tweak_indices_len, c->tweak_indices, c->is_xonly)); + CHECK(c->error == error); + } +} + +static void musig_test_vectors_noncegen(void) { + size_t i; + const struct musig_nonce_gen_vector *vector = &musig_nonce_gen_vector; + + for (i = 0; i < sizeof(vector->test_case)/sizeof(vector->test_case[0]); i++) { + const struct musig_nonce_gen_test_case *c = &vector->test_case[i]; + secp256k1_musig_keyagg_cache keyagg_cache; + secp256k1_musig_keyagg_cache *keyagg_cache_ptr = NULL; + unsigned char session_secrand32[32]; + secp256k1_musig_secnonce secnonce; + secp256k1_musig_pubnonce pubnonce; + const unsigned char *sk = NULL; + const unsigned char *msg = NULL; + const unsigned char *extra_in = NULL; + secp256k1_pubkey pk; + unsigned char pubnonce66[66]; + + memcpy(session_secrand32, c->rand_, 32); + if (c->has_sk) { + sk = c->sk; + } + if (c->has_aggpk) { + /* Create keyagg_cache from aggpk */ + secp256k1_keyagg_cache_internal cache_i; + secp256k1_xonly_pubkey aggpk; + memset(&cache_i, 0, sizeof(cache_i)); + CHECK(secp256k1_xonly_pubkey_parse(CTX, &aggpk, c->aggpk)); + CHECK(secp256k1_xonly_pubkey_load(CTX, &cache_i.pk, &aggpk)); + secp256k1_keyagg_cache_save(&keyagg_cache, &cache_i); + keyagg_cache_ptr = &keyagg_cache; + } + if (c->has_msg) { + msg = c->msg; + } + if (c->has_extra_in) { + extra_in = c->extra_in; + } + + CHECK(secp256k1_ec_pubkey_parse(CTX, &pk, c->pk, sizeof(c->pk))); + CHECK(secp256k1_musig_nonce_gen(CTX, &secnonce, &pubnonce, session_secrand32, sk, &pk, msg, keyagg_cache_ptr, extra_in) == 1); + CHECK(secp256k1_memcmp_var(&secnonce.data[4], c->expected_secnonce, 2*32) == 0); + /* The last element of the secnonce is the public key (uncompressed in + * secp256k1_musig_secnonce, compressed in the test vector secnonce). */ + CHECK(secp256k1_memcmp_var(&secnonce.data[4+2*32], &pk, sizeof(pk)) == 0); + CHECK(secp256k1_memcmp_var(&c->expected_secnonce[2*32], c->pk, sizeof(c->pk)) == 0); + + CHECK(secp256k1_musig_pubnonce_serialize(CTX, pubnonce66, &pubnonce) == 1); + CHECK(sizeof(c->expected_pubnonce) == sizeof(pubnonce66)); + CHECK(secp256k1_memcmp_var(pubnonce66, c->expected_pubnonce, sizeof(pubnonce66)) == 0); + } +} + + +static void musig_test_vectors_nonceagg(void) { + size_t i; + int j; + const struct musig_nonce_agg_vector *vector = &musig_nonce_agg_vector; + + for (i = 0; i < sizeof(vector->valid_case)/sizeof(vector->valid_case[0]); i++) { + const struct musig_nonce_agg_test_case *c = &vector->valid_case[i]; + secp256k1_musig_pubnonce pubnonce[2]; + const secp256k1_musig_pubnonce *pubnonce_ptr[2]; + secp256k1_musig_aggnonce aggnonce; + unsigned char aggnonce66[66]; + + for (j = 0; j < 2; j++) { + CHECK(secp256k1_musig_pubnonce_parse(CTX, &pubnonce[j], vector->pnonces[c->pnonce_indices[j]]) == 1); + pubnonce_ptr[j] = &pubnonce[j]; + } + CHECK(secp256k1_musig_nonce_agg(CTX, &aggnonce, pubnonce_ptr, 2)); + CHECK(secp256k1_musig_aggnonce_serialize(CTX, aggnonce66, &aggnonce)); + CHECK(secp256k1_memcmp_var(aggnonce66, c->expected, 33) == 0); + } + for (i = 0; i < sizeof(vector->error_case)/sizeof(vector->error_case[0]); i++) { + const struct musig_nonce_agg_test_case *c = &vector->error_case[i]; + secp256k1_musig_pubnonce pubnonce[2]; + for (j = 0; j < 2; j++) { + int expected = c->invalid_nonce_idx != j; + CHECK(expected == secp256k1_musig_pubnonce_parse(CTX, &pubnonce[j], vector->pnonces[c->pnonce_indices[j]])); + } + } +} + +static void musig_test_set_secnonce(secp256k1_musig_secnonce *secnonce, const unsigned char *secnonce64, const secp256k1_pubkey *pubkey) { + secp256k1_ge pk; + secp256k1_scalar k[2]; + + secp256k1_scalar_set_b32(&k[0], &secnonce64[0], NULL); + secp256k1_scalar_set_b32(&k[1], &secnonce64[32], NULL); + CHECK(secp256k1_pubkey_load(CTX, &pk, pubkey)); + secp256k1_musig_secnonce_save(secnonce, k, &pk); +} + +static void musig_test_vectors_signverify(void) { + size_t i; + const struct musig_sign_verify_vector *vector = &musig_sign_verify_vector; + + for (i = 0; i < sizeof(vector->valid_case)/sizeof(vector->valid_case[0]); i++) { + const struct musig_valid_case *c = &vector->valid_case[i]; + enum MUSIG_ERROR error; + secp256k1_musig_keyagg_cache keyagg_cache; + secp256k1_pubkey pubkey; + secp256k1_musig_pubnonce pubnonce; + secp256k1_musig_aggnonce aggnonce; + secp256k1_musig_session session; + secp256k1_musig_partial_sig partial_sig; + secp256k1_musig_secnonce secnonce; + secp256k1_keypair keypair; + unsigned char partial_sig32[32]; + + CHECK(secp256k1_keypair_create(CTX, &keypair, vector->sk)); + CHECK(musig_vectors_keyagg_and_tweak(&error, &keyagg_cache, NULL, vector->pubkeys, NULL, c->key_indices_len, c->key_indices, 0, NULL, NULL)); + + CHECK(secp256k1_musig_aggnonce_parse(CTX, &aggnonce, vector->aggnonces[c->aggnonce_index])); + CHECK(secp256k1_musig_nonce_process(CTX, &session, &aggnonce, vector->msgs[c->msg_index], &keyagg_cache)); + + CHECK(secp256k1_ec_pubkey_parse(CTX, &pubkey, vector->pubkeys[0], sizeof(vector->pubkeys[0]))); + musig_test_set_secnonce(&secnonce, vector->secnonces[0], &pubkey); + CHECK(secp256k1_musig_partial_sign(CTX, &partial_sig, &secnonce, &keypair, &keyagg_cache, &session)); + CHECK(secp256k1_musig_partial_sig_serialize(CTX, partial_sig32, &partial_sig)); + CHECK(secp256k1_memcmp_var(partial_sig32, c->expected, sizeof(partial_sig32)) == 0); + + CHECK(secp256k1_musig_pubnonce_parse(CTX, &pubnonce, vector->pubnonces[0])); + CHECK(secp256k1_musig_partial_sig_verify(CTX, &partial_sig, &pubnonce, &pubkey, &keyagg_cache, &session)); + } + for (i = 0; i < sizeof(vector->sign_error_case)/sizeof(vector->sign_error_case[0]); i++) { + const struct musig_sign_error_case *c = &vector->sign_error_case[i]; + enum MUSIG_ERROR error; + secp256k1_musig_keyagg_cache keyagg_cache; + secp256k1_pubkey pubkey; + secp256k1_musig_aggnonce aggnonce; + secp256k1_musig_session session; + secp256k1_musig_partial_sig partial_sig; + secp256k1_musig_secnonce secnonce; + secp256k1_keypair keypair; + int expected; + + if (i == 0) { + /* Skip this vector since the implementation does not error out when + * the signing key does not belong to any pubkey. */ + continue; + } + expected = c->error != MUSIG_PUBKEY; + CHECK(expected == musig_vectors_keyagg_and_tweak(&error, &keyagg_cache, NULL, vector->pubkeys, NULL, c->key_indices_len, c->key_indices, 0, NULL, NULL)); + CHECK(expected || c->error == error); + if (!expected) { + continue; + } + + expected = c->error != MUSIG_AGGNONCE; + CHECK(expected == secp256k1_musig_aggnonce_parse(CTX, &aggnonce, vector->aggnonces[c->aggnonce_index])); + if (!expected) { + continue; + } + CHECK(secp256k1_musig_nonce_process(CTX, &session, &aggnonce, vector->msgs[c->msg_index], &keyagg_cache)); + + CHECK(secp256k1_ec_pubkey_parse(CTX, &pubkey, vector->pubkeys[0], sizeof(vector->pubkeys[0]))); + musig_test_set_secnonce(&secnonce, vector->secnonces[c->secnonce_index], &pubkey); + expected = c->error != MUSIG_SECNONCE; + if (expected) { + CHECK(secp256k1_musig_partial_sign(CTX, &partial_sig, &secnonce, &keypair, &keyagg_cache, &session)); + } else { + CHECK_ILLEGAL(CTX, secp256k1_musig_partial_sign(CTX, &partial_sig, &secnonce, &keypair, &keyagg_cache, &session)); + } + } + for (i = 0; i < sizeof(vector->verify_fail_case)/sizeof(vector->verify_fail_case[0]); i++) { + const struct musig_verify_fail_error_case *c = &vector->verify_fail_case[i]; + enum MUSIG_ERROR error; + secp256k1_musig_keyagg_cache keyagg_cache; + secp256k1_musig_aggnonce aggnonce; + secp256k1_musig_session session; + secp256k1_musig_partial_sig partial_sig; + enum { NUM_PUBNONCES = 3 }; + secp256k1_musig_pubnonce pubnonce[NUM_PUBNONCES]; + const secp256k1_musig_pubnonce *pubnonce_ptr[NUM_PUBNONCES]; + secp256k1_pubkey pubkey; + int expected; + size_t j; + + CHECK(NUM_PUBNONCES <= c->nonce_indices_len); + for (j = 0; j < c->nonce_indices_len; j++) { + CHECK(secp256k1_musig_pubnonce_parse(CTX, &pubnonce[j], vector->pubnonces[c->nonce_indices[j]])); + pubnonce_ptr[j] = &pubnonce[j]; + } + + CHECK(musig_vectors_keyagg_and_tweak(&error, &keyagg_cache, NULL, vector->pubkeys, NULL, c->key_indices_len, c->key_indices, 0, NULL, NULL)); + CHECK(secp256k1_musig_nonce_agg(CTX, &aggnonce, pubnonce_ptr, c->nonce_indices_len) == 1); + CHECK(secp256k1_musig_nonce_process(CTX, &session, &aggnonce, vector->msgs[c->msg_index], &keyagg_cache)); + + CHECK(secp256k1_ec_pubkey_parse(CTX, &pubkey, vector->pubkeys[c->signer_index], sizeof(vector->pubkeys[0]))); + + expected = c->error != MUSIG_SIG; + CHECK(expected == secp256k1_musig_partial_sig_parse(CTX, &partial_sig, c->sig)); + if (!expected) { + continue; + } + expected = c->error != MUSIG_SIG_VERIFY; + CHECK(expected == secp256k1_musig_partial_sig_verify(CTX, &partial_sig, pubnonce, &pubkey, &keyagg_cache, &session)); + } + for (i = 0; i < sizeof(vector->verify_error_case)/sizeof(vector->verify_error_case[0]); i++) { + const struct musig_verify_fail_error_case *c = &vector->verify_error_case[i]; + enum MUSIG_ERROR error; + secp256k1_musig_keyagg_cache keyagg_cache; + secp256k1_musig_pubnonce pubnonce; + int expected; + + expected = c->error != MUSIG_PUBKEY; + CHECK(expected == musig_vectors_keyagg_and_tweak(&error, &keyagg_cache, NULL, vector->pubkeys, NULL, c->key_indices_len, c->key_indices, 0, NULL, NULL)); + CHECK(expected || c->error == error); + if (!expected) { + continue; + } + expected = c->error != MUSIG_PUBNONCE; + CHECK(expected == secp256k1_musig_pubnonce_parse(CTX, &pubnonce, vector->pubnonces[c->nonce_indices[c->signer_index]])); + } +} + +static void musig_test_vectors_tweak(void) { + size_t i; + const struct musig_tweak_vector *vector = &musig_tweak_vector; + secp256k1_pubkey pubkey; + secp256k1_musig_aggnonce aggnonce; + secp256k1_musig_secnonce secnonce; + + CHECK(secp256k1_musig_aggnonce_parse(CTX, &aggnonce, vector->aggnonce)); + CHECK(secp256k1_ec_pubkey_parse(CTX, &pubkey, vector->pubkeys[0], sizeof(vector->pubkeys[0]))); + + for (i = 0; i < sizeof(vector->valid_case)/sizeof(vector->valid_case[0]); i++) { + const struct musig_tweak_case *c = &vector->valid_case[i]; + enum MUSIG_ERROR error; + secp256k1_musig_keyagg_cache keyagg_cache; + secp256k1_musig_pubnonce pubnonce; + secp256k1_musig_session session; + secp256k1_musig_partial_sig partial_sig; + secp256k1_keypair keypair; + unsigned char partial_sig32[32]; + + musig_test_set_secnonce(&secnonce, vector->secnonce, &pubkey); + + CHECK(secp256k1_keypair_create(CTX, &keypair, vector->sk)); + CHECK(musig_vectors_keyagg_and_tweak(&error, &keyagg_cache, NULL, vector->pubkeys, vector->tweaks, c->key_indices_len, c->key_indices, c->tweak_indices_len, c->tweak_indices, c->is_xonly)); + + CHECK(secp256k1_musig_nonce_process(CTX, &session, &aggnonce, vector->msg, &keyagg_cache)); + + CHECK(secp256k1_musig_partial_sign(CTX, &partial_sig, &secnonce, &keypair, &keyagg_cache, &session)); + CHECK(secp256k1_musig_partial_sig_serialize(CTX, partial_sig32, &partial_sig)); + CHECK(secp256k1_memcmp_var(partial_sig32, c->expected, sizeof(partial_sig32)) == 0); + + CHECK(secp256k1_musig_pubnonce_parse(CTX, &pubnonce, vector->pubnonces[c->nonce_indices[c->signer_index]])); + CHECK(secp256k1_musig_partial_sig_verify(CTX, &partial_sig, &pubnonce, &pubkey, &keyagg_cache, &session)); + } + for (i = 0; i < sizeof(vector->error_case)/sizeof(vector->error_case[0]); i++) { + const struct musig_tweak_case *c = &vector->error_case[i]; + enum MUSIG_ERROR error; + secp256k1_musig_keyagg_cache keyagg_cache; + CHECK(!musig_vectors_keyagg_and_tweak(&error, &keyagg_cache, NULL, vector->pubkeys, vector->tweaks, c->key_indices_len, c->key_indices, c->tweak_indices_len, c->tweak_indices, c->is_xonly)); + CHECK(error == MUSIG_TWEAK); + } +} + +static void musig_test_vectors_sigagg(void) { + size_t i, j; + const struct musig_sig_agg_vector *vector = &musig_sig_agg_vector; + + for (i = 0; i < sizeof(vector->valid_case)/sizeof(vector->valid_case[0]); i++) { + const struct musig_sig_agg_case *c = &vector->valid_case[i]; + enum MUSIG_ERROR error; + unsigned char final_sig[64]; + secp256k1_musig_keyagg_cache keyagg_cache; + unsigned char agg_pk32[32]; + secp256k1_xonly_pubkey agg_pk; + secp256k1_musig_aggnonce aggnonce; + secp256k1_musig_session session; + secp256k1_musig_partial_sig partial_sig[(sizeof(vector->psigs)/sizeof(vector->psigs[0]))]; + const secp256k1_musig_partial_sig *partial_sig_ptr[(sizeof(vector->psigs)/sizeof(vector->psigs[0]))]; + + CHECK(musig_vectors_keyagg_and_tweak(&error, &keyagg_cache, agg_pk32, vector->pubkeys, vector->tweaks, c->key_indices_len, c->key_indices, c->tweak_indices_len, c->tweak_indices, c->is_xonly)); + CHECK(secp256k1_musig_aggnonce_parse(CTX, &aggnonce, c->aggnonce)); + CHECK(secp256k1_musig_nonce_process(CTX, &session, &aggnonce, vector->msg, &keyagg_cache)); + for (j = 0; j < c->psig_indices_len; j++) { + CHECK(secp256k1_musig_partial_sig_parse(CTX, &partial_sig[j], vector->psigs[c->psig_indices[j]])); + partial_sig_ptr[j] = &partial_sig[j]; + } + + CHECK(secp256k1_musig_partial_sig_agg(CTX, final_sig, &session, partial_sig_ptr, c->psig_indices_len) == 1); + CHECK(secp256k1_memcmp_var(final_sig, c->expected, sizeof(final_sig)) == 0); + + CHECK(secp256k1_xonly_pubkey_parse(CTX, &agg_pk, agg_pk32)); + CHECK(secp256k1_schnorrsig_verify(CTX, final_sig, vector->msg, sizeof(vector->msg), &agg_pk) == 1); + } + for (i = 0; i < sizeof(vector->error_case)/sizeof(vector->error_case[0]); i++) { + const struct musig_sig_agg_case *c = &vector->error_case[i]; + secp256k1_musig_partial_sig partial_sig[(sizeof(vector->psigs)/sizeof(vector->psigs[0]))]; + for (j = 0; j < c->psig_indices_len; j++) { + int expected = c->invalid_sig_idx != (int)j; + CHECK(expected == secp256k1_musig_partial_sig_parse(CTX, &partial_sig[j], vector->psigs[c->psig_indices[j]])); + } + } +} + +/* Since the BIP doesn't provide static test vectors for nonce_gen_counter, we + * define a static test here */ +static void musig_test_static_nonce_gen_counter(void) { + secp256k1_musig_secnonce secnonce; + secp256k1_musig_pubnonce pubnonce; + unsigned char pubnonce66[66]; + secp256k1_pubkey pk; + secp256k1_keypair keypair; + uint64_t nonrepeating_cnt = 0; + unsigned char sk[32] = { + 0xEE, 0xC1, 0xCB, 0x7D, 0x1B, 0x72, 0x54, 0xC5, + 0xCA, 0xB0, 0xD9, 0xC6, 0x1A, 0xB0, 0x2E, 0x64, + 0x3D, 0x46, 0x4A, 0x59, 0xFE, 0x6C, 0x96, 0xA7, + 0xEF, 0xE8, 0x71, 0xF0, 0x7C, 0x5A, 0xEF, 0x54, + }; + unsigned char expected_secnonce[64] = { + 0x84, 0x2F, 0x13, 0x80, 0xCD, 0x17, 0xA1, 0x98, + 0xFC, 0x3D, 0xAD, 0x3B, 0x7D, 0xA7, 0x49, 0x29, + 0x41, 0xF4, 0x69, 0x76, 0xF2, 0x70, 0x2F, 0xF7, + 0xC6, 0x6F, 0x24, 0xF4, 0x72, 0x03, 0x6A, 0xF1, + 0xDA, 0x3F, 0x95, 0x2D, 0xDE, 0x4A, 0x2D, 0xA6, + 0xB6, 0x32, 0x57, 0x07, 0xCE, 0x87, 0xA4, 0xE3, + 0x61, 0x6D, 0x06, 0xFC, 0x5F, 0x81, 0xA9, 0xC9, + 0x93, 0x86, 0xD2, 0x0A, 0x99, 0xCE, 0xCF, 0x99, + }; + unsigned char expected_pubnonce[66] = { + 0x03, 0xA5, 0xB9, 0xB6, 0x90, 0x79, 0x42, 0xEA, + 0xCD, 0xDA, 0x49, 0xA3, 0x66, 0x01, 0x6E, 0xC2, + 0xE6, 0x24, 0x04, 0xA1, 0xBF, 0x4A, 0xB6, 0xD4, + 0xDB, 0x82, 0x06, 0x7B, 0xC3, 0xAD, 0xF0, 0x86, + 0xD7, 0x03, 0x32, 0x05, 0xDB, 0x9E, 0xB3, 0x4D, + 0x5C, 0x7C, 0xE0, 0x28, 0x48, 0xCA, 0xC6, 0x8A, + 0x83, 0xED, 0x73, 0xE3, 0x88, 0x34, 0x77, 0xF5, + 0x63, 0xF2, 0x3C, 0xE9, 0xA1, 0x1A, 0x77, 0x21, + 0xEC, 0x64, + }; + + CHECK(secp256k1_keypair_create(CTX, &keypair, sk)); + CHECK(secp256k1_keypair_pub(CTX, &pk, &keypair)); + CHECK(secp256k1_musig_nonce_gen_counter(CTX, &secnonce, &pubnonce, nonrepeating_cnt, &keypair, NULL, NULL, NULL) == 1); + + CHECK(secp256k1_memcmp_var(&secnonce.data[4], expected_secnonce, 2*32) == 0); + CHECK(secp256k1_memcmp_var(&secnonce.data[4+2*32], &pk, sizeof(pk)) == 0); + + CHECK(secp256k1_musig_pubnonce_serialize(CTX, pubnonce66, &pubnonce) == 1); + CHECK(secp256k1_memcmp_var(pubnonce66, expected_pubnonce, sizeof(pubnonce66)) == 0); +} + +static void run_musig_tests(void) { + int i; + + for (i = 0; i < COUNT; i++) { + musig_simple_test(); + } + musig_api_tests(); + musig_nonce_test(); + for (i = 0; i < COUNT; i++) { + /* Run multiple times to ensure that pk and nonce have different y + * parities */ + musig_tweak_test(); + } + sha256_tag_test(); + musig_test_vectors_keyagg(); + musig_test_vectors_noncegen(); + musig_test_vectors_nonceagg(); + musig_test_vectors_signverify(); + musig_test_vectors_tweak(); + musig_test_vectors_sigagg(); + + musig_test_static_nonce_gen_counter(); +} + +#endif diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/musig/vectors.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/musig/vectors.h new file mode 100644 index 00000000000..8407c2a69a9 --- /dev/null +++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/musig/vectors.h @@ -0,0 +1,346 @@ +/** + * Automatically generated by ./tools/test_vectors_musig2_generate.py. + * + * The test vectors for the KeySort function are included in this file. They can + * be found in src/modules/extrakeys/tests_impl.h. */ + +enum MUSIG_ERROR { + MUSIG_PUBKEY, + MUSIG_TWEAK, + MUSIG_PUBNONCE, + MUSIG_AGGNONCE, + MUSIG_SECNONCE, + MUSIG_SIG, + MUSIG_SIG_VERIFY, + MUSIG_OTHER +}; + +struct musig_key_agg_valid_test_case { + size_t key_indices_len; + size_t key_indices[4]; + unsigned char expected[32]; +}; + +struct musig_key_agg_error_test_case { + size_t key_indices_len; + size_t key_indices[4]; + size_t tweak_indices_len; + size_t tweak_indices[1]; + int is_xonly[1]; + enum MUSIG_ERROR error; +}; + +struct musig_key_agg_vector { + unsigned char pubkeys[7][33]; + unsigned char tweaks[2][32]; + struct musig_key_agg_valid_test_case valid_case[4]; + struct musig_key_agg_error_test_case error_case[5]; +}; + +static const struct musig_key_agg_vector musig_key_agg_vector = { + { + { 0x02, 0xF9, 0x30, 0x8A, 0x01, 0x92, 0x58, 0xC3, 0x10, 0x49, 0x34, 0x4F, 0x85, 0xF8, 0x9D, 0x52, 0x29, 0xB5, 0x31, 0xC8, 0x45, 0x83, 0x6F, 0x99, 0xB0, 0x86, 0x01, 0xF1, 0x13, 0xBC, 0xE0, 0x36, 0xF9 }, + { 0x03, 0xDF, 0xF1, 0xD7, 0x7F, 0x2A, 0x67, 0x1C, 0x5F, 0x36, 0x18, 0x37, 0x26, 0xDB, 0x23, 0x41, 0xBE, 0x58, 0xFE, 0xAE, 0x1D, 0xA2, 0xDE, 0xCE, 0xD8, 0x43, 0x24, 0x0F, 0x7B, 0x50, 0x2B, 0xA6, 0x59 }, + { 0x02, 0x35, 0x90, 0xA9, 0x4E, 0x76, 0x8F, 0x8E, 0x18, 0x15, 0xC2, 0xF2, 0x4B, 0x4D, 0x80, 0xA8, 0xE3, 0x14, 0x93, 0x16, 0xC3, 0x51, 0x8C, 0xE7, 0xB7, 0xAD, 0x33, 0x83, 0x68, 0xD0, 0x38, 0xCA, 0x66 }, + { 0x02, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x05 }, + { 0x02, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFC, 0x30 }, + { 0x04, 0xF9, 0x30, 0x8A, 0x01, 0x92, 0x58, 0xC3, 0x10, 0x49, 0x34, 0x4F, 0x85, 0xF8, 0x9D, 0x52, 0x29, 0xB5, 0x31, 0xC8, 0x45, 0x83, 0x6F, 0x99, 0xB0, 0x86, 0x01, 0xF1, 0x13, 0xBC, 0xE0, 0x36, 0xF9 }, + { 0x03, 0x93, 0x5F, 0x97, 0x2D, 0xA0, 0x13, 0xF8, 0x0A, 0xE0, 0x11, 0x89, 0x0F, 0xA8, 0x9B, 0x67, 0xA2, 0x7B, 0x7B, 0xE6, 0xCC, 0xB2, 0x4D, 0x32, 0x74, 0xD1, 0x8B, 0x2D, 0x40, 0x67, 0xF2, 0x61, 0xA9 } + }, + { + { 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xBA, 0xAE, 0xDC, 0xE6, 0xAF, 0x48, 0xA0, 0x3B, 0xBF, 0xD2, 0x5E, 0x8C, 0xD0, 0x36, 0x41, 0x41 }, + { 0x25, 0x2E, 0x4B, 0xD6, 0x74, 0x10, 0xA7, 0x6C, 0xDF, 0x93, 0x3D, 0x30, 0xEA, 0xA1, 0x60, 0x82, 0x14, 0x03, 0x7F, 0x1B, 0x10, 0x5A, 0x01, 0x3E, 0xCC, 0xD3, 0xC5, 0xC1, 0x84, 0xA6, 0x11, 0x0B } + }, + { + { 3, { 0, 1, 2 }, { 0x90, 0x53, 0x9E, 0xED, 0xE5, 0x65, 0xF5, 0xD0, 0x54, 0xF3, 0x2C, 0xC0, 0xC2, 0x20, 0x12, 0x68, 0x89, 0xED, 0x1E, 0x5D, 0x19, 0x3B, 0xAF, 0x15, 0xAE, 0xF3, 0x44, 0xFE, 0x59, 0xD4, 0x61, 0x0C }}, + { 3, { 2, 1, 0 }, { 0x62, 0x04, 0xDE, 0x8B, 0x08, 0x34, 0x26, 0xDC, 0x6E, 0xAF, 0x95, 0x02, 0xD2, 0x70, 0x24, 0xD5, 0x3F, 0xC8, 0x26, 0xBF, 0x7D, 0x20, 0x12, 0x14, 0x8A, 0x05, 0x75, 0x43, 0x5D, 0xF5, 0x4B, 0x2B }}, + { 3, { 0, 0, 0 }, { 0xB4, 0x36, 0xE3, 0xBA, 0xD6, 0x2B, 0x8C, 0xD4, 0x09, 0x96, 0x9A, 0x22, 0x47, 0x31, 0xC1, 0x93, 0xD0, 0x51, 0x16, 0x2D, 0x8C, 0x5A, 0xE8, 0xB1, 0x09, 0x30, 0x61, 0x27, 0xDA, 0x3A, 0xA9, 0x35 }}, + { 4, { 0, 0, 1, 1 }, { 0x69, 0xBC, 0x22, 0xBF, 0xA5, 0xD1, 0x06, 0x30, 0x6E, 0x48, 0xA2, 0x06, 0x79, 0xDE, 0x1D, 0x73, 0x89, 0x38, 0x61, 0x24, 0xD0, 0x75, 0x71, 0xD0, 0xD8, 0x72, 0x68, 0x60, 0x28, 0xC2, 0x6A, 0x3E }}, + }, + { + { 2, { 0, 3 }, 0, { 0 }, { 0 }, MUSIG_PUBKEY }, + { 2, { 0, 4 }, 0, { 0 }, { 0 }, MUSIG_PUBKEY }, + { 2, { 5, 0 }, 0, { 0 }, { 0 }, MUSIG_PUBKEY }, + { 2, { 0, 1 }, 1, { 0 }, { 1 }, MUSIG_TWEAK }, + { 1, { 6 }, 1, { 1 }, { 0 }, MUSIG_TWEAK }, + }, +}; + +struct musig_nonce_gen_test_case { + unsigned char rand_[32]; + int has_sk; + unsigned char sk[32]; + unsigned char pk[33]; + int has_aggpk; + unsigned char aggpk[32]; + int has_msg; + unsigned char msg[32]; + int has_extra_in; + unsigned char extra_in[32]; + unsigned char expected_secnonce[97]; + unsigned char expected_pubnonce[66]; +}; + +struct musig_nonce_gen_vector { + struct musig_nonce_gen_test_case test_case[2]; +}; + +static const struct musig_nonce_gen_vector musig_nonce_gen_vector = { + { + { { 0x0F, 0x0F, 0x0F, 0x0F, 0x0F, 0x0F, 0x0F, 0x0F, 0x0F, 0x0F, 0x0F, 0x0F, 0x0F, 0x0F, 0x0F, 0x0F, 0x0F, 0x0F, 0x0F, 0x0F, 0x0F, 0x0F, 0x0F, 0x0F, 0x0F, 0x0F, 0x0F, 0x0F, 0x0F, 0x0F, 0x0F, 0x0F }, 1 , { 0x02, 0x02, 0x02, 0x02, 0x02, 0x02, 0x02, 0x02, 0x02, 0x02, 0x02, 0x02, 0x02, 0x02, 0x02, 0x02, 0x02, 0x02, 0x02, 0x02, 0x02, 0x02, 0x02, 0x02, 0x02, 0x02, 0x02, 0x02, 0x02, 0x02, 0x02, 0x02 }, { 0x02, 0x4D, 0x4B, 0x6C, 0xD1, 0x36, 0x10, 0x32, 0xCA, 0x9B, 0xD2, 0xAE, 0xB9, 0xD9, 0x00, 0xAA, 0x4D, 0x45, 0xD9, 0xEA, 0xD8, 0x0A, 0xC9, 0x42, 0x33, 0x74, 0xC4, 0x51, 0xA7, 0x25, 0x4D, 0x07, 0x66 }, 1 , { 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07 }, 1 , { 0x01, 0x01, 0x01, 0x01, 0x01, 0x01, 0x01, 0x01, 0x01, 0x01, 0x01, 0x01, 0x01, 0x01, 0x01, 0x01, 0x01, 0x01, 0x01, 0x01, 0x01, 0x01, 0x01, 0x01, 0x01, 0x01, 0x01, 0x01, 0x01, 0x01, 0x01, 0x01 }, 1 , { 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08 }, { 0xB1, 0x14, 0xE5, 0x02, 0xBE, 0xAA, 0x4E, 0x30, 0x1D, 0xD0, 0x8A, 0x50, 0x26, 0x41, 0x72, 0xC8, 0x4E, 0x41, 0x65, 0x0E, 0x6C, 0xB7, 0x26, 0xB4, 0x10, 0xC0, 0x69, 0x4D, 0x59, 0xEF, 0xFB, 0x64, 0x95, 0xB5, 0xCA, 0xF2, 0x8D, 0x04, 0x5B, 0x97, 0x3D, 0x63, 0xE3, 0xC9, 0x9A, 0x44, 0xB8, 0x07, 0xBD, 0xE3, 0x75, 0xFD, 0x6C, 0xB3, 0x9E, 0x46, 0xDC, 0x4A, 0x51, 0x17, 0x08, 0xD0, 0xE9, 0xD2, 0x02, 0x4D, 0x4B, 0x6C, 0xD1, 0x36, 0x10, 0x32, 0xCA, 0x9B, 0xD2, 0xAE, 0xB9, 0xD9, 0x00, 0xAA, 0x4D, 0x45, 0xD9, 0xEA, 0xD8, 0x0A, 0xC9, 0x42, 0x33, 0x74, 0xC4, 0x51, 0xA7, 0x25, 0x4D, 0x07, 0x66 }, { 0x02, 0xF7, 0xBE, 0x70, 0x89, 0xE8, 0x37, 0x6E, 0xB3, 0x55, 0x27, 0x23, 0x68, 0x76, 0x6B, 0x17, 0xE8, 0x8E, 0x7D, 0xB7, 0x20, 0x47, 0xD0, 0x5E, 0x56, 0xAA, 0x88, 0x1E, 0xA5, 0x2B, 0x3B, 0x35, 0xDF, 0x02, 0xC2, 0x9C, 0x80, 0x46, 0xFD, 0xD0, 0xDE, 0xD4, 0xC7, 0xE5, 0x58, 0x69, 0x13, 0x72, 0x00, 0xFB, 0xDB, 0xFE, 0x2E, 0xB6, 0x54, 0x26, 0x7B, 0x6D, 0x70, 0x13, 0x60, 0x2C, 0xAE, 0xD3, 0x11, 0x5A } }, + { { 0x0F, 0x0F, 0x0F, 0x0F, 0x0F, 0x0F, 0x0F, 0x0F, 0x0F, 0x0F, 0x0F, 0x0F, 0x0F, 0x0F, 0x0F, 0x0F, 0x0F, 0x0F, 0x0F, 0x0F, 0x0F, 0x0F, 0x0F, 0x0F, 0x0F, 0x0F, 0x0F, 0x0F, 0x0F, 0x0F, 0x0F, 0x0F }, 0 , { 0 }, { 0x02, 0xF9, 0x30, 0x8A, 0x01, 0x92, 0x58, 0xC3, 0x10, 0x49, 0x34, 0x4F, 0x85, 0xF8, 0x9D, 0x52, 0x29, 0xB5, 0x31, 0xC8, 0x45, 0x83, 0x6F, 0x99, 0xB0, 0x86, 0x01, 0xF1, 0x13, 0xBC, 0xE0, 0x36, 0xF9 }, 0 , { 0 }, 0 , { 0 }, 0 , { 0 }, { 0x89, 0xBD, 0xD7, 0x87, 0xD0, 0x28, 0x4E, 0x5E, 0x4D, 0x5F, 0xC5, 0x72, 0xE4, 0x9E, 0x31, 0x6B, 0xAB, 0x7E, 0x21, 0xE3, 0xB1, 0x83, 0x0D, 0xE3, 0x7D, 0xFE, 0x80, 0x15, 0x6F, 0xA4, 0x1A, 0x6D, 0x0B, 0x17, 0xAE, 0x8D, 0x02, 0x4C, 0x53, 0x67, 0x96, 0x99, 0xA6, 0xFD, 0x79, 0x44, 0xD9, 0xC4, 0xA3, 0x66, 0xB5, 0x14, 0xBA, 0xF4, 0x30, 0x88, 0xE0, 0x70, 0x8B, 0x10, 0x23, 0xDD, 0x28, 0x97, 0x02, 0xF9, 0x30, 0x8A, 0x01, 0x92, 0x58, 0xC3, 0x10, 0x49, 0x34, 0x4F, 0x85, 0xF8, 0x9D, 0x52, 0x29, 0xB5, 0x31, 0xC8, 0x45, 0x83, 0x6F, 0x99, 0xB0, 0x86, 0x01, 0xF1, 0x13, 0xBC, 0xE0, 0x36, 0xF9 }, { 0x02, 0xC9, 0x6E, 0x7C, 0xB1, 0xE8, 0xAA, 0x5D, 0xAC, 0x64, 0xD8, 0x72, 0x94, 0x79, 0x14, 0x19, 0x8F, 0x60, 0x7D, 0x90, 0xEC, 0xDE, 0x52, 0x00, 0xDE, 0x52, 0x97, 0x8A, 0xD5, 0xDE, 0xD6, 0x3C, 0x00, 0x02, 0x99, 0xEC, 0x51, 0x17, 0xC2, 0xD2, 0x9E, 0xDE, 0xE8, 0xA2, 0x09, 0x25, 0x87, 0xC3, 0x90, 0x9B, 0xE6, 0x94, 0xD5, 0xCF, 0xF0, 0x66, 0x7D, 0x6C, 0x02, 0xEA, 0x40, 0x59, 0xF7, 0xCD, 0x97, 0x86 } }, + }, +}; + +struct musig_nonce_agg_test_case { + size_t pnonce_indices[2]; + /* if valid case */ + unsigned char expected[66]; + /* if error case */ + int invalid_nonce_idx; +}; + +struct musig_nonce_agg_vector { + unsigned char pnonces[7][66]; + struct musig_nonce_agg_test_case valid_case[2]; + struct musig_nonce_agg_test_case error_case[3]; +}; + +static const struct musig_nonce_agg_vector musig_nonce_agg_vector = { + { + { 0x02, 0x01, 0x51, 0xC8, 0x0F, 0x43, 0x56, 0x48, 0xDF, 0x67, 0xA2, 0x2B, 0x74, 0x9C, 0xD7, 0x98, 0xCE, 0x54, 0xE0, 0x32, 0x1D, 0x03, 0x4B, 0x92, 0xB7, 0x09, 0xB5, 0x67, 0xD6, 0x0A, 0x42, 0xE6, 0x66, 0x03, 0xBA, 0x47, 0xFB, 0xC1, 0x83, 0x44, 0x37, 0xB3, 0x21, 0x2E, 0x89, 0xA8, 0x4D, 0x84, 0x25, 0xE7, 0xBF, 0x12, 0xE0, 0x24, 0x5D, 0x98, 0x26, 0x22, 0x68, 0xEB, 0xDC, 0xB3, 0x85, 0xD5, 0x06, 0x41 }, + { 0x03, 0xFF, 0x40, 0x6F, 0xFD, 0x8A, 0xDB, 0x9C, 0xD2, 0x98, 0x77, 0xE4, 0x98, 0x50, 0x14, 0xF6, 0x6A, 0x59, 0xF6, 0xCD, 0x01, 0xC0, 0xE8, 0x8C, 0xAA, 0x8E, 0x5F, 0x31, 0x66, 0xB1, 0xF6, 0x76, 0xA6, 0x02, 0x48, 0xC2, 0x64, 0xCD, 0xD5, 0x7D, 0x3C, 0x24, 0xD7, 0x99, 0x90, 0xB0, 0xF8, 0x65, 0x67, 0x4E, 0xB6, 0x2A, 0x0F, 0x90, 0x18, 0x27, 0x7A, 0x95, 0x01, 0x1B, 0x41, 0xBF, 0xC1, 0x93, 0xB8, 0x33 }, + { 0x02, 0x01, 0x51, 0xC8, 0x0F, 0x43, 0x56, 0x48, 0xDF, 0x67, 0xA2, 0x2B, 0x74, 0x9C, 0xD7, 0x98, 0xCE, 0x54, 0xE0, 0x32, 0x1D, 0x03, 0x4B, 0x92, 0xB7, 0x09, 0xB5, 0x67, 0xD6, 0x0A, 0x42, 0xE6, 0x66, 0x02, 0x79, 0xBE, 0x66, 0x7E, 0xF9, 0xDC, 0xBB, 0xAC, 0x55, 0xA0, 0x62, 0x95, 0xCE, 0x87, 0x0B, 0x07, 0x02, 0x9B, 0xFC, 0xDB, 0x2D, 0xCE, 0x28, 0xD9, 0x59, 0xF2, 0x81, 0x5B, 0x16, 0xF8, 0x17, 0x98 }, + { 0x03, 0xFF, 0x40, 0x6F, 0xFD, 0x8A, 0xDB, 0x9C, 0xD2, 0x98, 0x77, 0xE4, 0x98, 0x50, 0x14, 0xF6, 0x6A, 0x59, 0xF6, 0xCD, 0x01, 0xC0, 0xE8, 0x8C, 0xAA, 0x8E, 0x5F, 0x31, 0x66, 0xB1, 0xF6, 0x76, 0xA6, 0x03, 0x79, 0xBE, 0x66, 0x7E, 0xF9, 0xDC, 0xBB, 0xAC, 0x55, 0xA0, 0x62, 0x95, 0xCE, 0x87, 0x0B, 0x07, 0x02, 0x9B, 0xFC, 0xDB, 0x2D, 0xCE, 0x28, 0xD9, 0x59, 0xF2, 0x81, 0x5B, 0x16, 0xF8, 0x17, 0x98 }, + { 0x04, 0xFF, 0x40, 0x6F, 0xFD, 0x8A, 0xDB, 0x9C, 0xD2, 0x98, 0x77, 0xE4, 0x98, 0x50, 0x14, 0xF6, 0x6A, 0x59, 0xF6, 0xCD, 0x01, 0xC0, 0xE8, 0x8C, 0xAA, 0x8E, 0x5F, 0x31, 0x66, 0xB1, 0xF6, 0x76, 0xA6, 0x02, 0x48, 0xC2, 0x64, 0xCD, 0xD5, 0x7D, 0x3C, 0x24, 0xD7, 0x99, 0x90, 0xB0, 0xF8, 0x65, 0x67, 0x4E, 0xB6, 0x2A, 0x0F, 0x90, 0x18, 0x27, 0x7A, 0x95, 0x01, 0x1B, 0x41, 0xBF, 0xC1, 0x93, 0xB8, 0x33 }, + { 0x03, 0xFF, 0x40, 0x6F, 0xFD, 0x8A, 0xDB, 0x9C, 0xD2, 0x98, 0x77, 0xE4, 0x98, 0x50, 0x14, 0xF6, 0x6A, 0x59, 0xF6, 0xCD, 0x01, 0xC0, 0xE8, 0x8C, 0xAA, 0x8E, 0x5F, 0x31, 0x66, 0xB1, 0xF6, 0x76, 0xA6, 0x02, 0x48, 0xC2, 0x64, 0xCD, 0xD5, 0x7D, 0x3C, 0x24, 0xD7, 0x99, 0x90, 0xB0, 0xF8, 0x65, 0x67, 0x4E, 0xB6, 0x2A, 0x0F, 0x90, 0x18, 0x27, 0x7A, 0x95, 0x01, 0x1B, 0x41, 0xBF, 0xC1, 0x93, 0xB8, 0x31 }, + { 0x03, 0xFF, 0x40, 0x6F, 0xFD, 0x8A, 0xDB, 0x9C, 0xD2, 0x98, 0x77, 0xE4, 0x98, 0x50, 0x14, 0xF6, 0x6A, 0x59, 0xF6, 0xCD, 0x01, 0xC0, 0xE8, 0x8C, 0xAA, 0x8E, 0x5F, 0x31, 0x66, 0xB1, 0xF6, 0x76, 0xA6, 0x02, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFC, 0x30 } + }, + { + { { 0, 1 }, { 0x03, 0x5F, 0xE1, 0x87, 0x3B, 0x4F, 0x29, 0x67, 0xF5, 0x2F, 0xEA, 0x4A, 0x06, 0xAD, 0x5A, 0x8E, 0xCC, 0xBE, 0x9D, 0x0F, 0xD7, 0x30, 0x68, 0x01, 0x2C, 0x89, 0x4E, 0x2E, 0x87, 0xCC, 0xB5, 0x80, 0x4B, 0x02, 0x47, 0x25, 0x37, 0x73, 0x45, 0xBD, 0xE0, 0xE9, 0xC3, 0x3A, 0xF3, 0xC4, 0x3C, 0x0A, 0x29, 0xA9, 0x24, 0x9F, 0x2F, 0x29, 0x56, 0xFA, 0x8C, 0xFE, 0xB5, 0x5C, 0x85, 0x73, 0xD0, 0x26, 0x2D, 0xC8 }, 0 }, + { { 2, 3 }, { 0x03, 0x5F, 0xE1, 0x87, 0x3B, 0x4F, 0x29, 0x67, 0xF5, 0x2F, 0xEA, 0x4A, 0x06, 0xAD, 0x5A, 0x8E, 0xCC, 0xBE, 0x9D, 0x0F, 0xD7, 0x30, 0x68, 0x01, 0x2C, 0x89, 0x4E, 0x2E, 0x87, 0xCC, 0xB5, 0x80, 0x4B, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 }, 0 }, + }, + { + { { 0, 4 }, { 0 }, 1 }, + { { 5, 1 }, { 0 }, 0 }, + { { 6, 1 }, { 0 }, 0 }, + }, +}; + +/* Omit pubnonces in the test vectors because our partial signature verification + * implementation is able to accept the aggnonce directly. */ +struct musig_valid_case { + size_t key_indices_len; + size_t key_indices[3]; + size_t aggnonce_index; + size_t msg_index; + size_t signer_index; + unsigned char expected[32]; +}; + +struct musig_sign_error_case { + size_t key_indices_len; + size_t key_indices[3]; + size_t aggnonce_index; + size_t msg_index; + size_t secnonce_index; + enum MUSIG_ERROR error; +}; + +struct musig_verify_fail_error_case { + unsigned char sig[32]; + size_t key_indices_len; + size_t key_indices[3]; + size_t nonce_indices_len; + size_t nonce_indices[3]; + size_t msg_index; + size_t signer_index; + enum MUSIG_ERROR error; +}; + +struct musig_sign_verify_vector { + unsigned char sk[32]; + unsigned char pubkeys[4][33]; + unsigned char secnonces[2][194]; + unsigned char pubnonces[5][194]; + unsigned char aggnonces[5][66]; + unsigned char msgs[1][32]; + struct musig_valid_case valid_case[4]; + struct musig_sign_error_case sign_error_case[6]; + struct musig_verify_fail_error_case verify_fail_case[3]; + struct musig_verify_fail_error_case verify_error_case[2]; +}; + +static const struct musig_sign_verify_vector musig_sign_verify_vector = { + { 0x7F, 0xB9, 0xE0, 0xE6, 0x87, 0xAD, 0xA1, 0xEE, 0xBF, 0x7E, 0xCF, 0xE2, 0xF2, 0x1E, 0x73, 0xEB, 0xDB, 0x51, 0xA7, 0xD4, 0x50, 0x94, 0x8D, 0xFE, 0x8D, 0x76, 0xD7, 0xF2, 0xD1, 0x00, 0x76, 0x71 }, + { + { 0x03, 0x93, 0x5F, 0x97, 0x2D, 0xA0, 0x13, 0xF8, 0x0A, 0xE0, 0x11, 0x89, 0x0F, 0xA8, 0x9B, 0x67, 0xA2, 0x7B, 0x7B, 0xE6, 0xCC, 0xB2, 0x4D, 0x32, 0x74, 0xD1, 0x8B, 0x2D, 0x40, 0x67, 0xF2, 0x61, 0xA9 }, + { 0x02, 0xF9, 0x30, 0x8A, 0x01, 0x92, 0x58, 0xC3, 0x10, 0x49, 0x34, 0x4F, 0x85, 0xF8, 0x9D, 0x52, 0x29, 0xB5, 0x31, 0xC8, 0x45, 0x83, 0x6F, 0x99, 0xB0, 0x86, 0x01, 0xF1, 0x13, 0xBC, 0xE0, 0x36, 0xF9 }, + { 0x02, 0xDF, 0xF1, 0xD7, 0x7F, 0x2A, 0x67, 0x1C, 0x5F, 0x36, 0x18, 0x37, 0x26, 0xDB, 0x23, 0x41, 0xBE, 0x58, 0xFE, 0xAE, 0x1D, 0xA2, 0xDE, 0xCE, 0xD8, 0x43, 0x24, 0x0F, 0x7B, 0x50, 0x2B, 0xA6, 0x61 }, + { 0x02, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x07 } + }, + { + { 0x50, 0x8B, 0x81, 0xA6, 0x11, 0xF1, 0x00, 0xA6, 0xB2, 0xB6, 0xB2, 0x96, 0x56, 0x59, 0x08, 0x98, 0xAF, 0x48, 0x8B, 0xCF, 0x2E, 0x1F, 0x55, 0xCF, 0x22, 0xE5, 0xCF, 0xB8, 0x44, 0x21, 0xFE, 0x61, 0xFA, 0x27, 0xFD, 0x49, 0xB1, 0xD5, 0x00, 0x85, 0xB4, 0x81, 0x28, 0x5E, 0x1C, 0xA2, 0x05, 0xD5, 0x5C, 0x82, 0xCC, 0x1B, 0x31, 0xFF, 0x5C, 0xD5, 0x4A, 0x48, 0x98, 0x29, 0x35, 0x59, 0x01, 0xF7, 0x03, 0x93, 0x5F, 0x97, 0x2D, 0xA0, 0x13, 0xF8, 0x0A, 0xE0, 0x11, 0x89, 0x0F, 0xA8, 0x9B, 0x67, 0xA2, 0x7B, 0x7B, 0xE6, 0xCC, 0xB2, 0x4D, 0x32, 0x74, 0xD1, 0x8B, 0x2D, 0x40, 0x67, 0xF2, 0x61, 0xA9 }, + { 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x03, 0x93, 0x5F, 0x97, 0x2D, 0xA0, 0x13, 0xF8, 0x0A, 0xE0, 0x11, 0x89, 0x0F, 0xA8, 0x9B, 0x67, 0xA2, 0x7B, 0x7B, 0xE6, 0xCC, 0xB2, 0x4D, 0x32, 0x74, 0xD1, 0x8B, 0x2D, 0x40, 0x67, 0xF2, 0x61, 0xA9 } + }, + { + { 0x03, 0x37, 0xC8, 0x78, 0x21, 0xAF, 0xD5, 0x0A, 0x86, 0x44, 0xD8, 0x20, 0xA8, 0xF3, 0xE0, 0x2E, 0x49, 0x9C, 0x93, 0x18, 0x65, 0xC2, 0x36, 0x0F, 0xB4, 0x3D, 0x0A, 0x0D, 0x20, 0xDA, 0xFE, 0x07, 0xEA, 0x02, 0x87, 0xBF, 0x89, 0x1D, 0x2A, 0x6D, 0xEA, 0xEB, 0xAD, 0xC9, 0x09, 0x35, 0x2A, 0xA9, 0x40, 0x5D, 0x14, 0x28, 0xC1, 0x5F, 0x4B, 0x75, 0xF0, 0x4D, 0xAE, 0x64, 0x2A, 0x95, 0xC2, 0x54, 0x84, 0x80 }, + { 0x02, 0x79, 0xBE, 0x66, 0x7E, 0xF9, 0xDC, 0xBB, 0xAC, 0x55, 0xA0, 0x62, 0x95, 0xCE, 0x87, 0x0B, 0x07, 0x02, 0x9B, 0xFC, 0xDB, 0x2D, 0xCE, 0x28, 0xD9, 0x59, 0xF2, 0x81, 0x5B, 0x16, 0xF8, 0x17, 0x98, 0x02, 0x79, 0xBE, 0x66, 0x7E, 0xF9, 0xDC, 0xBB, 0xAC, 0x55, 0xA0, 0x62, 0x95, 0xCE, 0x87, 0x0B, 0x07, 0x02, 0x9B, 0xFC, 0xDB, 0x2D, 0xCE, 0x28, 0xD9, 0x59, 0xF2, 0x81, 0x5B, 0x16, 0xF8, 0x17, 0x98 }, + { 0x03, 0x2D, 0xE2, 0x66, 0x26, 0x28, 0xC9, 0x0B, 0x03, 0xF5, 0xE7, 0x20, 0x28, 0x4E, 0xB5, 0x2F, 0xF7, 0xD7, 0x1F, 0x42, 0x84, 0xF6, 0x27, 0xB6, 0x8A, 0x85, 0x3D, 0x78, 0xC7, 0x8E, 0x1F, 0xFE, 0x93, 0x03, 0xE4, 0xC5, 0x52, 0x4E, 0x83, 0xFF, 0xE1, 0x49, 0x3B, 0x90, 0x77, 0xCF, 0x1C, 0xA6, 0xBE, 0xB2, 0x09, 0x0C, 0x93, 0xD9, 0x30, 0x32, 0x10, 0x71, 0xAD, 0x40, 0xB2, 0xF4, 0x4E, 0x59, 0x90, 0x46 }, + { 0x02, 0x37, 0xC8, 0x78, 0x21, 0xAF, 0xD5, 0x0A, 0x86, 0x44, 0xD8, 0x20, 0xA8, 0xF3, 0xE0, 0x2E, 0x49, 0x9C, 0x93, 0x18, 0x65, 0xC2, 0x36, 0x0F, 0xB4, 0x3D, 0x0A, 0x0D, 0x20, 0xDA, 0xFE, 0x07, 0xEA, 0x03, 0x87, 0xBF, 0x89, 0x1D, 0x2A, 0x6D, 0xEA, 0xEB, 0xAD, 0xC9, 0x09, 0x35, 0x2A, 0xA9, 0x40, 0x5D, 0x14, 0x28, 0xC1, 0x5F, 0x4B, 0x75, 0xF0, 0x4D, 0xAE, 0x64, 0x2A, 0x95, 0xC2, 0x54, 0x84, 0x80 }, + { 0x02, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x09, 0x02, 0x87, 0xBF, 0x89, 0x1D, 0x2A, 0x6D, 0xEA, 0xEB, 0xAD, 0xC9, 0x09, 0x35, 0x2A, 0xA9, 0x40, 0x5D, 0x14, 0x28, 0xC1, 0x5F, 0x4B, 0x75, 0xF0, 0x4D, 0xAE, 0x64, 0x2A, 0x95, 0xC2, 0x54, 0x84, 0x80 } + }, + { + { 0x02, 0x84, 0x65, 0xFC, 0xF0, 0xBB, 0xDB, 0xCF, 0x44, 0x3A, 0xAB, 0xCC, 0xE5, 0x33, 0xD4, 0x2B, 0x4B, 0x5A, 0x10, 0x96, 0x6A, 0xC0, 0x9A, 0x49, 0x65, 0x5E, 0x8C, 0x42, 0xDA, 0xAB, 0x8F, 0xCD, 0x61, 0x03, 0x74, 0x96, 0xA3, 0xCC, 0x86, 0x92, 0x6D, 0x45, 0x2C, 0xAF, 0xCF, 0xD5, 0x5D, 0x25, 0x97, 0x2C, 0xA1, 0x67, 0x5D, 0x54, 0x93, 0x10, 0xDE, 0x29, 0x6B, 0xFF, 0x42, 0xF7, 0x2E, 0xEE, 0xA8, 0xC9 }, + { 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 }, + { 0x04, 0x84, 0x65, 0xFC, 0xF0, 0xBB, 0xDB, 0xCF, 0x44, 0x3A, 0xAB, 0xCC, 0xE5, 0x33, 0xD4, 0x2B, 0x4B, 0x5A, 0x10, 0x96, 0x6A, 0xC0, 0x9A, 0x49, 0x65, 0x5E, 0x8C, 0x42, 0xDA, 0xAB, 0x8F, 0xCD, 0x61, 0x03, 0x74, 0x96, 0xA3, 0xCC, 0x86, 0x92, 0x6D, 0x45, 0x2C, 0xAF, 0xCF, 0xD5, 0x5D, 0x25, 0x97, 0x2C, 0xA1, 0x67, 0x5D, 0x54, 0x93, 0x10, 0xDE, 0x29, 0x6B, 0xFF, 0x42, 0xF7, 0x2E, 0xEE, 0xA8, 0xC9 }, + { 0x02, 0x84, 0x65, 0xFC, 0xF0, 0xBB, 0xDB, 0xCF, 0x44, 0x3A, 0xAB, 0xCC, 0xE5, 0x33, 0xD4, 0x2B, 0x4B, 0x5A, 0x10, 0x96, 0x6A, 0xC0, 0x9A, 0x49, 0x65, 0x5E, 0x8C, 0x42, 0xDA, 0xAB, 0x8F, 0xCD, 0x61, 0x02, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x09 }, + { 0x02, 0x84, 0x65, 0xFC, 0xF0, 0xBB, 0xDB, 0xCF, 0x44, 0x3A, 0xAB, 0xCC, 0xE5, 0x33, 0xD4, 0x2B, 0x4B, 0x5A, 0x10, 0x96, 0x6A, 0xC0, 0x9A, 0x49, 0x65, 0x5E, 0x8C, 0x42, 0xDA, 0xAB, 0x8F, 0xCD, 0x61, 0x02, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFC, 0x30 } + }, + { + { 0xF9, 0x54, 0x66, 0xD0, 0x86, 0x77, 0x0E, 0x68, 0x99, 0x64, 0x66, 0x42, 0x19, 0x26, 0x6F, 0xE5, 0xED, 0x21, 0x5C, 0x92, 0xAE, 0x20, 0xBA, 0xB5, 0xC9, 0xD7, 0x9A, 0xDD, 0xDD, 0xF3, 0xC0, 0xCF } + }, + { + { 3, { 0, 1, 2 }, 0, 0, 0, { 0x01, 0x2A, 0xBB, 0xCB, 0x52, 0xB3, 0x01, 0x6A, 0xC0, 0x3A, 0xD8, 0x23, 0x95, 0xA1, 0xA4, 0x15, 0xC4, 0x8B, 0x93, 0xDE, 0xF7, 0x87, 0x18, 0xE6, 0x2A, 0x7A, 0x90, 0x05, 0x2F, 0xE2, 0x24, 0xFB }}, + { 3, { 1, 0, 2 }, 0, 0, 1, { 0x9F, 0xF2, 0xF7, 0xAA, 0xA8, 0x56, 0x15, 0x0C, 0xC8, 0x81, 0x92, 0x54, 0x21, 0x8D, 0x3A, 0xDE, 0xEB, 0x05, 0x35, 0x26, 0x90, 0x51, 0x89, 0x77, 0x24, 0xF9, 0xDB, 0x37, 0x89, 0x51, 0x3A, 0x52 }}, + { 3, { 1, 2, 0 }, 0, 0, 2, { 0xFA, 0x23, 0xC3, 0x59, 0xF6, 0xFA, 0xC4, 0xE7, 0x79, 0x6B, 0xB9, 0x3B, 0xC9, 0xF0, 0x53, 0x2A, 0x95, 0x46, 0x8C, 0x53, 0x9B, 0xA2, 0x0F, 0xF8, 0x6D, 0x7C, 0x76, 0xED, 0x92, 0x22, 0x79, 0x00 }}, + { 2, { 0, 1 }, 1, 0, 0, { 0xAE, 0x38, 0x60, 0x64, 0xB2, 0x61, 0x05, 0x40, 0x47, 0x98, 0xF7, 0x5D, 0xE2, 0xEB, 0x9A, 0xF5, 0xED, 0xA5, 0x38, 0x7B, 0x06, 0x4B, 0x83, 0xD0, 0x49, 0xCB, 0x7C, 0x5E, 0x08, 0x87, 0x95, 0x31 }}, + }, + { + { 2, { 1, 2 }, 0, 0, 0, MUSIG_PUBKEY }, + { 3, { 1, 0, 3 }, 0, 0, 0, MUSIG_PUBKEY }, + { 3, { 1, 2, 0 }, 2, 0, 0, MUSIG_AGGNONCE }, + { 3, { 1, 2, 0 }, 3, 0, 0, MUSIG_AGGNONCE }, + { 3, { 1, 2, 0 }, 4, 0, 0, MUSIG_AGGNONCE }, + { 3, { 0, 1, 2 }, 0, 0, 1, MUSIG_SECNONCE }, + }, + { + { { 0xFE, 0xD5, 0x44, 0x34, 0xAD, 0x4C, 0xFE, 0x95, 0x3F, 0xC5, 0x27, 0xDC, 0x6A, 0x5E, 0x5B, 0xE8, 0xF6, 0x23, 0x49, 0x07, 0xB7, 0xC1, 0x87, 0x55, 0x95, 0x57, 0xCE, 0x87, 0xA0, 0x54, 0x1C, 0x46 }, 3, { 0, 1, 2 }, 3, { 0, 1, 2 }, 0, 0, MUSIG_SIG_VERIFY }, + { { 0x01, 0x2A, 0xBB, 0xCB, 0x52, 0xB3, 0x01, 0x6A, 0xC0, 0x3A, 0xD8, 0x23, 0x95, 0xA1, 0xA4, 0x15, 0xC4, 0x8B, 0x93, 0xDE, 0xF7, 0x87, 0x18, 0xE6, 0x2A, 0x7A, 0x90, 0x05, 0x2F, 0xE2, 0x24, 0xFB }, 3, { 0, 1, 2 }, 3, { 0, 1, 2 }, 0, 1, MUSIG_SIG_VERIFY }, + { { 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xBA, 0xAE, 0xDC, 0xE6, 0xAF, 0x48, 0xA0, 0x3B, 0xBF, 0xD2, 0x5E, 0x8C, 0xD0, 0x36, 0x41, 0x41 }, 3, { 0, 1, 2 }, 3, { 0, 1, 2 }, 0, 0, MUSIG_SIG }, + }, + { + { { 0x01, 0x2A, 0xBB, 0xCB, 0x52, 0xB3, 0x01, 0x6A, 0xC0, 0x3A, 0xD8, 0x23, 0x95, 0xA1, 0xA4, 0x15, 0xC4, 0x8B, 0x93, 0xDE, 0xF7, 0x87, 0x18, 0xE6, 0x2A, 0x7A, 0x90, 0x05, 0x2F, 0xE2, 0x24, 0xFB }, 3, { 0, 1, 2 }, 3, { 4, 1, 2 }, 0, 0, MUSIG_PUBNONCE }, + { { 0x01, 0x2A, 0xBB, 0xCB, 0x52, 0xB3, 0x01, 0x6A, 0xC0, 0x3A, 0xD8, 0x23, 0x95, 0xA1, 0xA4, 0x15, 0xC4, 0x8B, 0x93, 0xDE, 0xF7, 0x87, 0x18, 0xE6, 0x2A, 0x7A, 0x90, 0x05, 0x2F, 0xE2, 0x24, 0xFB }, 3, { 3, 1, 2 }, 3, { 0, 1, 2 }, 0, 0, MUSIG_PUBKEY }, + }, +}; + +struct musig_tweak_case { + size_t key_indices_len; + size_t key_indices[3]; + size_t nonce_indices_len; + size_t nonce_indices[3]; + size_t tweak_indices_len; + size_t tweak_indices[4]; + int is_xonly[4]; + size_t signer_index; + unsigned char expected[32]; +}; + +struct musig_tweak_vector { + unsigned char sk[32]; + unsigned char secnonce[97]; + unsigned char aggnonce[66]; + unsigned char msg[32]; + unsigned char pubkeys[3][33]; + unsigned char pubnonces[3][194]; + unsigned char tweaks[5][32]; + struct musig_tweak_case valid_case[5]; + struct musig_tweak_case error_case[1]; +}; + +static const struct musig_tweak_vector musig_tweak_vector = { + { 0x7F, 0xB9, 0xE0, 0xE6, 0x87, 0xAD, 0xA1, 0xEE, 0xBF, 0x7E, 0xCF, 0xE2, 0xF2, 0x1E, 0x73, 0xEB, 0xDB, 0x51, 0xA7, 0xD4, 0x50, 0x94, 0x8D, 0xFE, 0x8D, 0x76, 0xD7, 0xF2, 0xD1, 0x00, 0x76, 0x71 }, + { 0x50, 0x8B, 0x81, 0xA6, 0x11, 0xF1, 0x00, 0xA6, 0xB2, 0xB6, 0xB2, 0x96, 0x56, 0x59, 0x08, 0x98, 0xAF, 0x48, 0x8B, 0xCF, 0x2E, 0x1F, 0x55, 0xCF, 0x22, 0xE5, 0xCF, 0xB8, 0x44, 0x21, 0xFE, 0x61, 0xFA, 0x27, 0xFD, 0x49, 0xB1, 0xD5, 0x00, 0x85, 0xB4, 0x81, 0x28, 0x5E, 0x1C, 0xA2, 0x05, 0xD5, 0x5C, 0x82, 0xCC, 0x1B, 0x31, 0xFF, 0x5C, 0xD5, 0x4A, 0x48, 0x98, 0x29, 0x35, 0x59, 0x01, 0xF7, 0x03, 0x93, 0x5F, 0x97, 0x2D, 0xA0, 0x13, 0xF8, 0x0A, 0xE0, 0x11, 0x89, 0x0F, 0xA8, 0x9B, 0x67, 0xA2, 0x7B, 0x7B, 0xE6, 0xCC, 0xB2, 0x4D, 0x32, 0x74, 0xD1, 0x8B, 0x2D, 0x40, 0x67, 0xF2, 0x61, 0xA9 }, + { 0x02, 0x84, 0x65, 0xFC, 0xF0, 0xBB, 0xDB, 0xCF, 0x44, 0x3A, 0xAB, 0xCC, 0xE5, 0x33, 0xD4, 0x2B, 0x4B, 0x5A, 0x10, 0x96, 0x6A, 0xC0, 0x9A, 0x49, 0x65, 0x5E, 0x8C, 0x42, 0xDA, 0xAB, 0x8F, 0xCD, 0x61, 0x03, 0x74, 0x96, 0xA3, 0xCC, 0x86, 0x92, 0x6D, 0x45, 0x2C, 0xAF, 0xCF, 0xD5, 0x5D, 0x25, 0x97, 0x2C, 0xA1, 0x67, 0x5D, 0x54, 0x93, 0x10, 0xDE, 0x29, 0x6B, 0xFF, 0x42, 0xF7, 0x2E, 0xEE, 0xA8, 0xC9 }, + { 0xF9, 0x54, 0x66, 0xD0, 0x86, 0x77, 0x0E, 0x68, 0x99, 0x64, 0x66, 0x42, 0x19, 0x26, 0x6F, 0xE5, 0xED, 0x21, 0x5C, 0x92, 0xAE, 0x20, 0xBA, 0xB5, 0xC9, 0xD7, 0x9A, 0xDD, 0xDD, 0xF3, 0xC0, 0xCF }, + { + { 0x03, 0x93, 0x5F, 0x97, 0x2D, 0xA0, 0x13, 0xF8, 0x0A, 0xE0, 0x11, 0x89, 0x0F, 0xA8, 0x9B, 0x67, 0xA2, 0x7B, 0x7B, 0xE6, 0xCC, 0xB2, 0x4D, 0x32, 0x74, 0xD1, 0x8B, 0x2D, 0x40, 0x67, 0xF2, 0x61, 0xA9 }, + { 0x02, 0xF9, 0x30, 0x8A, 0x01, 0x92, 0x58, 0xC3, 0x10, 0x49, 0x34, 0x4F, 0x85, 0xF8, 0x9D, 0x52, 0x29, 0xB5, 0x31, 0xC8, 0x45, 0x83, 0x6F, 0x99, 0xB0, 0x86, 0x01, 0xF1, 0x13, 0xBC, 0xE0, 0x36, 0xF9 }, + { 0x02, 0xDF, 0xF1, 0xD7, 0x7F, 0x2A, 0x67, 0x1C, 0x5F, 0x36, 0x18, 0x37, 0x26, 0xDB, 0x23, 0x41, 0xBE, 0x58, 0xFE, 0xAE, 0x1D, 0xA2, 0xDE, 0xCE, 0xD8, 0x43, 0x24, 0x0F, 0x7B, 0x50, 0x2B, 0xA6, 0x59 } + }, + { + { 0x03, 0x37, 0xC8, 0x78, 0x21, 0xAF, 0xD5, 0x0A, 0x86, 0x44, 0xD8, 0x20, 0xA8, 0xF3, 0xE0, 0x2E, 0x49, 0x9C, 0x93, 0x18, 0x65, 0xC2, 0x36, 0x0F, 0xB4, 0x3D, 0x0A, 0x0D, 0x20, 0xDA, 0xFE, 0x07, 0xEA, 0x02, 0x87, 0xBF, 0x89, 0x1D, 0x2A, 0x6D, 0xEA, 0xEB, 0xAD, 0xC9, 0x09, 0x35, 0x2A, 0xA9, 0x40, 0x5D, 0x14, 0x28, 0xC1, 0x5F, 0x4B, 0x75, 0xF0, 0x4D, 0xAE, 0x64, 0x2A, 0x95, 0xC2, 0x54, 0x84, 0x80 }, + { 0x02, 0x79, 0xBE, 0x66, 0x7E, 0xF9, 0xDC, 0xBB, 0xAC, 0x55, 0xA0, 0x62, 0x95, 0xCE, 0x87, 0x0B, 0x07, 0x02, 0x9B, 0xFC, 0xDB, 0x2D, 0xCE, 0x28, 0xD9, 0x59, 0xF2, 0x81, 0x5B, 0x16, 0xF8, 0x17, 0x98, 0x02, 0x79, 0xBE, 0x66, 0x7E, 0xF9, 0xDC, 0xBB, 0xAC, 0x55, 0xA0, 0x62, 0x95, 0xCE, 0x87, 0x0B, 0x07, 0x02, 0x9B, 0xFC, 0xDB, 0x2D, 0xCE, 0x28, 0xD9, 0x59, 0xF2, 0x81, 0x5B, 0x16, 0xF8, 0x17, 0x98 }, + { 0x03, 0x2D, 0xE2, 0x66, 0x26, 0x28, 0xC9, 0x0B, 0x03, 0xF5, 0xE7, 0x20, 0x28, 0x4E, 0xB5, 0x2F, 0xF7, 0xD7, 0x1F, 0x42, 0x84, 0xF6, 0x27, 0xB6, 0x8A, 0x85, 0x3D, 0x78, 0xC7, 0x8E, 0x1F, 0xFE, 0x93, 0x03, 0xE4, 0xC5, 0x52, 0x4E, 0x83, 0xFF, 0xE1, 0x49, 0x3B, 0x90, 0x77, 0xCF, 0x1C, 0xA6, 0xBE, 0xB2, 0x09, 0x0C, 0x93, 0xD9, 0x30, 0x32, 0x10, 0x71, 0xAD, 0x40, 0xB2, 0xF4, 0x4E, 0x59, 0x90, 0x46 } + }, + { + { 0xE8, 0xF7, 0x91, 0xFF, 0x92, 0x25, 0xA2, 0xAF, 0x01, 0x02, 0xAF, 0xFF, 0x4A, 0x9A, 0x72, 0x3D, 0x96, 0x12, 0xA6, 0x82, 0xA2, 0x5E, 0xBE, 0x79, 0x80, 0x2B, 0x26, 0x3C, 0xDF, 0xCD, 0x83, 0xBB }, + { 0xAE, 0x2E, 0xA7, 0x97, 0xCC, 0x0F, 0xE7, 0x2A, 0xC5, 0xB9, 0x7B, 0x97, 0xF3, 0xC6, 0x95, 0x7D, 0x7E, 0x41, 0x99, 0xA1, 0x67, 0xA5, 0x8E, 0xB0, 0x8B, 0xCA, 0xFF, 0xDA, 0x70, 0xAC, 0x04, 0x55 }, + { 0xF5, 0x2E, 0xCB, 0xC5, 0x65, 0xB3, 0xD8, 0xBE, 0xA2, 0xDF, 0xD5, 0xB7, 0x5A, 0x4F, 0x45, 0x7E, 0x54, 0x36, 0x98, 0x09, 0x32, 0x2E, 0x41, 0x20, 0x83, 0x16, 0x26, 0xF2, 0x90, 0xFA, 0x87, 0xE0 }, + { 0x19, 0x69, 0xAD, 0x73, 0xCC, 0x17, 0x7F, 0xA0, 0xB4, 0xFC, 0xED, 0x6D, 0xF1, 0xF7, 0xBF, 0x99, 0x07, 0xE6, 0x65, 0xFD, 0xE9, 0xBA, 0x19, 0x6A, 0x74, 0xFE, 0xD0, 0xA3, 0xCF, 0x5A, 0xEF, 0x9D }, + { 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xBA, 0xAE, 0xDC, 0xE6, 0xAF, 0x48, 0xA0, 0x3B, 0xBF, 0xD2, 0x5E, 0x8C, 0xD0, 0x36, 0x41, 0x41 } + }, + { + { 3, { 1, 2, 0 }, 3, { 1, 2, 0 }, 1, { 0 }, { 1 }, 2, { 0xE2, 0x8A, 0x5C, 0x66, 0xE6, 0x1E, 0x17, 0x8C, 0x2B, 0xA1, 0x9D, 0xB7, 0x7B, 0x6C, 0xF9, 0xF7, 0xE2, 0xF0, 0xF5, 0x6C, 0x17, 0x91, 0x8C, 0xD1, 0x31, 0x35, 0xE6, 0x0C, 0xC8, 0x48, 0xFE, 0x91 }}, + { 3, { 1, 2, 0 }, 3, { 1, 2, 0 }, 1, { 0 }, { 0 }, 2, { 0x38, 0xB0, 0x76, 0x77, 0x98, 0x25, 0x2F, 0x21, 0xBF, 0x57, 0x02, 0xC4, 0x80, 0x28, 0xB0, 0x95, 0x42, 0x83, 0x20, 0xF7, 0x3A, 0x4B, 0x14, 0xDB, 0x1E, 0x25, 0xDE, 0x58, 0x54, 0x3D, 0x2D, 0x2D }}, + { 3, { 1, 2, 0 }, 3, { 1, 2, 0 }, 2, { 0, 1 }, { 0, 1 }, 2, { 0x40, 0x8A, 0x0A, 0x21, 0xC4, 0xA0, 0xF5, 0xDA, 0xCA, 0xF9, 0x64, 0x6A, 0xD6, 0xEB, 0x6F, 0xEC, 0xD7, 0xF7, 0xA1, 0x1F, 0x03, 0xED, 0x1F, 0x48, 0xDF, 0xFF, 0x21, 0x85, 0xBC, 0x2C, 0x24, 0x08 }}, + { 3, { 1, 2, 0 }, 3, { 1, 2, 0 }, 4, { 0, 1, 2, 3 }, { 0, 0, 1, 1 }, 2, { 0x45, 0xAB, 0xD2, 0x06, 0xE6, 0x1E, 0x3D, 0xF2, 0xEC, 0x9E, 0x26, 0x4A, 0x6F, 0xEC, 0x82, 0x92, 0x14, 0x1A, 0x63, 0x3C, 0x28, 0x58, 0x63, 0x88, 0x23, 0x55, 0x41, 0xF9, 0xAD, 0xE7, 0x54, 0x35 }}, + { 3, { 1, 2, 0 }, 3, { 1, 2, 0 }, 4, { 0, 1, 2, 3 }, { 1, 0, 1, 0 }, 2, { 0xB2, 0x55, 0xFD, 0xCA, 0xC2, 0x7B, 0x40, 0xC7, 0xCE, 0x78, 0x48, 0xE2, 0xD3, 0xB7, 0xBF, 0x5E, 0xA0, 0xED, 0x75, 0x6D, 0xA8, 0x15, 0x65, 0xAC, 0x80, 0x4C, 0xCC, 0xA3, 0xE1, 0xD5, 0xD2, 0x39 }}, + }, + { + { 3, { 1, 2, 0 }, 3, { 1, 2, 0 }, 1, { 4 }, { 0 }, 2, { 0 }}, + }, +}; + +/* Omit pubnonces in the test vectors because they're only needed for + * implementations that do not directly accept an aggnonce. */ +struct musig_sig_agg_case { + size_t key_indices_len; + size_t key_indices[2]; + size_t tweak_indices_len; + size_t tweak_indices[3]; + int is_xonly[3]; + unsigned char aggnonce[66]; + size_t psig_indices_len; + size_t psig_indices[2]; + /* if valid case */ + unsigned char expected[64]; + /* if error case */ + int invalid_sig_idx; +}; + +struct musig_sig_agg_vector { + unsigned char pubkeys[4][33]; + unsigned char tweaks[3][32]; + unsigned char psigs[9][32]; + unsigned char msg[32]; + struct musig_sig_agg_case valid_case[4]; + struct musig_sig_agg_case error_case[1]; +}; + +static const struct musig_sig_agg_vector musig_sig_agg_vector = { + { + { 0x03, 0x93, 0x5F, 0x97, 0x2D, 0xA0, 0x13, 0xF8, 0x0A, 0xE0, 0x11, 0x89, 0x0F, 0xA8, 0x9B, 0x67, 0xA2, 0x7B, 0x7B, 0xE6, 0xCC, 0xB2, 0x4D, 0x32, 0x74, 0xD1, 0x8B, 0x2D, 0x40, 0x67, 0xF2, 0x61, 0xA9 }, + { 0x02, 0xD2, 0xDC, 0x6F, 0x5D, 0xF7, 0xC5, 0x6A, 0xCF, 0x38, 0xC7, 0xFA, 0x0A, 0xE7, 0xA7, 0x59, 0xAE, 0x30, 0xE1, 0x9B, 0x37, 0x35, 0x9D, 0xFD, 0xE0, 0x15, 0x87, 0x23, 0x24, 0xC7, 0xEF, 0x6E, 0x05 }, + { 0x03, 0xC7, 0xFB, 0x10, 0x1D, 0x97, 0xFF, 0x93, 0x0A, 0xCD, 0x0C, 0x67, 0x60, 0x85, 0x2E, 0xF6, 0x4E, 0x69, 0x08, 0x3D, 0xE0, 0xB0, 0x6A, 0xC6, 0x33, 0x57, 0x24, 0x75, 0x4B, 0xB4, 0xB0, 0x52, 0x2C }, + { 0x02, 0x35, 0x24, 0x33, 0xB2, 0x1E, 0x7E, 0x05, 0xD3, 0xB4, 0x52, 0xB8, 0x1C, 0xAE, 0x56, 0x6E, 0x06, 0xD2, 0xE0, 0x03, 0xEC, 0xE1, 0x6D, 0x10, 0x74, 0xAA, 0xBA, 0x42, 0x89, 0xE0, 0xE3, 0xD5, 0x81 } + }, + { + { 0xB5, 0x11, 0xDA, 0x49, 0x21, 0x82, 0xA9, 0x1B, 0x0F, 0xFB, 0x9A, 0x98, 0x02, 0x0D, 0x55, 0xF2, 0x60, 0xAE, 0x86, 0xD7, 0xEC, 0xBD, 0x03, 0x99, 0xC7, 0x38, 0x3D, 0x59, 0xA5, 0xF2, 0xAF, 0x7C }, + { 0xA8, 0x15, 0xFE, 0x04, 0x9E, 0xE3, 0xC5, 0xAA, 0xB6, 0x63, 0x10, 0x47, 0x7F, 0xBC, 0x8B, 0xCC, 0xCA, 0xC2, 0xF3, 0x39, 0x5F, 0x59, 0xF9, 0x21, 0xC3, 0x64, 0xAC, 0xD7, 0x8A, 0x2F, 0x48, 0xDC }, + { 0x75, 0x44, 0x8A, 0x87, 0x27, 0x4B, 0x05, 0x64, 0x68, 0xB9, 0x77, 0xBE, 0x06, 0xEB, 0x1E, 0x9F, 0x65, 0x75, 0x77, 0xB7, 0x32, 0x0B, 0x0A, 0x33, 0x76, 0xEA, 0x51, 0xFD, 0x42, 0x0D, 0x18, 0xA8 } + }, + { + { 0xB1, 0x5D, 0x2C, 0xD3, 0xC3, 0xD2, 0x2B, 0x04, 0xDA, 0xE4, 0x38, 0xCE, 0x65, 0x3F, 0x6B, 0x4E, 0xCF, 0x04, 0x2F, 0x42, 0xCF, 0xDE, 0xD7, 0xC4, 0x1B, 0x64, 0xAA, 0xF9, 0xB4, 0xAF, 0x53, 0xFB }, + { 0x61, 0x93, 0xD6, 0xAC, 0x61, 0xB3, 0x54, 0xE9, 0x10, 0x5B, 0xBD, 0xC8, 0x93, 0x7A, 0x34, 0x54, 0xA6, 0xD7, 0x05, 0xB6, 0xD5, 0x73, 0x22, 0xA5, 0xA4, 0x72, 0xA0, 0x2C, 0xE9, 0x9F, 0xCB, 0x64 }, + { 0x9A, 0x87, 0xD3, 0xB7, 0x9E, 0xC6, 0x72, 0x28, 0xCB, 0x97, 0x87, 0x8B, 0x76, 0x04, 0x9B, 0x15, 0xDB, 0xD0, 0x5B, 0x81, 0x58, 0xD1, 0x7B, 0x5B, 0x91, 0x14, 0xD3, 0xC2, 0x26, 0x88, 0x75, 0x05 }, + { 0x66, 0xF8, 0x2E, 0xA9, 0x09, 0x23, 0x68, 0x9B, 0x85, 0x5D, 0x36, 0xC6, 0xB7, 0xE0, 0x32, 0xFB, 0x99, 0x70, 0x30, 0x14, 0x81, 0xB9, 0x9E, 0x01, 0xCD, 0xB4, 0xD6, 0xAC, 0x7C, 0x34, 0x7A, 0x15 }, + { 0x4F, 0x5A, 0xEE, 0x41, 0x51, 0x08, 0x48, 0xA6, 0x44, 0x7D, 0xCD, 0x1B, 0xBC, 0x78, 0x45, 0x7E, 0xF6, 0x90, 0x24, 0x94, 0x4C, 0x87, 0xF4, 0x02, 0x50, 0xD3, 0xEF, 0x2C, 0x25, 0xD3, 0x3E, 0xFE }, + { 0xDD, 0xEF, 0x42, 0x7B, 0xBB, 0x84, 0x7C, 0xC0, 0x27, 0xBE, 0xFF, 0x4E, 0xDB, 0x01, 0x03, 0x81, 0x48, 0x91, 0x78, 0x32, 0x25, 0x3E, 0xBC, 0x35, 0x5F, 0xC3, 0x3F, 0x4A, 0x8E, 0x2F, 0xCC, 0xE4 }, + { 0x97, 0xB8, 0x90, 0xA2, 0x6C, 0x98, 0x1D, 0xA8, 0x10, 0x2D, 0x3B, 0xC2, 0x94, 0x15, 0x9D, 0x17, 0x1D, 0x72, 0x81, 0x0F, 0xDF, 0x7C, 0x6A, 0x69, 0x1D, 0xEF, 0x02, 0xF0, 0xF7, 0xAF, 0x3F, 0xDC }, + { 0x53, 0xFA, 0x9E, 0x08, 0xBA, 0x52, 0x43, 0xCB, 0xCB, 0x0D, 0x79, 0x7C, 0x5E, 0xE8, 0x3B, 0xC6, 0x72, 0x8E, 0x53, 0x9E, 0xB7, 0x6C, 0x2D, 0x0B, 0xF0, 0xF9, 0x71, 0xEE, 0x4E, 0x90, 0x99, 0x71 }, + { 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xBA, 0xAE, 0xDC, 0xE6, 0xAF, 0x48, 0xA0, 0x3B, 0xBF, 0xD2, 0x5E, 0x8C, 0xD0, 0x36, 0x41, 0x41 } + }, + { 0x59, 0x9C, 0x67, 0xEA, 0x41, 0x0D, 0x00, 0x5B, 0x9D, 0xA9, 0x08, 0x17, 0xCF, 0x03, 0xED, 0x3B, 0x1C, 0x86, 0x8E, 0x4D, 0xA4, 0xED, 0xF0, 0x0A, 0x58, 0x80, 0xB0, 0x08, 0x2C, 0x23, 0x78, 0x69 }, + { + { 2, { 0, 1 }, 0, { 0 }, { 0 }, { 0x03, 0x41, 0x43, 0x27, 0x22, 0xC5, 0xCD, 0x02, 0x68, 0xD8, 0x29, 0xC7, 0x02, 0xCF, 0x0D, 0x1C, 0xBC, 0xE5, 0x70, 0x33, 0xEE, 0xD2, 0x01, 0xFD, 0x33, 0x51, 0x91, 0x38, 0x52, 0x27, 0xC3, 0x21, 0x0C, 0x03, 0xD3, 0x77, 0xF2, 0xD2, 0x58, 0xB6, 0x4A, 0xAD, 0xC0, 0xE1, 0x6F, 0x26, 0x46, 0x23, 0x23, 0xD7, 0x01, 0xD2, 0x86, 0x04, 0x6A, 0x2E, 0xA9, 0x33, 0x65, 0x65, 0x6A, 0xFD, 0x98, 0x75, 0x98, 0x2B }, 2, { 0, 1 }, { 0x04, 0x1D, 0xA2, 0x22, 0x23, 0xCE, 0x65, 0xC9, 0x2C, 0x9A, 0x0D, 0x6C, 0x2C, 0xAC, 0x82, 0x8A, 0xAF, 0x1E, 0xEE, 0x56, 0x30, 0x4F, 0xEC, 0x37, 0x1D, 0xDF, 0x91, 0xEB, 0xB2, 0xB9, 0xEF, 0x09, 0x12, 0xF1, 0x03, 0x80, 0x25, 0x85, 0x7F, 0xED, 0xEB, 0x3F, 0xF6, 0x96, 0xF8, 0xB9, 0x9F, 0xA4, 0xBB, 0x2C, 0x58, 0x12, 0xF6, 0x09, 0x5A, 0x2E, 0x00, 0x04, 0xEC, 0x99, 0xCE, 0x18, 0xDE, 0x1E }, 0 }, + { 2, { 0, 2 }, 0, { 0 }, { 0 }, { 0x02, 0x24, 0xAF, 0xD3, 0x6C, 0x90, 0x20, 0x84, 0x05, 0x8B, 0x51, 0xB5, 0xD3, 0x66, 0x76, 0xBB, 0xA4, 0xDC, 0x97, 0xC7, 0x75, 0x87, 0x37, 0x68, 0xE5, 0x88, 0x22, 0xF8, 0x7F, 0xE4, 0x37, 0xD7, 0x92, 0x02, 0x8C, 0xB1, 0x59, 0x29, 0x09, 0x9E, 0xEE, 0x2F, 0x5D, 0xAE, 0x40, 0x4C, 0xD3, 0x93, 0x57, 0x59, 0x1B, 0xA3, 0x2E, 0x9A, 0xF4, 0xE1, 0x62, 0xB8, 0xD3, 0xE7, 0xCB, 0x5E, 0xFE, 0x31, 0xCB, 0x20 }, 2, { 2, 3 }, { 0x10, 0x69, 0xB6, 0x7E, 0xC3, 0xD2, 0xF3, 0xC7, 0xC0, 0x82, 0x91, 0xAC, 0xCB, 0x17, 0xA9, 0xC9, 0xB8, 0xF2, 0x81, 0x9A, 0x52, 0xEB, 0x5D, 0xF8, 0x72, 0x6E, 0x17, 0xE7, 0xD6, 0xB5, 0x2E, 0x9F, 0x01, 0x80, 0x02, 0x60, 0xA7, 0xE9, 0xDA, 0xC4, 0x50, 0xF4, 0xBE, 0x52, 0x2D, 0xE4, 0xCE, 0x12, 0xBA, 0x91, 0xAE, 0xAF, 0x2B, 0x42, 0x79, 0x21, 0x9E, 0xF7, 0x4B, 0xE1, 0xD2, 0x86, 0xAD, 0xD9 }, 0 }, + { 2, { 0, 2 }, 1, { 0 }, { 0 }, { 0x02, 0x08, 0xC5, 0xC4, 0x38, 0xC7, 0x10, 0xF4, 0xF9, 0x6A, 0x61, 0xE9, 0xFF, 0x3C, 0x37, 0x75, 0x88, 0x14, 0xB8, 0xC3, 0xAE, 0x12, 0xBF, 0xEA, 0x0E, 0xD2, 0xC8, 0x7F, 0xF6, 0x95, 0x4F, 0xF1, 0x86, 0x02, 0x0B, 0x18, 0x16, 0xEA, 0x10, 0x4B, 0x4F, 0xCA, 0x2D, 0x30, 0x4D, 0x73, 0x3E, 0x0E, 0x19, 0xCE, 0xAD, 0x51, 0x30, 0x3F, 0xF6, 0x42, 0x0B, 0xFD, 0x22, 0x23, 0x35, 0xCA, 0xA4, 0x02, 0x91, 0x6D }, 2, { 4, 5 }, { 0x5C, 0x55, 0x8E, 0x1D, 0xCA, 0xDE, 0x86, 0xDA, 0x0B, 0x2F, 0x02, 0x62, 0x6A, 0x51, 0x2E, 0x30, 0xA2, 0x2C, 0xF5, 0x25, 0x5C, 0xAE, 0xA7, 0xEE, 0x32, 0xC3, 0x8E, 0x9A, 0x71, 0xA0, 0xE9, 0x14, 0x8B, 0xA6, 0xC0, 0xE6, 0xEC, 0x76, 0x83, 0xB6, 0x42, 0x20, 0xF0, 0x29, 0x86, 0x96, 0xF1, 0xB8, 0x78, 0xCD, 0x47, 0xB1, 0x07, 0xB8, 0x1F, 0x71, 0x88, 0x81, 0x2D, 0x59, 0x39, 0x71, 0xE0, 0xCC }, 0 }, + { 2, { 0, 3 }, 3, { 0, 1, 2 }, { 1, 0, 1 }, { 0x02, 0xB5, 0xAD, 0x07, 0xAF, 0xCD, 0x99, 0xB6, 0xD9, 0x2C, 0xB4, 0x33, 0xFB, 0xD2, 0xA2, 0x8F, 0xDE, 0xB9, 0x8E, 0xAE, 0x2E, 0xB0, 0x9B, 0x60, 0x14, 0xEF, 0x0F, 0x81, 0x97, 0xCD, 0x58, 0x40, 0x33, 0x02, 0xE8, 0x61, 0x69, 0x10, 0xF9, 0x29, 0x3C, 0xF6, 0x92, 0xC4, 0x9F, 0x35, 0x1D, 0xB8, 0x6B, 0x25, 0xE3, 0x52, 0x90, 0x1F, 0x0E, 0x23, 0x7B, 0xAF, 0xDA, 0x11, 0xF1, 0xC1, 0xCE, 0xF2, 0x9F, 0xFD }, 2, { 6, 7 }, { 0x83, 0x9B, 0x08, 0x82, 0x0B, 0x68, 0x1D, 0xBA, 0x8D, 0xAF, 0x4C, 0xC7, 0xB1, 0x04, 0xE8, 0xF2, 0x63, 0x8F, 0x93, 0x88, 0xF8, 0xD7, 0xA5, 0x55, 0xDC, 0x17, 0xB6, 0xE6, 0x97, 0x1D, 0x74, 0x26, 0xCE, 0x07, 0xBF, 0x6A, 0xB0, 0x1F, 0x1D, 0xB5, 0x0E, 0x4E, 0x33, 0x71, 0x92, 0x95, 0xF4, 0x09, 0x45, 0x72, 0xB7, 0x98, 0x68, 0xE4, 0x40, 0xFB, 0x3D, 0xEF, 0xD3, 0xFA, 0xC1, 0xDB, 0x58, 0x9E }, 0 }, + }, + { + { 2, { 0, 3 }, 3, { 0, 1, 2 }, { 1, 0, 1 }, { 0x02, 0xB5, 0xAD, 0x07, 0xAF, 0xCD, 0x99, 0xB6, 0xD9, 0x2C, 0xB4, 0x33, 0xFB, 0xD2, 0xA2, 0x8F, 0xDE, 0xB9, 0x8E, 0xAE, 0x2E, 0xB0, 0x9B, 0x60, 0x14, 0xEF, 0x0F, 0x81, 0x97, 0xCD, 0x58, 0x40, 0x33, 0x02, 0xE8, 0x61, 0x69, 0x10, 0xF9, 0x29, 0x3C, 0xF6, 0x92, 0xC4, 0x9F, 0x35, 0x1D, 0xB8, 0x6B, 0x25, 0xE3, 0x52, 0x90, 0x1F, 0x0E, 0x23, 0x7B, 0xAF, 0xDA, 0x11, 0xF1, 0xC1, 0xCE, 0xF2, 0x9F, 0xFD }, 2, { 7, 8 }, { 0 }, 1 }, + }, +}; +enum { MUSIG_VECTORS_MAX_PUBKEYS = 7 }; diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/schnorrsig/bench_impl.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/schnorrsig/bench_impl.h new file mode 100644 index 00000000000..93a878ede3e --- /dev/null +++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/schnorrsig/bench_impl.h @@ -0,0 +1,104 @@ +/*********************************************************************** + * Copyright (c) 2018-2020 Andrew Poelstra, Jonas Nick * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_MODULE_SCHNORRSIG_BENCH_H +#define SECP256K1_MODULE_SCHNORRSIG_BENCH_H + +#include "../../../include/secp256k1_schnorrsig.h" + +#define MSGLEN 32 + +typedef struct { + secp256k1_context *ctx; + int n; + + const secp256k1_keypair **keypairs; + const unsigned char **pk; + const unsigned char **sigs; + const unsigned char **msgs; +} bench_schnorrsig_data; + +static void bench_schnorrsig_sign(void* arg, int iters) { + bench_schnorrsig_data *data = (bench_schnorrsig_data *)arg; + int i; + unsigned char msg[MSGLEN] = {0}; + unsigned char sig[64]; + + for (i = 0; i < iters; i++) { + msg[0] = i; + msg[1] = i >> 8; + CHECK(secp256k1_schnorrsig_sign_custom(data->ctx, sig, msg, MSGLEN, data->keypairs[i], NULL)); + } +} + +static void bench_schnorrsig_verify(void* arg, int iters) { + bench_schnorrsig_data *data = (bench_schnorrsig_data *)arg; + int i; + + for (i = 0; i < iters; i++) { + secp256k1_xonly_pubkey pk; + CHECK(secp256k1_xonly_pubkey_parse(data->ctx, &pk, data->pk[i]) == 1); + CHECK(secp256k1_schnorrsig_verify(data->ctx, data->sigs[i], data->msgs[i], MSGLEN, &pk)); + } +} + +static void run_schnorrsig_bench(int iters, int argc, char** argv) { + int i; + bench_schnorrsig_data data; + int d = argc == 1; + + data.ctx = secp256k1_context_create(SECP256K1_CONTEXT_NONE); + data.keypairs = (const secp256k1_keypair **)malloc(iters * sizeof(secp256k1_keypair *)); + data.pk = (const unsigned char **)malloc(iters * sizeof(unsigned char *)); + data.msgs = (const unsigned char **)malloc(iters * sizeof(unsigned char *)); + data.sigs = (const unsigned char **)malloc(iters * sizeof(unsigned char *)); + + CHECK(MSGLEN >= 4); + for (i = 0; i < iters; i++) { + unsigned char sk[32]; + unsigned char *msg = (unsigned char *)malloc(MSGLEN); + unsigned char *sig = (unsigned char *)malloc(64); + secp256k1_keypair *keypair = (secp256k1_keypair *)malloc(sizeof(*keypair)); + unsigned char *pk_char = (unsigned char *)malloc(32); + secp256k1_xonly_pubkey pk; + msg[0] = sk[0] = i; + msg[1] = sk[1] = i >> 8; + msg[2] = sk[2] = i >> 16; + msg[3] = sk[3] = i >> 24; + memset(&msg[4], 'm', MSGLEN - 4); + memset(&sk[4], 's', 28); + + data.keypairs[i] = keypair; + data.pk[i] = pk_char; + data.msgs[i] = msg; + data.sigs[i] = sig; + + CHECK(secp256k1_keypair_create(data.ctx, keypair, sk)); + CHECK(secp256k1_schnorrsig_sign_custom(data.ctx, sig, msg, MSGLEN, keypair, NULL)); + CHECK(secp256k1_keypair_xonly_pub(data.ctx, &pk, NULL, keypair)); + CHECK(secp256k1_xonly_pubkey_serialize(data.ctx, pk_char, &pk) == 1); + } + + if (d || have_flag(argc, argv, "schnorrsig") || have_flag(argc, argv, "sign") || have_flag(argc, argv, "schnorrsig_sign")) run_benchmark("schnorrsig_sign", bench_schnorrsig_sign, NULL, NULL, (void *) &data, 10, iters); + if (d || have_flag(argc, argv, "schnorrsig") || have_flag(argc, argv, "verify") || have_flag(argc, argv, "schnorrsig_verify")) run_benchmark("schnorrsig_verify", bench_schnorrsig_verify, NULL, NULL, (void *) &data, 10, iters); + + for (i = 0; i < iters; i++) { + free((void *)data.keypairs[i]); + free((void *)data.pk[i]); + free((void *)data.msgs[i]); + free((void *)data.sigs[i]); + } + + /* Casting to (void *) avoids a stupid warning in MSVC. */ + free((void *)data.keypairs); + free((void *)data.pk); + free((void *)data.msgs); + free((void *)data.sigs); + + secp256k1_context_destroy(data.ctx); +} + +#endif diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/schnorrsig/main_impl.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/schnorrsig/main_impl.h new file mode 100644 index 00000000000..2ed7be677fd --- /dev/null +++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/schnorrsig/main_impl.h @@ -0,0 +1,271 @@ +/*********************************************************************** + * Copyright (c) 2018-2020 Andrew Poelstra, Jonas Nick * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_MODULE_SCHNORRSIG_MAIN_H +#define SECP256K1_MODULE_SCHNORRSIG_MAIN_H + +#include "../../../include/secp256k1.h" +#include "../../../include/secp256k1_schnorrsig.h" +#include "../../hash.h" + +/* Initializes SHA256 with fixed midstate. This midstate was computed by applying + * SHA256 to SHA256("BIP0340/nonce")||SHA256("BIP0340/nonce"). */ +static void secp256k1_nonce_function_bip340_sha256_tagged(secp256k1_sha256 *sha) { + secp256k1_sha256_initialize(sha); + sha->s[0] = 0x46615b35ul; + sha->s[1] = 0xf4bfbff7ul; + sha->s[2] = 0x9f8dc671ul; + sha->s[3] = 0x83627ab3ul; + sha->s[4] = 0x60217180ul; + sha->s[5] = 0x57358661ul; + sha->s[6] = 0x21a29e54ul; + sha->s[7] = 0x68b07b4cul; + + sha->bytes = 64; +} + +/* Initializes SHA256 with fixed midstate. This midstate was computed by applying + * SHA256 to SHA256("BIP0340/aux")||SHA256("BIP0340/aux"). */ +static void secp256k1_nonce_function_bip340_sha256_tagged_aux(secp256k1_sha256 *sha) { + secp256k1_sha256_initialize(sha); + sha->s[0] = 0x24dd3219ul; + sha->s[1] = 0x4eba7e70ul; + sha->s[2] = 0xca0fabb9ul; + sha->s[3] = 0x0fa3166dul; + sha->s[4] = 0x3afbe4b1ul; + sha->s[5] = 0x4c44df97ul; + sha->s[6] = 0x4aac2739ul; + sha->s[7] = 0x249e850aul; + + sha->bytes = 64; +} + +/* algo argument for nonce_function_bip340 to derive the nonce exactly as stated in BIP-340 + * by using the correct tagged hash function. */ +static const unsigned char bip340_algo[] = {'B', 'I', 'P', '0', '3', '4', '0', '/', 'n', 'o', 'n', 'c', 'e'}; + +static const unsigned char schnorrsig_extraparams_magic[4] = SECP256K1_SCHNORRSIG_EXTRAPARAMS_MAGIC; + +static int nonce_function_bip340(unsigned char *nonce32, const unsigned char *msg, size_t msglen, const unsigned char *key32, const unsigned char *xonly_pk32, const unsigned char *algo, size_t algolen, void *data) { + secp256k1_sha256 sha; + unsigned char masked_key[32]; + int i; + + if (algo == NULL) { + return 0; + } + + if (data != NULL) { + secp256k1_nonce_function_bip340_sha256_tagged_aux(&sha); + secp256k1_sha256_write(&sha, data, 32); + secp256k1_sha256_finalize(&sha, masked_key); + for (i = 0; i < 32; i++) { + masked_key[i] ^= key32[i]; + } + } else { + /* Precomputed TaggedHash("BIP0340/aux", 0x0000...00); */ + static const unsigned char ZERO_MASK[32] = { + 84, 241, 105, 207, 201, 226, 229, 114, + 116, 128, 68, 31, 144, 186, 37, 196, + 136, 244, 97, 199, 11, 94, 165, 220, + 170, 247, 175, 105, 39, 10, 165, 20 + }; + for (i = 0; i < 32; i++) { + masked_key[i] = key32[i] ^ ZERO_MASK[i]; + } + } + + /* Tag the hash with algo which is important to avoid nonce reuse across + * algorithms. If this nonce function is used in BIP-340 signing as defined + * in the spec, an optimized tagging implementation is used. */ + if (algolen == sizeof(bip340_algo) + && secp256k1_memcmp_var(algo, bip340_algo, algolen) == 0) { + secp256k1_nonce_function_bip340_sha256_tagged(&sha); + } else { + secp256k1_sha256_initialize_tagged(&sha, algo, algolen); + } + + /* Hash masked-key||pk||msg using the tagged hash as per the spec */ + secp256k1_sha256_write(&sha, masked_key, 32); + secp256k1_sha256_write(&sha, xonly_pk32, 32); + secp256k1_sha256_write(&sha, msg, msglen); + secp256k1_sha256_finalize(&sha, nonce32); + secp256k1_sha256_clear(&sha); + secp256k1_memclear(masked_key, sizeof(masked_key)); + + return 1; +} + +const secp256k1_nonce_function_hardened secp256k1_nonce_function_bip340 = nonce_function_bip340; + +/* Initializes SHA256 with fixed midstate. This midstate was computed by applying + * SHA256 to SHA256("BIP0340/challenge")||SHA256("BIP0340/challenge"). */ +static void secp256k1_schnorrsig_sha256_tagged(secp256k1_sha256 *sha) { + secp256k1_sha256_initialize(sha); + sha->s[0] = 0x9cecba11ul; + sha->s[1] = 0x23925381ul; + sha->s[2] = 0x11679112ul; + sha->s[3] = 0xd1627e0ful; + sha->s[4] = 0x97c87550ul; + sha->s[5] = 0x003cc765ul; + sha->s[6] = 0x90f61164ul; + sha->s[7] = 0x33e9b66aul; + sha->bytes = 64; +} + +static void secp256k1_schnorrsig_challenge(secp256k1_scalar* e, const unsigned char *r32, const unsigned char *msg, size_t msglen, const unsigned char *pubkey32) +{ + unsigned char buf[32]; + secp256k1_sha256 sha; + + /* tagged hash(r.x, pk.x, msg) */ + secp256k1_schnorrsig_sha256_tagged(&sha); + secp256k1_sha256_write(&sha, r32, 32); + secp256k1_sha256_write(&sha, pubkey32, 32); + secp256k1_sha256_write(&sha, msg, msglen); + secp256k1_sha256_finalize(&sha, buf); + /* Set scalar e to the challenge hash modulo the curve order as per + * BIP340. */ + secp256k1_scalar_set_b32(e, buf, NULL); +} + +static int secp256k1_schnorrsig_sign_internal(const secp256k1_context* ctx, unsigned char *sig64, const unsigned char *msg, size_t msglen, const secp256k1_keypair *keypair, secp256k1_nonce_function_hardened noncefp, void *ndata) { + secp256k1_scalar sk; + secp256k1_scalar e; + secp256k1_scalar k; + secp256k1_gej rj; + secp256k1_ge pk; + secp256k1_ge r; + unsigned char buf[32] = { 0 }; + unsigned char pk_buf[32]; + unsigned char seckey[32]; + int ret = 1; + + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(secp256k1_ecmult_gen_context_is_built(&ctx->ecmult_gen_ctx)); + ARG_CHECK(sig64 != NULL); + ARG_CHECK(msg != NULL || msglen == 0); + ARG_CHECK(keypair != NULL); + + if (noncefp == NULL) { + noncefp = secp256k1_nonce_function_bip340; + } + + ret &= secp256k1_keypair_load(ctx, &sk, &pk, keypair); + /* Because we are signing for a x-only pubkey, the secret key is negated + * before signing if the point corresponding to the secret key does not + * have an even Y. */ + if (secp256k1_fe_is_odd(&pk.y)) { + secp256k1_scalar_negate(&sk, &sk); + } + + secp256k1_scalar_get_b32(seckey, &sk); + secp256k1_fe_get_b32(pk_buf, &pk.x); + ret &= !!noncefp(buf, msg, msglen, seckey, pk_buf, bip340_algo, sizeof(bip340_algo), ndata); + secp256k1_scalar_set_b32(&k, buf, NULL); + ret &= !secp256k1_scalar_is_zero(&k); + secp256k1_scalar_cmov(&k, &secp256k1_scalar_one, !ret); + + secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &rj, &k); + secp256k1_ge_set_gej(&r, &rj); + + /* We declassify r to allow using it as a branch point. This is fine + * because r is not a secret. */ + secp256k1_declassify(ctx, &r, sizeof(r)); + secp256k1_fe_normalize_var(&r.y); + if (secp256k1_fe_is_odd(&r.y)) { + secp256k1_scalar_negate(&k, &k); + } + secp256k1_fe_normalize_var(&r.x); + secp256k1_fe_get_b32(&sig64[0], &r.x); + + secp256k1_schnorrsig_challenge(&e, &sig64[0], msg, msglen, pk_buf); + secp256k1_scalar_mul(&e, &e, &sk); + secp256k1_scalar_add(&e, &e, &k); + secp256k1_scalar_get_b32(&sig64[32], &e); + + secp256k1_memczero(sig64, 64, !ret); + secp256k1_scalar_clear(&k); + secp256k1_scalar_clear(&sk); + secp256k1_memclear(seckey, sizeof(seckey)); + secp256k1_gej_clear(&rj); + + return ret; +} + +int secp256k1_schnorrsig_sign32(const secp256k1_context* ctx, unsigned char *sig64, const unsigned char *msg32, const secp256k1_keypair *keypair, const unsigned char *aux_rand32) { + /* We cast away const from the passed aux_rand32 argument since we know the default nonce function does not modify it. */ + return secp256k1_schnorrsig_sign_internal(ctx, sig64, msg32, 32, keypair, secp256k1_nonce_function_bip340, (unsigned char*)aux_rand32); +} + +int secp256k1_schnorrsig_sign(const secp256k1_context* ctx, unsigned char *sig64, const unsigned char *msg32, const secp256k1_keypair *keypair, const unsigned char *aux_rand32) { + return secp256k1_schnorrsig_sign32(ctx, sig64, msg32, keypair, aux_rand32); +} + +int secp256k1_schnorrsig_sign_custom(const secp256k1_context* ctx, unsigned char *sig64, const unsigned char *msg, size_t msglen, const secp256k1_keypair *keypair, secp256k1_schnorrsig_extraparams *extraparams) { + secp256k1_nonce_function_hardened noncefp = NULL; + void *ndata = NULL; + VERIFY_CHECK(ctx != NULL); + + if (extraparams != NULL) { + ARG_CHECK(secp256k1_memcmp_var(extraparams->magic, + schnorrsig_extraparams_magic, + sizeof(extraparams->magic)) == 0); + noncefp = extraparams->noncefp; + ndata = extraparams->ndata; + } + return secp256k1_schnorrsig_sign_internal(ctx, sig64, msg, msglen, keypair, noncefp, ndata); +} + +int secp256k1_schnorrsig_verify(const secp256k1_context* ctx, const unsigned char *sig64, const unsigned char *msg, size_t msglen, const secp256k1_xonly_pubkey *pubkey) { + secp256k1_scalar s; + secp256k1_scalar e; + secp256k1_gej rj; + secp256k1_ge pk; + secp256k1_gej pkj; + secp256k1_fe rx; + secp256k1_ge r; + unsigned char buf[32]; + int overflow; + + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(sig64 != NULL); + ARG_CHECK(msg != NULL || msglen == 0); + ARG_CHECK(pubkey != NULL); + + if (!secp256k1_fe_set_b32_limit(&rx, &sig64[0])) { + return 0; + } + + secp256k1_scalar_set_b32(&s, &sig64[32], &overflow); + if (overflow) { + return 0; + } + + if (!secp256k1_xonly_pubkey_load(ctx, &pk, pubkey)) { + return 0; + } + + /* Compute e. */ + secp256k1_fe_get_b32(buf, &pk.x); + secp256k1_schnorrsig_challenge(&e, &sig64[0], msg, msglen, buf); + + /* Compute rj = s*G + (-e)*pkj */ + secp256k1_scalar_negate(&e, &e); + secp256k1_gej_set_ge(&pkj, &pk); + secp256k1_ecmult(&rj, &pkj, &e, &s); + + secp256k1_ge_set_gej_var(&r, &rj); + if (secp256k1_ge_is_infinity(&r)) { + return 0; + } + + secp256k1_fe_normalize_var(&r.y); + return !secp256k1_fe_is_odd(&r.y) && + secp256k1_fe_equal(&rx, &r.x); +} + +#endif diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/schnorrsig/tests_exhaustive_impl.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/schnorrsig/tests_exhaustive_impl.h new file mode 100644 index 00000000000..601b54975d0 --- /dev/null +++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/schnorrsig/tests_exhaustive_impl.h @@ -0,0 +1,214 @@ +/*********************************************************************** + * Copyright (c) 2020 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_MODULE_SCHNORRSIG_TESTS_EXHAUSTIVE_H +#define SECP256K1_MODULE_SCHNORRSIG_TESTS_EXHAUSTIVE_H + +#include "../../../include/secp256k1_schnorrsig.h" +#include "main_impl.h" + +static const unsigned char invalid_pubkey_bytes[][32] = { + /* 0 */ + { + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 + }, + /* 2 */ + { + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 + }, + /* order */ + { + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + ((EXHAUSTIVE_TEST_ORDER + 0UL) >> 24) & 0xFF, + ((EXHAUSTIVE_TEST_ORDER + 0UL) >> 16) & 0xFF, + ((EXHAUSTIVE_TEST_ORDER + 0UL) >> 8) & 0xFF, + (EXHAUSTIVE_TEST_ORDER + 0UL) & 0xFF + }, + /* order + 1 */ + { + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + ((EXHAUSTIVE_TEST_ORDER + 1UL) >> 24) & 0xFF, + ((EXHAUSTIVE_TEST_ORDER + 1UL) >> 16) & 0xFF, + ((EXHAUSTIVE_TEST_ORDER + 1UL) >> 8) & 0xFF, + (EXHAUSTIVE_TEST_ORDER + 1UL) & 0xFF + }, + /* field size */ + { + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFC, 0x2F + }, + /* field size + 1 (note that 1 is legal) */ + { + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFC, 0x30 + }, + /* 2^256 - 1 */ + { + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF + } +}; + +#define NUM_INVALID_KEYS (sizeof(invalid_pubkey_bytes) / sizeof(invalid_pubkey_bytes[0])) + +static int secp256k1_hardened_nonce_function_smallint(unsigned char *nonce32, const unsigned char *msg, + size_t msglen, + const unsigned char *key32, const unsigned char *xonly_pk32, + const unsigned char *algo, size_t algolen, + void* data) { + secp256k1_scalar s; + int *idata = data; + (void)msg; + (void)msglen; + (void)key32; + (void)xonly_pk32; + (void)algo; + (void)algolen; + secp256k1_scalar_set_int(&s, *idata); + secp256k1_scalar_get_b32(nonce32, &s); + return 1; +} + +static void test_exhaustive_schnorrsig_verify(const secp256k1_context *ctx, const secp256k1_xonly_pubkey* pubkeys, unsigned char (*xonly_pubkey_bytes)[32], const int* parities) { + int d; + uint64_t iter = 0; + /* Iterate over the possible public keys to verify against (through their corresponding DL d). */ + for (d = 1; d <= EXHAUSTIVE_TEST_ORDER / 2; ++d) { + int actual_d; + unsigned k; + unsigned char pk32[32]; + memcpy(pk32, xonly_pubkey_bytes[d - 1], 32); + actual_d = parities[d - 1] ? EXHAUSTIVE_TEST_ORDER - d : d; + /* Iterate over the possible valid first 32 bytes in the signature, through their corresponding DL k. + Values above EXHAUSTIVE_TEST_ORDER/2 refer to the entries in invalid_pubkey_bytes. */ + for (k = 1; k <= EXHAUSTIVE_TEST_ORDER / 2 + NUM_INVALID_KEYS; ++k) { + unsigned char sig64[64]; + int actual_k = -1; + int e_done[EXHAUSTIVE_TEST_ORDER] = {0}; + int e_count_done = 0; + if (skip_section(&iter)) continue; + if (k <= EXHAUSTIVE_TEST_ORDER / 2) { + memcpy(sig64, xonly_pubkey_bytes[k - 1], 32); + actual_k = parities[k - 1] ? EXHAUSTIVE_TEST_ORDER - k : k; + } else { + memcpy(sig64, invalid_pubkey_bytes[k - 1 - EXHAUSTIVE_TEST_ORDER / 2], 32); + } + /* Randomly generate messages until all challenges have been hit. */ + while (e_count_done < EXHAUSTIVE_TEST_ORDER) { + secp256k1_scalar e; + unsigned char msg32[32]; + testrand256(msg32); + secp256k1_schnorrsig_challenge(&e, sig64, msg32, sizeof(msg32), pk32); + /* Only do work if we hit a challenge we haven't tried before. */ + if (!e_done[e]) { + /* Iterate over the possible valid last 32 bytes in the signature. + 0..order=that s value; order+1=random bytes */ + int count_valid = 0; + unsigned int s; + for (s = 0; s <= EXHAUSTIVE_TEST_ORDER + 1; ++s) { + int expect_valid, valid; + if (s <= EXHAUSTIVE_TEST_ORDER) { + memset(sig64 + 32, 0, 32); + secp256k1_write_be32(sig64 + 60, s); + expect_valid = actual_k != -1 && s != EXHAUSTIVE_TEST_ORDER && + (s == (actual_k + actual_d * e) % EXHAUSTIVE_TEST_ORDER); + } else { + testrand256(sig64 + 32); + expect_valid = 0; + } + valid = secp256k1_schnorrsig_verify(ctx, sig64, msg32, sizeof(msg32), &pubkeys[d - 1]); + CHECK(valid == expect_valid); + count_valid += valid; + } + /* Exactly one s value must verify, unless R is illegal. */ + CHECK(count_valid == (actual_k != -1)); + /* Don't retry other messages that result in the same challenge. */ + e_done[e] = 1; + ++e_count_done; + } + } + } + } +} + +static void test_exhaustive_schnorrsig_sign(const secp256k1_context *ctx, unsigned char (*xonly_pubkey_bytes)[32], const secp256k1_keypair* keypairs, const int* parities) { + int d, k; + uint64_t iter = 0; + secp256k1_schnorrsig_extraparams extraparams = SECP256K1_SCHNORRSIG_EXTRAPARAMS_INIT; + + /* Loop over keys. */ + for (d = 1; d < EXHAUSTIVE_TEST_ORDER; ++d) { + int actual_d = d; + if (parities[d - 1]) actual_d = EXHAUSTIVE_TEST_ORDER - d; + /* Loop over nonces. */ + for (k = 1; k < EXHAUSTIVE_TEST_ORDER; ++k) { + int e_done[EXHAUSTIVE_TEST_ORDER] = {0}; + int e_count_done = 0; + unsigned char msg32[32]; + unsigned char sig64[64]; + int actual_k = k; + if (skip_section(&iter)) continue; + extraparams.noncefp = secp256k1_hardened_nonce_function_smallint; + extraparams.ndata = &k; + if (parities[k - 1]) actual_k = EXHAUSTIVE_TEST_ORDER - k; + /* Generate random messages until all challenges have been tried. */ + while (e_count_done < EXHAUSTIVE_TEST_ORDER) { + secp256k1_scalar e; + testrand256(msg32); + secp256k1_schnorrsig_challenge(&e, xonly_pubkey_bytes[k - 1], msg32, sizeof(msg32), xonly_pubkey_bytes[d - 1]); + /* Only do work if we hit a challenge we haven't tried before. */ + if (!e_done[e]) { + secp256k1_scalar expected_s = (actual_k + e * actual_d) % EXHAUSTIVE_TEST_ORDER; + unsigned char expected_s_bytes[32]; + secp256k1_scalar_get_b32(expected_s_bytes, &expected_s); + /* Invoke the real function to construct a signature. */ + CHECK(secp256k1_schnorrsig_sign_custom(ctx, sig64, msg32, sizeof(msg32), &keypairs[d - 1], &extraparams)); + /* The first 32 bytes must match the xonly pubkey for the specified k. */ + CHECK(secp256k1_memcmp_var(sig64, xonly_pubkey_bytes[k - 1], 32) == 0); + /* The last 32 bytes must match the expected s value. */ + CHECK(secp256k1_memcmp_var(sig64 + 32, expected_s_bytes, 32) == 0); + /* Don't retry other messages that result in the same challenge. */ + e_done[e] = 1; + ++e_count_done; + } + } + } + } +} + +static void test_exhaustive_schnorrsig(const secp256k1_context *ctx) { + secp256k1_keypair keypair[EXHAUSTIVE_TEST_ORDER - 1]; + secp256k1_xonly_pubkey xonly_pubkey[EXHAUSTIVE_TEST_ORDER - 1]; + int parity[EXHAUSTIVE_TEST_ORDER - 1]; + unsigned char xonly_pubkey_bytes[EXHAUSTIVE_TEST_ORDER - 1][32]; + unsigned i; + + /* Verify that all invalid_pubkey_bytes are actually invalid. */ + for (i = 0; i < NUM_INVALID_KEYS; ++i) { + secp256k1_xonly_pubkey pk; + CHECK(!secp256k1_xonly_pubkey_parse(ctx, &pk, invalid_pubkey_bytes[i])); + } + + /* Construct keypairs and xonly-pubkeys for the entire group. */ + for (i = 1; i < EXHAUSTIVE_TEST_ORDER; ++i) { + secp256k1_scalar scalar_i; + unsigned char buf[32]; + secp256k1_scalar_set_int(&scalar_i, i); + secp256k1_scalar_get_b32(buf, &scalar_i); + CHECK(secp256k1_keypair_create(ctx, &keypair[i - 1], buf)); + CHECK(secp256k1_keypair_xonly_pub(ctx, &xonly_pubkey[i - 1], &parity[i - 1], &keypair[i - 1])); + CHECK(secp256k1_xonly_pubkey_serialize(ctx, xonly_pubkey_bytes[i - 1], &xonly_pubkey[i - 1])); + } + + test_exhaustive_schnorrsig_sign(ctx, xonly_pubkey_bytes, keypair, parity); + test_exhaustive_schnorrsig_verify(ctx, xonly_pubkey, xonly_pubkey_bytes, parity); +} + +#endif diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/schnorrsig/tests_impl.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/schnorrsig/tests_impl.h new file mode 100644 index 00000000000..2d716a01f89 --- /dev/null +++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/modules/schnorrsig/tests_impl.h @@ -0,0 +1,982 @@ +/*********************************************************************** + * Copyright (c) 2018-2020 Andrew Poelstra, Jonas Nick * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_MODULE_SCHNORRSIG_TESTS_H +#define SECP256K1_MODULE_SCHNORRSIG_TESTS_H + +#include "../../../include/secp256k1_schnorrsig.h" + +/* Checks that a bit flip in the n_flip-th argument (that has n_bytes many + * bytes) changes the hash function + */ +static void nonce_function_bip340_bitflip(unsigned char **args, size_t n_flip, size_t n_bytes, size_t msglen, size_t algolen) { + unsigned char nonces[2][32]; + CHECK(nonce_function_bip340(nonces[0], args[0], msglen, args[1], args[2], args[3], algolen, args[4]) == 1); + testrand_flip(args[n_flip], n_bytes); + CHECK(nonce_function_bip340(nonces[1], args[0], msglen, args[1], args[2], args[3], algolen, args[4]) == 1); + CHECK(secp256k1_memcmp_var(nonces[0], nonces[1], 32) != 0); +} + +static void run_nonce_function_bip340_tests(void) { + unsigned char tag[] = {'B', 'I', 'P', '0', '3', '4', '0', '/', 'n', 'o', 'n', 'c', 'e'}; + unsigned char aux_tag[] = {'B', 'I', 'P', '0', '3', '4', '0', '/', 'a', 'u', 'x'}; + unsigned char algo[] = {'B', 'I', 'P', '0', '3', '4', '0', '/', 'n', 'o', 'n', 'c', 'e'}; + size_t algolen = sizeof(algo); + secp256k1_sha256 sha; + secp256k1_sha256 sha_optimized; + unsigned char nonce[32], nonce_z[32]; + unsigned char msg[32]; + size_t msglen = sizeof(msg); + unsigned char key[32]; + unsigned char pk[32]; + unsigned char aux_rand[32]; + unsigned char *args[5]; + int i; + + /* Check that hash initialized by + * secp256k1_nonce_function_bip340_sha256_tagged has the expected + * state. */ + secp256k1_sha256_initialize_tagged(&sha, tag, sizeof(tag)); + secp256k1_nonce_function_bip340_sha256_tagged(&sha_optimized); + test_sha256_eq(&sha, &sha_optimized); + + /* Check that hash initialized by + * secp256k1_nonce_function_bip340_sha256_tagged_aux has the expected + * state. */ + secp256k1_sha256_initialize_tagged(&sha, aux_tag, sizeof(aux_tag)); + secp256k1_nonce_function_bip340_sha256_tagged_aux(&sha_optimized); + test_sha256_eq(&sha, &sha_optimized); + + testrand256(msg); + testrand256(key); + testrand256(pk); + testrand256(aux_rand); + + /* Check that a bitflip in an argument results in different nonces. */ + args[0] = msg; + args[1] = key; + args[2] = pk; + args[3] = algo; + args[4] = aux_rand; + for (i = 0; i < COUNT; i++) { + nonce_function_bip340_bitflip(args, 0, 32, msglen, algolen); + nonce_function_bip340_bitflip(args, 1, 32, msglen, algolen); + nonce_function_bip340_bitflip(args, 2, 32, msglen, algolen); + /* Flip algo special case "BIP0340/nonce" */ + nonce_function_bip340_bitflip(args, 3, algolen, msglen, algolen); + /* Flip algo again */ + nonce_function_bip340_bitflip(args, 3, algolen, msglen, algolen); + nonce_function_bip340_bitflip(args, 4, 32, msglen, algolen); + } + + /* NULL algo is disallowed */ + CHECK(nonce_function_bip340(nonce, msg, msglen, key, pk, NULL, 0, NULL) == 0); + CHECK(nonce_function_bip340(nonce, msg, msglen, key, pk, algo, algolen, NULL) == 1); + /* Other algo is fine */ + testrand_bytes_test(algo, algolen); + CHECK(nonce_function_bip340(nonce, msg, msglen, key, pk, algo, algolen, NULL) == 1); + + for (i = 0; i < COUNT; i++) { + unsigned char nonce2[32]; + uint32_t offset = testrand_int(msglen - 1); + size_t msglen_tmp = (msglen + offset) % msglen; + size_t algolen_tmp; + + /* Different msglen gives different nonce */ + CHECK(nonce_function_bip340(nonce2, msg, msglen_tmp, key, pk, algo, algolen, NULL) == 1); + CHECK(secp256k1_memcmp_var(nonce, nonce2, 32) != 0); + + /* Different algolen gives different nonce */ + offset = testrand_int(algolen - 1); + algolen_tmp = (algolen + offset) % algolen; + CHECK(nonce_function_bip340(nonce2, msg, msglen, key, pk, algo, algolen_tmp, NULL) == 1); + CHECK(secp256k1_memcmp_var(nonce, nonce2, 32) != 0); + } + + /* NULL aux_rand argument is allowed, and identical to passing all zero aux_rand. */ + memset(aux_rand, 0, 32); + CHECK(nonce_function_bip340(nonce_z, msg, msglen, key, pk, algo, algolen, &aux_rand) == 1); + CHECK(nonce_function_bip340(nonce, msg, msglen, key, pk, algo, algolen, NULL) == 1); + CHECK(secp256k1_memcmp_var(nonce_z, nonce, 32) == 0); +} + +static void test_schnorrsig_api(void) { + unsigned char sk1[32]; + unsigned char sk2[32]; + unsigned char sk3[32]; + unsigned char msg[32]; + secp256k1_keypair keypairs[3]; + secp256k1_keypair invalid_keypair = {{ 0 }}; + secp256k1_xonly_pubkey pk[3]; + secp256k1_xonly_pubkey zero_pk; + unsigned char sig[64]; + secp256k1_schnorrsig_extraparams extraparams = SECP256K1_SCHNORRSIG_EXTRAPARAMS_INIT; + secp256k1_schnorrsig_extraparams invalid_extraparams = {{ 0 }, NULL, NULL}; + + testrand256(sk1); + testrand256(sk2); + testrand256(sk3); + testrand256(msg); + CHECK(secp256k1_keypair_create(CTX, &keypairs[0], sk1) == 1); + CHECK(secp256k1_keypair_create(CTX, &keypairs[1], sk2) == 1); + CHECK(secp256k1_keypair_create(CTX, &keypairs[2], sk3) == 1); + CHECK(secp256k1_keypair_xonly_pub(CTX, &pk[0], NULL, &keypairs[0]) == 1); + CHECK(secp256k1_keypair_xonly_pub(CTX, &pk[1], NULL, &keypairs[1]) == 1); + CHECK(secp256k1_keypair_xonly_pub(CTX, &pk[2], NULL, &keypairs[2]) == 1); + memset(&zero_pk, 0, sizeof(zero_pk)); + + /** main test body **/ + CHECK(secp256k1_schnorrsig_sign32(CTX, sig, msg, &keypairs[0], NULL) == 1); + CHECK_ILLEGAL(CTX, secp256k1_schnorrsig_sign32(CTX, NULL, msg, &keypairs[0], NULL)); + CHECK_ILLEGAL(CTX, secp256k1_schnorrsig_sign32(CTX, sig, NULL, &keypairs[0], NULL)); + CHECK_ILLEGAL(CTX, secp256k1_schnorrsig_sign32(CTX, sig, msg, NULL, NULL)); + CHECK_ILLEGAL(CTX, secp256k1_schnorrsig_sign32(CTX, sig, msg, &invalid_keypair, NULL)); + CHECK_ILLEGAL(STATIC_CTX, secp256k1_schnorrsig_sign32(STATIC_CTX, sig, msg, &keypairs[0], NULL)); + + CHECK(secp256k1_schnorrsig_sign_custom(CTX, sig, msg, sizeof(msg), &keypairs[0], &extraparams) == 1); + CHECK_ILLEGAL(CTX, secp256k1_schnorrsig_sign_custom(CTX, NULL, msg, sizeof(msg), &keypairs[0], &extraparams)); + CHECK_ILLEGAL(CTX, secp256k1_schnorrsig_sign_custom(CTX, sig, NULL, sizeof(msg), &keypairs[0], &extraparams)); + CHECK(secp256k1_schnorrsig_sign_custom(CTX, sig, NULL, 0, &keypairs[0], &extraparams) == 1); + CHECK_ILLEGAL(CTX, secp256k1_schnorrsig_sign_custom(CTX, sig, msg, sizeof(msg), NULL, &extraparams)); + CHECK_ILLEGAL(CTX, secp256k1_schnorrsig_sign_custom(CTX, sig, msg, sizeof(msg), &invalid_keypair, &extraparams)); + CHECK(secp256k1_schnorrsig_sign_custom(CTX, sig, msg, sizeof(msg), &keypairs[0], NULL) == 1); + CHECK_ILLEGAL(CTX, secp256k1_schnorrsig_sign_custom(CTX, sig, msg, sizeof(msg), &keypairs[0], &invalid_extraparams)); + CHECK_ILLEGAL(STATIC_CTX, secp256k1_schnorrsig_sign_custom(STATIC_CTX, sig, msg, sizeof(msg), &keypairs[0], &extraparams)); + + CHECK(secp256k1_schnorrsig_sign32(CTX, sig, msg, &keypairs[0], NULL) == 1); + CHECK(secp256k1_schnorrsig_verify(CTX, sig, msg, sizeof(msg), &pk[0]) == 1); + CHECK_ILLEGAL(CTX, secp256k1_schnorrsig_verify(CTX, NULL, msg, sizeof(msg), &pk[0])); + CHECK_ILLEGAL(CTX, secp256k1_schnorrsig_verify(CTX, sig, NULL, sizeof(msg), &pk[0])); + CHECK(secp256k1_schnorrsig_verify(CTX, sig, NULL, 0, &pk[0]) == 0); + CHECK_ILLEGAL(CTX, secp256k1_schnorrsig_verify(CTX, sig, msg, sizeof(msg), NULL)); + CHECK_ILLEGAL(CTX, secp256k1_schnorrsig_verify(CTX, sig, msg, sizeof(msg), &zero_pk)); +} + +/* Checks that hash initialized by secp256k1_schnorrsig_sha256_tagged has the + * expected state. */ +static void test_schnorrsig_sha256_tagged(void) { + unsigned char tag[] = {'B', 'I', 'P', '0', '3', '4', '0', '/', 'c', 'h', 'a', 'l', 'l', 'e', 'n', 'g', 'e'}; + secp256k1_sha256 sha; + secp256k1_sha256 sha_optimized; + + secp256k1_sha256_initialize_tagged(&sha, (unsigned char *) tag, sizeof(tag)); + secp256k1_schnorrsig_sha256_tagged(&sha_optimized); + test_sha256_eq(&sha, &sha_optimized); +} + +/* Helper function for schnorrsig_bip_vectors + * Signs the message and checks that it's the same as expected_sig. */ +static void test_schnorrsig_bip_vectors_check_signing(const unsigned char *sk, const unsigned char *pk_serialized, const unsigned char *aux_rand, const unsigned char *msg, size_t msglen, const unsigned char *expected_sig) { + unsigned char sig[64]; + secp256k1_keypair keypair; + secp256k1_xonly_pubkey pk, pk_expected; + + secp256k1_schnorrsig_extraparams extraparams = SECP256K1_SCHNORRSIG_EXTRAPARAMS_INIT; + extraparams.ndata = (unsigned char*)aux_rand; + + CHECK(secp256k1_keypair_create(CTX, &keypair, sk)); + CHECK(secp256k1_schnorrsig_sign_custom(CTX, sig, msg, msglen, &keypair, &extraparams)); + CHECK(secp256k1_memcmp_var(sig, expected_sig, 64) == 0); + if (msglen == 32) { + memset(sig, 0, 64); + CHECK(secp256k1_schnorrsig_sign32(CTX, sig, msg, &keypair, aux_rand)); + CHECK(secp256k1_memcmp_var(sig, expected_sig, 64) == 0); + } + + CHECK(secp256k1_xonly_pubkey_parse(CTX, &pk_expected, pk_serialized)); + CHECK(secp256k1_keypair_xonly_pub(CTX, &pk, NULL, &keypair)); + CHECK(secp256k1_memcmp_var(&pk, &pk_expected, sizeof(pk)) == 0); + CHECK(secp256k1_schnorrsig_verify(CTX, sig, msg, msglen, &pk)); +} + +/* Helper function for schnorrsig_bip_vectors + * Checks that both verify and verify_batch (TODO) return the same value as expected. */ +static void test_schnorrsig_bip_vectors_check_verify(const unsigned char *pk_serialized, const unsigned char *msg, size_t msglen, const unsigned char *sig, int expected) { + secp256k1_xonly_pubkey pk; + + CHECK(secp256k1_xonly_pubkey_parse(CTX, &pk, pk_serialized)); + CHECK(expected == secp256k1_schnorrsig_verify(CTX, sig, msg, msglen, &pk)); +} + +/* Test vectors according to BIP-340 ("Schnorr Signatures for secp256k1"). See + * https://github.com/bitcoin/bips/blob/master/bip-0340/test-vectors.csv. */ +static void test_schnorrsig_bip_vectors(void) { + { + /* Test vector 0 */ + const unsigned char sk[32] = { + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x03 + }; + const unsigned char pk[32] = { + 0xF9, 0x30, 0x8A, 0x01, 0x92, 0x58, 0xC3, 0x10, + 0x49, 0x34, 0x4F, 0x85, 0xF8, 0x9D, 0x52, 0x29, + 0xB5, 0x31, 0xC8, 0x45, 0x83, 0x6F, 0x99, 0xB0, + 0x86, 0x01, 0xF1, 0x13, 0xBC, 0xE0, 0x36, 0xF9 + }; + const unsigned char aux_rand[32] = { + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 + }; + const unsigned char msg[32] = { + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 + }; + const unsigned char sig[64] = { + 0xE9, 0x07, 0x83, 0x1F, 0x80, 0x84, 0x8D, 0x10, + 0x69, 0xA5, 0x37, 0x1B, 0x40, 0x24, 0x10, 0x36, + 0x4B, 0xDF, 0x1C, 0x5F, 0x83, 0x07, 0xB0, 0x08, + 0x4C, 0x55, 0xF1, 0xCE, 0x2D, 0xCA, 0x82, 0x15, + 0x25, 0xF6, 0x6A, 0x4A, 0x85, 0xEA, 0x8B, 0x71, + 0xE4, 0x82, 0xA7, 0x4F, 0x38, 0x2D, 0x2C, 0xE5, + 0xEB, 0xEE, 0xE8, 0xFD, 0xB2, 0x17, 0x2F, 0x47, + 0x7D, 0xF4, 0x90, 0x0D, 0x31, 0x05, 0x36, 0xC0 + }; + test_schnorrsig_bip_vectors_check_signing(sk, pk, aux_rand, msg, sizeof(msg), sig); + test_schnorrsig_bip_vectors_check_verify(pk, msg, sizeof(msg), sig, 1); + } + { + /* Test vector 1 */ + const unsigned char sk[32] = { + 0xB7, 0xE1, 0x51, 0x62, 0x8A, 0xED, 0x2A, 0x6A, + 0xBF, 0x71, 0x58, 0x80, 0x9C, 0xF4, 0xF3, 0xC7, + 0x62, 0xE7, 0x16, 0x0F, 0x38, 0xB4, 0xDA, 0x56, + 0xA7, 0x84, 0xD9, 0x04, 0x51, 0x90, 0xCF, 0xEF + }; + const unsigned char pk[32] = { + 0xDF, 0xF1, 0xD7, 0x7F, 0x2A, 0x67, 0x1C, 0x5F, + 0x36, 0x18, 0x37, 0x26, 0xDB, 0x23, 0x41, 0xBE, + 0x58, 0xFE, 0xAE, 0x1D, 0xA2, 0xDE, 0xCE, 0xD8, + 0x43, 0x24, 0x0F, 0x7B, 0x50, 0x2B, 0xA6, 0x59 + }; + const unsigned char aux_rand[32] = { + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01 + }; + const unsigned char msg[32] = { + 0x24, 0x3F, 0x6A, 0x88, 0x85, 0xA3, 0x08, 0xD3, + 0x13, 0x19, 0x8A, 0x2E, 0x03, 0x70, 0x73, 0x44, + 0xA4, 0x09, 0x38, 0x22, 0x29, 0x9F, 0x31, 0xD0, + 0x08, 0x2E, 0xFA, 0x98, 0xEC, 0x4E, 0x6C, 0x89 + }; + const unsigned char sig[64] = { + 0x68, 0x96, 0xBD, 0x60, 0xEE, 0xAE, 0x29, 0x6D, + 0xB4, 0x8A, 0x22, 0x9F, 0xF7, 0x1D, 0xFE, 0x07, + 0x1B, 0xDE, 0x41, 0x3E, 0x6D, 0x43, 0xF9, 0x17, + 0xDC, 0x8D, 0xCF, 0x8C, 0x78, 0xDE, 0x33, 0x41, + 0x89, 0x06, 0xD1, 0x1A, 0xC9, 0x76, 0xAB, 0xCC, + 0xB2, 0x0B, 0x09, 0x12, 0x92, 0xBF, 0xF4, 0xEA, + 0x89, 0x7E, 0xFC, 0xB6, 0x39, 0xEA, 0x87, 0x1C, + 0xFA, 0x95, 0xF6, 0xDE, 0x33, 0x9E, 0x4B, 0x0A + }; + test_schnorrsig_bip_vectors_check_signing(sk, pk, aux_rand, msg, sizeof(msg), sig); + test_schnorrsig_bip_vectors_check_verify(pk, msg, sizeof(msg), sig, 1); + } + { + /* Test vector 2 */ + const unsigned char sk[32] = { + 0xC9, 0x0F, 0xDA, 0xA2, 0x21, 0x68, 0xC2, 0x34, + 0xC4, 0xC6, 0x62, 0x8B, 0x80, 0xDC, 0x1C, 0xD1, + 0x29, 0x02, 0x4E, 0x08, 0x8A, 0x67, 0xCC, 0x74, + 0x02, 0x0B, 0xBE, 0xA6, 0x3B, 0x14, 0xE5, 0xC9 + }; + const unsigned char pk[32] = { + 0xDD, 0x30, 0x8A, 0xFE, 0xC5, 0x77, 0x7E, 0x13, + 0x12, 0x1F, 0xA7, 0x2B, 0x9C, 0xC1, 0xB7, 0xCC, + 0x01, 0x39, 0x71, 0x53, 0x09, 0xB0, 0x86, 0xC9, + 0x60, 0xE1, 0x8F, 0xD9, 0x69, 0x77, 0x4E, 0xB8 + }; + const unsigned char aux_rand[32] = { + 0xC8, 0x7A, 0xA5, 0x38, 0x24, 0xB4, 0xD7, 0xAE, + 0x2E, 0xB0, 0x35, 0xA2, 0xB5, 0xBB, 0xBC, 0xCC, + 0x08, 0x0E, 0x76, 0xCD, 0xC6, 0xD1, 0x69, 0x2C, + 0x4B, 0x0B, 0x62, 0xD7, 0x98, 0xE6, 0xD9, 0x06 + }; + const unsigned char msg[32] = { + 0x7E, 0x2D, 0x58, 0xD8, 0xB3, 0xBC, 0xDF, 0x1A, + 0xBA, 0xDE, 0xC7, 0x82, 0x90, 0x54, 0xF9, 0x0D, + 0xDA, 0x98, 0x05, 0xAA, 0xB5, 0x6C, 0x77, 0x33, + 0x30, 0x24, 0xB9, 0xD0, 0xA5, 0x08, 0xB7, 0x5C + }; + const unsigned char sig[64] = { + 0x58, 0x31, 0xAA, 0xEE, 0xD7, 0xB4, 0x4B, 0xB7, + 0x4E, 0x5E, 0xAB, 0x94, 0xBA, 0x9D, 0x42, 0x94, + 0xC4, 0x9B, 0xCF, 0x2A, 0x60, 0x72, 0x8D, 0x8B, + 0x4C, 0x20, 0x0F, 0x50, 0xDD, 0x31, 0x3C, 0x1B, + 0xAB, 0x74, 0x58, 0x79, 0xA5, 0xAD, 0x95, 0x4A, + 0x72, 0xC4, 0x5A, 0x91, 0xC3, 0xA5, 0x1D, 0x3C, + 0x7A, 0xDE, 0xA9, 0x8D, 0x82, 0xF8, 0x48, 0x1E, + 0x0E, 0x1E, 0x03, 0x67, 0x4A, 0x6F, 0x3F, 0xB7 + }; + test_schnorrsig_bip_vectors_check_signing(sk, pk, aux_rand, msg, sizeof(msg), sig); + test_schnorrsig_bip_vectors_check_verify(pk, msg, sizeof(msg), sig, 1); + } + { + /* Test vector 3 */ + const unsigned char sk[32] = { + 0x0B, 0x43, 0x2B, 0x26, 0x77, 0x93, 0x73, 0x81, + 0xAE, 0xF0, 0x5B, 0xB0, 0x2A, 0x66, 0xEC, 0xD0, + 0x12, 0x77, 0x30, 0x62, 0xCF, 0x3F, 0xA2, 0x54, + 0x9E, 0x44, 0xF5, 0x8E, 0xD2, 0x40, 0x17, 0x10 + }; + const unsigned char pk[32] = { + 0x25, 0xD1, 0xDF, 0xF9, 0x51, 0x05, 0xF5, 0x25, + 0x3C, 0x40, 0x22, 0xF6, 0x28, 0xA9, 0x96, 0xAD, + 0x3A, 0x0D, 0x95, 0xFB, 0xF2, 0x1D, 0x46, 0x8A, + 0x1B, 0x33, 0xF8, 0xC1, 0x60, 0xD8, 0xF5, 0x17 + }; + const unsigned char aux_rand[32] = { + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF + }; + const unsigned char msg[32] = { + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF + }; + const unsigned char sig[64] = { + 0x7E, 0xB0, 0x50, 0x97, 0x57, 0xE2, 0x46, 0xF1, + 0x94, 0x49, 0x88, 0x56, 0x51, 0x61, 0x1C, 0xB9, + 0x65, 0xEC, 0xC1, 0xA1, 0x87, 0xDD, 0x51, 0xB6, + 0x4F, 0xDA, 0x1E, 0xDC, 0x96, 0x37, 0xD5, 0xEC, + 0x97, 0x58, 0x2B, 0x9C, 0xB1, 0x3D, 0xB3, 0x93, + 0x37, 0x05, 0xB3, 0x2B, 0xA9, 0x82, 0xAF, 0x5A, + 0xF2, 0x5F, 0xD7, 0x88, 0x81, 0xEB, 0xB3, 0x27, + 0x71, 0xFC, 0x59, 0x22, 0xEF, 0xC6, 0x6E, 0xA3 + }; + test_schnorrsig_bip_vectors_check_signing(sk, pk, aux_rand, msg, sizeof(msg), sig); + test_schnorrsig_bip_vectors_check_verify(pk, msg, sizeof(msg), sig, 1); + } + { + /* Test vector 4 */ + const unsigned char pk[32] = { + 0xD6, 0x9C, 0x35, 0x09, 0xBB, 0x99, 0xE4, 0x12, + 0xE6, 0x8B, 0x0F, 0xE8, 0x54, 0x4E, 0x72, 0x83, + 0x7D, 0xFA, 0x30, 0x74, 0x6D, 0x8B, 0xE2, 0xAA, + 0x65, 0x97, 0x5F, 0x29, 0xD2, 0x2D, 0xC7, 0xB9 + }; + const unsigned char msg[32] = { + 0x4D, 0xF3, 0xC3, 0xF6, 0x8F, 0xCC, 0x83, 0xB2, + 0x7E, 0x9D, 0x42, 0xC9, 0x04, 0x31, 0xA7, 0x24, + 0x99, 0xF1, 0x78, 0x75, 0xC8, 0x1A, 0x59, 0x9B, + 0x56, 0x6C, 0x98, 0x89, 0xB9, 0x69, 0x67, 0x03 + }; + const unsigned char sig[64] = { + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x3B, 0x78, 0xCE, 0x56, 0x3F, + 0x89, 0xA0, 0xED, 0x94, 0x14, 0xF5, 0xAA, 0x28, + 0xAD, 0x0D, 0x96, 0xD6, 0x79, 0x5F, 0x9C, 0x63, + 0x76, 0xAF, 0xB1, 0x54, 0x8A, 0xF6, 0x03, 0xB3, + 0xEB, 0x45, 0xC9, 0xF8, 0x20, 0x7D, 0xEE, 0x10, + 0x60, 0xCB, 0x71, 0xC0, 0x4E, 0x80, 0xF5, 0x93, + 0x06, 0x0B, 0x07, 0xD2, 0x83, 0x08, 0xD7, 0xF4 + }; + test_schnorrsig_bip_vectors_check_verify(pk, msg, sizeof(msg), sig, 1); + } + { + /* Test vector 5 */ + const unsigned char pk[32] = { + 0xEE, 0xFD, 0xEA, 0x4C, 0xDB, 0x67, 0x77, 0x50, + 0xA4, 0x20, 0xFE, 0xE8, 0x07, 0xEA, 0xCF, 0x21, + 0xEB, 0x98, 0x98, 0xAE, 0x79, 0xB9, 0x76, 0x87, + 0x66, 0xE4, 0xFA, 0xA0, 0x4A, 0x2D, 0x4A, 0x34 + }; + secp256k1_xonly_pubkey pk_parsed; + /* No need to check the signature of the test vector as parsing the pubkey already fails */ + CHECK(!secp256k1_xonly_pubkey_parse(CTX, &pk_parsed, pk)); + } + { + /* Test vector 6 */ + const unsigned char pk[32] = { + 0xDF, 0xF1, 0xD7, 0x7F, 0x2A, 0x67, 0x1C, 0x5F, + 0x36, 0x18, 0x37, 0x26, 0xDB, 0x23, 0x41, 0xBE, + 0x58, 0xFE, 0xAE, 0x1D, 0xA2, 0xDE, 0xCE, 0xD8, + 0x43, 0x24, 0x0F, 0x7B, 0x50, 0x2B, 0xA6, 0x59 + }; + const unsigned char msg[32] = { + 0x24, 0x3F, 0x6A, 0x88, 0x85, 0xA3, 0x08, 0xD3, + 0x13, 0x19, 0x8A, 0x2E, 0x03, 0x70, 0x73, 0x44, + 0xA4, 0x09, 0x38, 0x22, 0x29, 0x9F, 0x31, 0xD0, + 0x08, 0x2E, 0xFA, 0x98, 0xEC, 0x4E, 0x6C, 0x89 + }; + const unsigned char sig[64] = { + 0xFF, 0xF9, 0x7B, 0xD5, 0x75, 0x5E, 0xEE, 0xA4, + 0x20, 0x45, 0x3A, 0x14, 0x35, 0x52, 0x35, 0xD3, + 0x82, 0xF6, 0x47, 0x2F, 0x85, 0x68, 0xA1, 0x8B, + 0x2F, 0x05, 0x7A, 0x14, 0x60, 0x29, 0x75, 0x56, + 0x3C, 0xC2, 0x79, 0x44, 0x64, 0x0A, 0xC6, 0x07, + 0xCD, 0x10, 0x7A, 0xE1, 0x09, 0x23, 0xD9, 0xEF, + 0x7A, 0x73, 0xC6, 0x43, 0xE1, 0x66, 0xBE, 0x5E, + 0xBE, 0xAF, 0xA3, 0x4B, 0x1A, 0xC5, 0x53, 0xE2 + }; + test_schnorrsig_bip_vectors_check_verify(pk, msg, sizeof(msg), sig, 0); + } + { + /* Test vector 7 */ + const unsigned char pk[32] = { + 0xDF, 0xF1, 0xD7, 0x7F, 0x2A, 0x67, 0x1C, 0x5F, + 0x36, 0x18, 0x37, 0x26, 0xDB, 0x23, 0x41, 0xBE, + 0x58, 0xFE, 0xAE, 0x1D, 0xA2, 0xDE, 0xCE, 0xD8, + 0x43, 0x24, 0x0F, 0x7B, 0x50, 0x2B, 0xA6, 0x59 + }; + const unsigned char msg[32] = { + 0x24, 0x3F, 0x6A, 0x88, 0x85, 0xA3, 0x08, 0xD3, + 0x13, 0x19, 0x8A, 0x2E, 0x03, 0x70, 0x73, 0x44, + 0xA4, 0x09, 0x38, 0x22, 0x29, 0x9F, 0x31, 0xD0, + 0x08, 0x2E, 0xFA, 0x98, 0xEC, 0x4E, 0x6C, 0x89 + }; + const unsigned char sig[64] = { + 0x1F, 0xA6, 0x2E, 0x33, 0x1E, 0xDB, 0xC2, 0x1C, + 0x39, 0x47, 0x92, 0xD2, 0xAB, 0x11, 0x00, 0xA7, + 0xB4, 0x32, 0xB0, 0x13, 0xDF, 0x3F, 0x6F, 0xF4, + 0xF9, 0x9F, 0xCB, 0x33, 0xE0, 0xE1, 0x51, 0x5F, + 0x28, 0x89, 0x0B, 0x3E, 0xDB, 0x6E, 0x71, 0x89, + 0xB6, 0x30, 0x44, 0x8B, 0x51, 0x5C, 0xE4, 0xF8, + 0x62, 0x2A, 0x95, 0x4C, 0xFE, 0x54, 0x57, 0x35, + 0xAA, 0xEA, 0x51, 0x34, 0xFC, 0xCD, 0xB2, 0xBD + }; + test_schnorrsig_bip_vectors_check_verify(pk, msg, sizeof(msg), sig, 0); + } + { + /* Test vector 8 */ + const unsigned char pk[32] = { + 0xDF, 0xF1, 0xD7, 0x7F, 0x2A, 0x67, 0x1C, 0x5F, + 0x36, 0x18, 0x37, 0x26, 0xDB, 0x23, 0x41, 0xBE, + 0x58, 0xFE, 0xAE, 0x1D, 0xA2, 0xDE, 0xCE, 0xD8, + 0x43, 0x24, 0x0F, 0x7B, 0x50, 0x2B, 0xA6, 0x59 + }; + const unsigned char msg[32] = { + 0x24, 0x3F, 0x6A, 0x88, 0x85, 0xA3, 0x08, 0xD3, + 0x13, 0x19, 0x8A, 0x2E, 0x03, 0x70, 0x73, 0x44, + 0xA4, 0x09, 0x38, 0x22, 0x29, 0x9F, 0x31, 0xD0, + 0x08, 0x2E, 0xFA, 0x98, 0xEC, 0x4E, 0x6C, 0x89 + }; + const unsigned char sig[64] = { + 0x6C, 0xFF, 0x5C, 0x3B, 0xA8, 0x6C, 0x69, 0xEA, + 0x4B, 0x73, 0x76, 0xF3, 0x1A, 0x9B, 0xCB, 0x4F, + 0x74, 0xC1, 0x97, 0x60, 0x89, 0xB2, 0xD9, 0x96, + 0x3D, 0xA2, 0xE5, 0x54, 0x3E, 0x17, 0x77, 0x69, + 0x96, 0x17, 0x64, 0xB3, 0xAA, 0x9B, 0x2F, 0xFC, + 0xB6, 0xEF, 0x94, 0x7B, 0x68, 0x87, 0xA2, 0x26, + 0xE8, 0xD7, 0xC9, 0x3E, 0x00, 0xC5, 0xED, 0x0C, + 0x18, 0x34, 0xFF, 0x0D, 0x0C, 0x2E, 0x6D, 0xA6 + }; + test_schnorrsig_bip_vectors_check_verify(pk, msg, sizeof(msg), sig, 0); + } + { + /* Test vector 9 */ + const unsigned char pk[32] = { + 0xDF, 0xF1, 0xD7, 0x7F, 0x2A, 0x67, 0x1C, 0x5F, + 0x36, 0x18, 0x37, 0x26, 0xDB, 0x23, 0x41, 0xBE, + 0x58, 0xFE, 0xAE, 0x1D, 0xA2, 0xDE, 0xCE, 0xD8, + 0x43, 0x24, 0x0F, 0x7B, 0x50, 0x2B, 0xA6, 0x59 + }; + const unsigned char msg[32] = { + 0x24, 0x3F, 0x6A, 0x88, 0x85, 0xA3, 0x08, 0xD3, + 0x13, 0x19, 0x8A, 0x2E, 0x03, 0x70, 0x73, 0x44, + 0xA4, 0x09, 0x38, 0x22, 0x29, 0x9F, 0x31, 0xD0, + 0x08, 0x2E, 0xFA, 0x98, 0xEC, 0x4E, 0x6C, 0x89 + }; + const unsigned char sig[64] = { + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x12, 0x3D, 0xDA, 0x83, 0x28, 0xAF, 0x9C, 0x23, + 0xA9, 0x4C, 0x1F, 0xEE, 0xCF, 0xD1, 0x23, 0xBA, + 0x4F, 0xB7, 0x34, 0x76, 0xF0, 0xD5, 0x94, 0xDC, + 0xB6, 0x5C, 0x64, 0x25, 0xBD, 0x18, 0x60, 0x51 + }; + test_schnorrsig_bip_vectors_check_verify(pk, msg, sizeof(msg), sig, 0); + } + { + /* Test vector 10 */ + const unsigned char pk[32] = { + 0xDF, 0xF1, 0xD7, 0x7F, 0x2A, 0x67, 0x1C, 0x5F, + 0x36, 0x18, 0x37, 0x26, 0xDB, 0x23, 0x41, 0xBE, + 0x58, 0xFE, 0xAE, 0x1D, 0xA2, 0xDE, 0xCE, 0xD8, + 0x43, 0x24, 0x0F, 0x7B, 0x50, 0x2B, 0xA6, 0x59 + }; + const unsigned char msg[32] = { + 0x24, 0x3F, 0x6A, 0x88, 0x85, 0xA3, 0x08, 0xD3, + 0x13, 0x19, 0x8A, 0x2E, 0x03, 0x70, 0x73, 0x44, + 0xA4, 0x09, 0x38, 0x22, 0x29, 0x9F, 0x31, 0xD0, + 0x08, 0x2E, 0xFA, 0x98, 0xEC, 0x4E, 0x6C, 0x89 + }; + const unsigned char sig[64] = { + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + 0x76, 0x15, 0xFB, 0xAF, 0x5A, 0xE2, 0x88, 0x64, + 0x01, 0x3C, 0x09, 0x97, 0x42, 0xDE, 0xAD, 0xB4, + 0xDB, 0xA8, 0x7F, 0x11, 0xAC, 0x67, 0x54, 0xF9, + 0x37, 0x80, 0xD5, 0xA1, 0x83, 0x7C, 0xF1, 0x97 + }; + test_schnorrsig_bip_vectors_check_verify(pk, msg, sizeof(msg), sig, 0); + } + { + /* Test vector 11 */ + const unsigned char pk[32] = { + 0xDF, 0xF1, 0xD7, 0x7F, 0x2A, 0x67, 0x1C, 0x5F, + 0x36, 0x18, 0x37, 0x26, 0xDB, 0x23, 0x41, 0xBE, + 0x58, 0xFE, 0xAE, 0x1D, 0xA2, 0xDE, 0xCE, 0xD8, + 0x43, 0x24, 0x0F, 0x7B, 0x50, 0x2B, 0xA6, 0x59 + }; + const unsigned char msg[32] = { + 0x24, 0x3F, 0x6A, 0x88, 0x85, 0xA3, 0x08, 0xD3, + 0x13, 0x19, 0x8A, 0x2E, 0x03, 0x70, 0x73, 0x44, + 0xA4, 0x09, 0x38, 0x22, 0x29, 0x9F, 0x31, 0xD0, + 0x08, 0x2E, 0xFA, 0x98, 0xEC, 0x4E, 0x6C, 0x89 + }; + const unsigned char sig[64] = { + 0x4A, 0x29, 0x8D, 0xAC, 0xAE, 0x57, 0x39, 0x5A, + 0x15, 0xD0, 0x79, 0x5D, 0xDB, 0xFD, 0x1D, 0xCB, + 0x56, 0x4D, 0xA8, 0x2B, 0x0F, 0x26, 0x9B, 0xC7, + 0x0A, 0x74, 0xF8, 0x22, 0x04, 0x29, 0xBA, 0x1D, + 0x69, 0xE8, 0x9B, 0x4C, 0x55, 0x64, 0xD0, 0x03, + 0x49, 0x10, 0x6B, 0x84, 0x97, 0x78, 0x5D, 0xD7, + 0xD1, 0xD7, 0x13, 0xA8, 0xAE, 0x82, 0xB3, 0x2F, + 0xA7, 0x9D, 0x5F, 0x7F, 0xC4, 0x07, 0xD3, 0x9B + }; + test_schnorrsig_bip_vectors_check_verify(pk, msg, sizeof(msg), sig, 0); + } + { + /* Test vector 12 */ + const unsigned char pk[32] = { + 0xDF, 0xF1, 0xD7, 0x7F, 0x2A, 0x67, 0x1C, 0x5F, + 0x36, 0x18, 0x37, 0x26, 0xDB, 0x23, 0x41, 0xBE, + 0x58, 0xFE, 0xAE, 0x1D, 0xA2, 0xDE, 0xCE, 0xD8, + 0x43, 0x24, 0x0F, 0x7B, 0x50, 0x2B, 0xA6, 0x59 + }; + const unsigned char msg[32] = { + 0x24, 0x3F, 0x6A, 0x88, 0x85, 0xA3, 0x08, 0xD3, + 0x13, 0x19, 0x8A, 0x2E, 0x03, 0x70, 0x73, 0x44, + 0xA4, 0x09, 0x38, 0x22, 0x29, 0x9F, 0x31, 0xD0, + 0x08, 0x2E, 0xFA, 0x98, 0xEC, 0x4E, 0x6C, 0x89 + }; + const unsigned char sig[64] = { + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFC, 0x2F, + 0x69, 0xE8, 0x9B, 0x4C, 0x55, 0x64, 0xD0, 0x03, + 0x49, 0x10, 0x6B, 0x84, 0x97, 0x78, 0x5D, 0xD7, + 0xD1, 0xD7, 0x13, 0xA8, 0xAE, 0x82, 0xB3, 0x2F, + 0xA7, 0x9D, 0x5F, 0x7F, 0xC4, 0x07, 0xD3, 0x9B + }; + test_schnorrsig_bip_vectors_check_verify(pk, msg, sizeof(msg), sig, 0); + } + { + /* Test vector 13 */ + const unsigned char pk[32] = { + 0xDF, 0xF1, 0xD7, 0x7F, 0x2A, 0x67, 0x1C, 0x5F, + 0x36, 0x18, 0x37, 0x26, 0xDB, 0x23, 0x41, 0xBE, + 0x58, 0xFE, 0xAE, 0x1D, 0xA2, 0xDE, 0xCE, 0xD8, + 0x43, 0x24, 0x0F, 0x7B, 0x50, 0x2B, 0xA6, 0x59 + }; + const unsigned char msg[32] = { + 0x24, 0x3F, 0x6A, 0x88, 0x85, 0xA3, 0x08, 0xD3, + 0x13, 0x19, 0x8A, 0x2E, 0x03, 0x70, 0x73, 0x44, + 0xA4, 0x09, 0x38, 0x22, 0x29, 0x9F, 0x31, 0xD0, + 0x08, 0x2E, 0xFA, 0x98, 0xEC, 0x4E, 0x6C, 0x89 + }; + const unsigned char sig[64] = { + 0x6C, 0xFF, 0x5C, 0x3B, 0xA8, 0x6C, 0x69, 0xEA, + 0x4B, 0x73, 0x76, 0xF3, 0x1A, 0x9B, 0xCB, 0x4F, + 0x74, 0xC1, 0x97, 0x60, 0x89, 0xB2, 0xD9, 0x96, + 0x3D, 0xA2, 0xE5, 0x54, 0x3E, 0x17, 0x77, 0x69, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, + 0xBA, 0xAE, 0xDC, 0xE6, 0xAF, 0x48, 0xA0, 0x3B, + 0xBF, 0xD2, 0x5E, 0x8C, 0xD0, 0x36, 0x41, 0x41 + }; + test_schnorrsig_bip_vectors_check_verify(pk, msg, sizeof(msg), sig, 0); + } + { + /* Test vector 14 */ + const unsigned char pk[32] = { + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFC, 0x30 + }; + secp256k1_xonly_pubkey pk_parsed; + /* No need to check the signature of the test vector as parsing the pubkey already fails */ + CHECK(!secp256k1_xonly_pubkey_parse(CTX, &pk_parsed, pk)); + } + { + /* Test vector 15 */ + const unsigned char sk[32] = { + 0x03, 0x40, 0x03, 0x40, 0x03, 0x40, 0x03, 0x40, + 0x03, 0x40, 0x03, 0x40, 0x03, 0x40, 0x03, 0x40, + 0x03, 0x40, 0x03, 0x40, 0x03, 0x40, 0x03, 0x40, + 0x03, 0x40, 0x03, 0x40, 0x03, 0x40, 0x03, 0x40, + }; + const unsigned char pk[32] = { + 0x77, 0x8C, 0xAA, 0x53, 0xB4, 0x39, 0x3A, 0xC4, + 0x67, 0x77, 0x4D, 0x09, 0x49, 0x7A, 0x87, 0x22, + 0x4B, 0xF9, 0xFA, 0xB6, 0xF6, 0xE6, 0x8B, 0x23, + 0x08, 0x64, 0x97, 0x32, 0x4D, 0x6F, 0xD1, 0x17, + }; + const unsigned char aux_rand[32] = { + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + }; + /* const unsigned char msg[0] = {}; */ + const unsigned char sig[64] = { + 0x71, 0x53, 0x5D, 0xB1, 0x65, 0xEC, 0xD9, 0xFB, + 0xBC, 0x04, 0x6E, 0x5F, 0xFA, 0xEA, 0x61, 0x18, + 0x6B, 0xB6, 0xAD, 0x43, 0x67, 0x32, 0xFC, 0xCC, + 0x25, 0x29, 0x1A, 0x55, 0x89, 0x54, 0x64, 0xCF, + 0x60, 0x69, 0xCE, 0x26, 0xBF, 0x03, 0x46, 0x62, + 0x28, 0xF1, 0x9A, 0x3A, 0x62, 0xDB, 0x8A, 0x64, + 0x9F, 0x2D, 0x56, 0x0F, 0xAC, 0x65, 0x28, 0x27, + 0xD1, 0xAF, 0x05, 0x74, 0xE4, 0x27, 0xAB, 0x63, + }; + test_schnorrsig_bip_vectors_check_signing(sk, pk, aux_rand, NULL, 0, sig); + test_schnorrsig_bip_vectors_check_verify(pk, NULL, 0, sig, 1); + } + { + /* Test vector 16 */ + const unsigned char sk[32] = { + 0x03, 0x40, 0x03, 0x40, 0x03, 0x40, 0x03, 0x40, + 0x03, 0x40, 0x03, 0x40, 0x03, 0x40, 0x03, 0x40, + 0x03, 0x40, 0x03, 0x40, 0x03, 0x40, 0x03, 0x40, + 0x03, 0x40, 0x03, 0x40, 0x03, 0x40, 0x03, 0x40, + }; + const unsigned char pk[32] = { + 0x77, 0x8C, 0xAA, 0x53, 0xB4, 0x39, 0x3A, 0xC4, + 0x67, 0x77, 0x4D, 0x09, 0x49, 0x7A, 0x87, 0x22, + 0x4B, 0xF9, 0xFA, 0xB6, 0xF6, 0xE6, 0x8B, 0x23, + 0x08, 0x64, 0x97, 0x32, 0x4D, 0x6F, 0xD1, 0x17, + }; + const unsigned char aux_rand[32] = { + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + }; + const unsigned char msg[] = { 0x11 }; + const unsigned char sig[64] = { + 0x08, 0xA2, 0x0A, 0x0A, 0xFE, 0xF6, 0x41, 0x24, + 0x64, 0x92, 0x32, 0xE0, 0x69, 0x3C, 0x58, 0x3A, + 0xB1, 0xB9, 0x93, 0x4A, 0xE6, 0x3B, 0x4C, 0x35, + 0x11, 0xF3, 0xAE, 0x11, 0x34, 0xC6, 0xA3, 0x03, + 0xEA, 0x31, 0x73, 0xBF, 0xEA, 0x66, 0x83, 0xBD, + 0x10, 0x1F, 0xA5, 0xAA, 0x5D, 0xBC, 0x19, 0x96, + 0xFE, 0x7C, 0xAC, 0xFC, 0x5A, 0x57, 0x7D, 0x33, + 0xEC, 0x14, 0x56, 0x4C, 0xEC, 0x2B, 0xAC, 0xBF, + }; + test_schnorrsig_bip_vectors_check_signing(sk, pk, aux_rand, msg, sizeof(msg), sig); + test_schnorrsig_bip_vectors_check_verify(pk, msg, sizeof(msg), sig, 1); + } + { + /* Test vector 17 */ + const unsigned char sk[32] = { + 0x03, 0x40, 0x03, 0x40, 0x03, 0x40, 0x03, 0x40, + 0x03, 0x40, 0x03, 0x40, 0x03, 0x40, 0x03, 0x40, + 0x03, 0x40, 0x03, 0x40, 0x03, 0x40, 0x03, 0x40, + 0x03, 0x40, 0x03, 0x40, 0x03, 0x40, 0x03, 0x40, + }; + const unsigned char pk[32] = { + 0x77, 0x8C, 0xAA, 0x53, 0xB4, 0x39, 0x3A, 0xC4, + 0x67, 0x77, 0x4D, 0x09, 0x49, 0x7A, 0x87, 0x22, + 0x4B, 0xF9, 0xFA, 0xB6, 0xF6, 0xE6, 0x8B, 0x23, + 0x08, 0x64, 0x97, 0x32, 0x4D, 0x6F, 0xD1, 0x17, + }; + const unsigned char aux_rand[32] = { + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + }; + const unsigned char msg[] = { + 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07, 0x08, + 0x09, 0x0A, 0x0B, 0x0C, 0x0D, 0x0E, 0x0F, 0x10, + 0x11, + }; + const unsigned char sig[64] = { + 0x51, 0x30, 0xF3, 0x9A, 0x40, 0x59, 0xB4, 0x3B, + 0xC7, 0xCA, 0xC0, 0x9A, 0x19, 0xEC, 0xE5, 0x2B, + 0x5D, 0x86, 0x99, 0xD1, 0xA7, 0x1E, 0x3C, 0x52, + 0xDA, 0x9A, 0xFD, 0xB6, 0xB5, 0x0A, 0xC3, 0x70, + 0xC4, 0xA4, 0x82, 0xB7, 0x7B, 0xF9, 0x60, 0xF8, + 0x68, 0x15, 0x40, 0xE2, 0x5B, 0x67, 0x71, 0xEC, + 0xE1, 0xE5, 0xA3, 0x7F, 0xD8, 0x0E, 0x5A, 0x51, + 0x89, 0x7C, 0x55, 0x66, 0xA9, 0x7E, 0xA5, 0xA5, + }; + test_schnorrsig_bip_vectors_check_signing(sk, pk, aux_rand, msg, sizeof(msg), sig); + test_schnorrsig_bip_vectors_check_verify(pk, msg, sizeof(msg), sig, 1); + } + { + /* Test vector 18 */ + const unsigned char sk[32] = { + 0x03, 0x40, 0x03, 0x40, 0x03, 0x40, 0x03, 0x40, + 0x03, 0x40, 0x03, 0x40, 0x03, 0x40, 0x03, 0x40, + 0x03, 0x40, 0x03, 0x40, 0x03, 0x40, 0x03, 0x40, + 0x03, 0x40, 0x03, 0x40, 0x03, 0x40, 0x03, 0x40, + }; + const unsigned char pk[32] = { + 0x77, 0x8C, 0xAA, 0x53, 0xB4, 0x39, 0x3A, 0xC4, + 0x67, 0x77, 0x4D, 0x09, 0x49, 0x7A, 0x87, 0x22, + 0x4B, 0xF9, 0xFA, 0xB6, 0xF6, 0xE6, 0x8B, 0x23, + 0x08, 0x64, 0x97, 0x32, 0x4D, 0x6F, 0xD1, 0x17, + }; + const unsigned char aux_rand[32] = { + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + }; + const unsigned char sig[64] = { + 0x40, 0x3B, 0x12, 0xB0, 0xD8, 0x55, 0x5A, 0x34, + 0x41, 0x75, 0xEA, 0x7E, 0xC7, 0x46, 0x56, 0x63, + 0x03, 0x32, 0x1E, 0x5D, 0xBF, 0xA8, 0xBE, 0x6F, + 0x09, 0x16, 0x35, 0x16, 0x3E, 0xCA, 0x79, 0xA8, + 0x58, 0x5E, 0xD3, 0xE3, 0x17, 0x08, 0x07, 0xE7, + 0xC0, 0x3B, 0x72, 0x0F, 0xC5, 0x4C, 0x7B, 0x23, + 0x89, 0x7F, 0xCB, 0xA0, 0xE9, 0xD0, 0xB4, 0xA0, + 0x68, 0x94, 0xCF, 0xD2, 0x49, 0xF2, 0x23, 0x67, + }; + unsigned char msg[100]; + memset(msg, 0x99, sizeof(msg)); + test_schnorrsig_bip_vectors_check_signing(sk, pk, aux_rand, msg, sizeof(msg), sig); + test_schnorrsig_bip_vectors_check_verify(pk, msg, sizeof(msg), sig, 1); + } +} + +/* Nonce function that returns constant 0 */ +static int nonce_function_failing(unsigned char *nonce32, const unsigned char *msg, size_t msglen, const unsigned char *key32, const unsigned char *xonly_pk32, const unsigned char *algo, size_t algolen, void *data) { + (void) msg; + (void) msglen; + (void) key32; + (void) xonly_pk32; + (void) algo; + (void) algolen; + (void) data; + (void) nonce32; + return 0; +} + +/* Nonce function that sets nonce to 0 */ +static int nonce_function_0(unsigned char *nonce32, const unsigned char *msg, size_t msglen, const unsigned char *key32, const unsigned char *xonly_pk32, const unsigned char *algo, size_t algolen, void *data) { + (void) msg; + (void) msglen; + (void) key32; + (void) xonly_pk32; + (void) algo; + (void) algolen; + (void) data; + + memset(nonce32, 0, 32); + return 1; +} + +/* Nonce function that sets nonce to 0xFF...0xFF */ +static int nonce_function_overflowing(unsigned char *nonce32, const unsigned char *msg, size_t msglen, const unsigned char *key32, const unsigned char *xonly_pk32, const unsigned char *algo, size_t algolen, void *data) { + (void) msg; + (void) msglen; + (void) key32; + (void) xonly_pk32; + (void) algo; + (void) algolen; + (void) data; + + memset(nonce32, 0xFF, 32); + return 1; +} + +static void test_schnorrsig_sign(void) { + unsigned char sk[32]; + secp256k1_xonly_pubkey pk; + secp256k1_keypair keypair; + const unsigned char msg[] = {'t', 'h', 'i', 's', ' ', 'i', 's', ' ', 'a', ' ', 'm', 's', 'g', ' ', 'f', 'o', 'r', ' ', 'a', ' ', 's', 'c', 'h', 'n', 'o', 'r', 'r', 's', 'i', 'g', '.', '.'}; + unsigned char sig[64]; + unsigned char sig2[64]; + unsigned char zeros64[64] = { 0 }; + secp256k1_schnorrsig_extraparams extraparams = SECP256K1_SCHNORRSIG_EXTRAPARAMS_INIT; + unsigned char aux_rand[32]; + + testrand256(sk); + testrand256(aux_rand); + CHECK(secp256k1_keypair_create(CTX, &keypair, sk)); + CHECK(secp256k1_keypair_xonly_pub(CTX, &pk, NULL, &keypair)); + CHECK(secp256k1_schnorrsig_sign32(CTX, sig, msg, &keypair, NULL) == 1); + CHECK(secp256k1_schnorrsig_verify(CTX, sig, msg, sizeof(msg), &pk)); + /* Check that deprecated alias gives the same result */ + CHECK(secp256k1_schnorrsig_sign(CTX, sig2, msg, &keypair, NULL) == 1); + CHECK(secp256k1_memcmp_var(sig, sig2, sizeof(sig)) == 0); + + /* Test different nonce functions */ + CHECK(secp256k1_schnorrsig_sign_custom(CTX, sig, msg, sizeof(msg), &keypair, &extraparams) == 1); + CHECK(secp256k1_schnorrsig_verify(CTX, sig, msg, sizeof(msg), &pk)); + memset(sig, 1, sizeof(sig)); + extraparams.noncefp = nonce_function_failing; + CHECK(secp256k1_schnorrsig_sign_custom(CTX, sig, msg, sizeof(msg), &keypair, &extraparams) == 0); + CHECK(secp256k1_memcmp_var(sig, zeros64, sizeof(sig)) == 0); + memset(&sig, 1, sizeof(sig)); + extraparams.noncefp = nonce_function_0; + CHECK(secp256k1_schnorrsig_sign_custom(CTX, sig, msg, sizeof(msg), &keypair, &extraparams) == 0); + CHECK(secp256k1_memcmp_var(sig, zeros64, sizeof(sig)) == 0); + memset(&sig, 1, sizeof(sig)); + extraparams.noncefp = nonce_function_overflowing; + CHECK(secp256k1_schnorrsig_sign_custom(CTX, sig, msg, sizeof(msg), &keypair, &extraparams) == 1); + CHECK(secp256k1_schnorrsig_verify(CTX, sig, msg, sizeof(msg), &pk)); + + /* When using the default nonce function, schnorrsig_sign_custom produces + * the same result as schnorrsig_sign with aux_rand = extraparams.ndata */ + extraparams.noncefp = NULL; + extraparams.ndata = aux_rand; + CHECK(secp256k1_schnorrsig_sign_custom(CTX, sig, msg, sizeof(msg), &keypair, &extraparams) == 1); + CHECK(secp256k1_schnorrsig_sign32(CTX, sig2, msg, &keypair, extraparams.ndata) == 1); + CHECK(secp256k1_memcmp_var(sig, sig2, sizeof(sig)) == 0); +} + +#define N_SIGS 3 +/* Creates N_SIGS valid signatures and verifies them with verify and + * verify_batch (TODO). Then flips some bits and checks that verification now + * fails. */ +static void test_schnorrsig_sign_verify(void) { + unsigned char sk[32]; + unsigned char msg[N_SIGS][32]; + unsigned char sig[N_SIGS][64]; + size_t i; + secp256k1_keypair keypair; + secp256k1_xonly_pubkey pk; + secp256k1_scalar s; + + testrand256(sk); + CHECK(secp256k1_keypair_create(CTX, &keypair, sk)); + CHECK(secp256k1_keypair_xonly_pub(CTX, &pk, NULL, &keypair)); + + for (i = 0; i < N_SIGS; i++) { + testrand256(msg[i]); + CHECK(secp256k1_schnorrsig_sign32(CTX, sig[i], msg[i], &keypair, NULL)); + CHECK(secp256k1_schnorrsig_verify(CTX, sig[i], msg[i], sizeof(msg[i]), &pk)); + } + + { + /* Flip a few bits in the signature and in the message and check that + * verify and verify_batch (TODO) fail */ + size_t sig_idx = testrand_int(N_SIGS); + size_t byte_idx = testrand_bits(5); + unsigned char xorbyte = testrand_int(254)+1; + sig[sig_idx][byte_idx] ^= xorbyte; + CHECK(!secp256k1_schnorrsig_verify(CTX, sig[sig_idx], msg[sig_idx], sizeof(msg[sig_idx]), &pk)); + sig[sig_idx][byte_idx] ^= xorbyte; + + byte_idx = testrand_bits(5); + sig[sig_idx][32+byte_idx] ^= xorbyte; + CHECK(!secp256k1_schnorrsig_verify(CTX, sig[sig_idx], msg[sig_idx], sizeof(msg[sig_idx]), &pk)); + sig[sig_idx][32+byte_idx] ^= xorbyte; + + byte_idx = testrand_bits(5); + msg[sig_idx][byte_idx] ^= xorbyte; + CHECK(!secp256k1_schnorrsig_verify(CTX, sig[sig_idx], msg[sig_idx], sizeof(msg[sig_idx]), &pk)); + msg[sig_idx][byte_idx] ^= xorbyte; + + /* Check that above bitflips have been reversed correctly */ + CHECK(secp256k1_schnorrsig_verify(CTX, sig[sig_idx], msg[sig_idx], sizeof(msg[sig_idx]), &pk)); + } + + /* Test overflowing s */ + CHECK(secp256k1_schnorrsig_sign32(CTX, sig[0], msg[0], &keypair, NULL)); + CHECK(secp256k1_schnorrsig_verify(CTX, sig[0], msg[0], sizeof(msg[0]), &pk)); + memset(&sig[0][32], 0xFF, 32); + CHECK(!secp256k1_schnorrsig_verify(CTX, sig[0], msg[0], sizeof(msg[0]), &pk)); + + /* Test negative s */ + CHECK(secp256k1_schnorrsig_sign32(CTX, sig[0], msg[0], &keypair, NULL)); + CHECK(secp256k1_schnorrsig_verify(CTX, sig[0], msg[0], sizeof(msg[0]), &pk)); + secp256k1_scalar_set_b32(&s, &sig[0][32], NULL); + secp256k1_scalar_negate(&s, &s); + secp256k1_scalar_get_b32(&sig[0][32], &s); + CHECK(!secp256k1_schnorrsig_verify(CTX, sig[0], msg[0], sizeof(msg[0]), &pk)); + + /* The empty message can be signed & verified */ + CHECK(secp256k1_schnorrsig_sign_custom(CTX, sig[0], NULL, 0, &keypair, NULL) == 1); + CHECK(secp256k1_schnorrsig_verify(CTX, sig[0], NULL, 0, &pk) == 1); + + { + /* Test varying message lengths */ + unsigned char msg_large[32 * 8]; + uint32_t msglen = testrand_int(sizeof(msg_large)); + for (i = 0; i < sizeof(msg_large); i += 32) { + testrand256(&msg_large[i]); + } + CHECK(secp256k1_schnorrsig_sign_custom(CTX, sig[0], msg_large, msglen, &keypair, NULL) == 1); + CHECK(secp256k1_schnorrsig_verify(CTX, sig[0], msg_large, msglen, &pk) == 1); + /* Verification for a random wrong message length fails */ + msglen = (msglen + (sizeof(msg_large) - 1)) % sizeof(msg_large); + CHECK(secp256k1_schnorrsig_verify(CTX, sig[0], msg_large, msglen, &pk) == 0); + } +} +#undef N_SIGS + +static void test_schnorrsig_taproot(void) { + unsigned char sk[32]; + secp256k1_keypair keypair; + secp256k1_xonly_pubkey internal_pk; + unsigned char internal_pk_bytes[32]; + secp256k1_xonly_pubkey output_pk; + unsigned char output_pk_bytes[32]; + unsigned char tweak[32]; + int pk_parity; + unsigned char msg[32]; + unsigned char sig[64]; + + /* Create output key */ + testrand256(sk); + CHECK(secp256k1_keypair_create(CTX, &keypair, sk) == 1); + CHECK(secp256k1_keypair_xonly_pub(CTX, &internal_pk, NULL, &keypair) == 1); + /* In actual taproot the tweak would be hash of internal_pk */ + CHECK(secp256k1_xonly_pubkey_serialize(CTX, tweak, &internal_pk) == 1); + CHECK(secp256k1_keypair_xonly_tweak_add(CTX, &keypair, tweak) == 1); + CHECK(secp256k1_keypair_xonly_pub(CTX, &output_pk, &pk_parity, &keypair) == 1); + CHECK(secp256k1_xonly_pubkey_serialize(CTX, output_pk_bytes, &output_pk) == 1); + + /* Key spend */ + testrand256(msg); + CHECK(secp256k1_schnorrsig_sign32(CTX, sig, msg, &keypair, NULL) == 1); + /* Verify key spend */ + CHECK(secp256k1_xonly_pubkey_parse(CTX, &output_pk, output_pk_bytes) == 1); + CHECK(secp256k1_schnorrsig_verify(CTX, sig, msg, sizeof(msg), &output_pk) == 1); + + /* Script spend */ + CHECK(secp256k1_xonly_pubkey_serialize(CTX, internal_pk_bytes, &internal_pk) == 1); + /* Verify script spend */ + CHECK(secp256k1_xonly_pubkey_parse(CTX, &internal_pk, internal_pk_bytes) == 1); + CHECK(secp256k1_xonly_pubkey_tweak_add_check(CTX, output_pk_bytes, pk_parity, &internal_pk, tweak) == 1); +} + +static void run_schnorrsig_tests(void) { + int i; + run_nonce_function_bip340_tests(); + + test_schnorrsig_api(); + test_schnorrsig_sha256_tagged(); + test_schnorrsig_bip_vectors(); + for (i = 0; i < COUNT; i++) { + test_schnorrsig_sign(); + test_schnorrsig_sign_verify(); + } + test_schnorrsig_taproot(); +} + +#endif diff --git a/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/wycheproof/ecdsa_secp256k1_sha256_bitcoin_test.h b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/wycheproof/ecdsa_secp256k1_sha256_bitcoin_test.h new file mode 100644 index 00000000000..736737fd61f --- /dev/null +++ b/vendor/github.com/ethereum/go-ethereum/crypto/secp256k1/libsecp256k1/src/wycheproof/ecdsa_secp256k1_sha256_bitcoin_test.h @@ -0,0 +1,1564 @@ +/* Note: this file was autogenerated using tests_wycheproof_generate.py. Do not edit. */ +#define SECP256K1_ECDSA_WYCHEPROOF_NUMBER_TESTVECTORS (463) + +typedef struct { + size_t pk_offset; + size_t msg_offset; + size_t msg_len; + size_t sig_offset; + size_t sig_len; + int expected_verify; +} wycheproof_ecdsa_testvector; + +static const unsigned char wycheproof_ecdsa_messages[] = { 0x31,0x32,0x33,0x34,0x30,0x30, + 0x32,0x35,0x35,0x38,0x35, + 0x34,0x32,0x36,0x34,0x37,0x39,0x37,0x32,0x34, + 0x37,0x31,0x33,0x38,0x36,0x38,0x34,0x38,0x39,0x31, + 0x31,0x30,0x33,0x35,0x39,0x33,0x33,0x31,0x36,0x36,0x38, + 0x33,0x39,0x34,0x39,0x34,0x30,0x31,0x32,0x31,0x35, + 0x31,0x33,0x34,0x34,0x32,0x39,0x33,0x30,0x37,0x39, + 0x33,0x37,0x30,0x36,0x32,0x31,0x31,0x37,0x31,0x32, + 0x33,0x34,0x33,0x36,0x38,0x38,0x37,0x31,0x32, + 0x31,0x33,0x35,0x31,0x35,0x33,0x30,0x33,0x37,0x30, + 0x36,0x35,0x35,0x33,0x32,0x30,0x33,0x31,0x32,0x36, + 0x31,0x35,0x36,0x34,0x33,0x34,0x36,0x36,0x30,0x33, + 0x34,0x34,0x32,0x39,0x35,0x33,0x39,0x31,0x31,0x37, + 0x31,0x30,0x39,0x35,0x33,0x32,0x36,0x31,0x33,0x35,0x31, + 0x35,0x39,0x38,0x37,0x33,0x35,0x30,0x30,0x34,0x31, + 0x33,0x34,0x36,0x33,0x30,0x30,0x36,0x38,0x37,0x38, + 0x39,0x38,0x31,0x37,0x33,0x32,0x30,0x32,0x38,0x37, + 0x33,0x32,0x32,0x32,0x30,0x34,0x31,0x30,0x34,0x36, + 0x36,0x36,0x36,0x36,0x33,0x30,0x37,0x31,0x30,0x34, + 0x31,0x30,0x33,0x35,0x39,0x35,0x31,0x38,0x39,0x38, + 0x31,0x38,0x34,0x36,0x35,0x39,0x37,0x31,0x39,0x35, + 0x33,0x31,0x33,0x36,0x30,0x34,0x36,0x31,0x38,0x39, + 0x32,0x36,0x36,0x33,0x37,0x38,0x34,0x32,0x35,0x34, + 0x31,0x36,0x35,0x32,0x31,0x30,0x30,0x35,0x32,0x34, + 0x35,0x37,0x34,0x38,0x30,0x38,0x31,0x36,0x39,0x36, + 0x36,0x33,0x34,0x33,0x39,0x31,0x33,0x34,0x36,0x38, + 0x31,0x35,0x34,0x31,0x31,0x30,0x33,0x35,0x39,0x38, + 0x31,0x30,0x34,0x37,0x38,0x35,0x38,0x30,0x31,0x32,0x38, + 0x31,0x30,0x35,0x33,0x36,0x32,0x38,0x35,0x35,0x36,0x38, + 0x39,0x35,0x33,0x39,0x30,0x34,0x31,0x30,0x35, + 0x39,0x37,0x38,0x38,0x34,0x38,0x30,0x33,0x39, + 0x33,0x36,0x31,0x30,0x36,0x37,0x32,0x34,0x34,0x32, + 0x31,0x30,0x35,0x34,0x32,0x34,0x30,0x37,0x30,0x35, + 0x35,0x31,0x37,0x34,0x34,0x34,0x38,0x31,0x39,0x37, + 0x31,0x39,0x36,0x37,0x35,0x36,0x31,0x32,0x35,0x31, + 0x33,0x34,0x34,0x37,0x32,0x35,0x33,0x33,0x34,0x33, + 0x33,0x36,0x38,0x32,0x36,0x34,0x33,0x31,0x38, + 0x33,0x32,0x36,0x31,0x31,0x39,0x38,0x36,0x30,0x38, + 0x39,0x36,0x37,0x38,0x37,0x38,0x31,0x30,0x39,0x34, + 0x34,0x39,0x35,0x38,0x38,0x32,0x33,0x38,0x32,0x33, + 0x38,0x32,0x34,0x36,0x33,0x37,0x38,0x33,0x37, + 0x31,0x31,0x30,0x32,0x30,0x38,0x33,0x33,0x37,0x37,0x36, + 0x31,0x33,0x33,0x38,0x37,0x31,0x36,0x34,0x38, + 0x33,0x32,0x32,0x31,0x34,0x34,0x31,0x36,0x32, + 0x31,0x30,0x36,0x38,0x36,0x36,0x35,0x35,0x35,0x34,0x36, + 0x36,0x32,0x31,0x35,0x35,0x32,0x34,0x36, + 0x37,0x30,0x33,0x30,0x38,0x31,0x38,0x37,0x37,0x34, + 0x35,0x39,0x32,0x34,0x35,0x32,0x33,0x37,0x34,0x34, + 0x31,0x34,0x39,0x35,0x35,0x38,0x36,0x36,0x32,0x31, + 0x34,0x30,0x30,0x35,0x33,0x31,0x34,0x34,0x30,0x36, + 0x33,0x30,0x39,0x36,0x34,0x35,0x37,0x35,0x31,0x32, + 0x32,0x37,0x38,0x34,0x30,0x32,0x35,0x36,0x32,0x30, + 0x32,0x36,0x31,0x38,0x37,0x38,0x37,0x34,0x31,0x38, + 0x31,0x36,0x34,0x32,0x36,0x32,0x35,0x32,0x36,0x32, + 0x36,0x38,0x32,0x34,0x31,0x38,0x39,0x34,0x33,0x36, + 0x34,0x38,0x34,0x32,0x34,0x35,0x34,0x32,0x35, + 0x4d,0x73,0x67, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x4d,0x65,0x73,0x73,0x61,0x67,0x65}; + +static const unsigned char wycheproof_ecdsa_public_keys[] = { 0x04,0xb8,0x38,0xff,0x44,0xe5,0xbc,0x17,0x7b,0xf2,0x11,0x89,0xd0,0x76,0x60,0x82,0xfc,0x9d,0x84,0x32,0x26,0x88,0x7f,0xc9,0x76,0x03,0x71,0x10,0x0b,0x7e,0xe2,0x0a,0x6f,0xf0,0xc9,0xd7,0x5b,0xfb,0xa7,0xb3,0x1a,0x6b,0xca,0x19,0x74,0x49,0x6e,0xeb,0x56,0xde,0x35,0x70,0x71,0x95,0x5d,0x83,0xc4,0xb1,0xba,0xda,0xa0,0xb2,0x18,0x32,0xe9, + 0x04,0x07,0x31,0x0f,0x90,0xa9,0xea,0xe1,0x49,0xa0,0x84,0x02,0xf5,0x41,0x94,0xa0,0xf7,0xb4,0xac,0x42,0x7b,0xf8,0xd9,0xbd,0x6c,0x76,0x81,0x07,0x1d,0xc4,0x7d,0xc3,0x62,0x26,0xa6,0xd3,0x7a,0xc4,0x6d,0x61,0xfd,0x60,0x0c,0x0b,0xf1,0xbf,0xf8,0x76,0x89,0xed,0x11,0x7d,0xda,0x6b,0x0e,0x59,0x31,0x8a,0xe0,0x10,0xa1,0x97,0xa2,0x6c,0xa0, + 0x04,0xbc,0x97,0xe7,0x58,0x5e,0xec,0xad,0x48,0xe1,0x66,0x83,0xbc,0x40,0x91,0x70,0x8e,0x1a,0x93,0x0c,0x68,0x3f,0xc4,0x70,0x01,0xd4,0xb3,0x83,0x59,0x4f,0x2c,0x4e,0x22,0x70,0x59,0x89,0xcf,0x69,0xda,0xea,0xdd,0x4e,0x4e,0x4b,0x81,0x51,0xed,0x88,0x8d,0xfe,0xc2,0x0f,0xb0,0x17,0x28,0xd8,0x9d,0x56,0xb3,0xf3,0x8f,0x2a,0xe9,0xc8,0xc5, + 0x04,0x44,0xad,0x33,0x9a,0xfb,0xc2,0x1e,0x9a,0xbf,0x7b,0x60,0x2a,0x5c,0xa5,0x35,0xea,0x37,0x81,0x35,0xb6,0xd1,0x0d,0x81,0x31,0x0b,0xdd,0x82,0x93,0xd1,0xdf,0x32,0x52,0xb6,0x3f,0xf7,0xd0,0x77,0x47,0x70,0xf8,0xfe,0x1d,0x17,0x22,0xfa,0x83,0xac,0xd0,0x2f,0x43,0x4e,0x4f,0xc1,0x10,0xa0,0xcc,0x8f,0x6d,0xdd,0xd3,0x7d,0x56,0xc4,0x63, + 0x04,0x12,0x60,0xc2,0x12,0x2c,0x9e,0x24,0x4e,0x1a,0xf5,0x15,0x1b,0xed,0xe0,0xc3,0xae,0x23,0xb5,0x4d,0x7c,0x59,0x68,0x81,0xd3,0xee,0xba,0xd2,0x1f,0x37,0xdd,0x87,0x8c,0x5c,0x9a,0x0c,0x1a,0x9a,0xde,0x76,0x73,0x7a,0x88,0x11,0xbd,0x6a,0x7f,0x92,0x87,0xc9,0x78,0xee,0x39,0x6a,0xa8,0x9c,0x11,0xe4,0x72,0x29,0xd2,0xcc,0xb5,0x52,0xf0, + 0x04,0x18,0x77,0x04,0x5b,0xe2,0x5d,0x34,0xa1,0xd0,0x60,0x0f,0x9d,0x5c,0x00,0xd0,0x64,0x5a,0x2a,0x54,0x37,0x9b,0x6c,0xee,0xfa,0xd2,0xe6,0xbf,0x5c,0x2a,0x33,0x52,0xce,0x82,0x1a,0x53,0x2c,0xc1,0x75,0x1e,0xe1,0xd3,0x6d,0x41,0xc3,0xd6,0xab,0x4e,0x9b,0x14,0x3e,0x44,0xec,0x46,0xd7,0x34,0x78,0xea,0x6a,0x79,0xa5,0xc0,0xe5,0x41,0x59, + 0x04,0x45,0x54,0x39,0xfc,0xc3,0xd2,0xde,0xec,0xed,0xde,0xae,0xce,0x60,0xe7,0xbd,0x17,0x30,0x4f,0x36,0xeb,0xb6,0x02,0xad,0xf5,0xa2,0x2e,0x0b,0x8f,0x1d,0xb4,0x6a,0x50,0xae,0xc3,0x8f,0xb2,0xba,0xf2,0x21,0xe9,0xa8,0xd1,0x88,0x7c,0x7b,0xf6,0x22,0x2d,0xd1,0x83,0x46,0x34,0xe7,0x72,0x63,0x31,0x5a,0xf6,0xd2,0x36,0x09,0xd0,0x4f,0x77, + 0x04,0x2e,0x1f,0x46,0x6b,0x02,0x4c,0x0c,0x3a,0xce,0x24,0x37,0xde,0x09,0x12,0x7f,0xed,0x04,0xb7,0x06,0xf9,0x4b,0x19,0xa2,0x1b,0xb1,0xc2,0xac,0xf3,0x5c,0xec,0xe7,0x18,0x04,0x49,0xae,0x35,0x23,0xd7,0x25,0x34,0xe9,0x64,0x97,0x2c,0xfd,0x3b,0x38,0xaf,0x0b,0xdd,0xd9,0x61,0x9e,0x5a,0xf2,0x23,0xe4,0xd1,0xa4,0x0f,0x34,0xcf,0x9f,0x1d, + 0x04,0x8e,0x7a,0xbd,0xbb,0xd1,0x8d,0xe7,0x45,0x23,0x74,0xc1,0x87,0x9a,0x1c,0x3b,0x01,0xd1,0x32,0x61,0xe7,0xd4,0x57,0x1c,0x3b,0x47,0xa1,0xc7,0x6c,0x55,0xa2,0x33,0x73,0x26,0xed,0x89,0x7c,0xd5,0x17,0xa4,0xf5,0x34,0x9d,0xb8,0x09,0x78,0x0f,0x6d,0x2f,0x2b,0x9f,0x62,0x99,0xd8,0xb5,0xa8,0x90,0x77,0xf1,0x11,0x9a,0x71,0x8f,0xd7,0xb3, + 0x04,0x7b,0x33,0x3d,0x43,0x40,0xd3,0xd7,0x18,0xdd,0x3e,0x6a,0xff,0x7d,0xe7,0xbb,0xf8,0xb7,0x2b,0xfd,0x61,0x6c,0x84,0x20,0x05,0x60,0x52,0x84,0x23,0x76,0xb9,0xaf,0x19,0x42,0x11,0x7c,0x5a,0xfe,0xac,0x75,0x5d,0x6f,0x37,0x6f,0xc6,0x32,0x9a,0x7d,0x76,0x05,0x1b,0x87,0x12,0x3a,0x4a,0x5d,0x0b,0xc4,0xa5,0x39,0x38,0x0f,0x03,0xde,0x7b, + 0x04,0xd3,0x0c,0xa4,0xa0,0xdd,0xb6,0x61,0x6c,0x85,0x1d,0x30,0xce,0xd6,0x82,0xc4,0x0f,0x83,0xc6,0x27,0x58,0xa1,0xf2,0x75,0x99,0x88,0xd6,0x76,0x3a,0x88,0xf1,0xc0,0xe5,0x03,0xa8,0x0d,0x54,0x15,0x65,0x0d,0x41,0x23,0x97,0x84,0xe8,0xe2,0xfb,0x12,0x35,0xe9,0xfe,0x99,0x1d,0x11,0x2e,0xbb,0x81,0x18,0x6c,0xbf,0x0d,0xa2,0xde,0x3a,0xff, + 0x04,0x48,0x96,0x9b,0x39,0x99,0x12,0x97,0xb3,0x32,0xa6,0x52,0xd3,0xee,0x6e,0x01,0xe9,0x09,0xb3,0x99,0x04,0xe7,0x1f,0xa2,0x35,0x4a,0x78,0x30,0xc7,0x75,0x0b,0xaf,0x24,0xb4,0x01,0x2d,0x1b,0x83,0x0d,0x19,0x9c,0xcb,0x1f,0xc9,0x72,0xb3,0x2b,0xfd,0xed,0x55,0xf0,0x9c,0xd6,0x2d,0x25,0x7e,0x5e,0x84,0x4e,0x27,0xe5,0x7a,0x15,0x94,0xec, + 0x04,0x02,0xef,0x4d,0x6d,0x6c,0xfd,0x5a,0x94,0xf1,0xd7,0x78,0x42,0x26,0xe3,0xe2,0xa6,0xc0,0xa4,0x36,0xc5,0x58,0x39,0x61,0x9f,0x38,0xfb,0x44,0x72,0xb5,0xf9,0xee,0x77,0x7e,0xb4,0xac,0xd4,0xee,0xbd,0xa5,0xcd,0x72,0x87,0x5f,0xfd,0x2a,0x2f,0x26,0x22,0x9c,0x2d,0xc6,0xb4,0x65,0x00,0x91,0x9a,0x43,0x2c,0x86,0x73,0x9f,0x3a,0xe8,0x66, + 0x04,0x46,0x4f,0x4f,0xf7,0x15,0x72,0x9c,0xae,0x50,0x72,0xca,0x3b,0xd8,0x01,0xd3,0x19,0x5b,0x67,0xae,0xc6,0x5e,0x9b,0x01,0xaa,0xd2,0x0a,0x29,0x43,0xdc,0xbc,0xb5,0x84,0xb1,0xaf,0xd2,0x9d,0x31,0xa3,0x9a,0x11,0xd5,0x70,0xaa,0x15,0x97,0x43,0x9b,0x3b,0x2d,0x19,0x71,0xbf,0x2f,0x1a,0xbf,0x15,0x43,0x2d,0x02,0x07,0xb1,0x0d,0x1d,0x08, + 0x04,0x15,0x7f,0x8f,0xdd,0xf3,0x73,0xeb,0x5f,0x49,0xcf,0xcf,0x10,0xd8,0xb8,0x53,0xcf,0x91,0xcb,0xcd,0x7d,0x66,0x5c,0x35,0x22,0xba,0x7d,0xd7,0x38,0xdd,0xb7,0x9a,0x4c,0xde,0xad,0xf1,0xa5,0xc4,0x48,0xea,0x3c,0x9f,0x41,0x91,0xa8,0x99,0x9a,0xbf,0xcc,0x75,0x7a,0xc6,0xd6,0x45,0x67,0xef,0x07,0x2c,0x47,0xfe,0xc6,0x13,0x44,0x3b,0x8f, + 0x04,0x09,0x34,0xa5,0x37,0x46,0x6c,0x07,0x43,0x0e,0x2c,0x48,0xfe,0xb9,0x90,0xbb,0x19,0xfb,0x78,0xce,0xcc,0x9c,0xee,0x42,0x4e,0xa4,0xd1,0x30,0x29,0x1a,0xa2,0x37,0xf0,0xd4,0xf9,0x2d,0x23,0xb4,0x62,0x80,0x4b,0x5b,0x68,0xc5,0x25,0x58,0xc0,0x1c,0x99,0x96,0xdb,0xf7,0x27,0xfc,0xca,0xbb,0xee,0xdb,0x96,0x21,0xa4,0x00,0x53,0x5a,0xfa, + 0x04,0xd6,0xef,0x20,0xbe,0x66,0xc8,0x93,0xf7,0x41,0xa9,0xbf,0x90,0xd9,0xb7,0x46,0x75,0xd1,0xc2,0xa3,0x12,0x96,0x39,0x7a,0xcb,0x3e,0xf1,0x74,0xfd,0x0b,0x30,0x0c,0x65,0x4a,0x0c,0x95,0x47,0x8c,0xa0,0x03,0x99,0x16,0x2d,0x7f,0x0f,0x2d,0xc8,0x9e,0xfd,0xc2,0xb2,0x8a,0x30,0xfb,0xab,0xe2,0x85,0x85,0x72,0x95,0xa4,0xb0,0xc4,0xe2,0x65, + 0x04,0xb7,0x29,0x1d,0x14,0x04,0xe0,0xc0,0xc0,0x7d,0xab,0x93,0x72,0x18,0x9f,0x4b,0xd5,0x8d,0x2c,0xea,0xa8,0xd1,0x5e,0xde,0x54,0x4d,0x95,0x14,0x54,0x5b,0xa9,0xee,0x06,0x29,0xc9,0xa6,0x3d,0x5e,0x30,0x87,0x69,0xcc,0x30,0xec,0x27,0x6a,0x41,0x0e,0x64,0x64,0xa2,0x7e,0xea,0xfd,0x9e,0x59,0x9d,0xb1,0x0f,0x05,0x3a,0x4f,0xe4,0xa8,0x29, + 0x04,0x6e,0x28,0x30,0x33,0x05,0xd6,0x42,0xcc,0xb9,0x23,0xb7,0x22,0xea,0x86,0xb2,0xa0,0xbc,0x8e,0x37,0x35,0xec,0xb2,0x6e,0x84,0x9b,0x19,0xc9,0xf7,0x6b,0x2f,0xdb,0xb8,0x18,0x6e,0x80,0xd6,0x4d,0x8c,0xab,0x16,0x4f,0x52,0x38,0xf5,0x31,0x84,0x61,0xbf,0x89,0xd4,0xd9,0x6e,0xe6,0x54,0x4c,0x81,0x6c,0x75,0x66,0x94,0x77,0x74,0xe0,0xf6, + 0x04,0x37,0x5b,0xda,0x93,0xf6,0xaf,0x92,0xfb,0x5f,0x8f,0x4b,0x1b,0x5f,0x05,0x34,0xe3,0xba,0xfa,0xb3,0x4c,0xb7,0xad,0x9f,0xb9,0xd0,0xb7,0x22,0xe4,0xa5,0xc3,0x02,0xa9,0xa0,0x0b,0x9f,0x38,0x7a,0x5a,0x39,0x60,0x97,0xaa,0x21,0x62,0xfc,0x5b,0xbc,0xf4,0xa5,0x26,0x33,0x72,0xf6,0x81,0xc9,0x4d,0xa5,0x1e,0x97,0x99,0x12,0x09,0x90,0xfd, + 0x04,0xd7,0x5b,0x68,0x21,0x6b,0xab,0xe0,0x3a,0xe2,0x57,0xe9,0x4b,0x4e,0x3b,0xf1,0xc5,0x2f,0x44,0xe3,0xdf,0x26,0x6d,0x15,0x24,0xff,0x8c,0x5e,0xa6,0x9d,0xa7,0x31,0x97,0xda,0x4b,0xff,0x9e,0xd1,0xc5,0x3f,0x44,0x91,0x7a,0x67,0xd7,0xb9,0x78,0x59,0x8e,0x89,0xdf,0x35,0x9e,0x3d,0x59,0x13,0xea,0xea,0x24,0xf3,0xae,0x25,0x9a,0xbc,0x44, + 0x04,0x78,0xbc,0xda,0x14,0x0a,0xed,0x23,0xd4,0x30,0xcb,0x23,0xc3,0xdc,0x0d,0x01,0xf4,0x23,0xdb,0x13,0x4e,0xe9,0x4a,0x3a,0x8c,0xb4,0x83,0xf2,0xde,0xac,0x2a,0xc6,0x53,0x11,0x81,0x14,0xf6,0xf3,0x30,0x45,0xd4,0xe9,0xed,0x91,0x07,0x08,0x50,0x07,0xbf,0xbd,0xdf,0x8f,0x58,0xfe,0x7a,0x1a,0x24,0x45,0xd6,0x6a,0x99,0x00,0x45,0x47,0x6e, + 0x04,0xbb,0x79,0xf6,0x18,0x57,0xf7,0x43,0xbf,0xa1,0xb6,0xe7,0x11,0x1c,0xe4,0x09,0x43,0x77,0x25,0x69,0x69,0xe4,0xe1,0x51,0x59,0x12,0x3d,0x95,0x48,0xac,0xc3,0xbe,0x6c,0x1f,0x9d,0x9f,0x88,0x60,0xdc,0xff,0xd3,0xeb,0x36,0xdd,0x6c,0x31,0xff,0x2e,0x72,0x26,0xc2,0x00,0x9c,0x4c,0x94,0xd8,0xd7,0xd2,0xb5,0x68,0x6b,0xf7,0xab,0xd6,0x77, + 0x04,0x93,0x59,0x18,0x27,0xd9,0xe6,0x71,0x3b,0x4e,0x9f,0xae,0xa6,0x2c,0x72,0xb2,0x8d,0xfe,0xfa,0x68,0xe0,0xc0,0x51,0x60,0xb5,0xd6,0xaa,0xe8,0x8f,0xd2,0xe3,0x6c,0x36,0x07,0x3f,0x55,0x45,0xad,0x5a,0xf4,0x10,0xaf,0x26,0xaf,0xff,0x68,0x65,0x4c,0xf7,0x2d,0x45,0xe4,0x93,0x48,0x93,0x11,0x20,0x32,0x47,0x34,0x7a,0x89,0x0f,0x45,0x18, + 0x04,0x31,0xed,0x30,0x81,0xae,0xfe,0x00,0x1e,0xb6,0x40,0x20,0x69,0xee,0x2c,0xcc,0x18,0x62,0x93,0x7b,0x85,0x99,0x51,0x44,0xdb,0xa9,0x50,0x39,0x43,0x58,0x7b,0xf0,0xda,0xda,0x01,0xb8,0xcc,0x4d,0xf3,0x4f,0x5a,0xb3,0xb1,0xa3,0x59,0x61,0x52,0x08,0x94,0x6e,0x5e,0xe3,0x5f,0x98,0xee,0x77,0x5b,0x8c,0xce,0xcd,0x86,0xcc,0xc1,0x65,0x0f, + 0x04,0x7d,0xff,0x66,0xfa,0x98,0x50,0x9f,0xf3,0xe2,0xe5,0x10,0x45,0xf4,0x39,0x05,0x23,0xdc,0xcd,0xa4,0x3a,0x3b,0xc2,0x88,0x5e,0x58,0xc2,0x48,0x09,0x09,0x90,0xee,0xa8,0x54,0xc7,0x6c,0x2b,0x9a,0xde,0xb6,0xbb,0x57,0x18,0x23,0xe0,0x7f,0xd7,0xc6,0x5c,0x86,0x39,0xcf,0x9d,0x90,0x52,0x60,0x06,0x4c,0x8e,0x76,0x75,0xce,0x6d,0x98,0xb4, + 0x04,0x42,0x80,0x50,0x9a,0xab,0x64,0xed,0xfc,0x0b,0x4a,0x29,0x67,0xe4,0xcb,0xce,0x84,0x9c,0xb5,0x44,0xe4,0xa7,0x73,0x13,0xc8,0xe6,0xec,0xe5,0x79,0xfb,0xd7,0x42,0x0a,0x2e,0x89,0xfe,0x5c,0xc1,0x92,0x7d,0x55,0x4e,0x6a,0x3b,0xb1,0x40,0x33,0xea,0x7c,0x92,0x2c,0xd7,0x5c,0xba,0x2c,0x74,0x15,0xfd,0xab,0x52,0xf2,0x0b,0x18,0x60,0xf1, + 0x04,0x4f,0x8d,0xf1,0x45,0x19,0x4e,0x3c,0x4f,0xc3,0xee,0xa2,0x6d,0x43,0xce,0x75,0xb4,0x02,0xd6,0xb1,0x74,0x72,0xdd,0xcb,0xb2,0x54,0xb8,0xa7,0x9b,0x0b,0xf3,0xd9,0xcb,0x2a,0xa2,0x0d,0x82,0x84,0x4c,0xb2,0x66,0x34,0x4e,0x71,0xca,0x78,0xf2,0xad,0x27,0xa7,0x5a,0x09,0xe5,0xbc,0x0f,0xa5,0x7e,0x4e,0xfd,0x9d,0x46,0x5a,0x08,0x88,0xdb, + 0x04,0x95,0x98,0xa5,0x7d,0xd6,0x7e,0xc3,0xe1,0x6b,0x58,0x7a,0x33,0x8a,0xa3,0xa1,0x0a,0x3a,0x39,0x13,0xb4,0x1a,0x3a,0xf3,0x2e,0x3e,0xd3,0xff,0x01,0x35,0x8c,0x6b,0x14,0x12,0x28,0x19,0xed,0xf8,0x07,0x4b,0xbc,0x52,0x1f,0x7d,0x4c,0xdc,0xe8,0x2f,0xef,0x7a,0x51,0x67,0x06,0xaf,0xfb,0xa1,0xd9,0x3d,0x9d,0xea,0x9c,0xca,0xe1,0xa2,0x07, + 0x04,0x91,0x71,0xfe,0xc3,0xca,0x20,0x80,0x6b,0xc0,0x84,0xf1,0x2f,0x07,0x60,0x91,0x1b,0x60,0x99,0x0b,0xd8,0x0e,0x5b,0x2a,0x71,0xca,0x03,0xa0,0x48,0xb2,0x0f,0x83,0x7e,0x63,0x4f,0xd1,0x78,0x63,0x76,0x1b,0x29,0x58,0xd2,0xbe,0x4e,0x14,0x9f,0x8d,0x3d,0x7a,0xbb,0xdc,0x18,0xbe,0x03,0xf4,0x51,0xab,0x6c,0x17,0xfa,0x0a,0x1f,0x83,0x30, + 0x04,0x77,0x7c,0x89,0x30,0xb6,0xe1,0xd2,0x71,0x10,0x0f,0xe6,0x8c,0xe9,0x3f,0x16,0x3f,0xa3,0x76,0x12,0xc5,0xff,0xf6,0x7f,0x4a,0x62,0xfc,0x3b,0xaf,0xaf,0x3d,0x17,0xa9,0xed,0x73,0xd8,0x6f,0x60,0xa5,0x1b,0x5e,0xd9,0x13,0x53,0xa3,0xb0,0x54,0xed,0xc0,0xaa,0x92,0xc9,0xeb,0xcb,0xd0,0xb7,0x5d,0x18,0x8f,0xdc,0x88,0x27,0x91,0xd6,0x8d, + 0x04,0xea,0xbc,0x24,0x8f,0x62,0x6e,0x0a,0x63,0xe1,0xeb,0x81,0xc4,0x3d,0x46,0x1a,0x39,0xa1,0xdb,0xa8,0x81,0xeb,0x6e,0xe2,0x15,0x2b,0x07,0xc3,0x2d,0x71,0xbc,0xf4,0x70,0x06,0x03,0xca,0xa8,0xb9,0xd3,0x3d,0xb1,0x3a,0xf4,0x4c,0x6e,0xfb,0xec,0x8a,0x19,0x8e,0xd6,0x12,0x4a,0xc9,0xeb,0x17,0xea,0xaf,0xd2,0x82,0x4a,0x54,0x5e,0xc0,0x00, + 0x04,0x9f,0x7a,0x13,0xad,0xa1,0x58,0xa5,0x5f,0x9d,0xdf,0x1a,0x45,0xf0,0x44,0xf0,0x73,0xd9,0xb8,0x00,0x30,0xef,0xdc,0xfc,0x9f,0x9f,0x58,0x41,0x8f,0xbc,0xea,0xf0,0x01,0xf8,0xad,0xa0,0x17,0x50,0x90,0xf8,0x0d,0x47,0x22,0x7d,0x67,0x13,0xb6,0x74,0x0f,0x9a,0x00,0x91,0xd8,0x8a,0x83,0x7d,0x0a,0x1c,0xd7,0x7b,0x58,0xa8,0xf2,0x8d,0x73, + 0x04,0x11,0xc4,0xf3,0xe4,0x61,0xcd,0x01,0x9b,0x5c,0x06,0xea,0x0c,0xea,0x4c,0x40,0x90,0xc3,0xcc,0x3e,0x3c,0x5d,0x9f,0x3c,0x6d,0x65,0xb4,0x36,0x82,0x6d,0xa9,0xb4,0xdb,0xbb,0xeb,0x7a,0x77,0xe4,0xcb,0xfd,0xa2,0x07,0x09,0x7c,0x43,0x42,0x37,0x05,0xf7,0x2c,0x80,0x47,0x6d,0xa3,0xda,0xc4,0x0a,0x48,0x3b,0x0a,0xb0,0xf2,0xea,0xd1,0xcb, + 0x04,0xe2,0xe1,0x86,0x82,0xd5,0x31,0x23,0xaa,0x01,0xa6,0xc5,0xd0,0x0b,0x0c,0x62,0x3d,0x67,0x1b,0x46,0x2e,0xa8,0x0b,0xdd,0xd6,0x52,0x27,0xfd,0x51,0x05,0x98,0x8a,0xa4,0x16,0x19,0x07,0xb3,0xfd,0x25,0x04,0x4a,0x94,0x9e,0xa4,0x1c,0x8e,0x2e,0xa8,0x45,0x9d,0xc6,0xf1,0x65,0x48,0x56,0xb8,0xb6,0x1b,0x31,0x54,0x3b,0xb1,0xb4,0x5b,0xdb, + 0x04,0x90,0xf8,0xd4,0xca,0x73,0xde,0x08,0xa6,0x56,0x4a,0xaf,0x00,0x52,0x47,0xb6,0xf0,0xff,0xe9,0x78,0x50,0x4d,0xce,0x52,0x60,0x5f,0x46,0xb7,0xc3,0xe5,0x61,0x97,0xda,0xfa,0xdb,0xe5,0x28,0xeb,0x70,0xd9,0xee,0x7e,0xa0,0xe7,0x07,0x02,0xdb,0x54,0xf7,0x21,0x51,0x4c,0x7b,0x86,0x04,0xac,0x2c,0xb2,0x14,0xf1,0xde,0xcb,0x7e,0x38,0x3d, + 0x04,0x82,0x4c,0x19,0x5c,0x73,0xcf,0xfd,0xf0,0x38,0xd1,0x01,0xbc,0xe1,0x68,0x7b,0x5c,0x3b,0x61,0x46,0xf3,0x95,0xc8,0x85,0x97,0x6f,0x77,0x53,0xb2,0x37,0x6b,0x94,0x8e,0x3c,0xde,0xfa,0x6f,0xc3,0x47,0xd1,0x3e,0x4d,0xcb,0xc6,0x3a,0x0b,0x03,0xa1,0x65,0x18,0x0c,0xd2,0xbe,0x14,0x31,0xa0,0xcf,0x74,0xce,0x1e,0xa2,0x50,0x82,0xd2,0xbc, + 0x04,0x27,0x88,0xa5,0x2f,0x07,0x8e,0xb3,0xf2,0x02,0xc4,0xfa,0x73,0xe0,0xd3,0x38,0x6f,0xaf,0x3d,0xf6,0xbe,0x85,0x60,0x03,0x63,0x6f,0x59,0x99,0x22,0xd4,0xf5,0x26,0x8f,0x30,0xb4,0xf2,0x07,0xc9,0x19,0xbb,0xdf,0x5e,0x67,0xa8,0xbe,0x42,0x65,0xa8,0x17,0x47,0x54,0xb3,0xab,0xa8,0xf1,0x6e,0x57,0x5b,0x77,0xff,0x4d,0x5a,0x7e,0xb6,0x4f, + 0x04,0xd5,0x33,0xb7,0x89,0xa4,0xaf,0x89,0x0f,0xa7,0xa8,0x2a,0x1f,0xae,0x58,0xc4,0x04,0xf9,0xa6,0x2a,0x50,0xb4,0x9a,0xda,0xfa,0xb3,0x49,0xc5,0x13,0xb4,0x15,0x08,0x74,0x01,0xb4,0x17,0x1b,0x80,0x3e,0x76,0xb3,0x4a,0x98,0x61,0xe1,0x0f,0x7b,0xc2,0x89,0xa0,0x66,0xfd,0x01,0xbd,0x29,0xf8,0x4c,0x98,0x7a,0x10,0xa5,0xfb,0x18,0xc2,0xd4, + 0x04,0x3a,0x31,0x50,0x79,0x8c,0x8a,0xf6,0x9d,0x1e,0x6e,0x98,0x1f,0x3a,0x45,0x40,0x2b,0xa1,0xd7,0x32,0xf4,0xbe,0x83,0x30,0xc5,0x16,0x4f,0x49,0xe1,0x0e,0xc5,0x55,0xb4,0x22,0x1b,0xd8,0x42,0xbc,0x5e,0x4d,0x97,0xef,0xf3,0x71,0x65,0xf6,0x0e,0x39,0x98,0xa4,0x24,0xd7,0x2a,0x45,0x0c,0xf9,0x5e,0xa4,0x77,0xc7,0x82,0x87,0xd0,0x34,0x3a, + 0x04,0x3b,0x37,0xdf,0x5f,0xb3,0x47,0xc6,0x9a,0x0f,0x17,0xd8,0x5c,0x0c,0x7c,0xa8,0x37,0x36,0x88,0x3a,0x82,0x5e,0x13,0x14,0x3d,0x0f,0xcf,0xc8,0x10,0x1e,0x85,0x1e,0x80,0x0d,0xe3,0xc0,0x90,0xb6,0xca,0x21,0xba,0x54,0x35,0x17,0x33,0x0c,0x04,0xb1,0x2f,0x94,0x8c,0x6b,0xad,0xf1,0x4a,0x63,0xab,0xff,0xdf,0x4e,0xf8,0xc7,0x53,0x70,0x26, + 0x04,0xfe,0xb5,0x16,0x3b,0x0e,0xce,0x30,0xff,0x3e,0x03,0xc7,0xd5,0x5c,0x43,0x80,0xfa,0x2f,0xa8,0x1e,0xe2,0xc0,0x35,0x49,0x42,0xff,0x6f,0x08,0xc9,0x9d,0x0c,0xd8,0x2c,0xe8,0x7d,0xe0,0x5e,0xe1,0xbd,0xa0,0x89,0xd3,0xe4,0xe2,0x48,0xfa,0x0f,0x72,0x11,0x02,0xac,0xff,0xfd,0xf5,0x0e,0x65,0x4b,0xe2,0x81,0x43,0x39,0x99,0xdf,0x89,0x7e, + 0x04,0x23,0x8c,0xed,0x00,0x1c,0xf2,0x2b,0x88,0x53,0xe0,0x2e,0xdc,0x89,0xcb,0xec,0xa5,0x05,0x0b,0xa7,0xe0,0x42,0xa7,0xa7,0x7f,0x93,0x82,0xcd,0x41,0x49,0x22,0x89,0x76,0x40,0x68,0x3d,0x30,0x94,0x64,0x38,0x40,0xf2,0x95,0x89,0x0a,0xa4,0xc1,0x8a,0xa3,0x9b,0x41,0xd7,0x7d,0xd0,0xfb,0x3b,0xb2,0x70,0x0e,0x4f,0x9e,0xc2,0x84,0xff,0xc2, + 0x04,0x96,0x1c,0xf6,0x48,0x17,0xc0,0x6c,0x0e,0x51,0xb3,0xc2,0x73,0x6c,0x92,0x2f,0xde,0x18,0xbd,0x8c,0x49,0x06,0xfc,0xd7,0xf5,0xef,0x66,0xc4,0x67,0x85,0x08,0xf3,0x5e,0xd2,0xc5,0xd1,0x81,0x68,0xcf,0xbe,0x70,0xf2,0xf1,0x23,0xbd,0x74,0x19,0x23,0x2b,0xb9,0x2d,0xd6,0x91,0x13,0xe2,0x94,0x10,0x61,0x88,0x94,0x81,0xc5,0xa0,0x27,0xbf, + 0x04,0x13,0x68,0x1e,0xae,0x16,0x8c,0xd4,0xea,0x7c,0xf2,0xe2,0xa4,0x5d,0x05,0x27,0x42,0xd1,0x0a,0x9f,0x64,0xe7,0x96,0x86,0x7d,0xbd,0xcb,0x82,0x9f,0xe0,0xb1,0x02,0x88,0x16,0x52,0x87,0x60,0xd1,0x77,0x37,0x6c,0x09,0xdf,0x79,0xde,0x39,0x55,0x7c,0x32,0x9c,0xc1,0x75,0x35,0x17,0xac,0xff,0xe8,0xfa,0x2e,0xc2,0x98,0x02,0x6b,0x83,0x84, + 0x04,0x5a,0xa7,0xab,0xfd,0xb6,0xb4,0x08,0x6d,0x54,0x33,0x25,0xe5,0xd7,0x9c,0x6e,0x95,0xce,0x42,0xf8,0x66,0xd2,0xbb,0x84,0x90,0x96,0x33,0xa0,0x4b,0xb1,0xaa,0x31,0xc2,0x91,0xc8,0x00,0x88,0x79,0x49,0x05,0xe1,0xda,0x33,0x33,0x6d,0x87,0x4e,0x2f,0x91,0xcc,0xf4,0x5c,0xc5,0x91,0x85,0xbe,0xde,0x5d,0xd6,0xf3,0xf7,0xac,0xaa,0xe1,0x8b, + 0x04,0x00,0x27,0x77,0x91,0xb3,0x05,0xa4,0x5b,0x2b,0x39,0x59,0x0b,0x2f,0x05,0xd3,0x39,0x2a,0x6c,0x81,0x82,0xce,0xf4,0xeb,0x54,0x01,0x20,0xe0,0xf5,0xc2,0x06,0xc3,0xe4,0x64,0x10,0x82,0x33,0xfb,0x0b,0x8c,0x3a,0xc8,0x92,0xd7,0x9e,0xf8,0xe0,0xfb,0xf9,0x2e,0xd1,0x33,0xad,0xdb,0x45,0x54,0x27,0x01,0x32,0x58,0x4d,0xc5,0x2e,0xef,0x41, + 0x04,0x6e,0xfa,0x09,0x2b,0x68,0xde,0x94,0x60,0xf0,0xbc,0xc9,0x19,0x00,0x5a,0x5f,0x6e,0x80,0xe1,0x9d,0xe9,0x89,0x68,0xbe,0x3c,0xd2,0xc7,0x70,0xa9,0x94,0x9b,0xfb,0x1a,0xc7,0x5e,0x6e,0x50,0x87,0xd6,0x55,0x0d,0x5f,0x9b,0xeb,0x1e,0x79,0xe5,0x02,0x93,0x07,0xbc,0x25,0x52,0x35,0xe2,0xd5,0xdc,0x99,0x24,0x1a,0xc3,0xab,0x88,0x6c,0x49, + 0x04,0x72,0xd4,0xa1,0x9c,0x4f,0x9d,0x2c,0xf5,0x84,0x8e,0xa4,0x04,0x45,0xb7,0x0d,0x46,0x96,0xb5,0xf0,0x2d,0x63,0x2c,0x0c,0x65,0x4c,0xc7,0xd7,0xee,0xb0,0xc6,0xd0,0x58,0xe8,0xc4,0xcd,0x99,0x43,0xe4,0x59,0x17,0x4c,0x7a,0xc0,0x1f,0xa7,0x42,0x19,0x8e,0x47,0xe6,0xc1,0x9a,0x6b,0xdb,0x0c,0x4f,0x6c,0x23,0x78,0x31,0xc1,0xb3,0xf9,0x42, + 0x04,0x2a,0x8e,0xa2,0xf5,0x0d,0xcc,0xed,0x0c,0x21,0x75,0x75,0xbd,0xfa,0x7c,0xd4,0x7d,0x1c,0x6f,0x10,0x00,0x41,0xec,0x0e,0x35,0x51,0x27,0x94,0xc1,0xbe,0x7e,0x74,0x02,0x58,0xf8,0xc1,0x71,0x22,0xed,0x30,0x3f,0xda,0x71,0x43,0xeb,0x58,0xbe,0xde,0x70,0x29,0x5b,0x65,0x32,0x66,0x01,0x3b,0x0b,0x0e,0xbd,0x3f,0x05,0x31,0x37,0xf6,0xec, + 0x04,0x88,0xde,0x68,0x9c,0xe9,0xaf,0x1e,0x94,0xbe,0x6a,0x20,0x89,0xc8,0xa8,0xb1,0x25,0x3f,0xfd,0xbb,0x6c,0x8e,0x9c,0x86,0x24,0x9b,0xa2,0x20,0x00,0x1a,0x4a,0xd3,0xb8,0x0c,0x49,0x98,0xe5,0x48,0x42,0xf4,0x13,0xb9,0xed,0xb1,0x82,0x5a,0xcb,0xb6,0x33,0x5e,0x81,0xe4,0xd1,0x84,0xb2,0xb0,0x1c,0x8b,0xeb,0xdc,0x85,0xd1,0xf2,0x89,0x46, + 0x04,0xfe,0xa2,0xd3,0x1f,0x70,0xf9,0x0d,0x5f,0xb3,0xe0,0x0e,0x18,0x6a,0xc4,0x2a,0xb3,0xc1,0x61,0x5c,0xee,0x71,0x4e,0x0b,0x4e,0x11,0x31,0xb3,0xd4,0xd8,0x22,0x5b,0xf7,0xb0,0x37,0xa1,0x8d,0xf2,0xac,0x15,0x34,0x3f,0x30,0xf7,0x40,0x67,0xdd,0xf2,0x9e,0x81,0x7d,0x5f,0x77,0xf8,0xdc,0xe0,0x57,0x14,0xda,0x59,0xc0,0x94,0xf0,0xcd,0xa9, + 0x04,0x72,0x58,0x91,0x1e,0x3d,0x42,0x33,0x49,0x16,0x64,0x79,0xdb,0xe0,0xb8,0x34,0x1a,0xf7,0xfb,0xd0,0x3d,0x0a,0x7e,0x10,0xed,0xcc,0xb3,0x6b,0x6c,0xee,0xa5,0xa3,0xdb,0x17,0xac,0x2b,0x89,0x92,0x79,0x11,0x28,0xfa,0x3b,0x96,0xdc,0x2f,0xbd,0x4c,0xa3,0xbf,0xa7,0x82,0xef,0x28,0x32,0xfc,0x66,0x56,0x94,0x3d,0xb1,0x8e,0x73,0x46,0xb0, + 0x04,0x4f,0x28,0x46,0x1d,0xea,0x64,0x47,0x4d,0x6b,0xb3,0x4d,0x14,0x99,0xc9,0x7d,0x37,0xb9,0xe9,0x56,0x33,0xdf,0x1c,0xee,0xea,0xac,0xd4,0x50,0x16,0xc9,0x8b,0x39,0x14,0xc8,0x81,0x88,0x10,0xb8,0xcc,0x06,0xdd,0xb4,0x0e,0x8a,0x12,0x61,0xc5,0x28,0xfa,0xa5,0x89,0x45,0x5d,0x5a,0x6d,0xf9,0x3b,0x77,0xbc,0x5e,0x0e,0x49,0x3c,0x74,0x70, + 0x04,0x74,0xf2,0xa8,0x14,0xfb,0x5d,0x8e,0xca,0x91,0xa6,0x9b,0x5e,0x60,0x71,0x27,0x32,0xb3,0x93,0x7d,0xe3,0x28,0x29,0xbe,0x97,0x4e,0xd7,0xb6,0x8c,0x5c,0x2f,0x5d,0x66,0xef,0xf0,0xf0,0x7c,0x56,0xf9,0x87,0xa6,0x57,0xf4,0x21,0x96,0x20,0x5f,0x58,0x8c,0x0f,0x1d,0x96,0xfd,0x8a,0x63,0xa5,0xf2,0x38,0xb4,0x8f,0x47,0x87,0x88,0xfe,0x3b, + 0x04,0x19,0x5b,0x51,0xa7,0xcc,0x4a,0x21,0xb8,0x27,0x4a,0x70,0xa9,0x0d,0xe7,0x79,0x81,0x4c,0x3c,0x8c,0xa3,0x58,0x32,0x82,0x08,0xc0,0x9a,0x29,0xf3,0x36,0xb8,0x2d,0x6a,0xb2,0x41,0x6b,0x7c,0x92,0xff,0xfd,0xc2,0x9c,0x3b,0x12,0x82,0xdd,0x2a,0x77,0xa4,0xd0,0x4d,0xf7,0xf7,0x45,0x20,0x47,0x39,0x3d,0x84,0x99,0x89,0xc5,0xce,0xe9,0xad, + 0x04,0x62,0x2f,0xc7,0x47,0x32,0x03,0x4b,0xec,0x2d,0xdf,0x3b,0xc1,0x6d,0x34,0xb3,0xd1,0xf7,0xa3,0x27,0xdd,0x2a,0x8c,0x19,0xba,0xb4,0xbb,0x4f,0xe3,0xa2,0x4b,0x58,0xaa,0x73,0x6b,0x2f,0x2f,0xae,0x76,0xf4,0xdf,0xae,0xcc,0x90,0x96,0x33,0x3b,0x01,0x32,0x8d,0x51,0xeb,0x3f,0xda,0x9c,0x92,0x27,0xe9,0x0d,0x0b,0x44,0x99,0x83,0xc4,0xf0, + 0x04,0x1f,0x7f,0x85,0xca,0xf2,0xd7,0x55,0x0e,0x7a,0xf9,0xb6,0x50,0x23,0xeb,0xb4,0xdc,0xe3,0x45,0x03,0x11,0x69,0x23,0x09,0xdb,0x26,0x99,0x69,0xb8,0x34,0xb6,0x11,0xc7,0x08,0x27,0xf4,0x5b,0x78,0x02,0x0e,0xcb,0xba,0xf4,0x84,0xfd,0xd5,0xbf,0xaa,0xe6,0x87,0x0f,0x11,0x84,0xc2,0x15,0x81,0xba,0xf6,0xef,0x82,0xbd,0x7b,0x53,0x0f,0x93, + 0x04,0x49,0xc1,0x97,0xdc,0x80,0xad,0x1d,0xa4,0x7a,0x43,0x42,0xb9,0x38,0x93,0xe8,0xe1,0xfb,0x0b,0xb9,0x4f,0xc3,0x3a,0x83,0xe7,0x83,0xc0,0x0b,0x24,0xc7,0x81,0x37,0x7a,0xef,0xc2,0x0d,0xa9,0x2b,0xac,0x76,0x29,0x51,0xf7,0x24,0x74,0xbe,0xcc,0x73,0x4d,0x4c,0xc2,0x2b,0xa8,0x1b,0x89,0x5e,0x28,0x2f,0xda,0xc4,0xdf,0x7a,0xf0,0xf3,0x7d, + 0x04,0xd8,0xcb,0x68,0x51,0x7b,0x61,0x6a,0x56,0x40,0x0a,0xa3,0x86,0x86,0x35,0xe5,0x4b,0x6f,0x69,0x95,0x98,0xa2,0xf6,0x16,0x77,0x57,0x65,0x49,0x80,0xba,0xf6,0xac,0xbe,0x7e,0xc8,0xcf,0x44,0x9c,0x84,0x9a,0xa0,0x34,0x61,0xa3,0x0e,0xfa,0xda,0x41,0x45,0x3c,0x57,0xc6,0xe6,0xfb,0xc9,0x3b,0xbc,0x6f,0xa4,0x9a,0xda,0x6d,0xc0,0x55,0x5c, + 0x04,0x03,0x07,0x13,0xfb,0x63,0xf2,0xaa,0x6f,0xe2,0xca,0xdf,0x1b,0x20,0xef,0xc2,0x59,0xc7,0x74,0x45,0xda,0xfa,0x87,0xda,0xc3,0x98,0xb8,0x40,0x65,0xca,0x34,0x7d,0xf3,0xb2,0x27,0x81,0x8d,0xe1,0xa3,0x9b,0x58,0x9c,0xb0,0x71,0xd8,0x3e,0x53,0x17,0xcc,0xcd,0xc2,0x33,0x8e,0x51,0xe3,0x12,0xfe,0x31,0xd8,0xdc,0x34,0xa4,0x80,0x17,0x50, + 0x04,0xba,0xbb,0x36,0x77,0xb0,0x95,0x58,0x02,0xd8,0xe9,0x29,0xa4,0x13,0x55,0x64,0x0e,0xaf,0x1e,0xa1,0x35,0x3f,0x8a,0x77,0x13,0x31,0xc4,0x94,0x6e,0x34,0x80,0xaf,0xa7,0x25,0x2f,0x19,0x6c,0x87,0xed,0x3d,0x2a,0x59,0xd3,0xb1,0xb5,0x59,0x13,0x7f,0xed,0x00,0x13,0xfe,0xce,0xfc,0x19,0xfb,0x5a,0x92,0x68,0x2b,0x9b,0xca,0x51,0xb9,0x50, + 0x04,0x1a,0xab,0x20,0x18,0x79,0x34,0x71,0x11,0x1a,0x8a,0x0e,0x9b,0x14,0x3f,0xde,0x02,0xfc,0x95,0x92,0x07,0x96,0xd3,0xa6,0x3d,0xe3,0x29,0xb4,0x24,0x39,0x6f,0xba,0x60,0xbb,0xe4,0x13,0x07,0x05,0x17,0x47,0x92,0x44,0x1b,0x31,0x8d,0x3a,0xa3,0x1d,0xfe,0x85,0x77,0x82,0x1e,0x9b,0x44,0x6e,0xc5,0x73,0xd2,0x72,0xe0,0x36,0xc4,0xeb,0xe9, + 0x04,0x8c,0xb0,0xb9,0x09,0x49,0x9c,0x83,0xea,0x80,0x6c,0xd8,0x85,0xb1,0xdd,0x46,0x7a,0x01,0x19,0xf0,0x6a,0x88,0xa0,0x27,0x6e,0xb0,0xcf,0xda,0x27,0x45,0x35,0xa8,0xff,0x47,0xb5,0x42,0x88,0x33,0xbc,0x3f,0x2c,0x8b,0xf9,0xd9,0x04,0x11,0x58,0xcf,0x33,0x71,0x8a,0x69,0x96,0x1c,0xd0,0x17,0x29,0xbc,0x00,0x11,0xd1,0xe5,0x86,0xab,0x75, + 0x04,0x8f,0x03,0xcf,0x1a,0x42,0x27,0x2b,0xb1,0x53,0x27,0x23,0x09,0x3f,0x72,0xe6,0xfe,0xea,0xc8,0x5e,0x17,0x00,0xe9,0xfb,0xe9,0xa6,0xa2,0xdd,0x64,0x2d,0x74,0xbf,0x5d,0x3b,0x89,0xa7,0x18,0x9d,0xad,0x8c,0xf7,0x5f,0xc2,0x2f,0x6f,0x15,0x8a,0xa2,0x7f,0x9c,0x2c,0xa0,0x0d,0xac,0xa7,0x85,0xbe,0x33,0x58,0xf2,0xbd,0xa3,0x86,0x2c,0xa0, + 0x04,0x44,0xde,0x3b,0x9c,0x7a,0x57,0xa8,0xc9,0xe8,0x20,0x95,0x27,0x53,0x42,0x1e,0x7d,0x98,0x7b,0xb3,0xd7,0x9f,0x71,0xf0,0x13,0x80,0x5c,0x89,0x7e,0x01,0x8f,0x8a,0xce,0xa2,0x46,0x07,0x58,0xc8,0xf9,0x8d,0x3f,0xdc,0xe1,0x21,0xa9,0x43,0x65,0x9e,0x37,0x2c,0x32,0x6f,0xff,0x2e,0x5f,0xc2,0xae,0x7f,0xa3,0xf7,0x9d,0xaa,0xe1,0x3c,0x12, + 0x04,0x6f,0xb8,0xb2,0xb4,0x8e,0x33,0x03,0x12,0x68,0xad,0x6a,0x51,0x74,0x84,0xdc,0x88,0x39,0xea,0x90,0xf6,0x66,0x9e,0xa0,0xc7,0xac,0x32,0x33,0xe2,0xac,0x31,0x39,0x4a,0x0a,0xc8,0xbb,0xe7,0xf7,0x3c,0x2f,0xf4,0xdf,0x99,0x78,0x72,0x7a,0xc1,0xdf,0xc2,0xfd,0x58,0x64,0x7d,0x20,0xf3,0x1f,0x99,0x10,0x53,0x16,0xb6,0x46,0x71,0xf2,0x04, + 0x04,0xbe,0xa7,0x11,0x22,0xa0,0x48,0x69,0x3e,0x90,0x5f,0xf6,0x02,0xb3,0xcf,0x9d,0xd1,0x8a,0xf6,0x9b,0x9f,0xc9,0xd8,0x43,0x1d,0x2b,0x1d,0xd2,0x6b,0x94,0x2c,0x95,0xe6,0xf4,0x3c,0x7b,0x8b,0x95,0xeb,0x62,0x08,0x2c,0x12,0xdb,0x9d,0xbd,0xa7,0xfe,0x38,0xe4,0x5c,0xbe,0x4a,0x48,0x86,0x90,0x7f,0xb8,0x1b,0xdb,0x0c,0x5e,0xa9,0x24,0x6c, + 0x04,0xda,0x91,0x8c,0x73,0x1b,0xa0,0x6a,0x20,0xcb,0x94,0xef,0x33,0xb7,0x78,0xe9,0x81,0xa4,0x04,0xa3,0x05,0xf1,0x94,0x1f,0xe3,0x36,0x66,0xb4,0x5b,0x03,0x35,0x31,0x56,0xe2,0xbb,0x26,0x94,0xf5,0x75,0xb4,0x51,0x83,0xbe,0x78,0xe5,0xc9,0xb5,0x21,0x0b,0xf3,0xbf,0x48,0x8f,0xd4,0xc8,0x29,0x45,0x16,0xd8,0x95,0x72,0xca,0x4f,0x53,0x91, + 0x04,0x30,0x07,0xe9,0x2c,0x39,0x37,0xda,0xde,0x79,0x64,0xdf,0xa3,0x5b,0x0e,0xff,0x03,0x1f,0x7e,0xb0,0x2a,0xed,0x0a,0x03,0x14,0x41,0x11,0x06,0xcd,0xeb,0x70,0xfe,0x3d,0x5a,0x75,0x46,0xfc,0x05,0x52,0x99,0x7b,0x20,0xe3,0xd6,0xf4,0x13,0xe7,0x5e,0x2c,0xb6,0x6e,0x11,0x63,0x22,0x69,0x71,0x14,0xb7,0x9b,0xac,0x73,0x4b,0xfc,0x4d,0xc5, + 0x04,0x60,0xe7,0x34,0xef,0x56,0x24,0xd3,0xcb,0xf0,0xdd,0xd3,0x75,0x01,0x1b,0xd6,0x63,0xd6,0xd6,0xae,0xbc,0x64,0x4e,0xb5,0x99,0xfd,0xf9,0x8d,0xbd,0xcd,0x18,0xce,0x9b,0xd2,0xd9,0x0b,0x3a,0xc3,0x1f,0x13,0x9a,0xf8,0x32,0xcc,0xcf,0x6c,0xcb,0xbb,0x2c,0x6e,0xa1,0x1f,0xa9,0x73,0x70,0xdc,0x99,0x06,0xda,0x47,0x4d,0x7d,0x8a,0x75,0x67, + 0x04,0x85,0xa9,0x00,0xe9,0x78,0x58,0xf6,0x93,0xc0,0xb7,0xdf,0xa2,0x61,0xe3,0x80,0xda,0xd6,0xea,0x04,0x6d,0x1f,0x65,0xdd,0xee,0xed,0xd5,0xf7,0xd8,0xaf,0x0b,0xa3,0x37,0x69,0x74,0x4d,0x15,0xad,0xd4,0xf6,0xc0,0xbc,0x3b,0x0d,0xa2,0xae,0xc9,0x3b,0x34,0xcb,0x8c,0x65,0xf9,0x34,0x0d,0xdf,0x74,0xe7,0xb0,0x00,0x9e,0xee,0xcc,0xce,0x3c, + 0x04,0x38,0x06,0x6f,0x75,0xd8,0x8e,0xfc,0x4c,0x93,0xde,0x36,0xf4,0x9e,0x03,0x7b,0x23,0x4c,0xc1,0x8b,0x1d,0xe5,0x60,0x87,0x50,0xa6,0x2c,0xab,0x03,0x45,0x40,0x10,0x46,0xa3,0xe8,0x4b,0xed,0x8c,0xfc,0xb8,0x19,0xef,0x4d,0x55,0x04,0x44,0xf2,0xce,0x4b,0x65,0x17,0x66,0xb6,0x9e,0x2e,0x29,0x01,0xf8,0x88,0x36,0xff,0x90,0x03,0x4f,0xed, + 0x04,0x98,0xf6,0x81,0x77,0xdc,0x95,0xc1,0xb4,0xcb,0xfa,0x52,0x45,0x48,0x8c,0xa5,0x23,0xa7,0xd5,0x62,0x94,0x70,0xd0,0x35,0xd6,0x21,0xa4,0x43,0xc7,0x2f,0x39,0xaa,0xbf,0xa3,0x3d,0x29,0x54,0x6f,0xa1,0xc6,0x48,0xf2,0xc7,0xd5,0xcc,0xf7,0x0c,0xf1,0xce,0x4a,0xb7,0x9b,0x5d,0xb1,0xac,0x05,0x9d,0xbe,0xcd,0x06,0x8d,0xbd,0xff,0x1b,0x89, + 0x04,0x5c,0x2b,0xbf,0xa2,0x3c,0x9b,0x9a,0xd0,0x7f,0x03,0x8a,0xa8,0x9b,0x49,0x30,0xbf,0x26,0x7d,0x94,0x01,0xe4,0x25,0x5d,0xe9,0xe8,0xda,0x0a,0x50,0x78,0xec,0x82,0x77,0xe3,0xe8,0x82,0xa3,0x1d,0x5e,0x6a,0x37,0x9e,0x07,0x93,0x98,0x3c,0xcd,0xed,0x39,0xb9,0x5c,0x43,0x53,0xab,0x2f,0xf0,0x1e,0xa5,0x36,0x9b,0xa4,0x7b,0x0c,0x31,0x91, + 0x04,0x2e,0xa7,0x13,0x34,0x32,0x33,0x9c,0x69,0xd2,0x7f,0x9b,0x26,0x72,0x81,0xbd,0x2d,0xdd,0x5f,0x19,0xd6,0x33,0x8d,0x40,0x0a,0x05,0xcd,0x36,0x47,0xb1,0x57,0xa3,0x85,0x35,0x47,0x80,0x82,0x98,0x44,0x8e,0xdb,0x5e,0x70,0x1a,0xde,0x84,0xcd,0x5f,0xb1,0xac,0x95,0x67,0xba,0x5e,0x8f,0xb6,0x8a,0x6b,0x93,0x3e,0xc4,0xb5,0xcc,0x84,0xcc, + 0x04,0x2e,0xa7,0x13,0x34,0x32,0x33,0x9c,0x69,0xd2,0x7f,0x9b,0x26,0x72,0x81,0xbd,0x2d,0xdd,0x5f,0x19,0xd6,0x33,0x8d,0x40,0x0a,0x05,0xcd,0x36,0x47,0xb1,0x57,0xa3,0x85,0xca,0xb8,0x7f,0x7d,0x67,0xbb,0x71,0x24,0xa1,0x8f,0xe5,0x21,0x7b,0x32,0xa0,0x4e,0x53,0x6a,0x98,0x45,0xa1,0x70,0x49,0x75,0x94,0x6c,0xc1,0x3a,0x4a,0x33,0x77,0x63, + 0x04,0x8a,0xa2,0xc6,0x4f,0xa9,0xc6,0x43,0x75,0x63,0xab,0xfb,0xcb,0xd0,0x0b,0x20,0x48,0xd4,0x8c,0x18,0xc1,0x52,0xa2,0xa6,0xf4,0x90,0x36,0xde,0x76,0x47,0xeb,0xe8,0x2e,0x1c,0xe6,0x43,0x87,0x99,0x5c,0x68,0xa0,0x60,0xfa,0x3b,0xc0,0x39,0x9b,0x05,0xcc,0x06,0xee,0xc7,0xd5,0x98,0xf7,0x50,0x41,0xa4,0x91,0x7e,0x69,0x2b,0x7f,0x51,0xff, + 0x04,0x39,0x14,0x27,0xff,0x7e,0xe7,0x80,0x13,0xc1,0x4a,0xec,0x7d,0x96,0xa8,0xa0,0x62,0x20,0x92,0x98,0xa7,0x83,0x83,0x5e,0x94,0xfd,0x65,0x49,0xd5,0x02,0xff,0xf7,0x1f,0xdd,0x66,0x24,0xec,0x34,0x3a,0xd9,0xfc,0xf4,0xd9,0x87,0x21,0x81,0xe5,0x9f,0x84,0x2f,0x9b,0xa4,0xcc,0xca,0xe0,0x9a,0x6c,0x09,0x72,0xfb,0x6a,0xc6,0xb4,0xc6,0xbd, + 0x04,0xe7,0x62,0xb8,0xa2,0x19,0xb4,0xf1,0x80,0x21,0x9c,0xc7,0xa9,0x05,0x92,0x45,0xe4,0x96,0x1b,0xd1,0x91,0xc0,0x38,0x99,0x78,0x9c,0x7a,0x34,0xb8,0x9e,0x8c,0x13,0x8e,0xc1,0x53,0x3e,0xf0,0x41,0x9b,0xb7,0x37,0x6e,0x0b,0xfd,0xe9,0x31,0x9d,0x10,0xa0,0x69,0x68,0x79,0x1d,0x9e,0xa0,0xee,0xd9,0xc1,0xce,0x63,0x45,0xae,0xd9,0x75,0x9e, + 0x04,0x9a,0xed,0xb0,0xd2,0x81,0xdb,0x16,0x4e,0x13,0x00,0x00,0xc5,0x69,0x7f,0xae,0x0f,0x30,0x5e,0xf8,0x48,0xbe,0x6f,0xff,0xb4,0x3a,0xc5,0x93,0xfb,0xb9,0x50,0xe9,0x52,0xfa,0x6f,0x63,0x33,0x59,0xbd,0xcd,0x82,0xb5,0x6b,0x0b,0x9f,0x96,0x5b,0x03,0x77,0x89,0xd4,0x6b,0x9a,0x81,0x41,0xb7,0x91,0xb2,0xae,0xfa,0x71,0x3f,0x96,0xc1,0x75, + 0x04,0x8a,0xd4,0x45,0xdb,0x62,0x81,0x62,0x60,0xe4,0xe6,0x87,0xfd,0x18,0x84,0xe4,0x8b,0x9f,0xc0,0x63,0x6d,0x03,0x15,0x47,0xd6,0x33,0x15,0xe7,0x92,0xe1,0x9b,0xfa,0xee,0x1d,0xe6,0x4f,0x99,0xd5,0xf1,0xcd,0x8b,0x6e,0xc9,0xcb,0x0f,0x78,0x7a,0x65,0x4a,0xe8,0x69,0x93,0xba,0x3d,0xb1,0x00,0x8e,0xf4,0x3c,0xff,0x06,0x84,0xcb,0x22,0xbd, + 0x04,0x1f,0x57,0x99,0xc9,0x5b,0xe8,0x90,0x63,0xb2,0x4f,0x26,0xe4,0x0c,0xb9,0x28,0xc1,0xa8,0x68,0xa7,0x6f,0xb0,0x09,0x46,0x07,0xe8,0x04,0x3d,0xb4,0x09,0xc9,0x1c,0x32,0xe7,0x57,0x24,0xe8,0x13,0xa4,0x19,0x1e,0x3a,0x83,0x90,0x07,0xf0,0x8e,0x2e,0x89,0x73,0x88,0xb0,0x6d,0x4a,0x00,0xde,0x6d,0xe6,0x0e,0x53,0x6d,0x91,0xfa,0xb5,0x66, + 0x04,0xa3,0x33,0x1a,0x4e,0x1b,0x42,0x23,0xec,0x2c,0x02,0x7e,0xdd,0x48,0x2c,0x92,0x8a,0x14,0xed,0x35,0x8d,0x93,0xf1,0xd4,0x21,0x7d,0x39,0xab,0xf6,0x9f,0xcb,0x5c,0xcc,0x28,0xd6,0x84,0xd2,0xaa,0xab,0xcd,0x63,0x83,0x77,0x5c,0xaa,0x62,0x39,0xde,0x26,0xd4,0xc6,0x93,0x7b,0xb6,0x03,0xec,0xb4,0x19,0x60,0x82,0xf4,0xcf,0xfd,0x50,0x9d, + 0x04,0x3f,0x39,0x52,0x19,0x97,0x74,0xc7,0xcf,0x39,0xb3,0x8b,0x66,0xcb,0x10,0x42,0xa6,0x26,0x0d,0x86,0x80,0x80,0x38,0x45,0xe4,0xd4,0x33,0xad,0xba,0x3b,0xb2,0x48,0x18,0x5e,0xa4,0x95,0xb6,0x8c,0xbc,0x7e,0xd4,0x17,0x3e,0xe6,0x3c,0x90,0x42,0xdc,0x50,0x26,0x25,0xc7,0xeb,0x7e,0x21,0xfb,0x02,0xca,0x9a,0x91,0x14,0xe0,0xa3,0xa1,0x8d, + 0x04,0xcd,0xfb,0x8c,0x0f,0x42,0x2e,0x14,0x4e,0x13,0x7c,0x24,0x12,0xc8,0x6c,0x17,0x1f,0x5f,0xe3,0xfa,0x3f,0x5b,0xbb,0x54,0x4e,0x90,0x76,0x28,0x8f,0x3c,0xed,0x78,0x6e,0x05,0x4f,0xd0,0x72,0x1b,0x77,0xc1,0x1c,0x79,0xbe,0xac,0xb3,0xc9,0x42,0x11,0xb0,0xa1,0x9b,0xda,0x08,0x65,0x2e,0xfe,0xaf,0x92,0x51,0x3a,0x3b,0x0a,0x16,0x36,0x98, + 0x04,0x73,0x59,0x8a,0x6a,0x1c,0x68,0x27,0x8f,0xa6,0xbf,0xd0,0xce,0x40,0x64,0xe6,0x82,0x35,0xbc,0x1c,0x0f,0x6b,0x20,0xa9,0x28,0x10,0x8b,0xe3,0x36,0x73,0x0f,0x87,0xe3,0xcb,0xae,0x61,0x25,0x19,0xb5,0x03,0x2e,0xcc,0x85,0xae,0xd8,0x11,0x27,0x1a,0x95,0xfe,0x79,0x39,0xd5,0xd3,0x46,0x01,0x40,0xba,0x31,0x8f,0x4d,0x14,0xab,0xa3,0x1d, + 0x04,0x58,0xde,0xbd,0x9a,0x7e,0xe2,0xc9,0xd5,0x91,0x32,0x47,0x8a,0x54,0x40,0xae,0x4d,0x5d,0x7e,0xd4,0x37,0x30,0x83,0x69,0xf9,0x2e,0xa8,0x6c,0x82,0x18,0x3f,0x10,0xa1,0x67,0x73,0xe7,0x6f,0x5e,0xdb,0xf4,0xda,0x0e,0x4f,0x1b,0xdf,0xfa,0xc0,0xf5,0x72,0x57,0xe1,0xdf,0xa4,0x65,0x84,0x29,0x31,0x30,0x9a,0x24,0x24,0x5f,0xda,0x6a,0x5d, + 0x04,0x8b,0x90,0x4d,0xe4,0x79,0x67,0x34,0x0c,0x5f,0x8c,0x35,0x72,0xa7,0x20,0x92,0x4e,0xf7,0x57,0x86,0x37,0xfe,0xab,0x19,0x49,0xac,0xb2,0x41,0xa5,0xa6,0xac,0x3f,0x5b,0x95,0x09,0x04,0x49,0x6f,0x98,0x24,0xb1,0xd6,0x3f,0x33,0x13,0xba,0xe2,0x1b,0x89,0xfa,0xe8,0x9a,0xfd,0xfc,0x81,0x1b,0x5e,0xce,0x03,0xfd,0x5a,0xa3,0x01,0x86,0x4f, + 0x04,0xf4,0x89,0x2b,0x6d,0x52,0x5c,0x77,0x1e,0x03,0x5f,0x2a,0x25,0x27,0x08,0xf3,0x78,0x4e,0x48,0x23,0x86,0x04,0xb4,0xf9,0x4d,0xc5,0x6e,0xaa,0x1e,0x54,0x6d,0x94,0x1a,0x34,0x6b,0x1a,0xa0,0xbc,0xe6,0x8b,0x1c,0x50,0xe5,0xb5,0x2f,0x50,0x9f,0xb5,0x52,0x2e,0x5c,0x25,0xe0,0x28,0xbc,0x8f,0x86,0x34,0x02,0xed,0xb7,0xbc,0xad,0x8b,0x1b, + 0x04,0x79,0xbe,0x66,0x7e,0xf9,0xdc,0xbb,0xac,0x55,0xa0,0x62,0x95,0xce,0x87,0x0b,0x07,0x02,0x9b,0xfc,0xdb,0x2d,0xce,0x28,0xd9,0x59,0xf2,0x81,0x5b,0x16,0xf8,0x17,0x98,0x48,0x3a,0xda,0x77,0x26,0xa3,0xc4,0x65,0x5d,0xa4,0xfb,0xfc,0x0e,0x11,0x08,0xa8,0xfd,0x17,0xb4,0x48,0xa6,0x85,0x54,0x19,0x9c,0x47,0xd0,0x8f,0xfb,0x10,0xd4,0xb8, + 0x04,0x79,0xbe,0x66,0x7e,0xf9,0xdc,0xbb,0xac,0x55,0xa0,0x62,0x95,0xce,0x87,0x0b,0x07,0x02,0x9b,0xfc,0xdb,0x2d,0xce,0x28,0xd9,0x59,0xf2,0x81,0x5b,0x16,0xf8,0x17,0x98,0xb7,0xc5,0x25,0x88,0xd9,0x5c,0x3b,0x9a,0xa2,0x5b,0x04,0x03,0xf1,0xee,0xf7,0x57,0x02,0xe8,0x4b,0xb7,0x59,0x7a,0xab,0xe6,0x63,0xb8,0x2f,0x6f,0x04,0xef,0x27,0x77, + 0x04,0x78,0x2c,0x8e,0xd1,0x7e,0x3b,0x2a,0x78,0x3b,0x54,0x64,0xf3,0x3b,0x09,0x65,0x2a,0x71,0xc6,0x78,0xe0,0x5e,0xc5,0x1e,0x84,0xe2,0xbc,0xfc,0x66,0x3a,0x3d,0xe9,0x63,0xaf,0x9a,0xcb,0x42,0x80,0xb8,0xc7,0xf7,0xc4,0x2f,0x4e,0xf9,0xab,0xa6,0x24,0x5e,0xc1,0xec,0x17,0x12,0xfd,0x38,0xa0,0xfa,0x96,0x41,0x8d,0x8c,0xd6,0xaa,0x61,0x52, + 0x04,0x6e,0x82,0x35,0x55,0x45,0x29,0x14,0x09,0x91,0x82,0xc6,0xb2,0xc1,0xd6,0xf0,0xb5,0xd2,0x8d,0x50,0xcc,0xd0,0x05,0xaf,0x2c,0xe1,0xbb,0xa5,0x41,0xaa,0x40,0xca,0xff,0x00,0x00,0x00,0x01,0x06,0x04,0x92,0xd5,0xa5,0x67,0x3e,0x0f,0x25,0xd8,0xd5,0x0f,0xb7,0xe5,0x8c,0x49,0xd8,0x6d,0x46,0xd4,0x21,0x69,0x55,0xe0,0xaa,0x3d,0x40,0xe1, + 0x04,0x6e,0x82,0x35,0x55,0x45,0x29,0x14,0x09,0x91,0x82,0xc6,0xb2,0xc1,0xd6,0xf0,0xb5,0xd2,0x8d,0x50,0xcc,0xd0,0x05,0xaf,0x2c,0xe1,0xbb,0xa5,0x41,0xaa,0x40,0xca,0xff,0xff,0xff,0xff,0xfe,0xf9,0xfb,0x6d,0x2a,0x5a,0x98,0xc1,0xf0,0xda,0x27,0x2a,0xf0,0x48,0x1a,0x73,0xb6,0x27,0x92,0xb9,0x2b,0xde,0x96,0xaa,0x1e,0x55,0xc2,0xbb,0x4e, + 0x04,0x00,0x00,0x00,0x01,0x3f,0xd2,0x22,0x48,0xd6,0x4d,0x95,0xf7,0x3c,0x29,0xb4,0x8a,0xb4,0x86,0x31,0x85,0x0b,0xe5,0x03,0xfd,0x00,0xf8,0x46,0x8b,0x5f,0x0f,0x70,0xe0,0xf6,0xee,0x7a,0xa4,0x3b,0xc2,0xc6,0xfd,0x25,0xb1,0xd8,0x26,0x92,0x41,0xcb,0xdd,0x9d,0xbb,0x0d,0xac,0x96,0xdc,0x96,0x23,0x1f,0x43,0x07,0x05,0xf8,0x38,0x71,0x7d, + 0x04,0x25,0xaf,0xd6,0x89,0xac,0xab,0xae,0xd6,0x7c,0x1f,0x29,0x6d,0xe5,0x94,0x06,0xf8,0xc5,0x50,0xf5,0x71,0x46,0xa0,0xb4,0xec,0x2c,0x97,0x87,0x6d,0xff,0xff,0xff,0xff,0xfa,0x46,0xa7,0x6e,0x52,0x03,0x22,0xdf,0xbc,0x49,0x1e,0xc4,0xf0,0xcc,0x19,0x74,0x20,0xfc,0x4e,0xa5,0x88,0x3d,0x8f,0x6d,0xd5,0x3c,0x35,0x4b,0xc4,0xf6,0x7c,0x35, + 0x04,0xd1,0x2e,0x6c,0x66,0xb6,0x77,0x34,0xc3,0xc8,0x4d,0x26,0x01,0xcf,0x5d,0x35,0xdc,0x09,0x7e,0x27,0x63,0x7f,0x0a,0xca,0x4a,0x4f,0xdb,0x74,0xb6,0xaa,0xdd,0x3b,0xb9,0x3f,0x5b,0xdf,0xf8,0x8b,0xd5,0x73,0x6d,0xf8,0x98,0xe6,0x99,0x00,0x6e,0xd7,0x50,0xf1,0x1c,0xf0,0x7c,0x58,0x66,0xcd,0x7a,0xd7,0x0c,0x71,0x21,0xff,0xff,0xff,0xff, + 0x04,0x6d,0x4a,0x7f,0x60,0xd4,0x77,0x4a,0x4f,0x0a,0xa8,0xbb,0xde,0xdb,0x95,0x3c,0x7e,0xea,0x79,0x09,0x40,0x7e,0x31,0x64,0x75,0x56,0x64,0xbc,0x28,0x00,0x00,0x00,0x00,0xe6,0x59,0xd3,0x4e,0x4d,0xf3,0x8d,0x9e,0x8c,0x9e,0xaa,0xdf,0xba,0x36,0x61,0x2c,0x76,0x91,0x95,0xbe,0x86,0xc7,0x7a,0xac,0x3f,0x36,0xe7,0x8b,0x53,0x86,0x80,0xfb}; + +static const unsigned char wycheproof_ecdsa_signatures[] = { 0x30,0x46,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x21,0x00,0x90,0x0e,0x75,0xad,0x23,0x3f,0xcc,0x90,0x85,0x09,0xdb,0xff,0x59,0x22,0x64,0x7d,0xb3,0x7c,0x21,0xf4,0xaf,0xd3,0x20,0x3a,0xe8,0xdc,0x4a,0xe7,0x79,0x4b,0x0f,0x87, + 0x30,0x45,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x81,0x45,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x82,0x00,0x45,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x46,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x44,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x85,0x01,0x00,0x00,0x00,0x45,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x89,0x01,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x45,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x84,0x7f,0xff,0xff,0xff,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x84,0x80,0x00,0x00,0x00,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x84,0xff,0xff,0xff,0xff,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x85,0xff,0xff,0xff,0xff,0xff,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x88,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0xff,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x80,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30, + 0x30,0x47,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba,0x00,0x00, + 0x30,0x47,0x00,0x00,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x45,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba,0x00,0x00, + 0x30,0x47,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba,0x05,0x00, + 0x30,0x4a,0x49,0x81,0x77,0x30,0x45,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x49,0x25,0x00,0x30,0x45,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x47,0x30,0x45,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba,0x00,0x04,0xde,0xad,0xbe,0xef, + 0x30,0x4d,0xaa,0x00,0xbb,0x00,0xcd,0x00,0x30,0x45,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x4d,0x22,0x29,0xaa,0x00,0xbb,0x00,0xcd,0x00,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x4d,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x22,0x28,0xaa,0x00,0xbb,0x00,0xcd,0x00,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x81, + 0x30,0x4b,0xaa,0x02,0xaa,0xbb,0x30,0x45,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x80,0x30,0x45,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba,0x00,0x00, + 0x30,0x80,0x31,0x45,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba,0x00,0x00, + 0x05,0x00, + 0x2e,0x45,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x2f,0x45,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x31,0x45,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x32,0x45,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0xff,0x45,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x00, + 0x30,0x49,0x30,0x01,0x02,0x30,0x44,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x44,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31, + 0x30,0x44,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x82,0x10,0x46,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x30,0x80,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba,0x00,0x00, + 0x30,0x80,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba,0x00, + 0x30,0x80,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba,0x05,0x00,0x00,0x00, + 0x30,0x80,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba,0x06,0x08,0x11,0x22,0x00,0x00, + 0x30,0x80,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba,0x00,0x00,0xfe,0x02,0xbe,0xef, + 0x30,0x80,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba,0x00,0x02,0xbe,0xef, + 0x30,0x47,0x30,0x00,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x47,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba,0x30,0x00, + 0x30,0x48,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba,0x02,0x01,0x00, + 0x30,0x48,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba,0xbf,0x7f,0x00, + 0x30,0x49,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba,0xa0,0x02,0x05,0x00, + 0x30,0x47,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba,0xa0,0x00, + 0x30,0x47,0x30,0x45,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x23,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65, + 0x30,0x67,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x43,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x64,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x43,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xca,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x43,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x13,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x43,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x08,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x46,0x02,0x81,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x47,0x02,0x82,0x00,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x45,0x02,0x22,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x45,0x02,0x20,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x4a,0x02,0x85,0x01,0x00,0x00,0x00,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x4e,0x02,0x89,0x01,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x49,0x02,0x84,0x7f,0xff,0xff,0xff,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x49,0x02,0x84,0x80,0x00,0x00,0x00,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x49,0x02,0x84,0xff,0xff,0xff,0xff,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x4a,0x02,0x85,0xff,0xff,0xff,0xff,0xff,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x4d,0x02,0x88,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x45,0x02,0xff,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x45,0x02,0x80,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x22,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x23,0x02,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x24,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02, + 0x30,0x47,0x02,0x23,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x00,0x00,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x47,0x02,0x23,0x00,0x00,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x47,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x00,0x00,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x47,0x02,0x23,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x05,0x00,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x4a,0x22,0x26,0x49,0x81,0x77,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x49,0x22,0x25,0x25,0x00,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x4d,0x22,0x23,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x00,0x04,0xde,0xad,0xbe,0xef,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x24,0x02,0x81,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x4b,0x22,0x27,0xaa,0x02,0xaa,0xbb,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x49,0x22,0x80,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x00,0x00,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x49,0x22,0x80,0x03,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x00,0x00,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x24,0x05,0x00,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x45,0x00,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x45,0x01,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x45,0x03,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x45,0x04,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x45,0xff,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x24,0x02,0x00,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x49,0x22,0x25,0x02,0x01,0x00,0x02,0x20,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x45,0x02,0x21,0x02,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x45,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0xe5,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x44,0x02,0x20,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x44,0x02,0x20,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x82,0x10,0x48,0x02,0x82,0x10,0x22,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x46,0x02,0x22,0xff,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x25,0x09,0x01,0x80,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x25,0x02,0x01,0x00,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x43,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xbb, + 0x30,0x43,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa4,0x56,0xeb,0x31,0xba, + 0x30,0x43,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf7,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x43,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x01,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x46,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x81,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x47,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x82,0x00,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x45,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x21,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x45,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x1f,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x4a,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x85,0x01,0x00,0x00,0x00,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x4e,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x89,0x01,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x49,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x84,0x7f,0xff,0xff,0xff,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x49,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x84,0x80,0x00,0x00,0x00,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x49,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x84,0xff,0xff,0xff,0xff,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x4a,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x85,0xff,0xff,0xff,0xff,0xff,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x4d,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x88,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x45,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0xff,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x45,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x80,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x47,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x22,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba,0x00,0x00, + 0x30,0x47,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x22,0x00,0x00,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x47,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x22,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba,0x05,0x00, + 0x30,0x4a,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x22,0x25,0x49,0x81,0x77,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x49,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x22,0x24,0x25,0x00,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x4d,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x22,0x22,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba,0x00,0x04,0xde,0xad,0xbe,0xef, + 0x30,0x25,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x81, + 0x30,0x4b,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x22,0x26,0xaa,0x02,0xaa,0xbb,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x49,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x22,0x80,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba,0x00,0x00, + 0x30,0x49,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x22,0x80,0x03,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba,0x00,0x00, + 0x30,0x25,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x05,0x00, + 0x30,0x45,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x00,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x45,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x01,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x45,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x03,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x45,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x04,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x45,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0xff,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x25,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x00, + 0x30,0x49,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x22,0x24,0x02,0x01,0x6f,0x02,0x1f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x45,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6d,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x45,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0x3a, + 0x30,0x44,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x1f,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31, + 0x30,0x44,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x1f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x82,0x10,0x48,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x82,0x10,0x21,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x30,0x46,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x21,0xff,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x26,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x09,0x01,0x80, + 0x30,0x26,0x02,0x21,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x01,0x00, + 0x30,0x45,0x02,0x21,0x01,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x83,0xb9,0x0d,0xea,0xbc,0xa4,0xb0,0x5c,0x45,0x74,0xe4,0x9b,0x58,0x99,0xb9,0x64,0xa6,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x44,0x02,0x20,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x86,0x43,0xb0,0x30,0xef,0x46,0x1f,0x1b,0xcd,0xf5,0x3f,0xde,0x3e,0xf9,0x4c,0xe2,0x24,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x46,0x02,0x22,0x01,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x84,0x3f,0xad,0x3b,0xf4,0x85,0x3e,0x07,0xf7,0xc9,0x87,0x70,0xc9,0x9b,0xff,0xc4,0x64,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x45,0x02,0x21,0xff,0x7e,0xc1,0x08,0x63,0x31,0x05,0x65,0xa9,0x08,0x45,0x7f,0xa0,0xf1,0xb8,0x7a,0x7b,0x01,0xa0,0xf2,0x2a,0x0a,0x98,0x43,0xf6,0x4a,0xed,0xc3,0x34,0x36,0x7c,0xdc,0x9b,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x44,0x02,0x20,0x7e,0xc1,0x08,0x63,0x31,0x05,0x65,0xa9,0x08,0x45,0x7f,0xa0,0xf1,0xb8,0x7a,0x79,0xbc,0x4f,0xcf,0x10,0xb9,0xe0,0xe4,0x32,0x0a,0xc0,0x21,0xc1,0x06,0xb3,0x1d,0xdc,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x45,0x02,0x21,0xfe,0x7e,0xc1,0x08,0x63,0x31,0x05,0x65,0xa9,0x08,0x45,0x7f,0xa0,0xf1,0xb8,0x7a,0x7c,0x46,0xf2,0x15,0x43,0x5b,0x4f,0xa3,0xba,0x8b,0x1b,0x64,0xa7,0x66,0x46,0x9b,0x5a,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x45,0x02,0x21,0x01,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x4d,0x02,0x29,0x01,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x81,0x3e,0xf7,0x9c,0xce,0xfa,0x9a,0x56,0xf7,0xba,0x80,0x5f,0x0e,0x47,0x85,0x84,0xfe,0x5f,0x0d,0xd5,0xf5,0x67,0xbc,0x09,0xb5,0x12,0x3c,0xcb,0xc9,0x83,0x23,0x65,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x45,0x02,0x21,0x01,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x7f,0xc1,0xe1,0x97,0xd8,0xae,0xbe,0x20,0x3c,0x96,0xc8,0x72,0x32,0x27,0x21,0x72,0xfb,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x45,0x02,0x21,0xff,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x82,0x4c,0x83,0xde,0x0b,0x50,0x2c,0xdf,0xc5,0x17,0x23,0xb5,0x18,0x86,0xb4,0xf0,0x79,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x46,0x02,0x22,0x01,0x00,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9a,0x3b,0xb6,0x0f,0xa1,0xa1,0x48,0x15,0xbb,0xc0,0xa9,0x54,0xa0,0x75,0x8d,0x2c,0x72,0xba,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x44,0x02,0x20,0x90,0x0e,0x75,0xad,0x23,0x3f,0xcc,0x90,0x85,0x09,0xdb,0xff,0x59,0x22,0x64,0x7e,0xf8,0xcd,0x45,0x0e,0x00,0x8a,0x7f,0xff,0x29,0x09,0xec,0x5a,0xa9,0x14,0xce,0x46,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x45,0x02,0x21,0xfe,0x90,0x0e,0x75,0xad,0x23,0x3f,0xcc,0x90,0x85,0x09,0xdb,0xff,0x59,0x22,0x64,0x80,0x3e,0x1e,0x68,0x27,0x51,0x41,0xdf,0xc3,0x69,0x37,0x8d,0xcd,0xd8,0xde,0x8d,0x05,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x45,0x02,0x21,0x01,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x45,0x02,0x21,0xff,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x4d,0x02,0x29,0x01,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba,0x02,0x20,0x6f,0xf1,0x8a,0x52,0xdc,0xc0,0x33,0x6f,0x7a,0xf6,0x24,0x00,0xa6,0xdd,0x9b,0x81,0x07,0x32,0xba,0xf1,0xff,0x75,0x80,0x00,0xd6,0xf6,0x13,0xa5,0x56,0xeb,0x31,0xba, + 0x30,0x06,0x02,0x01,0x00,0x02,0x01,0x00, + 0x30,0x06,0x02,0x01,0x00,0x02,0x01,0x01, + 0x30,0x06,0x02,0x01,0x00,0x02,0x01,0xff, + 0x30,0x26,0x02,0x01,0x00,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x41, + 0x30,0x26,0x02,0x01,0x00,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x40, + 0x30,0x26,0x02,0x01,0x00,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x42, + 0x30,0x26,0x02,0x01,0x00,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xff,0xff,0xfc,0x2f, + 0x30,0x26,0x02,0x01,0x00,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xff,0xff,0xfc,0x30, + 0x30,0x06,0x02,0x01,0x01,0x02,0x01,0x00, + 0x30,0x06,0x02,0x01,0x01,0x02,0x01,0x01, + 0x30,0x06,0x02,0x01,0x01,0x02,0x01,0xff, + 0x30,0x26,0x02,0x01,0x01,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x41, + 0x30,0x26,0x02,0x01,0x01,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x40, + 0x30,0x26,0x02,0x01,0x01,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x42, + 0x30,0x26,0x02,0x01,0x01,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xff,0xff,0xfc,0x2f, + 0x30,0x26,0x02,0x01,0x01,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xff,0xff,0xfc,0x30, + 0x30,0x06,0x02,0x01,0xff,0x02,0x01,0x00, + 0x30,0x06,0x02,0x01,0xff,0x02,0x01,0x01, + 0x30,0x06,0x02,0x01,0xff,0x02,0x01,0xff, + 0x30,0x26,0x02,0x01,0xff,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x41, + 0x30,0x26,0x02,0x01,0xff,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x40, + 0x30,0x26,0x02,0x01,0xff,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x42, + 0x30,0x26,0x02,0x01,0xff,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xff,0xff,0xfc,0x2f, + 0x30,0x26,0x02,0x01,0xff,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xff,0xff,0xfc,0x30, + 0x30,0x26,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x41,0x02,0x01,0x00, + 0x30,0x26,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x41,0x02,0x01,0x01, + 0x30,0x26,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x41,0x02,0x01,0xff, + 0x30,0x46,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x41,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x41, + 0x30,0x46,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x41,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x40, + 0x30,0x46,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x41,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x42, + 0x30,0x46,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x41,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xff,0xff,0xfc,0x2f, + 0x30,0x46,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x41,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xff,0xff,0xfc,0x30, + 0x30,0x26,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x40,0x02,0x01,0x00, + 0x30,0x26,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x40,0x02,0x01,0x01, + 0x30,0x26,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x40,0x02,0x01,0xff, + 0x30,0x46,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x40,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x41, + 0x30,0x46,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x40,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x40, + 0x30,0x46,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x40,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x42, + 0x30,0x46,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x40,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xff,0xff,0xfc,0x2f, + 0x30,0x46,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x40,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xff,0xff,0xfc,0x30, + 0x30,0x26,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x42,0x02,0x01,0x00, + 0x30,0x26,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x42,0x02,0x01,0x01, + 0x30,0x26,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x42,0x02,0x01,0xff, + 0x30,0x46,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x42,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x41, + 0x30,0x46,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x42,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x40, + 0x30,0x46,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x42,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x42, + 0x30,0x46,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x42,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xff,0xff,0xfc,0x2f, + 0x30,0x46,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x42,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xff,0xff,0xfc,0x30, + 0x30,0x26,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xff,0xff,0xfc,0x2f,0x02,0x01,0x00, + 0x30,0x26,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xff,0xff,0xfc,0x2f,0x02,0x01,0x01, + 0x30,0x26,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xff,0xff,0xfc,0x2f,0x02,0x01,0xff, + 0x30,0x46,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xff,0xff,0xfc,0x2f,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x41, + 0x30,0x46,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xff,0xff,0xfc,0x2f,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x40, + 0x30,0x46,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xff,0xff,0xfc,0x2f,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x42, + 0x30,0x46,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xff,0xff,0xfc,0x2f,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xff,0xff,0xfc,0x2f, + 0x30,0x46,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xff,0xff,0xfc,0x2f,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xff,0xff,0xfc,0x30, + 0x30,0x26,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xff,0xff,0xfc,0x30,0x02,0x01,0x00, + 0x30,0x26,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xff,0xff,0xfc,0x30,0x02,0x01,0x01, + 0x30,0x26,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xff,0xff,0xfc,0x30,0x02,0x01,0xff, + 0x30,0x46,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xff,0xff,0xfc,0x30,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x41, + 0x30,0x46,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xff,0xff,0xfc,0x30,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x40, + 0x30,0x46,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xff,0xff,0xfc,0x30,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x42, + 0x30,0x46,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xff,0xff,0xfc,0x30,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xff,0xff,0xfc,0x2f, + 0x30,0x46,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xff,0xff,0xfc,0x30,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xff,0xff,0xfc,0x30, + 0x30,0x08,0x02,0x01,0x00,0x09,0x03,0x80,0xfe,0x01, + 0x30,0x06,0x02,0x01,0x00,0x09,0x01,0x42, + 0x30,0x06,0x02,0x01,0x00,0x01,0x01,0x01, + 0x30,0x06,0x02,0x01,0x00,0x01,0x01,0x00, + 0x30,0x05,0x02,0x01,0x00,0x05,0x00, + 0x30,0x05,0x02,0x01,0x00,0x0c,0x00, + 0x30,0x06,0x02,0x01,0x00,0x0c,0x01,0x30, + 0x30,0x05,0x02,0x01,0x00,0x30,0x00, + 0x30,0x08,0x02,0x01,0x00,0x30,0x03,0x02,0x01,0x00, + 0x30,0x08,0x02,0x01,0x01,0x09,0x03,0x80,0xfe,0x01, + 0x30,0x06,0x02,0x01,0x01,0x09,0x01,0x42, + 0x30,0x06,0x02,0x01,0x01,0x01,0x01,0x01, + 0x30,0x06,0x02,0x01,0x01,0x01,0x01,0x00, + 0x30,0x05,0x02,0x01,0x01,0x05,0x00, + 0x30,0x05,0x02,0x01,0x01,0x0c,0x00, + 0x30,0x06,0x02,0x01,0x01,0x0c,0x01,0x30, + 0x30,0x05,0x02,0x01,0x01,0x30,0x00, + 0x30,0x08,0x02,0x01,0x01,0x30,0x03,0x02,0x01,0x00, + 0x30,0x08,0x02,0x01,0xff,0x09,0x03,0x80,0xfe,0x01, + 0x30,0x06,0x02,0x01,0xff,0x09,0x01,0x42, + 0x30,0x06,0x02,0x01,0xff,0x01,0x01,0x01, + 0x30,0x06,0x02,0x01,0xff,0x01,0x01,0x00, + 0x30,0x05,0x02,0x01,0xff,0x05,0x00, + 0x30,0x05,0x02,0x01,0xff,0x0c,0x00, + 0x30,0x06,0x02,0x01,0xff,0x0c,0x01,0x30, + 0x30,0x05,0x02,0x01,0xff,0x30,0x00, + 0x30,0x08,0x02,0x01,0xff,0x30,0x03,0x02,0x01,0x00, + 0x30,0x28,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x41,0x09,0x03,0x80,0xfe,0x01, + 0x30,0x26,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x41,0x09,0x01,0x42, + 0x30,0x26,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x41,0x01,0x01,0x01, + 0x30,0x26,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x41,0x01,0x01,0x00, + 0x30,0x25,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x41,0x05,0x00, + 0x30,0x25,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x41,0x0c,0x00, + 0x30,0x26,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x41,0x0c,0x01,0x30, + 0x30,0x25,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x41,0x30,0x00, + 0x30,0x28,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x41,0x30,0x03,0x02,0x01,0x00, + 0x30,0x28,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xff,0xff,0xfc,0x2f,0x09,0x03,0x80,0xfe,0x01, + 0x30,0x26,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xff,0xff,0xfc,0x2f,0x09,0x01,0x42, + 0x30,0x26,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xff,0xff,0xfc,0x2f,0x01,0x01,0x01, + 0x30,0x26,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xff,0xff,0xfc,0x2f,0x01,0x01,0x00, + 0x30,0x25,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xff,0xff,0xfc,0x2f,0x05,0x00, + 0x30,0x25,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xff,0xff,0xfc,0x2f,0x0c,0x00, + 0x30,0x26,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xff,0xff,0xfc,0x2f,0x0c,0x01,0x30, + 0x30,0x25,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xff,0xff,0xfc,0x2f,0x30,0x00, + 0x30,0x28,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xff,0xff,0xfc,0x2f,0x30,0x03,0x02,0x01,0x00, + 0x30,0x0a,0x09,0x03,0x80,0xfe,0x01,0x09,0x03,0x80,0xfe,0x01, + 0x30,0x06,0x09,0x01,0x42,0x09,0x01,0x42, + 0x30,0x06,0x01,0x01,0x01,0x01,0x01,0x01, + 0x30,0x06,0x01,0x01,0x00,0x01,0x01,0x00, + 0x30,0x04,0x05,0x00,0x05,0x00, + 0x30,0x04,0x0c,0x00,0x0c,0x00, + 0x30,0x06,0x0c,0x01,0x30,0x0c,0x01,0x30, + 0x30,0x04,0x30,0x00,0x30,0x00, + 0x30,0x0a,0x30,0x03,0x02,0x01,0x00,0x30,0x03,0x02,0x01,0x00, + 0x30,0x08,0x09,0x03,0x80,0xfe,0x01,0x02,0x01,0x00, + 0x30,0x06,0x09,0x01,0x42,0x02,0x01,0x00, + 0x30,0x06,0x01,0x01,0x01,0x02,0x01,0x00, + 0x30,0x06,0x01,0x01,0x00,0x02,0x01,0x00, + 0x30,0x05,0x05,0x00,0x02,0x01,0x00, + 0x30,0x05,0x0c,0x00,0x02,0x01,0x00, + 0x30,0x06,0x0c,0x01,0x30,0x02,0x01,0x00, + 0x30,0x05,0x30,0x00,0x02,0x01,0x00, + 0x30,0x08,0x30,0x03,0x02,0x01,0x00,0x02,0x01,0x00, + 0x30,0x45,0x02,0x21,0x00,0xdd,0x1b,0x7d,0x09,0xa7,0xbd,0x82,0x18,0x96,0x10,0x34,0xa3,0x9a,0x87,0xfe,0xcf,0x53,0x14,0xf0,0x0c,0x4d,0x25,0xeb,0x58,0xa0,0x7a,0xc8,0x5e,0x85,0xea,0xb5,0x16,0x02,0x20,0x35,0x13,0x8c,0x40,0x1e,0xf8,0xd3,0x49,0x3d,0x65,0xc9,0x00,0x2f,0xe6,0x2b,0x43,0xae,0xe5,0x68,0x73,0x1b,0x74,0x45,0x48,0x35,0x89,0x96,0xd9,0xcc,0x42,0x7e,0x06, + 0x30,0x45,0x02,0x21,0x00,0x95,0xc2,0x92,0x67,0xd9,0x72,0xa0,0x43,0xd9,0x55,0x22,0x45,0x46,0x22,0x2b,0xba,0x34,0x3f,0xc1,0xd4,0xdb,0x0f,0xec,0x26,0x2a,0x33,0xac,0x61,0x30,0x56,0x96,0xae,0x02,0x20,0x6e,0xdf,0xe9,0x67,0x13,0xae,0xd5,0x6f,0x8a,0x28,0xa6,0x65,0x3f,0x57,0xe0,0xb8,0x29,0x71,0x2e,0x5e,0xdd,0xc6,0x7f,0x34,0x68,0x2b,0x24,0xf0,0x67,0x6b,0x26,0x40, + 0x30,0x44,0x02,0x20,0x28,0xf9,0x4a,0x89,0x4e,0x92,0x02,0x46,0x99,0xe3,0x45,0xfe,0x66,0x97,0x1e,0x3e,0xdc,0xd0,0x50,0x02,0x33,0x86,0x13,0x5a,0xb3,0x93,0x9d,0x55,0x08,0x98,0xfb,0x25,0x02,0x20,0x32,0x96,0x3e,0x5b,0xd4,0x1f,0xa5,0x91,0x1e,0xd8,0xf3,0x7d,0xeb,0x86,0xda,0xe0,0xa7,0x62,0xbb,0x61,0x21,0xc8,0x94,0x61,0x50,0x83,0xc5,0xd9,0x5e,0xa0,0x1d,0xb3, + 0x30,0x45,0x02,0x21,0x00,0xbe,0x26,0xb1,0x8f,0x95,0x49,0xf8,0x9f,0x41,0x1a,0x9b,0x52,0x53,0x6b,0x15,0xaa,0x27,0x0b,0x84,0x54,0x8d,0x0e,0x85,0x9a,0x19,0x52,0xa2,0x7a,0xf1,0xa7,0x7a,0xc6,0x02,0x20,0x70,0xc1,0xd4,0xfa,0x9c,0xd0,0x3c,0xc8,0xea,0xa8,0xd5,0x06,0xed,0xb9,0x7e,0xed,0x7b,0x83,0x58,0xb4,0x53,0xc8,0x8a,0xef,0xbb,0x88,0x0a,0x3f,0x0e,0x8d,0x47,0x2f, + 0x30,0x45,0x02,0x21,0x00,0xb1,0xa4,0xb1,0x47,0x8e,0x65,0xcc,0x3e,0xaf,0xdf,0x22,0x5d,0x12,0x98,0xb4,0x3f,0x2d,0xa1,0x9e,0x4b,0xcf,0xf7,0xea,0xcc,0x0a,0x2e,0x98,0xcd,0x4b,0x74,0xb1,0x14,0x02,0x20,0x17,0x9a,0xa3,0x1e,0x30,0x4c,0xc1,0x42,0xcf,0x50,0x73,0x17,0x17,0x51,0xb2,0x8f,0x3f,0x5e,0x0f,0xa8,0x8c,0x99,0x4e,0x7c,0x55,0xf1,0xbc,0x07,0xb8,0xd5,0x6c,0x16, + 0x30,0x44,0x02,0x20,0x32,0x53,0x32,0x02,0x12,0x61,0xf1,0xbd,0x18,0xf2,0x71,0x2a,0xa1,0xe2,0x25,0x2d,0xa2,0x37,0x96,0xda,0x8a,0x4b,0x1f,0xf6,0xea,0x18,0xca,0xfe,0xc7,0xe1,0x71,0xf2,0x02,0x20,0x40,0xb4,0xf5,0xe2,0x87,0xee,0x61,0xfc,0x3c,0x80,0x41,0x86,0x98,0x23,0x60,0x89,0x1e,0xaa,0x35,0xc7,0x5f,0x05,0xa4,0x3e,0xcd,0x48,0xb3,0x5d,0x98,0x4a,0x66,0x48, + 0x30,0x45,0x02,0x21,0x00,0xa2,0x3a,0xd1,0x8d,0x8f,0xc6,0x6d,0x81,0xaf,0x09,0x03,0x89,0x0c,0xbd,0x45,0x3a,0x55,0x4c,0xb0,0x4c,0xdc,0x1a,0x8c,0xa7,0xf7,0xf7,0x8e,0x53,0x67,0xed,0x88,0xa0,0x02,0x20,0x23,0xe3,0xeb,0x2c,0xe1,0xc0,0x4e,0xa7,0x48,0xc3,0x89,0xbd,0x97,0x37,0x4a,0xa9,0x41,0x3b,0x92,0x68,0x85,0x1c,0x04,0xdc,0xd9,0xf8,0x8e,0x78,0x81,0x3f,0xee,0x56, + 0x30,0x44,0x02,0x20,0x2b,0xde,0xa4,0x1c,0xda,0x63,0xa2,0xd1,0x4b,0xf4,0x73,0x53,0xbd,0x20,0x88,0x0a,0x69,0x09,0x01,0xde,0x7c,0xd6,0xe3,0xcc,0x6d,0x8e,0xd5,0xba,0x0c,0xdb,0x10,0x91,0x02,0x20,0x3c,0xea,0x66,0xbc,0xcf,0xc9,0xf9,0xbf,0x8c,0x7c,0xa4,0xe1,0xc1,0x45,0x7c,0xc9,0x14,0x5e,0x13,0xe9,0x36,0xd9,0x0b,0x3d,0x9c,0x77,0x86,0xb8,0xb2,0x6c,0xf4,0xc7, + 0x30,0x45,0x02,0x21,0x00,0xd7,0xcd,0x76,0xec,0x01,0xc1,0xb1,0x07,0x9e,0xba,0x9e,0x2a,0xa2,0xa3,0x97,0x24,0x3c,0x47,0x58,0xc9,0x8a,0x1b,0xa0,0xb7,0x40,0x4a,0x34,0x0b,0x9b,0x00,0xce,0xd6,0x02,0x20,0x35,0x75,0x00,0x1e,0x19,0xd9,0x22,0xe6,0xde,0x8b,0x3d,0x6c,0x84,0xea,0x43,0xb5,0xc3,0x33,0x81,0x06,0xcf,0x29,0x99,0x01,0x34,0xe7,0x66,0x9a,0x82,0x6f,0x78,0xe6, + 0x30,0x45,0x02,0x21,0x00,0xa8,0x72,0xc7,0x44,0xd9,0x36,0xdb,0x21,0xa1,0x0c,0x36,0x1d,0xd5,0xc9,0x06,0x33,0x55,0xf8,0x49,0x02,0x21,0x96,0x52,0xf6,0xfc,0x56,0xdc,0x95,0xa7,0x13,0x9d,0x96,0x02,0x20,0x40,0x0d,0xf7,0x57,0x5d,0x97,0x56,0x21,0x0e,0x9c,0xcc,0x77,0x16,0x2c,0x6b,0x59,0x3c,0x77,0x46,0xcf,0xb4,0x8a,0xc2,0x63,0xc4,0x27,0x50,0xb4,0x21,0xef,0x4b,0xb9, + 0x30,0x45,0x02,0x21,0x00,0x9f,0xa9,0xaf,0xe0,0x77,0x52,0xda,0x10,0xb3,0x6d,0x3a,0xfc,0xd0,0xfe,0x44,0xbf,0xc4,0x02,0x44,0xd7,0x52,0x03,0x59,0x9c,0xf8,0xf5,0x04,0x7f,0xa3,0x45,0x38,0x54,0x02,0x20,0x50,0xe0,0xa7,0xc0,0x13,0xbf,0xbf,0x51,0x81,0x97,0x36,0x97,0x2d,0x44,0xb4,0xb5,0x6b,0xc2,0xa2,0xb2,0xc1,0x80,0xdf,0x6e,0xc6,0x72,0xdf,0x17,0x14,0x10,0xd7,0x7a, + 0x30,0x45,0x02,0x21,0x00,0x88,0x56,0x40,0x38,0x4d,0x0d,0x91,0x0e,0xfb,0x17,0x7b,0x46,0xbe,0x6c,0x3d,0xc5,0xca,0xc8,0x1f,0x0b,0x88,0xc3,0x19,0x0b,0xb6,0xb5,0xf9,0x9c,0x26,0x41,0xf2,0x05,0x02,0x20,0x73,0x8e,0xd9,0xbf,0xf1,0x16,0x30,0x6d,0x9c,0xaa,0x0f,0x8f,0xc6,0x08,0xbe,0x24,0x3e,0x0b,0x56,0x77,0x79,0xd8,0xda,0xb0,0x3e,0x8e,0x19,0xd5,0x53,0xf1,0xdc,0x8e, + 0x30,0x44,0x02,0x20,0x2d,0x05,0x1f,0x91,0xc5,0xa9,0xd4,0x40,0xc5,0x67,0x69,0x85,0x71,0x04,0x83,0xbc,0x4f,0x1a,0x6c,0x61,0x1b,0x10,0xc9,0x5a,0x2f,0xf0,0x36,0x3d,0x90,0xc2,0xa4,0x58,0x02,0x20,0x6d,0xdf,0x94,0xe6,0xfb,0xa5,0xbe,0x58,0x68,0x33,0xd0,0xc5,0x3c,0xf2,0x16,0xad,0x39,0x48,0xf3,0x79,0x53,0xc2,0x6c,0x1c,0xf4,0x96,0x8e,0x9a,0x9e,0x82,0x43,0xdc, + 0x30,0x45,0x02,0x21,0x00,0xf3,0xac,0x25,0x23,0x96,0x74,0x82,0xf5,0x3d,0x50,0x85,0x22,0x71,0x2d,0x58,0x3f,0x43,0x79,0xcd,0x82,0x41,0x01,0xff,0x63,0x5e,0xa0,0x93,0x51,0x17,0xba,0xa5,0x4f,0x02,0x20,0x27,0xf1,0x08,0x12,0x22,0x73,0x97,0xe0,0x2c,0xea,0x96,0xfb,0x0e,0x68,0x07,0x61,0x63,0x6d,0xab,0x2b,0x08,0x0d,0x1f,0xc5,0xd1,0x16,0x85,0xcb,0xe8,0x50,0x0c,0xfe, + 0x30,0x45,0x02,0x21,0x00,0x96,0x44,0x7c,0xf6,0x8c,0x3a,0xb7,0x26,0x6e,0xd7,0x44,0x7d,0xe3,0xac,0x52,0xfe,0xd7,0xcc,0x08,0xcb,0xdf,0xea,0x39,0x1c,0x18,0xa9,0xb8,0xab,0x37,0x0b,0xc9,0x13,0x02,0x20,0x0f,0x5e,0x78,0x74,0xd3,0xac,0x0e,0x91,0x8f,0x01,0xc8,0x85,0xa1,0x63,0x91,0x77,0xc9,0x23,0xf8,0x66,0x0d,0x1c,0xeb,0xa1,0xca,0x1f,0x30,0x1b,0xc6,0x75,0xcd,0xbc, + 0x30,0x44,0x02,0x20,0x53,0x0a,0x08,0x32,0xb6,0x91,0xda,0x0b,0x56,0x19,0xa0,0xb1,0x1d,0xe6,0x87,0x7f,0x3c,0x09,0x71,0xba,0xaa,0x68,0xed,0x12,0x27,0x58,0xc2,0x9c,0xaa,0xf4,0x6b,0x72,0x02,0x20,0x6c,0x89,0xe4,0x4f,0x5e,0xb3,0x30,0x60,0xea,0x4b,0x46,0x31,0x8c,0x39,0x13,0x8e,0xae,0xde,0xc7,0x2d,0xe4,0x2b,0xa5,0x76,0x57,0x9a,0x6a,0x46,0x90,0xe3,0x39,0xf3, + 0x30,0x45,0x02,0x21,0x00,0x9c,0x54,0xc2,0x55,0x00,0xbd,0xe0,0xb9,0x2d,0x72,0xd6,0xec,0x48,0x3d,0xc2,0x48,0x2f,0x36,0x54,0x29,0x4c,0xa7,0x4d,0xe7,0x96,0xb6,0x81,0x25,0x5e,0xd5,0x8a,0x77,0x02,0x20,0x67,0x74,0x53,0xc6,0xb5,0x6f,0x52,0x76,0x31,0xc9,0xf6,0x7b,0x3f,0x3e,0xb6,0x21,0xfd,0x88,0x58,0x2b,0x4a,0xff,0x15,0x6d,0x2f,0x15,0x67,0xd6,0x21,0x1a,0x2a,0x33, + 0x30,0x45,0x02,0x21,0x00,0xe7,0x90,0x9d,0x41,0x43,0x9e,0x2f,0x6a,0xf2,0x91,0x36,0xc7,0x34,0x8c,0xa2,0x64,0x1a,0x2b,0x07,0x0d,0x5b,0x64,0xf9,0x1e,0xa9,0xda,0x70,0x70,0xc7,0xa2,0x61,0x8b,0x02,0x20,0x42,0xd7,0x82,0xf1,0x32,0xfa,0x1d,0x36,0xc2,0xc8,0x8b,0xa2,0x7c,0x3d,0x67,0x8d,0x80,0x18,0x4a,0x5d,0x1e,0xcc,0xac,0x75,0x01,0xf0,0xb4,0x7e,0x3d,0x20,0x50,0x08, + 0x30,0x44,0x02,0x20,0x59,0x24,0x87,0x32,0x09,0x59,0x31,0x35,0xa4,0xc3,0xda,0x7b,0xb3,0x81,0x22,0x7f,0x8a,0x4b,0x6a,0xa9,0xf3,0x4f,0xe5,0xbb,0x7f,0x8f,0xbc,0x13,0x1a,0x03,0x9f,0xfe,0x02,0x20,0x1f,0x1b,0xb1,0x1b,0x44,0x1c,0x8f,0xea,0xa4,0x0f,0x44,0x21,0x3d,0x9a,0x40,0x5e,0xd7,0x92,0xd5,0x9f,0xb4,0x9d,0x5b,0xcd,0xd9,0xa4,0x28,0x5a,0xe5,0x69,0x30,0x22, + 0x30,0x45,0x02,0x21,0x00,0xee,0xb6,0x92,0xc9,0xb2,0x62,0x96,0x9b,0x23,0x1c,0x38,0xb5,0xa7,0xf6,0x06,0x49,0xe0,0xc8,0x75,0xcd,0x64,0xdf,0x88,0xf3,0x3a,0xa5,0x71,0xfa,0x3d,0x29,0xab,0x0e,0x02,0x20,0x21,0x8b,0x3a,0x1e,0xb0,0x63,0x79,0xc2,0xc1,0x8c,0xf5,0x1b,0x06,0x43,0x07,0x86,0xd1,0xc6,0x4c,0xd2,0xd2,0x4c,0x9b,0x23,0x2b,0x23,0xe5,0xba,0xc7,0x98,0x9a,0xcd, + 0x30,0x45,0x02,0x21,0x00,0xa4,0x00,0x34,0x17,0x7f,0x36,0x09,0x1c,0x2b,0x65,0x36,0x84,0xa0,0xe3,0xeb,0x5d,0x4b,0xff,0x18,0xe4,0xd0,0x9f,0x66,0x4c,0x28,0x00,0xe7,0xca,0xfd,0xa1,0xda,0xf8,0x02,0x20,0x3a,0x3e,0xc2,0x98,0x53,0x70,0x4e,0x52,0x03,0x1c,0x58,0x92,0x7a,0x80,0x0a,0x96,0x83,0x53,0xad,0xc3,0xd9,0x73,0xbe,0xba,0x91,0x72,0xcb,0xbe,0xab,0x4d,0xd1,0x49, + 0x30,0x45,0x02,0x21,0x00,0xb5,0xd7,0x95,0xcc,0x75,0xce,0xa5,0xc4,0x34,0xfa,0x41,0x85,0x18,0x0c,0xd6,0xbd,0x21,0x22,0x3f,0x3d,0x5a,0x86,0xda,0x66,0x70,0xd7,0x1d,0x95,0x68,0x0d,0xad,0xbf,0x02,0x20,0x54,0xe4,0xd8,0x81,0x0a,0x00,0x1e,0xcb,0xb9,0xf7,0xca,0x1c,0x2e,0xbf,0xdb,0x9d,0x00,0x9e,0x90,0x31,0xa4,0x31,0xac,0xa3,0xc2,0x0a,0xb4,0xe0,0xd1,0x37,0x4e,0xc1, + 0x30,0x44,0x02,0x20,0x07,0xdc,0x24,0x78,0xd4,0x3c,0x12,0x32,0xa4,0x59,0x56,0x08,0xc6,0x44,0x26,0xc3,0x55,0x10,0x05,0x1a,0x63,0x1a,0xe6,0xa5,0xa6,0xeb,0x11,0x61,0xe5,0x7e,0x42,0xe1,0x02,0x20,0x4a,0x59,0xea,0x0f,0xdb,0x72,0xd1,0x21,0x65,0xce,0xa3,0xbf,0x1c,0xa8,0x6b,0xa9,0x75,0x17,0xbd,0x18,0x8d,0xb3,0xdb,0xd2,0x1a,0x5a,0x15,0x78,0x50,0x02,0x19,0x84, + 0x30,0x45,0x02,0x21,0x00,0xdd,0xd2,0x0c,0x4a,0x05,0x59,0x6c,0xa8,0x68,0xb5,0x58,0x83,0x9f,0xce,0x9f,0x65,0x11,0xdd,0xd8,0x3d,0x1c,0xcb,0x53,0xf8,0x2e,0x52,0x69,0xd5,0x59,0xa0,0x15,0x52,0x02,0x20,0x5b,0x91,0x73,0x47,0x29,0xd9,0x30,0x93,0xff,0x22,0x12,0x3c,0x4a,0x25,0x81,0x9d,0x7f,0xeb,0x66,0xa2,0x50,0x66,0x3f,0xc7,0x80,0xcb,0x66,0xfc,0x7b,0x6e,0x6d,0x17, + 0x30,0x45,0x02,0x21,0x00,0x9c,0xde,0x6e,0x0e,0xde,0x0a,0x00,0x3f,0x02,0xfd,0xa0,0xa0,0x1b,0x59,0xfa,0xcf,0xe5,0xde,0xc0,0x63,0x31,0x8f,0x27,0x9c,0xe2,0xde,0x7a,0x9b,0x10,0x62,0xf7,0xb7,0x02,0x20,0x28,0x86,0xa5,0xb8,0xc6,0x79,0xbd,0xf8,0x22,0x4c,0x66,0xf9,0x08,0xfd,0x62,0x05,0x49,0x2c,0xb7,0x0b,0x00,0x68,0xd4,0x6a,0xe4,0xf3,0x3a,0x41,0x49,0xb1,0x2a,0x52, + 0x30,0x45,0x02,0x21,0x00,0xc5,0x77,0x10,0x16,0xd0,0xdd,0x63,0x57,0x14,0x3c,0x89,0xf6,0x84,0xcd,0x74,0x04,0x23,0x50,0x25,0x54,0xc0,0xc5,0x9a,0xa8,0xc9,0x95,0x84,0xf1,0xff,0x38,0xf6,0x09,0x02,0x20,0x54,0xb4,0x05,0xf4,0x47,0x75,0x46,0x68,0x6e,0x46,0x4c,0x54,0x63,0xb4,0xfd,0x41,0x90,0x57,0x2e,0x58,0xd0,0xf7,0xe7,0x35,0x7f,0x6e,0x61,0x94,0x7d,0x20,0x71,0x5c, + 0x30,0x45,0x02,0x21,0x00,0xa2,0x4e,0xbc,0x0e,0xc2,0x24,0xbd,0x67,0xae,0x39,0x7c,0xbe,0x6f,0xa3,0x7b,0x31,0x25,0xad,0xbd,0x34,0x89,0x1a,0xbe,0x2d,0x7c,0x73,0x56,0x92,0x19,0x16,0xdf,0xe6,0x02,0x20,0x34,0xf6,0xeb,0x63,0x74,0x73,0x1b,0xbb,0xaf,0xc4,0x92,0x4f,0xb8,0xb0,0xbd,0xcd,0xda,0x49,0x45,0x6d,0x72,0x4c,0xda,0xe6,0x17,0x8d,0x87,0x01,0x4c,0xb5,0x3d,0x8c, + 0x30,0x44,0x02,0x20,0x25,0x57,0xd6,0x4a,0x7a,0xee,0x2e,0x09,0x31,0xc0,0x12,0xe4,0xfe,0xa1,0xcd,0x3a,0x2c,0x33,0x4e,0xda,0xe6,0x8c,0xde,0xb7,0x15,0x8c,0xaf,0x21,0xb6,0x8e,0x5a,0x24,0x02,0x20,0x7f,0x06,0xcd,0xbb,0x6a,0x90,0x02,0x3a,0x97,0x38,0x82,0xed,0x97,0xb0,0x80,0xfe,0x6b,0x05,0xaf,0x3e,0xc9,0x3d,0xb6,0xf1,0xa4,0x39,0x9a,0x69,0xed,0xf7,0x67,0x0d, + 0x30,0x45,0x02,0x21,0x00,0xc4,0xf2,0xec,0xcb,0xb6,0xa2,0x43,0x50,0xc8,0x46,0x64,0x50,0xb9,0xd6,0x1b,0x20,0x7e,0xe3,0x59,0xe0,0x37,0xb3,0xdc,0xed,0xb4,0x2a,0x3f,0x2e,0x6d,0xd6,0xae,0xb5,0x02,0x20,0x32,0x63,0xc6,0xb5,0x9a,0x2f,0x55,0xcd,0xd1,0xc6,0xe1,0x48,0x94,0xd5,0xe5,0x96,0x3b,0x28,0xbc,0x3e,0x24,0x69,0xac,0x9b,0xa1,0x19,0x79,0x91,0xca,0x7f,0xf9,0xc7, + 0x30,0x45,0x02,0x21,0x00,0xef,0xf0,0x47,0x81,0xc9,0xcb,0xcd,0x16,0x2d,0x0a,0x25,0xa6,0xe2,0xeb,0xcc,0xa4,0x35,0x06,0xc5,0x23,0x38,0x5c,0xb5,0x15,0xd4,0x9e,0xa3,0x8a,0x1b,0x12,0xfc,0xad,0x02,0x20,0x15,0xac,0xd7,0x31,0x94,0xc9,0x1a,0x95,0x47,0x85,0x34,0xf2,0x30,0x15,0xb6,0x72,0xeb,0xed,0x21,0x3e,0x45,0x42,0x4d,0xd2,0xc8,0xe2,0x6a,0xc8,0xb3,0xeb,0x34,0xa5, + 0x30,0x45,0x02,0x21,0x00,0xf5,0x8b,0x4e,0x31,0x10,0xa6,0x4b,0xf1,0xb5,0xdb,0x97,0x63,0x9e,0xe0,0xe5,0xa9,0xc8,0xdf,0xa4,0x9d,0xc5,0x9b,0x67,0x98,0x91,0xf5,0x20,0xfd,0xf0,0x58,0x4c,0x87,0x02,0x20,0x2c,0xd8,0xfe,0x51,0x88,0x8a,0xee,0x9d,0xb3,0xe0,0x75,0x44,0x0f,0xd4,0xdb,0x73,0xb5,0xc7,0x32,0xfb,0x87,0xb5,0x10,0xe9,0x70,0x93,0xd6,0x64,0x15,0xf6,0x2a,0xf7, + 0x30,0x45,0x02,0x21,0x00,0xf8,0xab,0xec,0xaa,0x4f,0x0c,0x50,0x2d,0xe4,0xbf,0x59,0x03,0xd4,0x84,0x17,0xf7,0x86,0xbf,0x92,0xe8,0xad,0x72,0xfe,0xc0,0xbd,0x7f,0xcb,0x78,0x00,0xc0,0xbb,0xe3,0x02,0x20,0x4c,0x7f,0x9e,0x23,0x10,0x76,0xa3,0x0b,0x7a,0xe3,0x6b,0x0c,0xeb,0xe6,0x9c,0xce,0xf1,0xcd,0x19,0x4f,0x7c,0xce,0x93,0xa5,0x58,0x8f,0xd6,0x81,0x4f,0x43,0x7c,0x0e, + 0x30,0x44,0x02,0x20,0x5d,0x5b,0x38,0xbd,0x37,0xad,0x49,0x8b,0x22,0x27,0xa6,0x33,0x26,0x8a,0x8c,0xca,0x87,0x9a,0x5c,0x7c,0x94,0xa4,0xe4,0x16,0xbd,0x0a,0x61,0x4d,0x09,0xe6,0x06,0xd2,0x02,0x20,0x12,0xb8,0xd6,0x64,0xea,0x99,0x91,0x06,0x2e,0xcb,0xb8,0x34,0xe5,0x84,0x00,0xe2,0x5c,0x46,0x00,0x7a,0xf8,0x4f,0x60,0x07,0xd7,0xf1,0x68,0x54,0x43,0x26,0x9a,0xfe, + 0x30,0x44,0x02,0x20,0x0c,0x1c,0xd9,0xfe,0x40,0x34,0xf0,0x86,0xa2,0xb5,0x2d,0x65,0xb9,0xd3,0x83,0x4d,0x72,0xae,0xbe,0x7f,0x33,0xdf,0xe8,0xf9,0x76,0xda,0x82,0x64,0x81,0x77,0xd8,0xe3,0x02,0x20,0x13,0x10,0x57,0x82,0xe3,0xd0,0xcf,0xe8,0x5c,0x27,0x78,0xde,0xc1,0xa8,0x48,0xb2,0x7a,0xc0,0xae,0x07,0x1a,0xa6,0xda,0x34,0x1a,0x95,0x53,0xa9,0x46,0xb4,0x1e,0x59, + 0x30,0x45,0x02,0x21,0x00,0xae,0x79,0x35,0xfb,0x96,0xff,0x24,0x6b,0x7b,0x5d,0x56,0x62,0x87,0x0d,0x1b,0xa5,0x87,0xb0,0x3d,0x6e,0x13,0x60,0xba,0xf4,0x79,0x88,0xb5,0xc0,0x2c,0xcc,0x1a,0x5b,0x02,0x20,0x5f,0x00,0xc3,0x23,0x27,0x20,0x83,0x78,0x2d,0x4a,0x59,0xf2,0xdf,0xd6,0x5e,0x49,0xde,0x06,0x93,0x62,0x70,0x16,0x90,0x0e,0xf7,0xe6,0x14,0x28,0x05,0x66,0x64,0xb3, + 0x30,0x44,0x02,0x20,0x00,0xa1,0x34,0xb5,0xc6,0xcc,0xbc,0xef,0xd4,0xc8,0x82,0xb9,0x45,0xba,0xeb,0x49,0x33,0x44,0x41,0x72,0x79,0x5f,0xa6,0x79,0x6a,0xae,0x14,0x90,0x67,0x54,0x70,0x98,0x02,0x20,0x56,0x6e,0x46,0x10,0x5d,0x24,0xd8,0x90,0x15,0x1e,0x3e,0xea,0x3e,0xbf,0x88,0xf5,0xb9,0x2b,0x3f,0x5e,0xc9,0x3a,0x21,0x77,0x65,0xa6,0xdc,0xbd,0x94,0xf2,0xc5,0x5b, + 0x30,0x44,0x02,0x20,0x2e,0x47,0x21,0x36,0x3a,0xd3,0x99,0x2c,0x13,0x9e,0x5a,0x1c,0x26,0x39,0x5d,0x2c,0x2d,0x77,0x78,0x24,0xaa,0x24,0xfd,0xe0,0x75,0xe0,0xd7,0x38,0x11,0x71,0x30,0x9d,0x02,0x20,0x74,0x0f,0x7c,0x49,0x44,0x18,0xe1,0x30,0x0d,0xd4,0x51,0x2f,0x78,0x2a,0x58,0x80,0x0b,0xff,0x6a,0x7a,0xbd,0xfd,0xd2,0x0f,0xbb,0xd4,0xf0,0x55,0x15,0xca,0x1a,0x4f, + 0x30,0x44,0x02,0x20,0x68,0x52,0xe9,0xd3,0xcd,0x9f,0xe3,0x73,0xc2,0xd5,0x04,0x87,0x79,0x67,0xd3,0x65,0xab,0x14,0x56,0x70,0x7b,0x68,0x17,0xa0,0x42,0x86,0x46,0x94,0xe1,0x96,0x0c,0xcf,0x02,0x20,0x06,0x4b,0x27,0xea,0x14,0x2b,0x30,0x88,0x7b,0x84,0xc8,0x6a,0xdc,0xcb,0x2f,0xa3,0x9a,0x69,0x11,0xad,0x21,0xfc,0x7e,0x81,0x9f,0x59,0x3b,0xe5,0x2b,0xc4,0xf3,0xbd, + 0x30,0x44,0x02,0x20,0x18,0x8a,0x8c,0x56,0x48,0xdc,0x79,0xea,0xce,0x15,0x8c,0xf8,0x86,0xc6,0x2b,0x54,0x68,0xf0,0x5f,0xd9,0x5f,0x03,0xa7,0x63,0x5c,0x5b,0x4c,0x31,0xf0,0x9a,0xf4,0xc5,0x02,0x20,0x36,0x36,0x1a,0x0b,0x57,0x1a,0x00,0xc6,0xcd,0x5e,0x68,0x6c,0xcb,0xfc,0xfa,0x70,0x3c,0x4f,0x97,0xe4,0x89,0x38,0x34,0x6d,0x0c,0x10,0x3f,0xdc,0x76,0xdc,0x58,0x67, + 0x30,0x45,0x02,0x21,0x00,0xa7,0x4f,0x1f,0xb9,0xa8,0x26,0x3f,0x62,0xfc,0x44,0x16,0xa5,0xb7,0xd5,0x84,0xf4,0x20,0x6f,0x39,0x96,0xbb,0x91,0xf6,0xfc,0x8e,0x73,0xb9,0xe9,0x2b,0xad,0x0e,0x13,0x02,0x20,0x68,0x15,0x03,0x2e,0x8c,0x7d,0x76,0xc3,0xab,0x06,0xa8,0x6f,0x33,0x24,0x9c,0xe9,0x94,0x01,0x48,0xcb,0x36,0xd1,0xf4,0x17,0xc2,0xe9,0x92,0xe8,0x01,0xaf,0xa3,0xfa, + 0x30,0x44,0x02,0x20,0x07,0x24,0x48,0x65,0xb7,0x2f,0xf3,0x7e,0x62,0xe3,0x14,0x6f,0x0d,0xc1,0x46,0x82,0xba,0xdd,0x71,0x97,0x79,0x91,0x35,0xf0,0xb0,0x0a,0xde,0x76,0x71,0x74,0x2b,0xfe,0x02,0x20,0x0d,0x80,0xc2,0x23,0x8e,0xdb,0x4e,0x4a,0x7a,0x86,0xa8,0xc5,0x7c,0xa9,0xaf,0x17,0x11,0xf4,0x06,0xf7,0xf5,0xda,0x02,0x99,0xaa,0x04,0xe2,0x93,0x2d,0x96,0x07,0x54, + 0x30,0x45,0x02,0x21,0x00,0xda,0x7f,0xdd,0x05,0xb5,0xba,0xda,0xbd,0x61,0x9d,0x80,0x5c,0x4e,0xe7,0xd9,0xa8,0x4f,0x84,0xdd,0xd5,0xcf,0x9c,0x5b,0xf4,0xd4,0x33,0x81,0x40,0xd6,0x89,0xef,0x08,0x02,0x20,0x28,0xf1,0xcf,0x4f,0xa1,0xc3,0xc5,0x86,0x2c,0xfa,0x14,0x9c,0x00,0x13,0xcf,0x5f,0xe6,0xcf,0x50,0x76,0xca,0xe0,0x00,0x51,0x10,0x63,0xe7,0xde,0x25,0xbb,0x38,0xe5, + 0x30,0x45,0x02,0x21,0x00,0xd3,0x02,0x7c,0x65,0x6f,0x6d,0x4f,0xdf,0xd8,0xed,0xe2,0x20,0x93,0xe3,0xc3,0x03,0xb0,0x13,0x3c,0x34,0x0d,0x61,0x5e,0x77,0x56,0xf6,0x25,0x3a,0xea,0x92,0x72,0x38,0x02,0x20,0x09,0xae,0xf0,0x60,0xc8,0xe4,0xce,0xf9,0x72,0x97,0x40,0x11,0x55,0x8d,0xf1,0x44,0xfe,0xd2,0x5c,0xa6,0x9a,0xe8,0xd0,0xb2,0xea,0xf1,0xa8,0xfe,0xef,0xbe,0xc4,0x17, + 0x30,0x44,0x02,0x20,0x0b,0xf6,0xc0,0x18,0x8d,0xc9,0x57,0x1c,0xd0,0xe2,0x1e,0xec,0xac,0x5f,0xbb,0x19,0xd2,0x43,0x49,0x88,0xe9,0xcc,0x10,0x24,0x45,0x93,0xef,0x3a,0x98,0x09,0x9f,0x69,0x02,0x20,0x48,0x64,0xa5,0x62,0x66,0x1f,0x92,0x21,0xec,0x88,0xe3,0xdd,0x0b,0xc2,0xf6,0xe2,0x7a,0xc1,0x28,0xc3,0x0c,0xc1,0xa8,0x0f,0x79,0xec,0x67,0x0a,0x22,0xb0,0x42,0xee, + 0x30,0x45,0x02,0x21,0x00,0xae,0x45,0x96,0x40,0xd5,0xd1,0x17,0x9b,0xe4,0x7a,0x47,0xfa,0x53,0x8e,0x16,0xd9,0x4d,0xde,0xa5,0x58,0x5e,0x7a,0x24,0x48,0x04,0xa5,0x17,0x42,0xc6,0x86,0x44,0x3a,0x02,0x20,0x6c,0x8e,0x30,0xe5,0x30,0xa6,0x34,0xfa,0xe8,0x0b,0x3c,0xeb,0x06,0x29,0x78,0xb3,0x9e,0xdb,0xe1,0x97,0x77,0xe0,0xa2,0x45,0x53,0xb6,0x88,0x86,0x18,0x1f,0xd8,0x97, + 0x30,0x44,0x02,0x20,0x1c,0xf3,0x51,0x7b,0xa3,0xbf,0x2a,0xb8,0xb9,0xea,0xd4,0xeb,0xb6,0xe8,0x66,0xcb,0x88,0xa1,0xde,0xac,0xb6,0xa7,0x85,0xd3,0xb6,0x3b,0x48,0x3c,0xa0,0x2a,0xc4,0x95,0x02,0x20,0x24,0x9a,0x79,0x8b,0x73,0x60,0x6f,0x55,0xf5,0xf1,0xc7,0x0d,0xe6,0x7c,0xb1,0xa0,0xcf,0xf9,0x5d,0x7d,0xc5,0x0b,0x3a,0x61,0x7d,0xf8,0x61,0xba,0xd3,0xc6,0xb1,0xc9, + 0x30,0x45,0x02,0x21,0x00,0xe6,0x9b,0x52,0x38,0x26,0x5e,0xa3,0x5d,0x77,0xe4,0xdd,0x17,0x22,0x88,0xd8,0xce,0xa1,0x98,0x10,0xa1,0x02,0x92,0x61,0x7d,0x59,0x76,0x51,0x9d,0xc5,0x75,0x7c,0xb8,0x02,0x20,0x4b,0x03,0xc5,0xbc,0x47,0xe8,0x26,0xbd,0xb2,0x73,0x28,0xab,0xd3,0x8d,0x30,0x56,0xd7,0x74,0x76,0xb2,0x13,0x0f,0x3d,0xf6,0xec,0x48,0x91,0xaf,0x08,0xba,0x1e,0x29, + 0x30,0x44,0x02,0x20,0x5f,0x9d,0x7d,0x7c,0x87,0x0d,0x08,0x5f,0xc1,0xd4,0x9f,0xff,0x69,0xe4,0xa2,0x75,0x81,0x28,0x00,0xd2,0xcf,0x89,0x73,0xe7,0x32,0x58,0x66,0xcb,0x40,0xfa,0x2b,0x6f,0x02,0x20,0x6d,0x1f,0x54,0x91,0xd9,0xf7,0x17,0xa5,0x97,0xa1,0x5f,0xd5,0x40,0x40,0x64,0x86,0xd7,0x6a,0x44,0x69,0x7b,0x3f,0x0d,0x9d,0x6d,0xce,0xf6,0x66,0x9f,0x8a,0x0a,0x56, + 0x30,0x44,0x02,0x20,0x0a,0x7d,0x5b,0x19,0x59,0xf7,0x1d,0xf9,0xf8,0x17,0x14,0x6e,0xe4,0x9b,0xd5,0xc8,0x9b,0x43,0x1e,0x79,0x93,0xe2,0xfd,0xec,0xab,0x68,0x58,0x95,0x7d,0xa6,0x85,0xae,0x02,0x20,0x0f,0x8a,0xad,0x2d,0x25,0x46,0x90,0xbd,0xc1,0x3f,0x34,0xa4,0xfe,0xc4,0x4a,0x02,0xfd,0x74,0x5a,0x42,0x2d,0xf0,0x5c,0xcb,0xb5,0x46,0x35,0xa8,0xb8,0x6b,0x96,0x09, + 0x30,0x44,0x02,0x20,0x79,0xe8,0x8b,0xf5,0x76,0xb7,0x4b,0xc0,0x7c,0xa1,0x42,0x39,0x5f,0xda,0x28,0xf0,0x3d,0x3d,0x5e,0x64,0x0b,0x0b,0x4f,0xf0,0x75,0x2c,0x6d,0x94,0xcd,0x55,0x34,0x08,0x02,0x20,0x32,0xce,0xa0,0x5b,0xd2,0xd7,0x06,0xc8,0xf6,0x03,0x6a,0x50,0x7e,0x2a,0xb7,0x76,0x60,0x04,0xf0,0x90,0x4e,0x2e,0x5c,0x58,0x62,0x74,0x9c,0x00,0x73,0x24,0x5d,0x6a, + 0x30,0x45,0x02,0x21,0x00,0x9d,0x54,0xe0,0x37,0xa0,0x02,0x12,0xb3,0x77,0xbc,0x88,0x74,0x79,0x8b,0x8d,0xa0,0x80,0x56,0x4b,0xbd,0xf7,0xe0,0x75,0x91,0xb8,0x61,0x28,0x58,0x09,0xd0,0x14,0x88,0x02,0x20,0x18,0xb4,0xe5,0x57,0x66,0x7a,0x82,0xbd,0x95,0x96,0x5f,0x07,0x06,0xf8,0x1a,0x29,0x24,0x3f,0xbd,0xd8,0x69,0x68,0xa7,0xeb,0xeb,0x43,0x06,0x9d,0xb3,0xb1,0x8c,0x7f, + 0x30,0x44,0x02,0x20,0x26,0x64,0xf1,0xff,0xa9,0x82,0xfe,0xdb,0xcc,0x7c,0xab,0x1b,0x8b,0xc6,0xe2,0xcb,0x42,0x02,0x18,0xd2,0xa6,0x07,0x7a,0xd0,0x8e,0x59,0x1b,0xa9,0xfe,0xab,0x33,0xbd,0x02,0x20,0x49,0xf5,0xc7,0xcb,0x51,0x5e,0x83,0x87,0x2a,0x3d,0x41,0xb4,0xcd,0xb8,0x5f,0x24,0x2a,0xd9,0xd6,0x1a,0x5b,0xfc,0x01,0xde,0xbf,0xbb,0x52,0xc6,0xc8,0x4b,0xa7,0x28, + 0x30,0x44,0x02,0x20,0x58,0x27,0x51,0x83,0x44,0x84,0x4f,0xd6,0xa7,0xde,0x73,0xcb,0xb0,0xa6,0xbe,0xfd,0xea,0x7b,0x13,0xd2,0xde,0xe4,0x47,0x53,0x17,0xf0,0xf1,0x8f,0xfc,0x81,0x52,0x4b,0x02,0x20,0x4f,0x5c,0xcb,0x4e,0x0b,0x48,0x8b,0x5a,0x5d,0x76,0x0a,0xac,0xdd,0xb2,0xd7,0x91,0x97,0x0f,0xe4,0x3d,0xa6,0x1e,0xb3,0x0e,0x2e,0x90,0x20,0x8a,0x81,0x7e,0x46,0xdb, + 0x30,0x45,0x02,0x21,0x00,0x97,0xab,0x19,0xbd,0x13,0x9c,0xac,0x31,0x93,0x25,0x86,0x92,0x18,0xb1,0xbc,0xe1,0x11,0x87,0x5d,0x63,0xfb,0x12,0x09,0x8a,0x04,0xb0,0xcd,0x59,0xb6,0xfd,0xd3,0xa3,0x02,0x20,0x43,0x1d,0x9c,0xea,0x3a,0x24,0x38,0x47,0x30,0x3c,0xeb,0xda,0x56,0x47,0x64,0x31,0xd0,0x34,0x33,0x9f,0x31,0xd7,0x85,0xee,0x88,0x52,0xdb,0x4f,0x04,0x0d,0x49,0x21, + 0x30,0x44,0x02,0x20,0x52,0xc6,0x83,0x14,0x4e,0x44,0x11,0x9a,0xe2,0x01,0x37,0x49,0xd4,0x96,0x4e,0xf6,0x75,0x09,0x27,0x8f,0x6d,0x38,0xba,0x86,0x9a,0xdc,0xfa,0x69,0x97,0x0e,0x12,0x3d,0x02,0x20,0x34,0x79,0x91,0x01,0x67,0x40,0x8f,0x45,0xbd,0xa4,0x20,0xa6,0x26,0xec,0x9c,0x4e,0xc7,0x11,0xc1,0x27,0x4b,0xe0,0x92,0x19,0x8b,0x41,0x87,0xc0,0x18,0xb5,0x62,0xca, + 0x30,0x16,0x02,0x11,0x01,0x45,0x51,0x23,0x19,0x50,0xb7,0x5f,0xc4,0x40,0x2d,0xa1,0x72,0x2f,0xc9,0xba,0xeb,0x02,0x01,0x03, + 0x30,0x26,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xff,0xff,0xfc,0x2c,0x02,0x01,0x03, + 0x30,0x26,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x3f,0x02,0x01,0x03, + 0x30,0x44,0x02,0x20,0x7f,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfc,0x02,0x20,0x3e,0x9a,0x75,0x82,0x88,0x60,0x89,0xc6,0x2f,0xb8,0x40,0xcf,0x3b,0x83,0x06,0x1c,0xd1,0xcf,0xf3,0xae,0x43,0x41,0x80,0x8b,0xb5,0xbd,0xee,0x61,0x91,0x17,0x41,0x77, + 0x30,0x44,0x02,0x20,0x7f,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfc,0x02,0x20,0x24,0x23,0x8e,0x70,0xb4,0x31,0xb1,0xa6,0x4e,0xfd,0xf9,0x03,0x26,0x69,0x93,0x9d,0x4b,0x77,0xf2,0x49,0x50,0x3f,0xc6,0x90,0x5f,0xeb,0x75,0x40,0xde,0xa3,0xe6,0xd2, + 0x30,0x06,0x02,0x01,0x01,0x02,0x01,0x01, + 0x30,0x06,0x02,0x01,0x01,0x02,0x01,0x02, + 0x30,0x06,0x02,0x01,0x01,0x02,0x01,0x03, + 0x30,0x06,0x02,0x01,0x02,0x02,0x01,0x01, + 0x30,0x06,0x02,0x01,0x02,0x02,0x01,0x02, + 0x30,0x06,0x02,0x01,0x02,0x02,0x01,0x03, + 0x30,0x26,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x41,0x43,0x02,0x01,0x03, + 0x30,0x08,0x02,0x01,0x02,0x02,0x03,0xed,0x29,0x79, + 0x30,0x26,0x02,0x02,0x01,0x01,0x02,0x20,0x3a,0x74,0xe9,0xd3,0xa7,0x4e,0x9d,0x3a,0x74,0xe9,0xd3,0xa7,0x4e,0x9d,0x3a,0x74,0x9f,0x8a,0xb3,0x73,0x2a,0x0a,0x89,0x60,0x4a,0x09,0xbc,0xe5,0xb2,0x91,0x6d,0xa4, + 0x30,0x2b,0x02,0x07,0x2d,0x9b,0x4d,0x34,0x79,0x52,0xcc,0x02,0x20,0x03,0x43,0xae,0xfc,0x2f,0x25,0xd9,0x8b,0x88,0x2e,0x86,0xeb,0x9e,0x30,0xd5,0x5a,0x6e,0xb5,0x08,0xb5,0x16,0x51,0x0b,0x34,0x02,0x4a,0xe4,0xb6,0x36,0x23,0x30,0xb3, + 0x30,0x31,0x02,0x0d,0x10,0x33,0xe6,0x7e,0x37,0xb3,0x2b,0x44,0x55,0x80,0xbf,0x4e,0xfc,0x02,0x20,0x6f,0x90,0x6f,0x90,0x6f,0x90,0x6f,0x90,0x6f,0x90,0x6f,0x90,0x6f,0x90,0x6f,0x8f,0xe1,0xca,0xb5,0xee,0xfd,0xb2,0x14,0x06,0x1d,0xce,0x3b,0x22,0x78,0x9f,0x1d,0x6f, + 0x30,0x26,0x02,0x02,0x01,0x01,0x02,0x20,0x78,0x32,0x66,0xe9,0x0f,0x43,0xda,0xfe,0x5c,0xd9,0xb3,0xb0,0xbe,0x86,0xde,0x22,0xf9,0xde,0x83,0x67,0x7d,0x0f,0x50,0x71,0x3a,0x46,0x8e,0xc7,0x2f,0xcf,0x5d,0x57, + 0x30,0x31,0x02,0x0d,0x06,0x25,0x22,0xbb,0xd3,0xec,0xbe,0x7c,0x39,0xe9,0x3e,0x7c,0x26,0x02,0x20,0x78,0x32,0x66,0xe9,0x0f,0x43,0xda,0xfe,0x5c,0xd9,0xb3,0xb0,0xbe,0x86,0xde,0x22,0xf9,0xde,0x83,0x67,0x7d,0x0f,0x50,0x71,0x3a,0x46,0x8e,0xc7,0x2f,0xcf,0x5d,0x57, + 0x30,0x45,0x02,0x21,0x00,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe,0xba,0xae,0xdc,0xe6,0xaf,0x48,0xa0,0x3b,0xbf,0xd2,0x5e,0x8c,0xd0,0x36,0x40,0xc1,0x02,0x20,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x54,0xe8,0xe4,0xf4,0x4c,0xe5,0x18,0x35,0x69,0x3f,0xf0,0xca,0x2e,0xf0,0x12,0x15,0xc0, + 0x30,0x16,0x02,0x09,0x00,0x9c,0x44,0xfe,0xbf,0x31,0xc3,0x59,0x4d,0x02,0x09,0x00,0x83,0x9e,0xd2,0x82,0x47,0xc2,0xb0,0x6b, + 0x30,0x1e,0x02,0x0d,0x09,0xdf,0x8b,0x68,0x24,0x30,0xbe,0xef,0x6f,0x5f,0xd7,0xc7,0xcf,0x02,0x0d,0x0f,0xd0,0xa6,0x2e,0x13,0x77,0x8f,0x42,0x22,0xa0,0xd6,0x1c,0x8a, + 0x30,0x26,0x02,0x11,0x00,0x8a,0x59,0x8e,0x56,0x3a,0x89,0xf5,0x26,0xc3,0x2e,0xbe,0xc8,0xde,0x26,0x36,0x7a,0x02,0x11,0x00,0x84,0xf6,0x33,0xe2,0x04,0x26,0x30,0xe9,0x9d,0xd0,0xf1,0xe1,0x6f,0x7a,0x04,0xbf, + 0x30,0x2e,0x02,0x15,0x00,0xaa,0x6e,0xeb,0x58,0x23,0xf7,0xfa,0x31,0xb4,0x66,0xbb,0x47,0x37,0x97,0xf0,0xd0,0x31,0x4c,0x0b,0xdf,0x02,0x15,0x00,0xe2,0x97,0x7c,0x47,0x9e,0x6d,0x25,0x70,0x3c,0xeb,0xbc,0x6b,0xd5,0x61,0x93,0x8c,0xc9,0xd1,0xbf,0xb9, + 0x30,0x25,0x02,0x20,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x54,0xe8,0xe4,0xf4,0x4c,0xe5,0x18,0x35,0x69,0x3f,0xf0,0xca,0x2e,0xf0,0x12,0x15,0xc1,0x02,0x01,0x01, + 0x30,0x25,0x02,0x20,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x54,0xe8,0xe4,0xf4,0x4c,0xe5,0x18,0x35,0x69,0x3f,0xf0,0xca,0x2e,0xf0,0x12,0x15,0xc1,0x02,0x01,0x00, + 0x30,0x44,0x02,0x20,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x54,0xe8,0xe4,0xf4,0x4c,0xe5,0x18,0x35,0x69,0x3f,0xf0,0xca,0x2e,0xf0,0x12,0x15,0xc1,0x02,0x20,0x41,0x9d,0x98,0x1c,0x51,0x5a,0xf8,0xcc,0x82,0x54,0x5a,0xac,0x0c,0x85,0xe9,0xe3,0x08,0xfb,0xb2,0xea,0xb6,0xac,0xd7,0xed,0x49,0x7e,0x0b,0x41,0x45,0xa1,0x8f,0xd9, + 0x30,0x44,0x02,0x20,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x54,0xe8,0xe4,0xf4,0x4c,0xe5,0x18,0x35,0x69,0x3f,0xf0,0xca,0x2e,0xf0,0x12,0x15,0xc1,0x02,0x20,0x1b,0x21,0x71,0x7a,0xd7,0x1d,0x23,0xbb,0xac,0x60,0xa9,0xad,0x0b,0xaf,0x75,0xb0,0x63,0xc9,0xfd,0xf5,0x2a,0x00,0xeb,0xf9,0x9d,0x02,0x21,0x72,0x91,0x09,0x93,0xc9, + 0x30,0x44,0x02,0x20,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x54,0xe8,0xe4,0xf4,0x4c,0xe5,0x18,0x35,0x69,0x3f,0xf0,0xca,0x2e,0xf0,0x12,0x15,0xc1,0x02,0x20,0x2f,0x58,0x8f,0x66,0x01,0x8f,0x3d,0xd1,0x4d,0xb3,0xe2,0x8e,0x77,0x99,0x64,0x87,0xe3,0x24,0x86,0xb5,0x21,0xed,0x8e,0x5a,0x20,0xf0,0x65,0x91,0x95,0x17,0x77,0xe9, + 0x30,0x44,0x02,0x20,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x54,0xe8,0xe4,0xf4,0x4c,0xe5,0x18,0x35,0x69,0x3f,0xf0,0xca,0x2e,0xf0,0x12,0x15,0xc1,0x02,0x20,0x09,0x1a,0x08,0x87,0x0f,0xf4,0xda,0xf9,0x12,0x3b,0x30,0xc2,0x0e,0x8c,0x4f,0xc8,0x50,0x57,0x58,0xdc,0xf4,0x07,0x4f,0xca,0xff,0x21,0x70,0xc9,0xbf,0xcf,0x74,0xf4, + 0x30,0x44,0x02,0x20,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x54,0xe8,0xe4,0xf4,0x4c,0xe5,0x18,0x35,0x69,0x3f,0xf0,0xca,0x2e,0xf0,0x12,0x15,0xc1,0x02,0x20,0x7c,0x37,0x0d,0xc0,0xce,0x8c,0x59,0xa8,0xb2,0x73,0xcb,0xa4,0x4a,0x7c,0x11,0x91,0xfc,0x31,0x86,0xdc,0x03,0xca,0xb9,0x6b,0x05,0x67,0x31,0x2d,0xf0,0xd0,0xb2,0x50, + 0x30,0x44,0x02,0x20,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x54,0xe8,0xe4,0xf4,0x4c,0xe5,0x18,0x35,0x69,0x3f,0xf0,0xca,0x2e,0xf0,0x12,0x15,0xc1,0x02,0x20,0x70,0xb5,0x9a,0x7d,0x1e,0xe7,0x7a,0x2f,0x9e,0x04,0x91,0xc2,0xa7,0xcf,0xcd,0x0e,0xd0,0x4d,0xf4,0xa3,0x51,0x92,0xf6,0x13,0x2d,0xcc,0x66,0x8c,0x79,0xa6,0x16,0x0e, + 0x30,0x44,0x02,0x20,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x54,0xe8,0xe4,0xf4,0x4c,0xe5,0x18,0x35,0x69,0x3f,0xf0,0xca,0x2e,0xf0,0x12,0x15,0xc1,0x02,0x20,0x27,0x36,0xd7,0x6e,0x41,0x22,0x46,0xe0,0x97,0x14,0x8e,0x2b,0xf6,0x29,0x15,0x61,0x4e,0xb7,0xc4,0x28,0x91,0x3a,0x58,0xeb,0x5e,0x9c,0xd4,0x67,0x4a,0x94,0x23,0xde, + 0x30,0x44,0x02,0x20,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x54,0xe8,0xe4,0xf4,0x4c,0xe5,0x18,0x35,0x69,0x3f,0xf0,0xca,0x2e,0xf0,0x12,0x15,0xc1,0x02,0x20,0x4a,0x1e,0x12,0x83,0x1f,0xbe,0x93,0x62,0x7b,0x02,0xd6,0xe7,0xf2,0x4b,0xcc,0xdd,0x6e,0xf4,0xb2,0xd0,0xf4,0x67,0x39,0xea,0xf3,0xb1,0xea,0xf0,0xca,0x11,0x77,0x70, + 0x30,0x44,0x02,0x20,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x54,0xe8,0xe4,0xf4,0x4c,0xe5,0x18,0x35,0x69,0x3f,0xf0,0xca,0x2e,0xf0,0x12,0x15,0xc1,0x02,0x20,0x06,0xc7,0x78,0xd4,0xdf,0xff,0x7d,0xee,0x06,0xed,0x88,0xbc,0x4e,0x0e,0xd3,0x4f,0xc5,0x53,0xaa,0xd6,0x7c,0xaf,0x79,0x6f,0x2a,0x1c,0x64,0x87,0xc1,0xb2,0xe8,0x77, + 0x30,0x44,0x02,0x20,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x54,0xe8,0xe4,0xf4,0x4c,0xe5,0x18,0x35,0x69,0x3f,0xf0,0xca,0x2e,0xf0,0x12,0x15,0xc1,0x02,0x20,0x4d,0xe4,0x59,0xef,0x91,0x59,0xaf,0xa0,0x57,0xfe,0xb3,0xec,0x40,0xfe,0xf0,0x1c,0x45,0xb8,0x09,0xf4,0xab,0x29,0x6e,0xa4,0x8c,0x20,0x6d,0x42,0x49,0xa2,0xb4,0x51, + 0x30,0x44,0x02,0x20,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x54,0xe8,0xe4,0xf4,0x4c,0xe5,0x18,0x35,0x69,0x3f,0xf0,0xca,0x2e,0xf0,0x12,0x15,0xc1,0x02,0x20,0x74,0x5d,0x29,0x49,0x78,0x00,0x73,0x02,0x03,0x35,0x02,0xe1,0xac,0xc4,0x8b,0x63,0xae,0x65,0x00,0xbe,0x43,0xad,0xbe,0xa1,0xb2,0x58,0xd6,0xb4,0x23,0xdb,0xb4,0x16, + 0x30,0x44,0x02,0x20,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x54,0xe8,0xe4,0xf4,0x4c,0xe5,0x18,0x35,0x69,0x3f,0xf0,0xca,0x2e,0xf0,0x12,0x15,0xc1,0x02,0x20,0x7b,0x2a,0x78,0x5e,0x38,0x96,0xf5,0x9b,0x2d,0x69,0xda,0x57,0x64,0x8e,0x80,0xad,0x3c,0x13,0x3a,0x75,0x0a,0x28,0x47,0xfd,0x20,0x98,0xcc,0xd9,0x02,0x04,0x2b,0x6c, + 0x30,0x44,0x02,0x20,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x54,0xe8,0xe4,0xf4,0x4c,0xe5,0x18,0x35,0x69,0x3f,0xf0,0xca,0x2e,0xf0,0x12,0x15,0xc1,0x02,0x20,0x71,0xae,0x94,0xa7,0x2c,0xa8,0x96,0x87,0x5e,0x7a,0xa4,0xa4,0xc3,0xd2,0x9a,0xfd,0xb4,0xb3,0x5b,0x69,0x96,0x27,0x3e,0x63,0xc4,0x7a,0xc5,0x19,0x25,0x6c,0x5e,0xb1, + 0x30,0x44,0x02,0x20,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x54,0xe8,0xe4,0xf4,0x4c,0xe5,0x18,0x35,0x69,0x3f,0xf0,0xca,0x2e,0xf0,0x12,0x15,0xc1,0x02,0x20,0x0f,0xa5,0x27,0xfa,0x73,0x43,0xc0,0xbc,0x9e,0xc3,0x5a,0x62,0x78,0xbf,0xbf,0xf4,0xd8,0x33,0x01,0xb1,0x54,0xfc,0x4b,0xd1,0x4a,0xee,0x7e,0xb9,0x34,0x45,0xb5,0xf9, + 0x30,0x44,0x02,0x20,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x54,0xe8,0xe4,0xf4,0x4c,0xe5,0x18,0x35,0x69,0x3f,0xf0,0xca,0x2e,0xf0,0x12,0x15,0xc1,0x02,0x20,0x65,0x39,0xc0,0xad,0xad,0xd0,0x52,0x5f,0xf4,0x26,0x22,0x16,0x4c,0xe9,0x31,0x43,0x48,0xbd,0x08,0x63,0xb4,0xc8,0x0e,0x93,0x6b,0x23,0xca,0x04,0x14,0x26,0x46,0x71, + 0x30,0x44,0x02,0x20,0x7f,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0x5d,0x57,0x6e,0x73,0x57,0xa4,0x50,0x1d,0xdf,0xe9,0x2f,0x46,0x68,0x1b,0x20,0xa0,0x02,0x20,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x54,0xe8,0xe4,0xf4,0x4c,0xe5,0x18,0x35,0x69,0x3f,0xf0,0xca,0x2e,0xf0,0x12,0x15,0xc0, + 0x30,0x44,0x02,0x20,0x7f,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0x5d,0x57,0x6e,0x73,0x57,0xa4,0x50,0x1d,0xdf,0xe9,0x2f,0x46,0x68,0x1b,0x20,0xa0,0x02,0x20,0x7f,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0x5d,0x57,0x6e,0x73,0x57,0xa4,0x50,0x1d,0xdf,0xe9,0x2f,0x46,0x68,0x1b,0x20,0xa0, + 0x30,0x44,0x02,0x20,0x7f,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0x5d,0x57,0x6e,0x73,0x57,0xa4,0x50,0x1d,0xdf,0xe9,0x2f,0x46,0x68,0x1b,0x20,0xa0,0x02,0x20,0x7f,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0x5d,0x57,0x6e,0x73,0x57,0xa4,0x50,0x1d,0xdf,0xe9,0x2f,0x46,0x68,0x1b,0x20,0xa1, + 0x30,0x44,0x02,0x20,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x54,0xe8,0xe4,0xf4,0x4c,0xe5,0x18,0x35,0x69,0x3f,0xf0,0xca,0x2e,0xf0,0x12,0x15,0xb8,0x02,0x20,0x44,0xa5,0xad,0x0b,0xd0,0x63,0x6d,0x9e,0x12,0xbc,0x9e,0x0a,0x6b,0xdd,0x5e,0x1b,0xba,0x77,0xf5,0x23,0x84,0x21,0x93,0xb3,0xb8,0x2e,0x44,0x8e,0x05,0xd5,0xf1,0x1e, + 0x30,0x44,0x02,0x20,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x54,0xe8,0xe4,0xf4,0x4c,0xe5,0x18,0x35,0x69,0x3f,0xf0,0xca,0x2e,0xf0,0x12,0x15,0xb8,0x02,0x20,0x44,0xa5,0xad,0x0b,0xd0,0x63,0x6d,0x9e,0x12,0xbc,0x9e,0x0a,0x6b,0xdd,0x5e,0x1b,0xba,0x77,0xf5,0x23,0x84,0x21,0x93,0xb3,0xb8,0x2e,0x44,0x8e,0x05,0xd5,0xf1,0x1e, + 0x30,0x44,0x02,0x20,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x54,0xe8,0xe4,0xf4,0x4c,0xe5,0x18,0x35,0x69,0x3f,0xf0,0xca,0x2e,0xf0,0x12,0x15,0xb8,0x02,0x20,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x54,0xe8,0xe4,0xf4,0x4c,0xe5,0x18,0x35,0x69,0x3f,0xf0,0xca,0x2e,0xf0,0x12,0x15,0xb8, + 0x30,0x44,0x02,0x20,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x54,0xe8,0xe4,0xf4,0x4c,0xe5,0x18,0x35,0x69,0x3f,0xf0,0xca,0x2e,0xf0,0x12,0x15,0xb8,0x02,0x20,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x54,0xe8,0xe4,0xf4,0x4c,0xe5,0x18,0x35,0x69,0x3f,0xf0,0xca,0x2e,0xf0,0x12,0x15,0xb8, + 0x30,0x44,0x02,0x20,0x7f,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfc,0x02,0x20,0x16,0xe1,0xe4,0x59,0x45,0x76,0x79,0xdf,0x5b,0x94,0x34,0xae,0x23,0xf4,0x74,0xb3,0xe8,0xd2,0xa7,0x0b,0xd6,0xb5,0xdb,0xe6,0x92,0xba,0x16,0xda,0x01,0xf1,0xfb,0x0a, + 0x30,0x44,0x02,0x20,0x7f,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfc,0x02,0x20,0x1c,0x94,0x0f,0x31,0x3f,0x92,0x64,0x7b,0xe2,0x57,0xec,0xcd,0x7e,0xd0,0x8b,0x0b,0xae,0xf3,0xf0,0x47,0x8f,0x25,0x87,0x1b,0x53,0x63,0x53,0x02,0xc5,0xf6,0x31,0x4a, + 0x30,0x44,0x02,0x20,0x7f,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfc,0x02,0x20,0x15,0xd9,0x4a,0x85,0x07,0x7b,0x49,0x3f,0x91,0xcb,0x71,0x01,0xec,0x63,0xe1,0xb0,0x1b,0xe5,0x8b,0x59,0x4e,0x85,0x5f,0x45,0x05,0x0a,0x8c,0x14,0x06,0x2d,0x68,0x9b, + 0x30,0x44,0x02,0x20,0x7f,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfc,0x02,0x20,0x5b,0x1d,0x27,0xa7,0x69,0x4c,0x14,0x62,0x44,0xa5,0xad,0x0b,0xd0,0x63,0x6d,0x9d,0x9e,0xf3,0xb9,0xfb,0x58,0x38,0x54,0x18,0xd9,0xc9,0x82,0x10,0x50,0x77,0xd1,0xb7, + 0x30,0x44,0x02,0x20,0x7f,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfc,0x02,0x20,0x2d,0x85,0x89,0x6b,0x3e,0xb9,0xdb,0xb5,0xa5,0x2f,0x42,0xf9,0xc9,0x26,0x1e,0xd3,0xfc,0x46,0x64,0x4e,0xc6,0x5f,0x06,0xad,0xe3,0xfd,0x78,0xf2,0x57,0xe4,0x34,0x32, + 0x30,0x44,0x02,0x20,0x7f,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfc,0x02,0x20,0x5b,0x0b,0x12,0xd6,0x7d,0x73,0xb7,0x6b,0x4a,0x5e,0x85,0xf3,0x92,0x4c,0x3d,0xa7,0xf8,0x8c,0xc8,0x9d,0x8c,0xbe,0x0d,0x5b,0xc7,0xfa,0xf1,0xe4,0xaf,0xc8,0x68,0x64, + 0x30,0x44,0x02,0x20,0x7f,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfc,0x02,0x20,0x69,0x4c,0x14,0x62,0x44,0xa5,0xad,0x0b,0xd0,0x63,0x6d,0x9e,0x12,0xbc,0x9e,0x09,0xe6,0x0e,0x68,0xb9,0x0d,0x0b,0x5e,0x6c,0x5d,0xdd,0xd0,0xcb,0x69,0x4d,0x87,0x99, + 0x30,0x44,0x02,0x20,0x7f,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfc,0x02,0x20,0x3d,0x7f,0x48,0x7c,0x07,0xbf,0xc5,0xf3,0x08,0x46,0x93,0x8a,0x3d,0xce,0xf6,0x96,0x44,0x47,0x07,0xcf,0x96,0x77,0x25,0x4a,0x92,0xb0,0x6c,0x63,0xab,0x86,0x7d,0x22, + 0x30,0x44,0x02,0x20,0x7f,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfc,0x02,0x20,0x6c,0x76,0x48,0xfc,0x0f,0xbf,0x8a,0x06,0xad,0xb8,0xb8,0x39,0xf9,0x7b,0x4f,0xf7,0xa8,0x00,0xf1,0x1b,0x1e,0x37,0xc5,0x93,0xb2,0x61,0x39,0x45,0x99,0x79,0x2b,0xa4, + 0x30,0x44,0x02,0x20,0x7f,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfc,0x02,0x20,0x64,0x1c,0x9c,0x5d,0x79,0x0d,0xc0,0x9c,0xdd,0x3d,0xfa,0xbb,0x62,0xcd,0xf4,0x53,0xe6,0x97,0x47,0xa7,0xe3,0xd7,0xaa,0x1a,0x71,0x41,0x89,0xef,0x53,0x17,0x1a,0x99, + 0x30,0x44,0x02,0x20,0x7f,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfc,0x02,0x20,0x29,0x79,0x8c,0x5c,0x45,0xbd,0xf5,0x8b,0x4a,0x7b,0x2f,0xdc,0x2c,0x46,0xab,0x4a,0xf1,0x21,0x8c,0x7e,0xeb,0x9f,0x0f,0x27,0xa8,0x8f,0x12,0x67,0x67,0x4d,0xe3,0xb0, + 0x30,0x44,0x02,0x20,0x7f,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfc,0x02,0x20,0x0b,0x70,0xf2,0x2c,0xa2,0xbb,0x3c,0xef,0xad,0xca,0x1a,0x57,0x11,0xfa,0x3a,0x59,0xf4,0x69,0x53,0x85,0xeb,0x5a,0xed,0xf3,0x49,0x5d,0x0b,0x6d,0x00,0xf8,0xfd,0x85, + 0x30,0x44,0x02,0x20,0x7f,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfc,0x02,0x20,0x16,0xe1,0xe4,0x59,0x45,0x76,0x79,0xdf,0x5b,0x94,0x34,0xae,0x23,0xf4,0x74,0xb3,0xe8,0xd2,0xa7,0x0b,0xd6,0xb5,0xdb,0xe6,0x92,0xba,0x16,0xda,0x01,0xf1,0xfb,0x0a, + 0x30,0x44,0x02,0x20,0x7f,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfc,0x02,0x20,0x22,0x52,0xd6,0x85,0xe8,0x31,0xb6,0xcf,0x09,0x5e,0x4f,0x05,0x35,0xee,0xaf,0x0d,0xdd,0x3b,0xfa,0x91,0xc2,0x10,0xc9,0xd9,0xdc,0x17,0x22,0x47,0x02,0xea,0xf8,0x8f, + 0x30,0x44,0x02,0x20,0x7f,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfc,0x02,0x20,0x75,0x13,0x5a,0xbd,0x7c,0x42,0x5b,0x60,0x37,0x1a,0x47,0x7f,0x09,0xce,0x0f,0x27,0x4f,0x64,0xa8,0xc6,0xb0,0x61,0xa0,0x7b,0x5d,0x63,0xe9,0x3c,0x65,0x04,0x6c,0x53, + 0x30,0x44,0x02,0x20,0x7f,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfc,0x02,0x20,0x2a,0xaa,0xaa,0xaa,0xaa,0xaa,0xaa,0xaa,0xaa,0xaa,0xaa,0xaa,0xaa,0xaa,0xaa,0xaa,0x3e,0x3a,0x49,0xa2,0x3a,0x6d,0x8a,0xbe,0x95,0x46,0x1f,0x84,0x45,0x67,0x6b,0x17, + 0x30,0x44,0x02,0x20,0x7f,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfc,0x02,0x20,0x3e,0x88,0x83,0x77,0xac,0x6c,0x71,0xac,0x9d,0xec,0x3f,0xdb,0x9b,0x56,0xc9,0xfe,0xaf,0x0c,0xfa,0xca,0x9f,0x82,0x7f,0xc5,0xeb,0x65,0xfc,0x3e,0xac,0x81,0x12,0x10, + 0x30,0x44,0x02,0x20,0x7f,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfc,0x02,0x20,0x30,0xbb,0xb7,0x94,0xdb,0x58,0x83,0x63,0xb4,0x06,0x79,0xf6,0xc1,0x82,0xa5,0x0d,0x3c,0xe9,0x67,0x9a,0xcd,0xd3,0xff,0xbe,0x36,0xd7,0x81,0x3d,0xac,0xbd,0xc8,0x18, + 0x30,0x44,0x02,0x20,0x7f,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfc,0x02,0x20,0x2c,0x37,0xfd,0x99,0x56,0x22,0xc4,0xfb,0x7f,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xc7,0xce,0xe7,0x45,0x11,0x0c,0xb4,0x5a,0xb5,0x58,0xed,0x7c,0x90,0xc1,0x5a,0x2f, + 0x30,0x44,0x02,0x20,0x7f,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfc,0x02,0x20,0x7f,0xd9,0x95,0x62,0x2c,0x4f,0xb7,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0x5d,0x88,0x3f,0xfa,0xb5,0xb3,0x26,0x52,0xcc,0xdc,0xaa,0x29,0x0f,0xcc,0xb9,0x7d, + 0x30,0x43,0x02,0x20,0x7f,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfc,0x02,0x1f,0x4c,0xd5,0x3b,0xa7,0x60,0x8f,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0x9e,0x5c,0xf1,0x43,0xe2,0x53,0x96,0x26,0x19,0x0a,0x3a,0xb0,0x9c,0xce,0x47, + 0x30,0x44,0x02,0x20,0x7f,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfc,0x02,0x20,0x56,0x22,0xc4,0xfb,0x7f,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0x92,0x8a,0x8f,0x1c,0x7a,0xc7,0xbe,0xc1,0x80,0x8b,0x9f,0x61,0xc0,0x1e,0xc3,0x27, + 0x30,0x44,0x02,0x20,0x7f,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfc,0x02,0x20,0x44,0x10,0x41,0x04,0x10,0x41,0x04,0x10,0x41,0x04,0x10,0x41,0x04,0x10,0x41,0x03,0xb8,0x78,0x53,0xfd,0x3b,0x7d,0x3f,0x8e,0x17,0x51,0x25,0xb4,0x38,0x2f,0x25,0xed, + 0x30,0x44,0x02,0x20,0x7f,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfc,0x02,0x20,0x27,0x39,0xce,0x73,0x9c,0xe7,0x39,0xce,0x73,0x9c,0xe7,0x39,0xce,0x73,0x9c,0xe7,0x05,0x56,0x02,0x98,0xd1,0xf2,0xf0,0x8d,0xc4,0x19,0xac,0x27,0x3a,0x5b,0x54,0xd9, + 0x30,0x44,0x02,0x20,0x7f,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfc,0x02,0x20,0x48,0x88,0x88,0x88,0x88,0x88,0x88,0x88,0x88,0x88,0x88,0x88,0x88,0x88,0x88,0x88,0x31,0xc8,0x3a,0xe8,0x2e,0xbe,0x08,0x98,0x77,0x6b,0x4c,0x69,0xd1,0x1f,0x88,0xde, + 0x30,0x44,0x02,0x20,0x7f,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfc,0x02,0x20,0x64,0x92,0x49,0x24,0x92,0x49,0x24,0x92,0x49,0x24,0x92,0x49,0x24,0x92,0x49,0x24,0x06,0xdd,0x3a,0x19,0xb8,0xd5,0xfb,0x87,0x52,0x35,0x96,0x3c,0x59,0x3b,0xd2,0xd3, + 0x30,0x44,0x02,0x20,0x7f,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfc,0x02,0x20,0x6a,0xaa,0xaa,0xaa,0xaa,0xaa,0xaa,0xaa,0xaa,0xaa,0xaa,0xaa,0xaa,0xaa,0xaa,0xaa,0x3e,0x3a,0x49,0xa2,0x3a,0x6d,0x8a,0xbe,0x95,0x46,0x1f,0x84,0x45,0x67,0x6b,0x15, + 0x30,0x44,0x02,0x20,0x7f,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfc,0x02,0x20,0x2a,0xaa,0xaa,0xaa,0xaa,0xaa,0xaa,0xaa,0xaa,0xaa,0xaa,0xaa,0xaa,0xaa,0xaa,0xaa,0x3e,0x3a,0x49,0xa2,0x3a,0x6d,0x8a,0xbe,0x95,0x46,0x1f,0x84,0x45,0x67,0x6b,0x17, + 0x30,0x44,0x02,0x20,0x7f,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfc,0x02,0x20,0x3f,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfe, + 0x30,0x44,0x02,0x20,0x7f,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xfc,0x02,0x20,0x18,0x5d,0xdb,0xca,0x6d,0xac,0x41,0xb1,0xda,0x03,0x3c,0xfb,0x60,0xc1,0x52,0x86,0x9e,0x74,0xb3,0xcd,0x66,0xe9,0xff,0xdf,0x1b,0x6b,0xc0,0x9e,0xd6,0x5e,0xe4,0x0c, + 0x30,0x44,0x02,0x20,0x32,0xb0,0xd1,0x0d,0x8d,0x0e,0x04,0xbc,0x8d,0x4d,0x06,0x4d,0x27,0x06,0x99,0xe8,0x7c,0xff,0xc9,0xb4,0x9c,0x5c,0x20,0x73,0x0e,0x1c,0x26,0xf6,0x10,0x5d,0xdc,0xda,0x02,0x20,0x29,0xed,0x3d,0x67,0xb3,0xd5,0x05,0xbe,0x95,0x58,0x0d,0x77,0xd5,0xb7,0x92,0xb4,0x36,0x88,0x11,0x79,0xb2,0xb6,0xb2,0xe0,0x4c,0x5f,0xe5,0x92,0xd3,0x8d,0x82,0xd9, + 0x30,0x44,0x02,0x20,0x32,0xb0,0xd1,0x0d,0x8d,0x0e,0x04,0xbc,0x8d,0x4d,0x06,0x4d,0x27,0x06,0x99,0xe8,0x7c,0xff,0xc9,0xb4,0x9c,0x5c,0x20,0x73,0x0e,0x1c,0x26,0xf6,0x10,0x5d,0xdc,0xda,0x02,0x20,0x29,0xed,0x3d,0x67,0xb3,0xd5,0x05,0xbe,0x95,0x58,0x0d,0x77,0xd5,0xb7,0x92,0xb4,0x36,0x88,0x11,0x79,0xb2,0xb6,0xb2,0xe0,0x4c,0x5f,0xe5,0x92,0xd3,0x8d,0x82,0xd9, + 0x30,0x44,0x02,0x20,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x54,0xe8,0xe4,0xf4,0x4c,0xe5,0x18,0x35,0x69,0x3f,0xf0,0xca,0x2e,0xf0,0x12,0x15,0xc0,0x02,0x20,0x33,0x33,0x33,0x33,0x33,0x33,0x33,0x33,0x33,0x33,0x33,0x33,0x33,0x33,0x33,0x32,0xf2,0x22,0xf8,0xfa,0xef,0xdb,0x53,0x3f,0x26,0x5d,0x46,0x1c,0x29,0xa4,0x73,0x73, + 0x30,0x45,0x02,0x21,0x00,0xc6,0x04,0x7f,0x94,0x41,0xed,0x7d,0x6d,0x30,0x45,0x40,0x6e,0x95,0xc0,0x7c,0xd8,0x5c,0x77,0x8e,0x4b,0x8c,0xef,0x3c,0xa7,0xab,0xac,0x09,0xb9,0x5c,0x70,0x9e,0xe5,0x02,0x20,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x54,0xe8,0xe4,0xf4,0x4c,0xe5,0x18,0x35,0x69,0x3f,0xf0,0xca,0x2e,0xf0,0x12,0x15,0xc0, + 0x30,0x45,0x02,0x21,0x00,0xc6,0x04,0x7f,0x94,0x41,0xed,0x7d,0x6d,0x30,0x45,0x40,0x6e,0x95,0xc0,0x7c,0xd8,0x5c,0x77,0x8e,0x4b,0x8c,0xef,0x3c,0xa7,0xab,0xac,0x09,0xb9,0x5c,0x70,0x9e,0xe5,0x02,0x20,0x49,0x24,0x92,0x49,0x24,0x92,0x49,0x24,0x92,0x49,0x24,0x92,0x49,0x24,0x92,0x48,0xc7,0x9f,0xac,0xd4,0x32,0x14,0xc0,0x11,0x12,0x3c,0x1b,0x03,0xa9,0x34,0x12,0xa5, + 0x30,0x45,0x02,0x21,0x00,0xc6,0x04,0x7f,0x94,0x41,0xed,0x7d,0x6d,0x30,0x45,0x40,0x6e,0x95,0xc0,0x7c,0xd8,0x5c,0x77,0x8e,0x4b,0x8c,0xef,0x3c,0xa7,0xab,0xac,0x09,0xb9,0x5c,0x70,0x9e,0xe5,0x02,0x20,0x66,0x66,0x66,0x66,0x66,0x66,0x66,0x66,0x66,0x66,0x66,0x66,0x66,0x66,0x66,0x65,0xe4,0x45,0xf1,0xf5,0xdf,0xb6,0xa6,0x7e,0x4c,0xba,0x8c,0x38,0x53,0x48,0xe6,0xe7, + 0x30,0x45,0x02,0x21,0x00,0xc6,0x04,0x7f,0x94,0x41,0xed,0x7d,0x6d,0x30,0x45,0x40,0x6e,0x95,0xc0,0x7c,0xd8,0x5c,0x77,0x8e,0x4b,0x8c,0xef,0x3c,0xa7,0xab,0xac,0x09,0xb9,0x5c,0x70,0x9e,0xe5,0x02,0x20,0x66,0x66,0x66,0x66,0x66,0x66,0x66,0x66,0x66,0x66,0x66,0x66,0x66,0x66,0x66,0x65,0xe4,0x45,0xf1,0xf5,0xdf,0xb6,0xa6,0x7e,0x4c,0xba,0x8c,0x38,0x53,0x48,0xe6,0xe7, + 0x30,0x45,0x02,0x21,0x00,0xc6,0x04,0x7f,0x94,0x41,0xed,0x7d,0x6d,0x30,0x45,0x40,0x6e,0x95,0xc0,0x7c,0xd8,0x5c,0x77,0x8e,0x4b,0x8c,0xef,0x3c,0xa7,0xab,0xac,0x09,0xb9,0x5c,0x70,0x9e,0xe5,0x02,0x20,0x49,0x24,0x92,0x49,0x24,0x92,0x49,0x24,0x92,0x49,0x24,0x92,0x49,0x24,0x92,0x48,0xc7,0x9f,0xac,0xd4,0x32,0x14,0xc0,0x11,0x12,0x3c,0x1b,0x03,0xa9,0x34,0x12,0xa5, + 0x30,0x45,0x02,0x21,0x00,0xc6,0x04,0x7f,0x94,0x41,0xed,0x7d,0x6d,0x30,0x45,0x40,0x6e,0x95,0xc0,0x7c,0xd8,0x5c,0x77,0x8e,0x4b,0x8c,0xef,0x3c,0xa7,0xab,0xac,0x09,0xb9,0x5c,0x70,0x9e,0xe5,0x02,0x20,0x0e,0xb1,0x0e,0x5a,0xb9,0x5f,0x2f,0x27,0x53,0x48,0xd8,0x2a,0xd2,0xe4,0xd7,0x94,0x9c,0x81,0x93,0x80,0x0d,0x8c,0x9c,0x75,0xdf,0x58,0xe3,0x43,0xf0,0xeb,0xba,0x7b, + 0x30,0x44,0x02,0x20,0x79,0xbe,0x66,0x7e,0xf9,0xdc,0xbb,0xac,0x55,0xa0,0x62,0x95,0xce,0x87,0x0b,0x07,0x02,0x9b,0xfc,0xdb,0x2d,0xce,0x28,0xd9,0x59,0xf2,0x81,0x5b,0x16,0xf8,0x17,0x98,0x02,0x20,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x54,0xe8,0xe4,0xf4,0x4c,0xe5,0x18,0x35,0x69,0x3f,0xf0,0xca,0x2e,0xf0,0x12,0x15,0xc0, + 0x30,0x44,0x02,0x20,0x79,0xbe,0x66,0x7e,0xf9,0xdc,0xbb,0xac,0x55,0xa0,0x62,0x95,0xce,0x87,0x0b,0x07,0x02,0x9b,0xfc,0xdb,0x2d,0xce,0x28,0xd9,0x59,0xf2,0x81,0x5b,0x16,0xf8,0x17,0x98,0x02,0x20,0x49,0x24,0x92,0x49,0x24,0x92,0x49,0x24,0x92,0x49,0x24,0x92,0x49,0x24,0x92,0x48,0xc7,0x9f,0xac,0xd4,0x32,0x14,0xc0,0x11,0x12,0x3c,0x1b,0x03,0xa9,0x34,0x12,0xa5, + 0x30,0x44,0x02,0x20,0x79,0xbe,0x66,0x7e,0xf9,0xdc,0xbb,0xac,0x55,0xa0,0x62,0x95,0xce,0x87,0x0b,0x07,0x02,0x9b,0xfc,0xdb,0x2d,0xce,0x28,0xd9,0x59,0xf2,0x81,0x5b,0x16,0xf8,0x17,0x98,0x02,0x20,0x66,0x66,0x66,0x66,0x66,0x66,0x66,0x66,0x66,0x66,0x66,0x66,0x66,0x66,0x66,0x65,0xe4,0x45,0xf1,0xf5,0xdf,0xb6,0xa6,0x7e,0x4c,0xba,0x8c,0x38,0x53,0x48,0xe6,0xe7, + 0x30,0x44,0x02,0x20,0x79,0xbe,0x66,0x7e,0xf9,0xdc,0xbb,0xac,0x55,0xa0,0x62,0x95,0xce,0x87,0x0b,0x07,0x02,0x9b,0xfc,0xdb,0x2d,0xce,0x28,0xd9,0x59,0xf2,0x81,0x5b,0x16,0xf8,0x17,0x98,0x02,0x20,0x66,0x66,0x66,0x66,0x66,0x66,0x66,0x66,0x66,0x66,0x66,0x66,0x66,0x66,0x66,0x65,0xe4,0x45,0xf1,0xf5,0xdf,0xb6,0xa6,0x7e,0x4c,0xba,0x8c,0x38,0x53,0x48,0xe6,0xe7, + 0x30,0x44,0x02,0x20,0x79,0xbe,0x66,0x7e,0xf9,0xdc,0xbb,0xac,0x55,0xa0,0x62,0x95,0xce,0x87,0x0b,0x07,0x02,0x9b,0xfc,0xdb,0x2d,0xce,0x28,0xd9,0x59,0xf2,0x81,0x5b,0x16,0xf8,0x17,0x98,0x02,0x20,0x49,0x24,0x92,0x49,0x24,0x92,0x49,0x24,0x92,0x49,0x24,0x92,0x49,0x24,0x92,0x48,0xc7,0x9f,0xac,0xd4,0x32,0x14,0xc0,0x11,0x12,0x3c,0x1b,0x03,0xa9,0x34,0x12,0xa5, + 0x30,0x44,0x02,0x20,0x79,0xbe,0x66,0x7e,0xf9,0xdc,0xbb,0xac,0x55,0xa0,0x62,0x95,0xce,0x87,0x0b,0x07,0x02,0x9b,0xfc,0xdb,0x2d,0xce,0x28,0xd9,0x59,0xf2,0x81,0x5b,0x16,0xf8,0x17,0x98,0x02,0x20,0x0e,0xb1,0x0e,0x5a,0xb9,0x5f,0x2f,0x27,0x53,0x48,0xd8,0x2a,0xd2,0xe4,0xd7,0x94,0x9c,0x81,0x93,0x80,0x0d,0x8c,0x9c,0x75,0xdf,0x58,0xe3,0x43,0xf0,0xeb,0xba,0x7b, + 0x30,0x45,0x02,0x21,0x00,0xbb,0x5a,0x52,0xf4,0x2f,0x9c,0x92,0x61,0xed,0x43,0x61,0xf5,0x94,0x22,0xa1,0xe3,0x00,0x36,0xe7,0xc3,0x2b,0x27,0x0c,0x88,0x07,0xa4,0x19,0xfe,0xca,0x60,0x50,0x23,0x02,0x20,0x24,0x92,0x49,0x24,0x92,0x49,0x24,0x92,0x49,0x24,0x92,0x49,0x24,0x92,0x49,0x24,0x63,0xcf,0xd6,0x6a,0x19,0x0a,0x60,0x08,0x89,0x1e,0x0d,0x81,0xd4,0x9a,0x09,0x52, + 0x30,0x44,0x02,0x20,0x44,0xa5,0xad,0x0b,0xd0,0x63,0x6d,0x9e,0x12,0xbc,0x9e,0x0a,0x6b,0xdd,0x5e,0x1b,0xba,0x77,0xf5,0x23,0x84,0x21,0x93,0xb3,0xb8,0x2e,0x44,0x8e,0x05,0xd5,0xf1,0x1e,0x02,0x20,0x24,0x92,0x49,0x24,0x92,0x49,0x24,0x92,0x49,0x24,0x92,0x49,0x24,0x92,0x49,0x24,0x63,0xcf,0xd6,0x6a,0x19,0x0a,0x60,0x08,0x89,0x1e,0x0d,0x81,0xd4,0x9a,0x09,0x52, + 0x30,0x45,0x02,0x21,0x00,0xbb,0x5a,0x52,0xf4,0x2f,0x9c,0x92,0x61,0xed,0x43,0x61,0xf5,0x94,0x22,0xa1,0xe3,0x00,0x36,0xe7,0xc3,0x2b,0x27,0x0c,0x88,0x07,0xa4,0x19,0xfe,0xca,0x60,0x50,0x23,0x02,0x20,0x24,0x92,0x49,0x24,0x92,0x49,0x24,0x92,0x49,0x24,0x92,0x49,0x24,0x92,0x49,0x24,0x63,0xcf,0xd6,0x6a,0x19,0x0a,0x60,0x08,0x89,0x1e,0x0d,0x81,0xd4,0x9a,0x09,0x52, + 0x30,0x44,0x02,0x20,0x44,0xa5,0xad,0x0b,0xd0,0x63,0x6d,0x9e,0x12,0xbc,0x9e,0x0a,0x6b,0xdd,0x5e,0x1b,0xba,0x77,0xf5,0x23,0x84,0x21,0x93,0xb3,0xb8,0x2e,0x44,0x8e,0x05,0xd5,0xf1,0x1e,0x02,0x20,0x24,0x92,0x49,0x24,0x92,0x49,0x24,0x92,0x49,0x24,0x92,0x49,0x24,0x92,0x49,0x24,0x63,0xcf,0xd6,0x6a,0x19,0x0a,0x60,0x08,0x89,0x1e,0x0d,0x81,0xd4,0x9a,0x09,0x52, + 0x30,0x45,0x02,0x21,0x00,0xf8,0x0a,0xe4,0xf9,0x6c,0xdb,0xc9,0xd8,0x53,0xf8,0x3d,0x47,0xaa,0xe2,0x25,0xbf,0x40,0x7d,0x51,0xc5,0x6b,0x77,0x76,0xcd,0x67,0xd0,0xdc,0x19,0x5d,0x99,0xa9,0xdc,0x02,0x20,0x4c,0xfc,0x1d,0x94,0x1e,0x08,0xcb,0x9a,0xce,0xad,0xde,0x0f,0x4c,0xce,0xad,0x76,0xb3,0x0d,0x33,0x2f,0xc4,0x42,0x11,0x5d,0x50,0xe6,0x73,0xe2,0x86,0x86,0xb7,0x0b, + 0x30,0x44,0x02,0x20,0x10,0x9c,0xd8,0xae,0x03,0x74,0x35,0x89,0x84,0xa8,0x24,0x9c,0x0a,0x84,0x36,0x28,0xf2,0x83,0x5f,0xfa,0xd1,0xdf,0x1a,0x9a,0x69,0xaa,0x2f,0xe7,0x23,0x55,0x54,0x5c,0x02,0x20,0x53,0x90,0xff,0x25,0x0a,0xc4,0x27,0x4e,0x1c,0xb2,0x5c,0xd6,0xca,0x64,0x91,0xf6,0xb9,0x12,0x81,0xe3,0x2f,0x5b,0x26,0x4d,0x87,0x97,0x7a,0xed,0x4a,0x94,0xe7,0x7b, + 0x30,0x45,0x02,0x21,0x00,0xd0,0x35,0xee,0x1f,0x17,0xfd,0xb0,0xb2,0x68,0x1b,0x16,0x3e,0x33,0xc3,0x59,0x93,0x26,0x59,0x99,0x0a,0xf7,0x7d,0xca,0x63,0x20,0x12,0xb3,0x0b,0x27,0xa0,0x57,0xb3,0x02,0x20,0x19,0x39,0xd9,0xf3,0xb2,0x85,0x8b,0xc1,0x3e,0x34,0x74,0xcb,0x50,0xe6,0xa8,0x2b,0xe4,0x4f,0xaa,0x71,0x94,0x0f,0x87,0x6c,0x1c,0xba,0x4c,0x3e,0x98,0x92,0x02,0xb6, + 0x30,0x44,0x02,0x20,0x4f,0x05,0x3f,0x56,0x3a,0xd3,0x4b,0x74,0xfd,0x8c,0x99,0x34,0xce,0x59,0xe7,0x9c,0x2e,0xb8,0xe6,0xec,0xa0,0xfe,0xf5,0xb3,0x23,0xca,0x67,0xd5,0xac,0x7e,0xd2,0x38,0x02,0x20,0x4d,0x4b,0x05,0xda,0xa0,0x71,0x9e,0x77,0x3d,0x86,0x17,0xdc,0xe5,0x63,0x1c,0x5f,0xd6,0xf5,0x9c,0x9b,0xdc,0x74,0x8e,0x4b,0x55,0xc9,0x70,0x04,0x0a,0xf0,0x1b,0xe5, + 0x30,0x44,0x02,0x20,0x6d,0x6a,0x4f,0x55,0x6c,0xcc,0xe1,0x54,0xe7,0xfb,0x9f,0x19,0xe7,0x6c,0x3d,0xec,0xa1,0x3d,0x59,0xcc,0x2a,0xeb,0x4e,0xca,0xd9,0x68,0xaa,0xb2,0xde,0xd4,0x59,0x65,0x02,0x20,0x53,0xb9,0xfa,0x74,0x80,0x3e,0xde,0x0f,0xc4,0x44,0x1b,0xf6,0x83,0xd5,0x6c,0x56,0x4d,0x3e,0x27,0x4e,0x09,0xcc,0xf4,0x73,0x90,0xba,0xdd,0x14,0x71,0xc0,0x5f,0xb7, + 0x30,0x44,0x02,0x21,0x00,0xaa,0xd5,0x03,0xde,0x9b,0x9f,0xd6,0x6b,0x94,0x8e,0x9a,0xcf,0x59,0x6f,0x0a,0x0e,0x65,0xe7,0x00,0xb2,0x8b,0x26,0xec,0x56,0xe6,0xe4,0x5e,0x84,0x64,0x89,0xb3,0xc4,0x02,0x1f,0x0d,0xdc,0x3a,0x2f,0x89,0xab,0xb8,0x17,0xbb,0x85,0xc0,0x62,0xce,0x02,0xf8,0x23,0xc6,0x3f,0xc2,0x6b,0x26,0x9e,0x0b,0xc9,0xb8,0x4d,0x81,0xa5,0xaa,0x12,0x3d, + 0x30,0x45,0x02,0x21,0x00,0x91,0x82,0xce,0xbd,0x3b,0xb8,0xab,0x57,0x2e,0x16,0x71,0x74,0x39,0x72,0x09,0xef,0x4b,0x1d,0x43,0x9a,0xf3,0xb2,0x00,0xcd,0xf0,0x03,0x62,0x00,0x89,0xe4,0x32,0x25,0x02,0x20,0x54,0x47,0x7c,0x98,0x2e,0xa0,0x19,0xd2,0xe1,0x00,0x04,0x97,0xfc,0x25,0xfc,0xee,0x1b,0xcc,0xae,0x55,0xf2,0xac,0x27,0x53,0x0a,0xe5,0x3b,0x29,0xc4,0xb3,0x56,0xa4, + 0x30,0x44,0x02,0x20,0x38,0x54,0xa3,0x99,0x8a,0xeb,0xdf,0x2d,0xbc,0x28,0xad,0xac,0x41,0x81,0x46,0x2c,0xca,0xc7,0x87,0x39,0x07,0xab,0x7f,0x21,0x2c,0x42,0xdb,0x0e,0x69,0xb5,0x6e,0xd8,0x02,0x20,0x3e,0xd3,0xf6,0xb8,0xa3,0x88,0xd0,0x2f,0x3e,0x4d,0xf9,0xf2,0xae,0x9c,0x1b,0xd2,0xc3,0x91,0x6a,0x68,0x64,0x60,0xdf,0xfc,0xd4,0x29,0x09,0xcd,0x7f,0x82,0x05,0x8e, + 0x30,0x45,0x02,0x21,0x00,0xe9,0x4d,0xbd,0xc3,0x87,0x95,0xfe,0x5c,0x90,0x4d,0x8f,0x16,0xd9,0x69,0xd3,0xb5,0x87,0xf0,0xa2,0x5d,0x2d,0xe9,0x0b,0x6d,0x8c,0x5c,0x53,0xff,0x88,0x7e,0x36,0x07,0x02,0x20,0x7a,0x94,0x73,0x69,0xc1,0x64,0x97,0x25,0x21,0xbb,0x8a,0xf4,0x06,0x81,0x3b,0x2d,0x9f,0x94,0xd2,0xae,0xaa,0x53,0xd4,0xc2,0x15,0xaa,0xa0,0xa2,0x57,0x8a,0x2c,0x5d, + 0x30,0x44,0x02,0x20,0x49,0xfc,0x10,0x2a,0x08,0xca,0x47,0xb6,0x0e,0x08,0x58,0xcd,0x02,0x84,0xd2,0x2c,0xdd,0xd7,0x23,0x3f,0x94,0xaa,0xff,0xbb,0x2d,0xb1,0xdd,0x2c,0xf0,0x84,0x25,0xe1,0x02,0x20,0x5b,0x16,0xfc,0xa5,0xa1,0x2c,0xdb,0x39,0x70,0x16,0x97,0xad,0x8e,0x39,0xff,0xd6,0xbd,0xec,0x00,0x24,0x29,0x8a,0xfa,0xa2,0x32,0x6a,0xea,0x09,0x20,0x0b,0x14,0xd6, + 0x30,0x44,0x02,0x20,0x41,0xef,0xa7,0xd3,0xf0,0x5a,0x00,0x10,0x67,0x5f,0xcb,0x91,0x8a,0x45,0xc6,0x93,0xda,0x4b,0x34,0x8d,0xf2,0x1a,0x59,0xd6,0xf9,0xcd,0x73,0xe0,0xd8,0x31,0xd6,0x7a,0x02,0x20,0x44,0x54,0xad,0xa6,0x93,0xe5,0xe2,0x6b,0x7b,0xd6,0x93,0x23,0x6d,0x34,0x0f,0x80,0x54,0x5c,0x83,0x45,0x77,0xb6,0xf7,0x3d,0x37,0x8c,0x7b,0xcc,0x53,0x42,0x44,0xda, + 0x30,0x45,0x02,0x21,0x00,0xb6,0x15,0x69,0x8c,0x35,0x8b,0x35,0x92,0x0d,0xd8,0x83,0xec,0xa6,0x25,0xa6,0xc5,0xf7,0x56,0x39,0x70,0xcd,0xfc,0x37,0x8f,0x8f,0xe0,0xce,0xe1,0x70,0x92,0x14,0x4c,0x02,0x20,0x25,0xf4,0x7b,0x32,0x6b,0x5b,0xe1,0xfb,0x61,0x0b,0x88,0x51,0x53,0xea,0x84,0xd4,0x1e,0xb4,0x71,0x6b,0xe6,0x6a,0x99,0x4e,0x87,0x79,0x98,0x9d,0xf1,0xc8,0x63,0xd4, + 0x30,0x45,0x02,0x21,0x00,0x87,0xcf,0x8c,0x0e,0xb8,0x2d,0x44,0xf6,0x9c,0x60,0xa2,0xff,0x54,0x57,0xd3,0xaa,0xa3,0x22,0xe7,0xec,0x61,0xae,0x5a,0xec,0xfd,0x67,0x8a,0xe1,0xc1,0x93,0x2b,0x0e,0x02,0x20,0x3a,0xdd,0x3b,0x11,0x58,0x15,0x04,0x7d,0x6e,0xb3,0x40,0xa3,0xe0,0x08,0x98,0x9e,0xaa,0x0f,0x87,0x08,0xd1,0x79,0x48,0x14,0x72,0x90,0x94,0xd0,0x8d,0x24,0x60,0xd3, + 0x30,0x44,0x02,0x20,0x62,0xf4,0x8e,0xf7,0x1a,0xce,0x27,0xbf,0x5a,0x01,0x83,0x4d,0xe1,0xf7,0xe3,0xf9,0x48,0xb9,0xdc,0xe1,0xca,0x1e,0x91,0x1d,0x5e,0x13,0xd3,0xb1,0x04,0x47,0x1d,0x82,0x02,0x20,0x5e,0xa8,0xf3,0x3f,0x0c,0x77,0x89,0x72,0xc4,0x58,0x20,0x80,0xde,0xda,0x9b,0x34,0x18,0x57,0xdd,0x64,0x51,0x4f,0x08,0x49,0xa0,0x5f,0x69,0x64,0xc2,0xe3,0x40,0x22, + 0x30,0x45,0x02,0x21,0x00,0xf6,0xb0,0xe2,0xf6,0xfe,0x02,0x0c,0xf7,0xc0,0xc2,0x01,0x37,0x43,0x43,0x44,0xed,0x7a,0xdd,0x6c,0x4b,0xe5,0x18,0x61,0xe2,0xd1,0x4c,0xbd,0xa4,0x72,0xa6,0xff,0xb4,0x02,0x20,0x64,0x16,0xc8,0xdd,0x3e,0x5c,0x52,0x82,0xb3,0x06,0xe8,0xdc,0x8f,0xf3,0x4a,0xb6,0x4c,0xc9,0x95,0x49,0x23,0x2d,0x67,0x8d,0x71,0x44,0x02,0xeb,0x6c,0xa7,0xaa,0x0f, + 0x30,0x45,0x02,0x21,0x00,0xdb,0x09,0xd8,0x46,0x0f,0x05,0xef,0xf2,0x3b,0xc7,0xe4,0x36,0xb6,0x7d,0xa5,0x63,0xfa,0x4b,0x4e,0xdb,0x58,0xac,0x24,0xce,0x20,0x1f,0xa8,0xa3,0x58,0x12,0x50,0x57,0x02,0x20,0x46,0xda,0x11,0x67,0x54,0x60,0x29,0x40,0xc8,0x99,0x9c,0x8d,0x66,0x5f,0x78,0x6c,0x50,0xf5,0x77,0x2c,0x0a,0x3c,0xdb,0xda,0x07,0x5e,0x77,0xea,0xbc,0x64,0xdf,0x16, + 0x30,0x44,0x02,0x20,0x59,0x2c,0x41,0xe1,0x65,0x17,0xf1,0x2f,0xca,0xbd,0x98,0x26,0x76,0x74,0xf9,0x74,0xb5,0x88,0xe9,0xf3,0x5d,0x35,0x40,0x6c,0x1a,0x7b,0xb2,0xed,0x1d,0x19,0xb7,0xb8,0x02,0x20,0x3e,0x65,0xa0,0x6b,0xd9,0xf8,0x3c,0xaa,0xeb,0x7b,0x00,0xf2,0x36,0x8d,0x7e,0x0d,0xec,0xe6,0xb1,0x22,0x21,0x26,0x9a,0x9b,0x5b,0x76,0x51,0x98,0xf8,0x40,0xa3,0xa1, + 0x30,0x45,0x02,0x21,0x00,0xbe,0x0d,0x70,0x88,0x7d,0x5e,0x40,0x82,0x1a,0x61,0xb6,0x80,0x47,0xde,0x4e,0xa0,0x3d,0xeb,0xfd,0xf5,0x1c,0xdf,0x4d,0x4b,0x19,0x55,0x58,0xb9,0x59,0xa0,0x32,0xb2,0x02,0x20,0x7d,0x99,0x4b,0x2d,0x8f,0x1d,0xbb,0xeb,0x13,0x53,0x4e,0xb3,0xf6,0xe5,0xdc,0xcd,0x85,0xf5,0xc4,0x13,0x3c,0x27,0xd9,0xe6,0x42,0x71,0xb1,0x82,0x6c,0xe1,0xf6,0x7d, + 0x30,0x45,0x02,0x21,0x00,0xfa,0xe9,0x2d,0xfc,0xb2,0xee,0x39,0x2d,0x27,0x0a,0xf3,0xa5,0x73,0x9f,0xaa,0x26,0xd4,0xf9,0x7b,0xfd,0x39,0xed,0x3c,0xbe,0xe4,0xd2,0x9e,0x26,0xaf,0x3b,0x20,0x6a,0x02,0x20,0x6c,0x9b,0xa3,0x7f,0x9f,0xaa,0x6a,0x1f,0xd3,0xf6,0x5f,0x23,0xb4,0xe8,0x53,0xd4,0x69,0x2a,0x72,0x74,0x24,0x0a,0x12,0xdb,0x7b,0xa3,0x88,0x48,0x30,0x63,0x0d,0x16, + 0x30,0x44,0x02,0x20,0x17,0x6a,0x25,0x57,0x56,0x6f,0xfa,0x51,0x8b,0x11,0x22,0x66,0x94,0xeb,0x98,0x02,0xed,0x20,0x98,0xbf,0xe2,0x78,0xe5,0x57,0x0f,0xe1,0xd5,0xd7,0xaf,0x18,0xa9,0x43,0x02,0x20,0x12,0x91,0xdf,0x6a,0x0e,0xd5,0xfc,0x0d,0x15,0x09,0x8e,0x70,0xbc,0xf1,0x3a,0x00,0x92,0x84,0xdf,0xd0,0x68,0x9d,0x3b,0xb4,0xbe,0x6c,0xee,0xb9,0xbe,0x14,0x87,0xc4, + 0x30,0x44,0x02,0x20,0x60,0xbe,0x20,0xc3,0xdb,0xc1,0x62,0xdd,0x34,0xd2,0x67,0x80,0x62,0x1c,0x10,0x4b,0xbe,0x5d,0xac,0xe6,0x30,0x17,0x1b,0x2d,0xae,0xf0,0xd8,0x26,0x40,0x9e,0xe5,0xc2,0x02,0x20,0x42,0x7f,0x7e,0x4d,0x88,0x9d,0x54,0x91,0x70,0xbd,0xa6,0xa9,0x40,0x9f,0xb1,0xcb,0x8b,0x0e,0x76,0x3d,0x13,0xee,0xa7,0xbd,0x97,0xf6,0x4c,0xf4,0x1d,0xc6,0xe4,0x97, + 0x30,0x45,0x02,0x21,0x00,0xed,0xf0,0x3c,0xf6,0x3f,0x65,0x88,0x83,0x28,0x9a,0x1a,0x59,0x3d,0x10,0x07,0x89,0x5b,0x9f,0x23,0x6d,0x27,0xc9,0xc1,0xf1,0x31,0x30,0x89,0xaa,0xed,0x6b,0x16,0xae,0x02,0x20,0x1a,0x4d,0xd6,0xfc,0x08,0x14,0xdc,0x52,0x3d,0x1f,0xef,0xa8,0x1c,0x64,0xfb,0xf5,0xe6,0x18,0xe6,0x51,0xe7,0x09,0x6f,0xcc,0xad,0xbb,0x94,0xcd,0x48,0xe5,0xe0,0xcd}; + +static const wycheproof_ecdsa_testvector testvectors[SECP256K1_ECDSA_WYCHEPROOF_NUMBER_TESTVECTORS] = { + /* tcId: 1. Signature malleability */ + {0, 0, 6, 0, 72, 0 }, + /* tcId: 2. valid */ + {0, 0, 6, 72, 71, 1 }, + /* tcId: 3. length of sequence [r, s] uses long form encoding */ + {0, 0, 6, 143, 72, 0 }, + /* tcId: 4. length of sequence [r, s] contains a leading 0 */ + {0, 0, 6, 215, 73, 0 }, + /* tcId: 5. length of sequence [r, s] uses 70 instead of 69 */ + {0, 0, 6, 288, 71, 0 }, + /* tcId: 6. length of sequence [r, s] uses 68 instead of 69 */ + {0, 0, 6, 359, 71, 0 }, + /* tcId: 7. uint32 overflow in length of sequence [r, s] */ + {0, 0, 6, 430, 76, 0 }, + /* tcId: 8. uint64 overflow in length of sequence [r, s] */ + {0, 0, 6, 506, 80, 0 }, + /* tcId: 9. length of sequence [r, s] = 2**31 - 1 */ + {0, 0, 6, 586, 75, 0 }, + /* tcId: 10. length of sequence [r, s] = 2**31 */ + {0, 0, 6, 661, 75, 0 }, + /* tcId: 11. length of sequence [r, s] = 2**32 - 1 */ + {0, 0, 6, 736, 75, 0 }, + /* tcId: 12. length of sequence [r, s] = 2**40 - 1 */ + {0, 0, 6, 811, 76, 0 }, + /* tcId: 13. length of sequence [r, s] = 2**64 - 1 */ + {0, 0, 6, 887, 79, 0 }, + /* tcId: 14. incorrect length of sequence [r, s] */ + {0, 0, 6, 966, 71, 0 }, + /* tcId: 15. replaced sequence [r, s] by an indefinite length tag without termination */ + {0, 0, 6, 1037, 71, 0 }, + /* tcId: 16. removing sequence [r, s] */ + {0, 0, 6, 1108, 0, 0 }, + /* tcId: 17. lonely sequence tag */ + {0, 0, 6, 1108, 1, 0 }, + /* tcId: 18. appending 0's to sequence [r, s] */ + {0, 0, 6, 1109, 73, 0 }, + /* tcId: 19. prepending 0's to sequence [r, s] */ + {0, 0, 6, 1182, 73, 0 }, + /* tcId: 20. appending unused 0's to sequence [r, s] */ + {0, 0, 6, 1255, 73, 0 }, + /* tcId: 21. appending null value to sequence [r, s] */ + {0, 0, 6, 1328, 73, 0 }, + /* tcId: 22. prepending garbage to sequence [r, s] */ + {0, 0, 6, 1401, 76, 0 }, + /* tcId: 23. prepending garbage to sequence [r, s] */ + {0, 0, 6, 1477, 75, 0 }, + /* tcId: 24. appending garbage to sequence [r, s] */ + {0, 0, 6, 1552, 79, 0 }, + /* tcId: 25. including undefined tags */ + {0, 0, 6, 1631, 79, 0 }, + /* tcId: 26. including undefined tags */ + {0, 0, 6, 1710, 79, 0 }, + /* tcId: 27. including undefined tags */ + {0, 0, 6, 1789, 79, 0 }, + /* tcId: 28. truncated length of sequence [r, s] */ + {0, 0, 6, 1868, 2, 0 }, + /* tcId: 29. including undefined tags to sequence [r, s] */ + {0, 0, 6, 1870, 77, 0 }, + /* tcId: 30. using composition with indefinite length for sequence [r, s] */ + {0, 0, 6, 1947, 75, 0 }, + /* tcId: 31. using composition with wrong tag for sequence [r, s] */ + {0, 0, 6, 2022, 75, 0 }, + /* tcId: 32. Replacing sequence [r, s] with NULL */ + {0, 0, 6, 2097, 2, 0 }, + /* tcId: 33. changing tag value of sequence [r, s] */ + {0, 0, 6, 2099, 71, 0 }, + /* tcId: 34. changing tag value of sequence [r, s] */ + {0, 0, 6, 2170, 71, 0 }, + /* tcId: 35. changing tag value of sequence [r, s] */ + {0, 0, 6, 2241, 71, 0 }, + /* tcId: 36. changing tag value of sequence [r, s] */ + {0, 0, 6, 2312, 71, 0 }, + /* tcId: 37. changing tag value of sequence [r, s] */ + {0, 0, 6, 2383, 71, 0 }, + /* tcId: 38. dropping value of sequence [r, s] */ + {0, 0, 6, 2454, 2, 0 }, + /* tcId: 39. using composition for sequence [r, s] */ + {0, 0, 6, 2456, 75, 0 }, + /* tcId: 40. truncated sequence [r, s] */ + {0, 0, 6, 2531, 70, 0 }, + /* tcId: 41. truncated sequence [r, s] */ + {0, 0, 6, 2601, 70, 0 }, + /* tcId: 42. sequence [r, s] of size 4166 to check for overflows */ + {0, 0, 6, 2671, 4170, 0 }, + /* tcId: 43. indefinite length */ + {0, 0, 6, 6841, 73, 0 }, + /* tcId: 44. indefinite length with truncated delimiter */ + {0, 0, 6, 6914, 72, 0 }, + /* tcId: 45. indefinite length with additional element */ + {0, 0, 6, 6986, 75, 0 }, + /* tcId: 46. indefinite length with truncated element */ + {0, 0, 6, 7061, 77, 0 }, + /* tcId: 47. indefinite length with garbage */ + {0, 0, 6, 7138, 77, 0 }, + /* tcId: 48. indefinite length with nonempty EOC */ + {0, 0, 6, 7215, 75, 0 }, + /* tcId: 49. prepend empty sequence */ + {0, 0, 6, 7290, 73, 0 }, + /* tcId: 50. append empty sequence */ + {0, 0, 6, 7363, 73, 0 }, + /* tcId: 51. append zero */ + {0, 0, 6, 7436, 74, 0 }, + /* tcId: 52. append garbage with high tag number */ + {0, 0, 6, 7510, 74, 0 }, + /* tcId: 53. append null with explicit tag */ + {0, 0, 6, 7584, 75, 0 }, + /* tcId: 54. append null with implicit tag */ + {0, 0, 6, 7659, 73, 0 }, + /* tcId: 55. sequence of sequence */ + {0, 0, 6, 7732, 73, 0 }, + /* tcId: 56. truncated sequence: removed last 1 elements */ + {0, 0, 6, 7805, 37, 0 }, + /* tcId: 57. repeating element in sequence */ + {0, 0, 6, 7842, 105, 0 }, + /* tcId: 58. flipped bit 0 in r */ + {0, 0, 6, 7947, 69, 0 }, + /* tcId: 59. flipped bit 32 in r */ + {0, 0, 6, 8016, 69, 0 }, + /* tcId: 60. flipped bit 48 in r */ + {0, 0, 6, 8085, 69, 0 }, + /* tcId: 61. flipped bit 64 in r */ + {0, 0, 6, 8154, 69, 0 }, + /* tcId: 62. length of r uses long form encoding */ + {0, 0, 6, 8223, 72, 0 }, + /* tcId: 63. length of r contains a leading 0 */ + {0, 0, 6, 8295, 73, 0 }, + /* tcId: 64. length of r uses 34 instead of 33 */ + {0, 0, 6, 8368, 71, 0 }, + /* tcId: 65. length of r uses 32 instead of 33 */ + {0, 0, 6, 8439, 71, 0 }, + /* tcId: 66. uint32 overflow in length of r */ + {0, 0, 6, 8510, 76, 0 }, + /* tcId: 67. uint64 overflow in length of r */ + {0, 0, 6, 8586, 80, 0 }, + /* tcId: 68. length of r = 2**31 - 1 */ + {0, 0, 6, 8666, 75, 0 }, + /* tcId: 69. length of r = 2**31 */ + {0, 0, 6, 8741, 75, 0 }, + /* tcId: 70. length of r = 2**32 - 1 */ + {0, 0, 6, 8816, 75, 0 }, + /* tcId: 71. length of r = 2**40 - 1 */ + {0, 0, 6, 8891, 76, 0 }, + /* tcId: 72. length of r = 2**64 - 1 */ + {0, 0, 6, 8967, 79, 0 }, + /* tcId: 73. incorrect length of r */ + {0, 0, 6, 9046, 71, 0 }, + /* tcId: 74. replaced r by an indefinite length tag without termination */ + {0, 0, 6, 9117, 71, 0 }, + /* tcId: 75. removing r */ + {0, 0, 6, 9188, 36, 0 }, + /* tcId: 76. lonely integer tag */ + {0, 0, 6, 9224, 37, 0 }, + /* tcId: 77. lonely integer tag */ + {0, 0, 6, 9261, 38, 0 }, + /* tcId: 78. appending 0's to r */ + {0, 0, 6, 9299, 73, 0 }, + /* tcId: 79. prepending 0's to r */ + {0, 0, 6, 9372, 73, 0 }, + /* tcId: 80. appending unused 0's to r */ + {0, 0, 6, 9445, 73, 0 }, + /* tcId: 81. appending null value to r */ + {0, 0, 6, 9518, 73, 0 }, + /* tcId: 82. prepending garbage to r */ + {0, 0, 6, 9591, 76, 0 }, + /* tcId: 83. prepending garbage to r */ + {0, 0, 6, 9667, 75, 0 }, + /* tcId: 84. appending garbage to r */ + {0, 0, 6, 9742, 79, 0 }, + /* tcId: 85. truncated length of r */ + {0, 0, 6, 9821, 38, 0 }, + /* tcId: 86. including undefined tags to r */ + {0, 0, 6, 9859, 77, 0 }, + /* tcId: 87. using composition with indefinite length for r */ + {0, 0, 6, 9936, 75, 0 }, + /* tcId: 88. using composition with wrong tag for r */ + {0, 0, 6, 10011, 75, 0 }, + /* tcId: 89. Replacing r with NULL */ + {0, 0, 6, 10086, 38, 0 }, + /* tcId: 90. changing tag value of r */ + {0, 0, 6, 10124, 71, 0 }, + /* tcId: 91. changing tag value of r */ + {0, 0, 6, 10195, 71, 0 }, + /* tcId: 92. changing tag value of r */ + {0, 0, 6, 10266, 71, 0 }, + /* tcId: 93. changing tag value of r */ + {0, 0, 6, 10337, 71, 0 }, + /* tcId: 94. changing tag value of r */ + {0, 0, 6, 10408, 71, 0 }, + /* tcId: 95. dropping value of r */ + {0, 0, 6, 10479, 38, 0 }, + /* tcId: 96. using composition for r */ + {0, 0, 6, 10517, 75, 0 }, + /* tcId: 97. modifying first byte of r */ + {0, 0, 6, 10592, 71, 0 }, + /* tcId: 98. modifying last byte of r */ + {0, 0, 6, 10663, 71, 0 }, + /* tcId: 99. truncated r */ + {0, 0, 6, 10734, 70, 0 }, + /* tcId: 100. truncated r */ + {0, 0, 6, 10804, 70, 0 }, + /* tcId: 101. r of size 4130 to check for overflows */ + {0, 0, 6, 10874, 4172, 0 }, + /* tcId: 102. leading ff in r */ + {0, 0, 6, 15046, 72, 0 }, + /* tcId: 103. replaced r by infinity */ + {0, 0, 6, 15118, 39, 0 }, + /* tcId: 104. replacing r with zero */ + {0, 0, 6, 15157, 39, 0 }, + /* tcId: 105. flipped bit 0 in s */ + {0, 0, 6, 15196, 69, 0 }, + /* tcId: 106. flipped bit 32 in s */ + {0, 0, 6, 15265, 69, 0 }, + /* tcId: 107. flipped bit 48 in s */ + {0, 0, 6, 15334, 69, 0 }, + /* tcId: 108. flipped bit 64 in s */ + {0, 0, 6, 15403, 69, 0 }, + /* tcId: 109. length of s uses long form encoding */ + {0, 0, 6, 15472, 72, 0 }, + /* tcId: 110. length of s contains a leading 0 */ + {0, 0, 6, 15544, 73, 0 }, + /* tcId: 111. length of s uses 33 instead of 32 */ + {0, 0, 6, 15617, 71, 0 }, + /* tcId: 112. length of s uses 31 instead of 32 */ + {0, 0, 6, 15688, 71, 0 }, + /* tcId: 113. uint32 overflow in length of s */ + {0, 0, 6, 15759, 76, 0 }, + /* tcId: 114. uint64 overflow in length of s */ + {0, 0, 6, 15835, 80, 0 }, + /* tcId: 115. length of s = 2**31 - 1 */ + {0, 0, 6, 15915, 75, 0 }, + /* tcId: 116. length of s = 2**31 */ + {0, 0, 6, 15990, 75, 0 }, + /* tcId: 117. length of s = 2**32 - 1 */ + {0, 0, 6, 16065, 75, 0 }, + /* tcId: 118. length of s = 2**40 - 1 */ + {0, 0, 6, 16140, 76, 0 }, + /* tcId: 119. length of s = 2**64 - 1 */ + {0, 0, 6, 16216, 79, 0 }, + /* tcId: 120. incorrect length of s */ + {0, 0, 6, 16295, 71, 0 }, + /* tcId: 121. replaced s by an indefinite length tag without termination */ + {0, 0, 6, 16366, 71, 0 }, + /* tcId: 122. appending 0's to s */ + {0, 0, 6, 16437, 73, 0 }, + /* tcId: 123. prepending 0's to s */ + {0, 0, 6, 16510, 73, 0 }, + /* tcId: 124. appending null value to s */ + {0, 0, 6, 16583, 73, 0 }, + /* tcId: 125. prepending garbage to s */ + {0, 0, 6, 16656, 76, 0 }, + /* tcId: 126. prepending garbage to s */ + {0, 0, 6, 16732, 75, 0 }, + /* tcId: 127. appending garbage to s */ + {0, 0, 6, 16807, 79, 0 }, + /* tcId: 128. truncated length of s */ + {0, 0, 6, 16886, 39, 0 }, + /* tcId: 129. including undefined tags to s */ + {0, 0, 6, 16925, 77, 0 }, + /* tcId: 130. using composition with indefinite length for s */ + {0, 0, 6, 17002, 75, 0 }, + /* tcId: 131. using composition with wrong tag for s */ + {0, 0, 6, 17077, 75, 0 }, + /* tcId: 132. Replacing s with NULL */ + {0, 0, 6, 17152, 39, 0 }, + /* tcId: 133. changing tag value of s */ + {0, 0, 6, 17191, 71, 0 }, + /* tcId: 134. changing tag value of s */ + {0, 0, 6, 17262, 71, 0 }, + /* tcId: 135. changing tag value of s */ + {0, 0, 6, 17333, 71, 0 }, + /* tcId: 136. changing tag value of s */ + {0, 0, 6, 17404, 71, 0 }, + /* tcId: 137. changing tag value of s */ + {0, 0, 6, 17475, 71, 0 }, + /* tcId: 138. dropping value of s */ + {0, 0, 6, 17546, 39, 0 }, + /* tcId: 139. using composition for s */ + {0, 0, 6, 17585, 75, 0 }, + /* tcId: 140. modifying first byte of s */ + {0, 0, 6, 17660, 71, 0 }, + /* tcId: 141. modifying last byte of s */ + {0, 0, 6, 17731, 71, 0 }, + /* tcId: 142. truncated s */ + {0, 0, 6, 17802, 70, 0 }, + /* tcId: 143. truncated s */ + {0, 0, 6, 17872, 70, 0 }, + /* tcId: 144. s of size 4129 to check for overflows */ + {0, 0, 6, 17942, 4172, 0 }, + /* tcId: 145. leading ff in s */ + {0, 0, 6, 22114, 72, 0 }, + /* tcId: 146. replaced s by infinity */ + {0, 0, 6, 22186, 40, 0 }, + /* tcId: 147. replacing s with zero */ + {0, 0, 6, 22226, 40, 0 }, + /* tcId: 148. replaced r by r + n */ + {0, 0, 6, 22266, 71, 0 }, + /* tcId: 149. replaced r by r - n */ + {0, 0, 6, 22337, 70, 0 }, + /* tcId: 150. replaced r by r + 256 * n */ + {0, 0, 6, 22407, 72, 0 }, + /* tcId: 151. replaced r by -r */ + {0, 0, 6, 22479, 71, 0 }, + /* tcId: 152. replaced r by n - r */ + {0, 0, 6, 22550, 70, 0 }, + /* tcId: 153. replaced r by -n - r */ + {0, 0, 6, 22620, 71, 0 }, + /* tcId: 154. replaced r by r + 2**256 */ + {0, 0, 6, 22691, 71, 0 }, + /* tcId: 155. replaced r by r + 2**320 */ + {0, 0, 6, 22762, 79, 0 }, + /* tcId: 156. replaced s by s + n */ + {0, 0, 6, 22841, 71, 0 }, + /* tcId: 157. replaced s by s - n */ + {0, 0, 6, 22912, 71, 0 }, + /* tcId: 158. replaced s by s + 256 * n */ + {0, 0, 6, 22983, 72, 0 }, + /* tcId: 159. replaced s by -s */ + {0, 0, 6, 23055, 70, 0 }, + /* tcId: 160. replaced s by -n - s */ + {0, 0, 6, 23125, 71, 0 }, + /* tcId: 161. replaced s by s + 2**256 */ + {0, 0, 6, 23196, 71, 0 }, + /* tcId: 162. replaced s by s - 2**256 */ + {0, 0, 6, 23267, 71, 0 }, + /* tcId: 163. replaced s by s + 2**320 */ + {0, 0, 6, 23338, 79, 0 }, + /* tcId: 164. Signature with special case values r=0 and s=0 */ + {0, 0, 6, 23417, 8, 0 }, + /* tcId: 165. Signature with special case values r=0 and s=1 */ + {0, 0, 6, 23425, 8, 0 }, + /* tcId: 166. Signature with special case values r=0 and s=-1 */ + {0, 0, 6, 23433, 8, 0 }, + /* tcId: 167. Signature with special case values r=0 and s=n */ + {0, 0, 6, 23441, 40, 0 }, + /* tcId: 168. Signature with special case values r=0 and s=n - 1 */ + {0, 0, 6, 23481, 40, 0 }, + /* tcId: 169. Signature with special case values r=0 and s=n + 1 */ + {0, 0, 6, 23521, 40, 0 }, + /* tcId: 170. Signature with special case values r=0 and s=p */ + {0, 0, 6, 23561, 40, 0 }, + /* tcId: 171. Signature with special case values r=0 and s=p + 1 */ + {0, 0, 6, 23601, 40, 0 }, + /* tcId: 172. Signature with special case values r=1 and s=0 */ + {0, 0, 6, 23641, 8, 0 }, + /* tcId: 173. Signature with special case values r=1 and s=1 */ + {0, 0, 6, 23649, 8, 0 }, + /* tcId: 174. Signature with special case values r=1 and s=-1 */ + {0, 0, 6, 23657, 8, 0 }, + /* tcId: 175. Signature with special case values r=1 and s=n */ + {0, 0, 6, 23665, 40, 0 }, + /* tcId: 176. Signature with special case values r=1 and s=n - 1 */ + {0, 0, 6, 23705, 40, 0 }, + /* tcId: 177. Signature with special case values r=1 and s=n + 1 */ + {0, 0, 6, 23745, 40, 0 }, + /* tcId: 178. Signature with special case values r=1 and s=p */ + {0, 0, 6, 23785, 40, 0 }, + /* tcId: 179. Signature with special case values r=1 and s=p + 1 */ + {0, 0, 6, 23825, 40, 0 }, + /* tcId: 180. Signature with special case values r=-1 and s=0 */ + {0, 0, 6, 23865, 8, 0 }, + /* tcId: 181. Signature with special case values r=-1 and s=1 */ + {0, 0, 6, 23873, 8, 0 }, + /* tcId: 182. Signature with special case values r=-1 and s=-1 */ + {0, 0, 6, 23881, 8, 0 }, + /* tcId: 183. Signature with special case values r=-1 and s=n */ + {0, 0, 6, 23889, 40, 0 }, + /* tcId: 184. Signature with special case values r=-1 and s=n - 1 */ + {0, 0, 6, 23929, 40, 0 }, + /* tcId: 185. Signature with special case values r=-1 and s=n + 1 */ + {0, 0, 6, 23969, 40, 0 }, + /* tcId: 186. Signature with special case values r=-1 and s=p */ + {0, 0, 6, 24009, 40, 0 }, + /* tcId: 187. Signature with special case values r=-1 and s=p + 1 */ + {0, 0, 6, 24049, 40, 0 }, + /* tcId: 188. Signature with special case values r=n and s=0 */ + {0, 0, 6, 24089, 40, 0 }, + /* tcId: 189. Signature with special case values r=n and s=1 */ + {0, 0, 6, 24129, 40, 0 }, + /* tcId: 190. Signature with special case values r=n and s=-1 */ + {0, 0, 6, 24169, 40, 0 }, + /* tcId: 191. Signature with special case values r=n and s=n */ + {0, 0, 6, 24209, 72, 0 }, + /* tcId: 192. Signature with special case values r=n and s=n - 1 */ + {0, 0, 6, 24281, 72, 0 }, + /* tcId: 193. Signature with special case values r=n and s=n + 1 */ + {0, 0, 6, 24353, 72, 0 }, + /* tcId: 194. Signature with special case values r=n and s=p */ + {0, 0, 6, 24425, 72, 0 }, + /* tcId: 195. Signature with special case values r=n and s=p + 1 */ + {0, 0, 6, 24497, 72, 0 }, + /* tcId: 196. Signature with special case values r=n - 1 and s=0 */ + {0, 0, 6, 24569, 40, 0 }, + /* tcId: 197. Signature with special case values r=n - 1 and s=1 */ + {0, 0, 6, 24609, 40, 0 }, + /* tcId: 198. Signature with special case values r=n - 1 and s=-1 */ + {0, 0, 6, 24649, 40, 0 }, + /* tcId: 199. Signature with special case values r=n - 1 and s=n */ + {0, 0, 6, 24689, 72, 0 }, + /* tcId: 200. Signature with special case values r=n - 1 and s=n - 1 */ + {0, 0, 6, 24761, 72, 0 }, + /* tcId: 201. Signature with special case values r=n - 1 and s=n + 1 */ + {0, 0, 6, 24833, 72, 0 }, + /* tcId: 202. Signature with special case values r=n - 1 and s=p */ + {0, 0, 6, 24905, 72, 0 }, + /* tcId: 203. Signature with special case values r=n - 1 and s=p + 1 */ + {0, 0, 6, 24977, 72, 0 }, + /* tcId: 204. Signature with special case values r=n + 1 and s=0 */ + {0, 0, 6, 25049, 40, 0 }, + /* tcId: 205. Signature with special case values r=n + 1 and s=1 */ + {0, 0, 6, 25089, 40, 0 }, + /* tcId: 206. Signature with special case values r=n + 1 and s=-1 */ + {0, 0, 6, 25129, 40, 0 }, + /* tcId: 207. Signature with special case values r=n + 1 and s=n */ + {0, 0, 6, 25169, 72, 0 }, + /* tcId: 208. Signature with special case values r=n + 1 and s=n - 1 */ + {0, 0, 6, 25241, 72, 0 }, + /* tcId: 209. Signature with special case values r=n + 1 and s=n + 1 */ + {0, 0, 6, 25313, 72, 0 }, + /* tcId: 210. Signature with special case values r=n + 1 and s=p */ + {0, 0, 6, 25385, 72, 0 }, + /* tcId: 211. Signature with special case values r=n + 1 and s=p + 1 */ + {0, 0, 6, 25457, 72, 0 }, + /* tcId: 212. Signature with special case values r=p and s=0 */ + {0, 0, 6, 25529, 40, 0 }, + /* tcId: 213. Signature with special case values r=p and s=1 */ + {0, 0, 6, 25569, 40, 0 }, + /* tcId: 214. Signature with special case values r=p and s=-1 */ + {0, 0, 6, 25609, 40, 0 }, + /* tcId: 215. Signature with special case values r=p and s=n */ + {0, 0, 6, 25649, 72, 0 }, + /* tcId: 216. Signature with special case values r=p and s=n - 1 */ + {0, 0, 6, 25721, 72, 0 }, + /* tcId: 217. Signature with special case values r=p and s=n + 1 */ + {0, 0, 6, 25793, 72, 0 }, + /* tcId: 218. Signature with special case values r=p and s=p */ + {0, 0, 6, 25865, 72, 0 }, + /* tcId: 219. Signature with special case values r=p and s=p + 1 */ + {0, 0, 6, 25937, 72, 0 }, + /* tcId: 220. Signature with special case values r=p + 1 and s=0 */ + {0, 0, 6, 26009, 40, 0 }, + /* tcId: 221. Signature with special case values r=p + 1 and s=1 */ + {0, 0, 6, 26049, 40, 0 }, + /* tcId: 222. Signature with special case values r=p + 1 and s=-1 */ + {0, 0, 6, 26089, 40, 0 }, + /* tcId: 223. Signature with special case values r=p + 1 and s=n */ + {0, 0, 6, 26129, 72, 0 }, + /* tcId: 224. Signature with special case values r=p + 1 and s=n - 1 */ + {0, 0, 6, 26201, 72, 0 }, + /* tcId: 225. Signature with special case values r=p + 1 and s=n + 1 */ + {0, 0, 6, 26273, 72, 0 }, + /* tcId: 226. Signature with special case values r=p + 1 and s=p */ + {0, 0, 6, 26345, 72, 0 }, + /* tcId: 227. Signature with special case values r=p + 1 and s=p + 1 */ + {0, 0, 6, 26417, 72, 0 }, + /* tcId: 228. Signature encoding contains incorrect types: r=0, s=0.25 */ + {0, 0, 6, 26489, 10, 0 }, + /* tcId: 229. Signature encoding contains incorrect types: r=0, s=nan */ + {0, 0, 6, 26499, 8, 0 }, + /* tcId: 230. Signature encoding contains incorrect types: r=0, s=True */ + {0, 0, 6, 26507, 8, 0 }, + /* tcId: 231. Signature encoding contains incorrect types: r=0, s=False */ + {0, 0, 6, 26515, 8, 0 }, + /* tcId: 232. Signature encoding contains incorrect types: r=0, s=Null */ + {0, 0, 6, 26523, 7, 0 }, + /* tcId: 233. Signature encoding contains incorrect types: r=0, s=empyt UTF-8 string */ + {0, 0, 6, 26530, 7, 0 }, + /* tcId: 234. Signature encoding contains incorrect types: r=0, s="0" */ + {0, 0, 6, 26537, 8, 0 }, + /* tcId: 235. Signature encoding contains incorrect types: r=0, s=empty list */ + {0, 0, 6, 26545, 7, 0 }, + /* tcId: 236. Signature encoding contains incorrect types: r=0, s=list containing 0 */ + {0, 0, 6, 26552, 10, 0 }, + /* tcId: 237. Signature encoding contains incorrect types: r=1, s=0.25 */ + {0, 0, 6, 26562, 10, 0 }, + /* tcId: 238. Signature encoding contains incorrect types: r=1, s=nan */ + {0, 0, 6, 26572, 8, 0 }, + /* tcId: 239. Signature encoding contains incorrect types: r=1, s=True */ + {0, 0, 6, 26580, 8, 0 }, + /* tcId: 240. Signature encoding contains incorrect types: r=1, s=False */ + {0, 0, 6, 26588, 8, 0 }, + /* tcId: 241. Signature encoding contains incorrect types: r=1, s=Null */ + {0, 0, 6, 26596, 7, 0 }, + /* tcId: 242. Signature encoding contains incorrect types: r=1, s=empyt UTF-8 string */ + {0, 0, 6, 26603, 7, 0 }, + /* tcId: 243. Signature encoding contains incorrect types: r=1, s="0" */ + {0, 0, 6, 26610, 8, 0 }, + /* tcId: 244. Signature encoding contains incorrect types: r=1, s=empty list */ + {0, 0, 6, 26618, 7, 0 }, + /* tcId: 245. Signature encoding contains incorrect types: r=1, s=list containing 0 */ + {0, 0, 6, 26625, 10, 0 }, + /* tcId: 246. Signature encoding contains incorrect types: r=-1, s=0.25 */ + {0, 0, 6, 26635, 10, 0 }, + /* tcId: 247. Signature encoding contains incorrect types: r=-1, s=nan */ + {0, 0, 6, 26645, 8, 0 }, + /* tcId: 248. Signature encoding contains incorrect types: r=-1, s=True */ + {0, 0, 6, 26653, 8, 0 }, + /* tcId: 249. Signature encoding contains incorrect types: r=-1, s=False */ + {0, 0, 6, 26661, 8, 0 }, + /* tcId: 250. Signature encoding contains incorrect types: r=-1, s=Null */ + {0, 0, 6, 26669, 7, 0 }, + /* tcId: 251. Signature encoding contains incorrect types: r=-1, s=empyt UTF-8 string */ + {0, 0, 6, 26676, 7, 0 }, + /* tcId: 252. Signature encoding contains incorrect types: r=-1, s="0" */ + {0, 0, 6, 26683, 8, 0 }, + /* tcId: 253. Signature encoding contains incorrect types: r=-1, s=empty list */ + {0, 0, 6, 26691, 7, 0 }, + /* tcId: 254. Signature encoding contains incorrect types: r=-1, s=list containing 0 */ + {0, 0, 6, 26698, 10, 0 }, + /* tcId: 255. Signature encoding contains incorrect types: r=n, s=0.25 */ + {0, 0, 6, 26708, 42, 0 }, + /* tcId: 256. Signature encoding contains incorrect types: r=n, s=nan */ + {0, 0, 6, 26750, 40, 0 }, + /* tcId: 257. Signature encoding contains incorrect types: r=n, s=True */ + {0, 0, 6, 26790, 40, 0 }, + /* tcId: 258. Signature encoding contains incorrect types: r=n, s=False */ + {0, 0, 6, 26830, 40, 0 }, + /* tcId: 259. Signature encoding contains incorrect types: r=n, s=Null */ + {0, 0, 6, 26870, 39, 0 }, + /* tcId: 260. Signature encoding contains incorrect types: r=n, s=empyt UTF-8 string */ + {0, 0, 6, 26909, 39, 0 }, + /* tcId: 261. Signature encoding contains incorrect types: r=n, s="0" */ + {0, 0, 6, 26948, 40, 0 }, + /* tcId: 262. Signature encoding contains incorrect types: r=n, s=empty list */ + {0, 0, 6, 26988, 39, 0 }, + /* tcId: 263. Signature encoding contains incorrect types: r=n, s=list containing 0 */ + {0, 0, 6, 27027, 42, 0 }, + /* tcId: 264. Signature encoding contains incorrect types: r=p, s=0.25 */ + {0, 0, 6, 27069, 42, 0 }, + /* tcId: 265. Signature encoding contains incorrect types: r=p, s=nan */ + {0, 0, 6, 27111, 40, 0 }, + /* tcId: 266. Signature encoding contains incorrect types: r=p, s=True */ + {0, 0, 6, 27151, 40, 0 }, + /* tcId: 267. Signature encoding contains incorrect types: r=p, s=False */ + {0, 0, 6, 27191, 40, 0 }, + /* tcId: 268. Signature encoding contains incorrect types: r=p, s=Null */ + {0, 0, 6, 27231, 39, 0 }, + /* tcId: 269. Signature encoding contains incorrect types: r=p, s=empyt UTF-8 string */ + {0, 0, 6, 27270, 39, 0 }, + /* tcId: 270. Signature encoding contains incorrect types: r=p, s="0" */ + {0, 0, 6, 27309, 40, 0 }, + /* tcId: 271. Signature encoding contains incorrect types: r=p, s=empty list */ + {0, 0, 6, 27349, 39, 0 }, + /* tcId: 272. Signature encoding contains incorrect types: r=p, s=list containing 0 */ + {0, 0, 6, 27388, 42, 0 }, + /* tcId: 273. Signature encoding contains incorrect types: r=0.25, s=0.25 */ + {0, 0, 6, 27430, 12, 0 }, + /* tcId: 274. Signature encoding contains incorrect types: r=nan, s=nan */ + {0, 0, 6, 27442, 8, 0 }, + /* tcId: 275. Signature encoding contains incorrect types: r=True, s=True */ + {0, 0, 6, 27450, 8, 0 }, + /* tcId: 276. Signature encoding contains incorrect types: r=False, s=False */ + {0, 0, 6, 27458, 8, 0 }, + /* tcId: 277. Signature encoding contains incorrect types: r=Null, s=Null */ + {0, 0, 6, 27466, 6, 0 }, + /* tcId: 278. Signature encoding contains incorrect types: r=empyt UTF-8 string, s=empyt UTF-8 string */ + {0, 0, 6, 27472, 6, 0 }, + /* tcId: 279. Signature encoding contains incorrect types: r="0", s="0" */ + {0, 0, 6, 27478, 8, 0 }, + /* tcId: 280. Signature encoding contains incorrect types: r=empty list, s=empty list */ + {0, 0, 6, 27486, 6, 0 }, + /* tcId: 281. Signature encoding contains incorrect types: r=list containing 0, s=list containing 0 */ + {0, 0, 6, 27492, 12, 0 }, + /* tcId: 282. Signature encoding contains incorrect types: r=0.25, s=0 */ + {0, 0, 6, 27504, 10, 0 }, + /* tcId: 283. Signature encoding contains incorrect types: r=nan, s=0 */ + {0, 0, 6, 27514, 8, 0 }, + /* tcId: 284. Signature encoding contains incorrect types: r=True, s=0 */ + {0, 0, 6, 27522, 8, 0 }, + /* tcId: 285. Signature encoding contains incorrect types: r=False, s=0 */ + {0, 0, 6, 27530, 8, 0 }, + /* tcId: 286. Signature encoding contains incorrect types: r=Null, s=0 */ + {0, 0, 6, 27538, 7, 0 }, + /* tcId: 287. Signature encoding contains incorrect types: r=empyt UTF-8 string, s=0 */ + {0, 0, 6, 27545, 7, 0 }, + /* tcId: 288. Signature encoding contains incorrect types: r="0", s=0 */ + {0, 0, 6, 27552, 8, 0 }, + /* tcId: 289. Signature encoding contains incorrect types: r=empty list, s=0 */ + {0, 0, 6, 27560, 7, 0 }, + /* tcId: 290. Signature encoding contains incorrect types: r=list containing 0, s=0 */ + {0, 0, 6, 27567, 10, 0 }, + /* tcId: 291. Edge case for Shamir multiplication */ + {0, 6, 5, 27577, 71, 1 }, + /* tcId: 292. special case hash */ + {0, 11, 9, 27648, 71, 1 }, + /* tcId: 293. special case hash */ + {0, 20, 10, 27719, 70, 1 }, + /* tcId: 294. special case hash */ + {0, 30, 11, 27789, 71, 1 }, + /* tcId: 295. special case hash */ + {0, 41, 10, 27860, 71, 1 }, + /* tcId: 296. special case hash */ + {0, 51, 10, 27931, 70, 1 }, + /* tcId: 297. special case hash */ + {0, 61, 10, 28001, 71, 1 }, + /* tcId: 298. special case hash */ + {0, 71, 9, 28072, 70, 1 }, + /* tcId: 299. special case hash */ + {0, 80, 10, 28142, 71, 1 }, + /* tcId: 300. special case hash */ + {0, 90, 10, 28213, 71, 1 }, + /* tcId: 301. special case hash */ + {0, 100, 10, 28284, 71, 1 }, + /* tcId: 302. special case hash */ + {0, 110, 10, 28355, 71, 1 }, + /* tcId: 303. special case hash */ + {0, 120, 11, 28426, 70, 1 }, + /* tcId: 304. special case hash */ + {0, 131, 10, 28496, 71, 1 }, + /* tcId: 305. special case hash */ + {0, 141, 10, 28567, 71, 1 }, + /* tcId: 306. special case hash */ + {0, 151, 10, 28638, 70, 1 }, + /* tcId: 307. special case hash */ + {0, 161, 10, 28708, 71, 1 }, + /* tcId: 308. special case hash */ + {0, 171, 10, 28779, 71, 1 }, + /* tcId: 309. special case hash */ + {0, 181, 10, 28850, 70, 1 }, + /* tcId: 310. special case hash */ + {0, 191, 10, 28920, 71, 1 }, + /* tcId: 311. special case hash */ + {0, 201, 10, 28991, 71, 1 }, + /* tcId: 312. special case hash */ + {0, 211, 10, 29062, 71, 1 }, + /* tcId: 313. special case hash */ + {0, 221, 10, 29133, 70, 1 }, + /* tcId: 314. special case hash */ + {0, 231, 10, 29203, 71, 1 }, + /* tcId: 315. special case hash */ + {0, 241, 10, 29274, 71, 1 }, + /* tcId: 316. special case hash */ + {0, 251, 10, 29345, 71, 1 }, + /* tcId: 317. special case hash */ + {0, 261, 11, 29416, 71, 1 }, + /* tcId: 318. special case hash */ + {0, 272, 11, 29487, 70, 1 }, + /* tcId: 319. special case hash */ + {0, 283, 9, 29557, 71, 1 }, + /* tcId: 320. special case hash */ + {0, 292, 9, 29628, 71, 1 }, + /* tcId: 321. special case hash */ + {0, 301, 10, 29699, 71, 1 }, + /* tcId: 322. special case hash */ + {0, 311, 10, 29770, 71, 1 }, + /* tcId: 323. special case hash */ + {0, 321, 10, 29841, 70, 1 }, + /* tcId: 324. special case hash */ + {0, 331, 10, 29911, 70, 1 }, + /* tcId: 325. special case hash */ + {0, 341, 10, 29981, 71, 1 }, + /* tcId: 326. special case hash */ + {0, 351, 9, 30052, 70, 1 }, + /* tcId: 327. special case hash */ + {0, 360, 10, 30122, 70, 1 }, + /* tcId: 328. special case hash */ + {0, 370, 10, 30192, 70, 1 }, + /* tcId: 329. special case hash */ + {0, 380, 10, 30262, 70, 1 }, + /* tcId: 330. special case hash */ + {0, 390, 9, 30332, 71, 1 }, + /* tcId: 331. special case hash */ + {0, 399, 11, 30403, 70, 1 }, + /* tcId: 332. special case hash */ + {0, 410, 9, 30473, 71, 1 }, + /* tcId: 333. special case hash */ + {0, 419, 9, 30544, 71, 1 }, + /* tcId: 334. special case hash */ + {0, 428, 11, 30615, 70, 1 }, + /* tcId: 335. special case hash */ + {0, 439, 8, 30685, 71, 1 }, + /* tcId: 336. special case hash */ + {0, 447, 10, 30756, 70, 1 }, + /* tcId: 337. special case hash */ + {0, 457, 10, 30826, 71, 1 }, + /* tcId: 338. special case hash */ + {0, 467, 10, 30897, 70, 1 }, + /* tcId: 339. special case hash */ + {0, 477, 10, 30967, 70, 1 }, + /* tcId: 340. special case hash */ + {0, 487, 10, 31037, 70, 1 }, + /* tcId: 341. special case hash */ + {0, 497, 10, 31107, 71, 1 }, + /* tcId: 342. special case hash */ + {0, 507, 10, 31178, 70, 1 }, + /* tcId: 343. special case hash */ + {0, 517, 10, 31248, 70, 1 }, + /* tcId: 344. special case hash */ + {0, 527, 10, 31318, 71, 1 }, + /* tcId: 345. special case hash */ + {0, 537, 9, 31389, 70, 1 }, + /* tcId: 346. k*G has a large x-coordinate */ + {65, 0, 6, 31459, 24, 1 }, + /* tcId: 347. r too large */ + {65, 0, 6, 31483, 40, 0 }, + /* tcId: 348. r,s are large */ + {130, 0, 6, 31523, 40, 1 }, + /* tcId: 349. r and s^-1 have a large Hamming weight */ + {195, 0, 6, 31563, 70, 1 }, + /* tcId: 350. r and s^-1 have a large Hamming weight */ + {260, 0, 6, 31633, 70, 1 }, + /* tcId: 351. small r and s */ + {325, 0, 6, 31703, 8, 1 }, + /* tcId: 352. small r and s */ + {390, 0, 6, 31711, 8, 1 }, + /* tcId: 353. small r and s */ + {455, 0, 6, 31719, 8, 1 }, + /* tcId: 354. small r and s */ + {520, 0, 6, 31727, 8, 1 }, + /* tcId: 355. small r and s */ + {585, 0, 6, 31735, 8, 1 }, + /* tcId: 356. small r and s */ + {650, 0, 6, 31743, 8, 1 }, + /* tcId: 357. r is larger than n */ + {650, 0, 6, 31751, 40, 0 }, + /* tcId: 358. s is larger than n */ + {715, 0, 6, 31791, 10, 0 }, + /* tcId: 359. small r and s^-1 */ + {780, 0, 6, 31801, 40, 1 }, + /* tcId: 360. smallish r and s^-1 */ + {845, 0, 6, 31841, 45, 1 }, + /* tcId: 361. 100-bit r and small s^-1 */ + {910, 0, 6, 31886, 51, 1 }, + /* tcId: 362. small r and 100 bit s^-1 */ + {975, 0, 6, 31937, 40, 1 }, + /* tcId: 363. 100-bit r and s^-1 */ + {1040, 0, 6, 31977, 51, 1 }, + /* tcId: 364. r and s^-1 are close to n */ + {1105, 0, 6, 32028, 71, 1 }, + /* tcId: 365. r and s are 64-bit integer */ + {1170, 0, 6, 32099, 24, 1 }, + /* tcId: 366. r and s are 100-bit integer */ + {1235, 0, 6, 32123, 32, 1 }, + /* tcId: 367. r and s are 128-bit integer */ + {1300, 0, 6, 32155, 40, 1 }, + /* tcId: 368. r and s are 160-bit integer */ + {1365, 0, 6, 32195, 48, 1 }, + /* tcId: 369. s == 1 */ + {1430, 0, 6, 32243, 39, 1 }, + /* tcId: 370. s == 0 */ + {1430, 0, 6, 32282, 39, 0 }, + /* tcId: 371. edge case modular inverse */ + {1495, 0, 6, 32321, 70, 1 }, + /* tcId: 372. edge case modular inverse */ + {1560, 0, 6, 32391, 70, 1 }, + /* tcId: 373. edge case modular inverse */ + {1625, 0, 6, 32461, 70, 1 }, + /* tcId: 374. edge case modular inverse */ + {1690, 0, 6, 32531, 70, 1 }, + /* tcId: 375. edge case modular inverse */ + {1755, 0, 6, 32601, 70, 1 }, + /* tcId: 376. edge case modular inverse */ + {1820, 0, 6, 32671, 70, 1 }, + /* tcId: 377. edge case modular inverse */ + {1885, 0, 6, 32741, 70, 1 }, + /* tcId: 378. edge case modular inverse */ + {1950, 0, 6, 32811, 70, 1 }, + /* tcId: 379. edge case modular inverse */ + {2015, 0, 6, 32881, 70, 1 }, + /* tcId: 380. edge case modular inverse */ + {2080, 0, 6, 32951, 70, 1 }, + /* tcId: 381. edge case modular inverse */ + {2145, 0, 6, 33021, 70, 1 }, + /* tcId: 382. edge case modular inverse */ + {2210, 0, 6, 33091, 70, 1 }, + /* tcId: 383. edge case modular inverse */ + {2275, 0, 6, 33161, 70, 1 }, + /* tcId: 384. edge case modular inverse */ + {2340, 0, 6, 33231, 70, 1 }, + /* tcId: 385. edge case modular inverse */ + {2405, 0, 6, 33301, 70, 1 }, + /* tcId: 386. point at infinity during verify */ + {2470, 0, 6, 33371, 70, 0 }, + /* tcId: 387. edge case for signature malleability */ + {2535, 0, 6, 33441, 70, 1 }, + /* tcId: 388. edge case for signature malleability */ + {2600, 0, 6, 33511, 70, 0 }, + /* tcId: 389. u1 == 1 */ + {2665, 0, 6, 33581, 70, 1 }, + /* tcId: 390. u1 == n - 1 */ + {2730, 0, 6, 33651, 70, 1 }, + /* tcId: 391. u2 == 1 */ + {2795, 0, 6, 33721, 70, 1 }, + /* tcId: 392. u2 == n - 1 */ + {2860, 0, 6, 33791, 70, 1 }, + /* tcId: 393. edge case for u1 */ + {2925, 0, 6, 33861, 70, 1 }, + /* tcId: 394. edge case for u1 */ + {2990, 0, 6, 33931, 70, 1 }, + /* tcId: 395. edge case for u1 */ + {3055, 0, 6, 34001, 70, 1 }, + /* tcId: 396. edge case for u1 */ + {3120, 0, 6, 34071, 70, 1 }, + /* tcId: 397. edge case for u1 */ + {3185, 0, 6, 34141, 70, 1 }, + /* tcId: 398. edge case for u1 */ + {3250, 0, 6, 34211, 70, 1 }, + /* tcId: 399. edge case for u1 */ + {3315, 0, 6, 34281, 70, 1 }, + /* tcId: 400. edge case for u1 */ + {3380, 0, 6, 34351, 70, 1 }, + /* tcId: 401. edge case for u1 */ + {3445, 0, 6, 34421, 70, 1 }, + /* tcId: 402. edge case for u1 */ + {3510, 0, 6, 34491, 70, 1 }, + /* tcId: 403. edge case for u1 */ + {3575, 0, 6, 34561, 70, 1 }, + /* tcId: 404. edge case for u1 */ + {3640, 0, 6, 34631, 70, 1 }, + /* tcId: 405. edge case for u1 */ + {3705, 0, 6, 34701, 70, 1 }, + /* tcId: 406. edge case for u1 */ + {3770, 0, 6, 34771, 70, 1 }, + /* tcId: 407. edge case for u1 */ + {3835, 0, 6, 34841, 70, 1 }, + /* tcId: 408. edge case for u2 */ + {3900, 0, 6, 34911, 70, 1 }, + /* tcId: 409. edge case for u2 */ + {3965, 0, 6, 34981, 70, 1 }, + /* tcId: 410. edge case for u2 */ + {4030, 0, 6, 35051, 70, 1 }, + /* tcId: 411. edge case for u2 */ + {4095, 0, 6, 35121, 70, 1 }, + /* tcId: 412. edge case for u2 */ + {4160, 0, 6, 35191, 70, 1 }, + /* tcId: 413. edge case for u2 */ + {4225, 0, 6, 35261, 69, 1 }, + /* tcId: 414. edge case for u2 */ + {4290, 0, 6, 35330, 70, 1 }, + /* tcId: 415. edge case for u2 */ + {4355, 0, 6, 35400, 70, 1 }, + /* tcId: 416. edge case for u2 */ + {4420, 0, 6, 35470, 70, 1 }, + /* tcId: 417. edge case for u2 */ + {4485, 0, 6, 35540, 70, 1 }, + /* tcId: 418. edge case for u2 */ + {4550, 0, 6, 35610, 70, 1 }, + /* tcId: 419. edge case for u2 */ + {4615, 0, 6, 35680, 70, 1 }, + /* tcId: 420. edge case for u2 */ + {4680, 0, 6, 35750, 70, 1 }, + /* tcId: 421. edge case for u2 */ + {4745, 0, 6, 35820, 70, 1 }, + /* tcId: 422. edge case for u2 */ + {4810, 0, 6, 35890, 70, 1 }, + /* tcId: 423. point duplication during verification */ + {4875, 0, 6, 35960, 70, 1 }, + /* tcId: 424. duplication bug */ + {4940, 0, 6, 36030, 70, 0 }, + /* tcId: 425. comparison with point at infinity */ + {5005, 0, 6, 36100, 70, 0 }, + /* tcId: 426. extreme value for k and edgecase s */ + {5070, 0, 6, 36170, 71, 1 }, + /* tcId: 427. extreme value for k and s^-1 */ + {5135, 0, 6, 36241, 71, 1 }, + /* tcId: 428. extreme value for k and s^-1 */ + {5200, 0, 6, 36312, 71, 1 }, + /* tcId: 429. extreme value for k and s^-1 */ + {5265, 0, 6, 36383, 71, 1 }, + /* tcId: 430. extreme value for k and s^-1 */ + {5330, 0, 6, 36454, 71, 1 }, + /* tcId: 431. extreme value for k */ + {5395, 0, 6, 36525, 71, 1 }, + /* tcId: 432. extreme value for k and edgecase s */ + {5460, 0, 6, 36596, 70, 1 }, + /* tcId: 433. extreme value for k and s^-1 */ + {5525, 0, 6, 36666, 70, 1 }, + /* tcId: 434. extreme value for k and s^-1 */ + {5590, 0, 6, 36736, 70, 1 }, + /* tcId: 435. extreme value for k and s^-1 */ + {5655, 0, 6, 36806, 70, 1 }, + /* tcId: 436. extreme value for k and s^-1 */ + {5720, 0, 6, 36876, 70, 1 }, + /* tcId: 437. extreme value for k */ + {5785, 0, 6, 36946, 70, 1 }, + /* tcId: 438. public key shares x-coordinate with generator */ + {5850, 0, 6, 37016, 71, 0 }, + /* tcId: 439. public key shares x-coordinate with generator */ + {5850, 0, 6, 37087, 70, 0 }, + /* tcId: 440. public key shares x-coordinate with generator */ + {5915, 0, 6, 37157, 71, 0 }, + /* tcId: 441. public key shares x-coordinate with generator */ + {5915, 0, 6, 37228, 70, 0 }, + /* tcId: 442. pseudorandom signature */ + {5980, 546, 0, 37298, 71, 1 }, + /* tcId: 443. pseudorandom signature */ + {5980, 546, 3, 37369, 70, 1 }, + /* tcId: 444. pseudorandom signature */ + {5980, 0, 6, 37439, 71, 1 }, + /* tcId: 445. pseudorandom signature */ + {5980, 549, 20, 37510, 70, 1 }, + /* tcId: 446. y-coordinate of the public key is small */ + {6045, 569, 7, 37580, 70, 1 }, + /* tcId: 447. y-coordinate of the public key is small */ + {6045, 569, 7, 37650, 70, 1 }, + /* tcId: 448. y-coordinate of the public key is small */ + {6045, 569, 7, 37720, 71, 1 }, + /* tcId: 449. y-coordinate of the public key is large */ + {6110, 569, 7, 37791, 70, 1 }, + /* tcId: 450. y-coordinate of the public key is large */ + {6110, 569, 7, 37861, 71, 1 }, + /* tcId: 451. y-coordinate of the public key is large */ + {6110, 569, 7, 37932, 70, 1 }, + /* tcId: 452. x-coordinate of the public key is small */ + {6175, 569, 7, 38002, 70, 1 }, + /* tcId: 453. x-coordinate of the public key is small */ + {6175, 569, 7, 38072, 71, 1 }, + /* tcId: 454. x-coordinate of the public key is small */ + {6175, 569, 7, 38143, 71, 1 }, + /* tcId: 455. x-coordinate of the public key has many trailing 1's */ + {6240, 569, 7, 38214, 70, 1 }, + /* tcId: 456. x-coordinate of the public key has many trailing 1's */ + {6240, 569, 7, 38284, 71, 1 }, + /* tcId: 457. x-coordinate of the public key has many trailing 1's */ + {6240, 569, 7, 38355, 71, 1 }, + /* tcId: 458. y-coordinate of the public key has many trailing 1's */ + {6305, 569, 7, 38426, 70, 1 }, + /* tcId: 459. y-coordinate of the public key has many trailing 1's */ + {6305, 569, 7, 38496, 71, 1 }, + /* tcId: 460. y-coordinate of the public key has many trailing 1's */ + {6305, 569, 7, 38567, 71, 1 }, + /* tcId: 461. x-coordinate of the public key has many trailing 0's */ + {6370, 569, 7, 38638, 70, 1 }, + /* tcId: 462. x-coordinate of the public key has many trailing 0's */ + {6370, 569, 7, 38708, 70, 1 }, + /* tcId: 463. x-coordinate of the public key has many trailing 0's */ + {6370, 569, 7, 38778, 71, 1 }, + +}; diff --git a/vendor/github.com/waku-org/go-discover/discover/common.go b/vendor/github.com/waku-org/go-discover/discover/common.go index b465ca84e54..654e482f518 100644 --- a/vendor/github.com/waku-org/go-discover/discover/common.go +++ b/vendor/github.com/waku-org/go-discover/discover/common.go @@ -20,12 +20,12 @@ import ( "crypto/ecdsa" "net" + "go.uber.org/zap" + "github.com/ethereum/go-ethereum/common/mclock" - "github.com/ethereum/go-ethereum/log" "github.com/ethereum/go-ethereum/p2p/enode" "github.com/ethereum/go-ethereum/p2p/enr" "github.com/ethereum/go-ethereum/p2p/netutil" - "github.com/waku-org/go-discover/discover/v5wire" ) // UDPConn is a network connection on which discovery can operate. @@ -46,19 +46,21 @@ type Config struct { PrivateKey *ecdsa.PrivateKey // These settings are optional: - NetRestrict *netutil.Netlist // list of allowed IP networks - Bootnodes []*enode.Node // list of bootstrap nodes - Unhandled chan<- ReadPacket // unhandled packets are sent on this channel - Log log.Logger // if set, log messages go here - ValidSchemes enr.IdentityScheme // allowed identity schemes - V5Config V5Config // DiscV5 settings - ValidNodeFn func(enode.Node) bool // function to validate a node before it's added to routing tables + NetRestrict *netutil.Netlist // list of allowed IP networks + Bootnodes []*enode.Node // list of bootstrap nodes + Unhandled chan<- ReadPacket // unhandled packets are sent on this channel + Log *zap.Logger // if set, log messages go here + + // V5ProtocolID configures the discv5 protocol identifier. + V5ProtocolID *[6]byte + + ValidSchemes enr.IdentityScheme // allowed identity schemes Clock mclock.Clock } func (cfg Config) withDefaults() Config { if cfg.Log == nil { - cfg.Log = log.Root() + cfg.Log = zap.NewNop() } if cfg.ValidSchemes == nil { cfg.ValidSchemes = enode.ValidSchemes @@ -66,9 +68,6 @@ func (cfg Config) withDefaults() Config { if cfg.Clock == nil { cfg.Clock = mclock.System{} } - if cfg.V5Config.ProtocolID == nil { - cfg.V5Config.ProtocolID = &v5wire.DefaultProtocolID - } return cfg } @@ -83,10 +82,3 @@ type ReadPacket struct { Data []byte Addr *net.UDPAddr } - -func min(x, y int) int { - if x > y { - return y - } - return x -} diff --git a/vendor/github.com/waku-org/go-discover/discover/lookup.go b/vendor/github.com/waku-org/go-discover/discover/lookup.go index b8d97b44e1c..cc868bbae69 100644 --- a/vendor/github.com/waku-org/go-discover/discover/lookup.go +++ b/vendor/github.com/waku-org/go-discover/discover/lookup.go @@ -140,7 +140,7 @@ func (it *lookup) slowdown() { } func (it *lookup) query(n *node, reply chan<- []*node) { - fails := it.tab.db.FindFails(n.ID(), n.IP()) + fails := it.tab.db.FindFails(n.ID(), n.IPAddr()) r, err := it.queryfunc(n) if errors.Is(err, errClosed) { // Avoid recording failures on shutdown. @@ -148,18 +148,15 @@ func (it *lookup) query(n *node, reply chan<- []*node) { return } else if len(r) == 0 { fails++ - it.tab.db.UpdateFindFails(n.ID(), n.IP(), fails) + it.tab.db.UpdateFindFails(n.ID(), n.IPAddr(), fails) // Remove the node from the local table if it fails to return anything useful too // many times, but only if there are enough other nodes in the bucket. - dropped := false if fails >= maxFindnodeFailures && it.tab.bucketLen(n.ID()) >= bucketSize/2 { - dropped = true it.tab.delete(n) } - it.tab.log.Trace("FINDNODE failed", "id", n.ID(), "failcount", fails, "dropped", dropped, "err", err) } else if fails > 0 { // Reset failure counter because it counts _consecutive_ failures. - it.tab.db.UpdateFindFails(n.ID(), n.IP(), 0) + it.tab.db.UpdateFindFails(n.ID(), n.IPAddr(), 0) } // Grab as many nodes as possible. Some of them might not be alive anymore, but we'll diff --git a/vendor/github.com/waku-org/go-discover/discover/metrics.go b/vendor/github.com/waku-org/go-discover/discover/metrics.go new file mode 100644 index 00000000000..f2193207fd7 --- /dev/null +++ b/vendor/github.com/waku-org/go-discover/discover/metrics.go @@ -0,0 +1,65 @@ +// Copyright 2023 The go-ethereum Authors +// This file is part of the go-ethereum library. +// +// The go-ethereum library is free software: you can redistribute it and/or modify +// it under the terms of the GNU Lesser General Public License as published by +// the Free Software Foundation, either version 3 of the License, or +// (at your option) any later version. +// +// The go-ethereum library is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU Lesser General Public License for more details. +// +// You should have received a copy of the GNU Lesser General Public License +// along with the go-ethereum library. If not, see . + +package discover + +import ( + "net" + + "github.com/ethereum/go-ethereum/metrics" +) + +const ( + moduleName = "discover" + // ingressMeterName is the prefix of the per-packet inbound metrics. + ingressMeterName = moduleName + "/ingress" + + // egressMeterName is the prefix of the per-packet outbound metrics. + egressMeterName = moduleName + "/egress" +) + +var ( + ingressTrafficMeter = metrics.NewRegisteredMeter(ingressMeterName, nil) + egressTrafficMeter = metrics.NewRegisteredMeter(egressMeterName, nil) +) + +// meteredConn is a wrapper around a net.UDPConn that meters both the +// inbound and outbound network traffic. +type meteredUdpConn struct { + UDPConn +} + +func newMeteredConn(conn UDPConn) UDPConn { + // Short circuit if metrics are disabled + if !metrics.Enabled() { + return conn + } + return &meteredUdpConn{UDPConn: conn} +} + +// Read delegates a network read to the underlying connection, bumping the udp ingress traffic meter along the way. +func (c *meteredUdpConn) ReadFromUDP(b []byte) (n int, addr *net.UDPAddr, err error) { + n, addr, err = c.UDPConn.ReadFromUDP(b) + ingressTrafficMeter.Mark(int64(n)) + return n, addr, err +} + +// Write delegates a network write to the underlying connection, bumping the udp egress traffic meter along the way. +func (c *meteredUdpConn) WriteToUDP(b []byte, addr *net.UDPAddr) (n int, err error) { + n, err = c.UDPConn.WriteToUDP(b, addr) + egressTrafficMeter.Mark(int64(n)) + return n, err +} diff --git a/vendor/github.com/waku-org/go-discover/discover/ntp.go b/vendor/github.com/waku-org/go-discover/discover/ntp.go index 48ceffe95b8..38b34063afd 100644 --- a/vendor/github.com/waku-org/go-discover/discover/ntp.go +++ b/vendor/github.com/waku-org/go-discover/discover/ntp.go @@ -20,12 +20,11 @@ package discover import ( - "fmt" "net" "sort" "time" - "github.com/ethereum/go-ethereum/log" + "go.uber.org/zap" ) const ( @@ -49,10 +48,10 @@ func checkClockDrift() { return } if drift < -driftThreshold || drift > driftThreshold { - log.Warn(fmt.Sprintf("System clock seems off by %v, which can prevent network connectivity", drift)) - log.Warn("Please enable network time synchronisation in system settings.") + zap.L().Warn("System clock seems off", zap.Duration("drift", drift)) + zap.L().Warn("Please enable network time synchronisation in system settings.") } else { - log.Debug("NTP sanity check done", "drift", drift) + zap.L().Debug("NTP sanity check done", zap.Duration("drift", drift)) } } diff --git a/vendor/github.com/waku-org/go-discover/discover/table.go b/vendor/github.com/waku-org/go-discover/discover/table.go index af77294ef7e..1846cc54c0c 100644 --- a/vendor/github.com/waku-org/go-discover/discover/table.go +++ b/vendor/github.com/waku-org/go-discover/discover/table.go @@ -32,8 +32,9 @@ import ( "sync" "time" + "go.uber.org/zap" + "github.com/ethereum/go-ethereum/common" - "github.com/ethereum/go-ethereum/log" "github.com/ethereum/go-ethereum/p2p/enode" "github.com/ethereum/go-ethereum/p2p/netutil" ) @@ -71,7 +72,7 @@ type Table struct { rand *mrand.Rand // source of randomness, periodically reseeded ips netutil.DistinctNetSet - log log.Logger + log *zap.Logger db *enode.DB // database of known nodes net transport refreshReq chan chan struct{} @@ -79,8 +80,6 @@ type Table struct { closeReq chan struct{} closed chan struct{} - nodeIsValidFn func(enode.Node) bool - nodeAddedHook func(*node) // for testing } @@ -101,27 +100,32 @@ type bucket struct { ips netutil.DistinctNetSet } -func newTable(t transport, db *enode.DB, bootnodes []*enode.Node, nodeIsValidFn func(enode.Node) bool, log log.Logger) (*Table, error) { +func newTable(t transport, db *enode.DB, bootnodes []*enode.Node, logger *zap.Logger) (*Table, error) { + buckets := [nBuckets]*bucket{} + for i := range buckets { + buckets[i] = &bucket{ + ips: netutil.DistinctNetSet{Subnet: bucketSubnet, Limit: bucketIPLimit}, + } + } + nursery := wrapNodes(bootnodes) + tab := &Table{ - net: t, - db: db, - refreshReq: make(chan chan struct{}), - initDone: make(chan struct{}), - closeReq: make(chan struct{}), - closed: make(chan struct{}), - rand: mrand.New(mrand.NewSource(0)), - ips: netutil.DistinctNetSet{Subnet: tableSubnet, Limit: tableIPLimit}, - nodeIsValidFn: nodeIsValidFn, - log: log, + mutex: sync.Mutex{}, + buckets: buckets, + nursery: nursery, + rand: mrand.New(mrand.NewSource(time.Now().UnixNano())), + ips: netutil.DistinctNetSet{}, + log: logger, + db: db, + net: t, + refreshReq: make(chan chan struct{}), + initDone: make(chan struct{}), + closeReq: make(chan struct{}), + closed: make(chan struct{}), } if err := tab.setFallbackNodes(bootnodes); err != nil { return nil, err } - for i := range tab.buckets { - tab.buckets[i] = &bucket{ - ips: netutil.DistinctNetSet{Subnet: bucketSubnet, Limit: bucketIPLimit}, - } - } tab.seedRand() tab.loadSeedNodes() @@ -312,8 +316,6 @@ func (tab *Table) loadSeedNodes() { tab.mutex.Unlock() for i := range seeds { seed := seeds[i] - age := log.Lazy{Fn: func() interface{} { return time.Since(tab.db.LastPongReceived(seed.ID(), seed.IP())) }} - tab.log.Trace("Found seed node in database", "id", seed.ID(), "addr", seed.addr(), "age", age) tab.addSeenNode(seed) } } @@ -332,32 +334,41 @@ func (tab *Table) doRevalidate(done chan<- struct{}) { // Ping the selected node and wait for a pong. remoteSeq, err := tab.net.ping(unwrapNode(last)) + logger := tab.log.With(zap.Stringer("id", last.ID()), zap.Stringer("addr", last.addr())) + // Also fetch record if the node replied and returned a higher sequence number. if last.Seq() < remoteSeq { n, err := tab.net.RequestENR(unwrapNode(last)) if err != nil { - tab.log.Debug("ENR request failed", "id", last.ID(), "addr", last.addr(), "err", err) + logger.Debug("ENR request failed", zap.Error(err)) } else { last = &node{Node: *n, addedAt: last.addedAt, livenessChecks: last.livenessChecks} } } + logger = logger.With(zap.Int("b", bi)) + tab.mutex.Lock() defer tab.mutex.Unlock() b := tab.buckets[bi] if err == nil { // The node responded, move it to the front. last.livenessChecks++ - tab.log.Debug("Revalidated node", "b", bi, "id", last.ID(), "checks", last.livenessChecks) + logger.Debug("Revalidated node", zap.Uint("checks", last.livenessChecks)) tab.bumpInBucket(b, last) return } + // No reply received, pick a replacement or delete the node if there aren't // any replacements. if r := tab.replace(b, last); r != nil { - tab.log.Debug("Replaced dead node", "b", bi, "id", last.ID(), "ip", last.IP(), "checks", last.livenessChecks, "r", r.ID(), "rip", r.IP()) + tab.log.Debug("Replaced dead node", + zap.Uint("checks", last.livenessChecks), + zap.Stringer("r", r.ID()), + zap.Stringer("rip", r.IP())) } else { - tab.log.Debug("Removed dead node", "b", bi, "id", last.ID(), "ip", last.IP(), "checks", last.livenessChecks) + tab.log.Debug("Removed dead node", + zap.Uint("checks", last.livenessChecks)) } } @@ -472,10 +483,6 @@ func (tab *Table) addSeenNode(n *node) { return } - if tab.nodeIsValidFn != nil && !tab.nodeIsValidFn(n.Node) { - return - } - tab.mutex.Lock() defer tab.mutex.Unlock() b := tab.bucket(n.ID()) @@ -518,10 +525,6 @@ func (tab *Table) addVerifiedNode(n *node) { return } - if tab.nodeIsValidFn != nil && !tab.nodeIsValidFn(n.Node) { - return - } - tab.mutex.Lock() defer tab.mutex.Unlock() b := tab.bucket(n.ID()) @@ -563,11 +566,11 @@ func (tab *Table) addIP(b *bucket, ip net.IP) bool { return true } if !tab.ips.Add(ip) { - tab.log.Debug("IP exceeds table limit", "ip", ip) + tab.log.Debug("IP exceeds table limit", zap.Stringer("ip", ip)) return false } if !b.ips.Add(ip) { - tab.log.Debug("IP exceeds bucket limit", "ip", ip) + tab.log.Debug("IP exceeds bucket limit", zap.Stringer("ip", ip)) tab.ips.Remove(ip) return false } @@ -687,15 +690,14 @@ func (h *nodesByDistance) push(n *node, maxElems int) { ix := sort.Search(len(h.entries), func(i int) bool { return enode.DistCmp(h.target, h.entries[i].ID(), n.ID()) > 0 }) + + end := len(h.entries) if len(h.entries) < maxElems { h.entries = append(h.entries, n) } - if ix == len(h.entries) { - // farther away than all nodes we already have. - // if there was room for it, the node is now the last element. - } else { - // slide existing entries down to make room - // this will overwrite the entry we just appended. + if ix < end { + // Slide existing entries down to make room. + // This will overwrite the entry we just appended. copy(h.entries[ix+1:], h.entries[ix:]) h.entries[ix] = n } diff --git a/vendor/github.com/waku-org/go-discover/discover/v4_udp.go b/vendor/github.com/waku-org/go-discover/discover/v4_udp.go index 00988c526c8..e678397b0e1 100644 --- a/vendor/github.com/waku-org/go-discover/discover/v4_udp.go +++ b/vendor/github.com/waku-org/go-discover/discover/v4_udp.go @@ -26,13 +26,16 @@ import ( "fmt" "io" "net" + "net/netip" "sync" "time" + "go.uber.org/zap" + "github.com/ethereum/go-ethereum/crypto" - "github.com/ethereum/go-ethereum/log" "github.com/ethereum/go-ethereum/p2p/enode" "github.com/ethereum/go-ethereum/p2p/netutil" + "github.com/waku-org/go-discover/discover/v4wire" ) @@ -66,7 +69,7 @@ const ( // UDPv4 implements the v4 wire protocol. type UDPv4 struct { conn UDPConn - log log.Logger + log *zap.Logger netrestrict *netutil.Netlist priv *ecdsa.PrivateKey localNode *enode.LocalNode @@ -130,7 +133,7 @@ func ListenV4(c UDPConn, ln *enode.LocalNode, cfg Config) (*UDPv4, error) { cfg = cfg.withDefaults() closeCtx, cancel := context.WithCancel(context.Background()) t := &UDPv4{ - conn: c, + conn: newMeteredConn(c), priv: cfg.PrivateKey, netrestrict: cfg.NetRestrict, localNode: ln, @@ -142,7 +145,7 @@ func ListenV4(c UDPConn, ln *enode.LocalNode, cfg Config) (*UDPv4, error) { log: cfg.Log, } - tab, err := newTable(t, ln.Database(), cfg.Bootnodes, cfg.ValidNodeFn, t.log) + tab, err := newTable(t, ln.Database(), cfg.Bootnodes, t.log) if err != nil { return nil, err } @@ -241,7 +244,7 @@ func (t *UDPv4) sendPing(toid enode.ID, toaddr *net.UDPAddr, callback func()) *r return matched, matched }) // Send the packet. - t.localNode.UDPContact(toaddr) + t.localNode.UDPContact(toaddr.AddrPort()) t.write(toaddr, toid, req.Name(), packet) return rm } @@ -311,7 +314,6 @@ func (t *UDPv4) findnode(toid enode.ID, toaddr *net.UDPAddr, target v4wire.Pubke nreceived++ n, err := t.nodeFromRPC(toaddr, rn) if err != nil { - t.log.Trace("Invalid neighbor node received", "ip", rn.IP, "addr", toaddr, "err", err) continue } nodes = append(nodes, n) @@ -506,7 +508,6 @@ func (t *UDPv4) send(toaddr *net.UDPAddr, toid enode.ID, req v4wire.Packet) ([]b func (t *UDPv4) write(toaddr *net.UDPAddr, toid enode.ID, what string, packet []byte) error { _, err := t.conn.WriteToUDP(packet, toaddr) - t.log.Trace(">> "+what, "id", toid, "addr", toaddr, "err", err) return err } @@ -522,12 +523,12 @@ func (t *UDPv4) readLoop(unhandled chan<- ReadPacket) { nbytes, from, err := t.conn.ReadFromUDP(buf) if netutil.IsTemporaryError(err) { // Ignore temporary read errors. - t.log.Debug("Temporary UDP read error", "err", err) + t.log.Debug("Temporary UDP read error", zap.Error(err)) continue } else if err != nil { // Shut down the loop for permanent errors. if !errors.Is(err, io.EOF) { - t.log.Debug("UDP read error", "err", err) + t.log.Debug("UDP read error", zap.Error(err)) } return } @@ -543,7 +544,10 @@ func (t *UDPv4) readLoop(unhandled chan<- ReadPacket) { func (t *UDPv4) handlePacket(from *net.UDPAddr, buf []byte) error { rawpacket, fromKey, hash, err := v4wire.Decode(buf) if err != nil { - t.log.Debug("Bad discv4 packet", "addr", from, "err", err) + t.log.Debug("bad discv4 packet", + zap.Stringer("addr", from), + zap.Error(err), + ) return err } packet := t.wrapPacket(rawpacket) @@ -551,7 +555,6 @@ func (t *UDPv4) handlePacket(from *net.UDPAddr, buf []byte) error { if err == nil && packet.preverify != nil { err = packet.preverify(packet, from, fromID, fromKey) } - t.log.Trace("<< "+packet.Name(), "id", fromID, "addr", from, "err", err) if err == nil && packet.handle != nil { packet.handle(packet, from, fromID, hash) } @@ -559,15 +562,15 @@ func (t *UDPv4) handlePacket(from *net.UDPAddr, buf []byte) error { } // checkBond checks if the given node has a recent enough endpoint proof. -func (t *UDPv4) checkBond(id enode.ID, ip net.IP) bool { - return time.Since(t.db.LastPongReceived(id, ip)) < bondExpiration +func (t *UDPv4) checkBond(id enode.ID, addr netip.Addr) bool { + return time.Since(t.db.LastPongReceived(id, addr)) < bondExpiration } // ensureBond solicits a ping from a node if we haven't seen a ping from it for a while. // This ensures there is a valid endpoint proof on the remote end. func (t *UDPv4) ensureBond(toid enode.ID, toaddr *net.UDPAddr) { - tooOld := time.Since(t.db.LastPingReceived(toid, toaddr.IP)) > bondExpiration - if tooOld || t.db.FindFails(toid, toaddr.IP) > maxFindnodeFailures { + tooOld := time.Since(t.db.LastPingReceived(toid, toaddr.AddrPort().Addr())) > bondExpiration + if tooOld || t.db.FindFails(toid, toaddr.AddrPort().Addr()) > maxFindnodeFailures { rm := t.sendPing(toid, toaddr, nil) <-rm.errc // Wait for them to ping back and process our pong. @@ -667,7 +670,7 @@ func (t *UDPv4) handlePing(h *packetHandlerV4, from *net.UDPAddr, fromID enode.I // Ping back if our last pong on file is too far in the past. n := wrapNode(enode.NewV4(h.senderKey, from.IP, int(req.From.TCP), from.Port)) - if time.Since(t.db.LastPongReceived(n.ID(), from.IP)) > bondExpiration { + if time.Since(t.db.LastPongReceived(n.ID(), from.AddrPort().Addr())) > bondExpiration { t.sendPing(fromID, from, func() { t.tab.addVerifiedNode(n) }) @@ -676,8 +679,8 @@ func (t *UDPv4) handlePing(h *packetHandlerV4, from *net.UDPAddr, fromID enode.I } // Update node database and endpoint predictor. - t.db.UpdateLastPingReceived(n.ID(), from.IP, time.Now()) - t.localNode.UDPEndpointStatement(from, &net.UDPAddr{IP: req.To.IP, Port: int(req.To.UDP)}) + t.db.UpdateLastPingReceived(n.ID(), from.AddrPort().Addr(), time.Now()) + t.localNode.UDPEndpointStatement(from.AddrPort(), req.To.UDPAddrPort()) } // PONG/v4 @@ -691,8 +694,8 @@ func (t *UDPv4) verifyPong(h *packetHandlerV4, from *net.UDPAddr, fromID enode.I if !t.handleReply(fromID, from.IP, req) { return errUnsolicitedReply } - t.localNode.UDPEndpointStatement(from, &net.UDPAddr{IP: req.To.IP, Port: int(req.To.UDP)}) - t.db.UpdateLastPongReceived(fromID, from.IP, time.Now()) + t.localNode.UDPEndpointStatement(from.AddrPort(), req.To.UDPAddrPort()) + t.db.UpdateLastPongReceived(fromID, from.AddrPort().Addr(), time.Now()) return nil } @@ -704,7 +707,7 @@ func (t *UDPv4) verifyFindnode(h *packetHandlerV4, from *net.UDPAddr, fromID eno if v4wire.Expired(req.Expiration) { return errExpired } - if !t.checkBond(fromID, from.IP) { + if !t.checkBond(fromID, from.AddrPort().Addr()) { // No endpoint proof pong exists, we don't process the packet. This prevents an // attack vector where the discovery protocol could be used to amplify traffic in a // DDOS attack. A malicious actor would send a findnode request with the IP address @@ -764,7 +767,7 @@ func (t *UDPv4) verifyENRRequest(h *packetHandlerV4, from *net.UDPAddr, fromID e if v4wire.Expired(req.Expiration) { return errExpired } - if !t.checkBond(fromID, from.IP) { + if !t.checkBond(fromID, from.AddrPort().Addr()) { return errUnknownNode } return nil diff --git a/vendor/github.com/waku-org/go-discover/discover/v4wire/v4wire.go b/vendor/github.com/waku-org/go-discover/discover/v4wire/v4wire.go index 3935068cd9d..dbcbefaa8b2 100644 --- a/vendor/github.com/waku-org/go-discover/discover/v4wire/v4wire.go +++ b/vendor/github.com/waku-org/go-discover/discover/v4wire/v4wire.go @@ -25,6 +25,7 @@ import ( "fmt" "math/big" "net" + "net/netip" "time" "github.com/ethereum/go-ethereum/common/math" @@ -151,13 +152,16 @@ type Endpoint struct { // NewEndpoint creates an endpoint. func NewEndpoint(addr *net.UDPAddr, tcpPort uint16) Endpoint { - ip := net.IP{} - if ip4 := addr.IP.To4(); ip4 != nil { - ip = ip4 - } else if ip6 := addr.IP.To16(); ip6 != nil { - ip = ip6 + return Endpoint{ + IP: addr.IP, + UDP: uint16(addr.Port), + TCP: tcpPort, } - return Endpoint{IP: ip, UDP: uint16(addr.Port), TCP: tcpPort} +} + +func (ep *Endpoint) UDPAddrPort() netip.AddrPort { + addr, _ := netip.AddrFromSlice(ep.IP) + return netip.AddrPortFrom(addr, ep.UDP) } type Packet interface { diff --git a/vendor/github.com/waku-org/go-discover/discover/v5_talk.go b/vendor/github.com/waku-org/go-discover/discover/v5_talk.go new file mode 100644 index 00000000000..cc030e1f506 --- /dev/null +++ b/vendor/github.com/waku-org/go-discover/discover/v5_talk.go @@ -0,0 +1,114 @@ +// Copyright 2023 The go-ethereum Authors +// This file is part of the go-ethereum library. +// +// The go-ethereum library is free software: you can redistribute it and/or modify +// it under the terms of the GNU Lesser General Public License as published by +// the Free Software Foundation, either version 3 of the License, or +// (at your option) any later version. +// +// The go-ethereum library is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU Lesser General Public License for more details. +// +// You should have received a copy of the GNU Lesser General Public License +// along with the go-ethereum library. If not, see . + +package discover + +import ( + "net" + "sync" + "time" + + "go.uber.org/zap" + + "github.com/ethereum/go-ethereum/p2p/enode" + "github.com/waku-org/go-discover/discover/v5wire" +) + +// This is a limit for the number of concurrent talk requests. +const maxActiveTalkRequests = 1024 + +// This is the timeout for acquiring a handler execution slot for a talk request. +// The timeout should be short enough to fit within the request timeout. +const talkHandlerLaunchTimeout = 400 * time.Millisecond + +// TalkRequestHandler callback processes a talk request and returns a response. +// +// Note that talk handlers are expected to come up with a response very quickly, within at +// most 200ms or so. If the handler takes longer than that, the remote end may time out +// and wont receive the response. +type TalkRequestHandler func(enode.ID, *net.UDPAddr, []byte) []byte + +type talkSystem struct { + transport *UDPv5 + + mutex sync.Mutex + handlers map[string]TalkRequestHandler + slots chan struct{} + lastLog time.Time + dropCount int +} + +func newTalkSystem(transport *UDPv5) *talkSystem { + t := &talkSystem{ + transport: transport, + handlers: make(map[string]TalkRequestHandler), + slots: make(chan struct{}, maxActiveTalkRequests), + } + for i := 0; i < cap(t.slots); i++ { + t.slots <- struct{}{} + } + return t +} + +// register adds a protocol handler. +func (t *talkSystem) register(protocol string, handler TalkRequestHandler) { + t.mutex.Lock() + t.handlers[protocol] = handler + t.mutex.Unlock() +} + +// handleRequest handles a talk request. +func (t *talkSystem) handleRequest(id enode.ID, addr *net.UDPAddr, req *v5wire.TalkRequest) { + t.mutex.Lock() + handler, ok := t.handlers[req.Protocol] + t.mutex.Unlock() + + if !ok { + resp := &v5wire.TalkResponse{ReqID: req.ReqID} + t.transport.sendResponse(id, addr, resp) + return + } + + // Wait for a slot to become available, then run the handler. + timeout := time.NewTimer(talkHandlerLaunchTimeout) + defer timeout.Stop() + select { + case <-t.slots: + go func() { + defer func() { t.slots <- struct{}{} }() + respMessage := handler(id, addr, req.Message) + resp := &v5wire.TalkResponse{ReqID: req.ReqID, Message: respMessage} + t.transport.sendFromAnotherThread(id, addr, resp) + }() + case <-timeout.C: + // Couldn't get it in time, drop the request. + if time.Since(t.lastLog) > 5*time.Second { + t.transport.log.Warn("Dropping TALKREQ due to overload", zap.Int("ndrop", t.dropCount)) + t.lastLog = time.Now() + t.dropCount++ + } + case <-t.transport.closeCtx.Done(): + // Transport closed, drop the request. + } +} + +// wait blocks until all active requests have finished, and prevents new request +// handlers from being launched. +func (t *talkSystem) wait() { + for i := 0; i < cap(t.slots); i++ { + <-t.slots + } +} diff --git a/vendor/github.com/waku-org/go-discover/discover/v5_udp.go b/vendor/github.com/waku-org/go-discover/discover/v5_udp.go index d9a0e232001..ad9106cde16 100644 --- a/vendor/github.com/waku-org/go-discover/discover/v5_udp.go +++ b/vendor/github.com/waku-org/go-discover/discover/v5_udp.go @@ -24,25 +24,25 @@ import ( "errors" "fmt" "io" - "math" "net" + "net/netip" "sync" "time" - "github.com/waku-org/go-discover/discover/v5wire" + "go.uber.org/zap" "github.com/ethereum/go-ethereum/common/mclock" - "github.com/ethereum/go-ethereum/log" "github.com/ethereum/go-ethereum/p2p/enode" "github.com/ethereum/go-ethereum/p2p/enr" "github.com/ethereum/go-ethereum/p2p/netutil" + + "github.com/waku-org/go-discover/discover/v5wire" ) const ( lookupRequestLimit = 3 // max requests against a single node during lookup findnodeResultLimit = 16 // applies in FINDNODE handler totalNodesResponseLimit = 5 // applies in waitForNodes - nodesResponseItemLimit = 3 // applies in sendNodes respTimeoutV5 = 700 * time.Millisecond ) @@ -69,13 +69,15 @@ type UDPv5 struct { priv *ecdsa.PrivateKey localNode *enode.LocalNode db *enode.DB - log log.Logger + log *zap.Logger clock mclock.Clock validSchemes enr.IdentityScheme + // misc buffers used during message handling + logcontext []interface{} + // talkreq handler registry - trlock sync.Mutex - trhandlers map[string]TalkRequestHandler + talk *talkSystem // channels into dispatch packetInCh chan ReadPacket @@ -83,6 +85,8 @@ type UDPv5 struct { callCh chan *callV5 callDoneCh chan *callV5 respTimeoutCh chan *callTimeout + sendCh chan sendRequest + unhandled chan<- ReadPacket // state of dispatch codec codecV5 @@ -97,12 +101,18 @@ type UDPv5 struct { wg sync.WaitGroup } -// TalkRequestHandler callback processes a talk request and optionally returns a reply -type TalkRequestHandler func(enode.ID, *net.UDPAddr, []byte) []byte +type sendRequest struct { + destID enode.ID + destAddr *net.UDPAddr + msg v5wire.Packet +} // callV5 represents a remote procedure call against another node. type callV5 struct { - node *enode.Node + id enode.ID + addr *net.UDPAddr + node *enode.Node // This is required to perform handshakes. + packet v5wire.Packet responseType byte // expected packet type of response reqid []byte @@ -141,7 +151,7 @@ func newUDPv5(ctx context.Context, conn UDPConn, ln *enode.LocalNode, cfg Config cfg = cfg.withDefaults() t := &UDPv5{ // static fields - conn: conn, + conn: newMeteredConn(conn), localNode: ln, db: ln.Database(), netrestrict: cfg.NetRestrict, @@ -149,15 +159,16 @@ func newUDPv5(ctx context.Context, conn UDPConn, ln *enode.LocalNode, cfg Config log: cfg.Log, validSchemes: cfg.ValidSchemes, clock: cfg.Clock, - trhandlers: make(map[string]TalkRequestHandler), // channels into dispatch packetInCh: make(chan ReadPacket, 1), readNextCh: make(chan struct{}, 1), callCh: make(chan *callV5), callDoneCh: make(chan *callV5), + sendCh: make(chan sendRequest), respTimeoutCh: make(chan *callTimeout), + unhandled: cfg.Unhandled, // state of dispatch - codec: v5wire.NewCodec(ln, cfg.PrivateKey, cfg.Clock, *cfg.V5Config.ProtocolID), + codec: v5wire.NewCodec(ln, cfg.PrivateKey, cfg.Clock, cfg.V5ProtocolID), activeCallByNode: make(map[enode.ID]*callV5), activeCallByAuth: make(map[v5wire.Nonce]*callV5), callQueue: make(map[enode.ID][]*callV5), @@ -165,7 +176,8 @@ func newUDPv5(ctx context.Context, conn UDPConn, ln *enode.LocalNode, cfg Config closeCtx: closeCtx, cancelCloseCtx: cancelCloseCtx, } - tab, err := newTable(t, t.db, cfg.Bootnodes, cfg.ValidNodeFn, cfg.Log) + t.talk = newTalkSystem(t) + tab, err := newTable(t, t.db, cfg.Bootnodes, cfg.Log) if err != nil { return nil, err } @@ -183,6 +195,7 @@ func (t *UDPv5) Close() { t.closeOnce.Do(func() { t.cancelCloseCtx() t.conn.Close() + t.talk.wait() t.wg.Wait() t.tab.close() }) @@ -238,15 +251,26 @@ func (t *UDPv5) LocalNode() *enode.LocalNode { // whenever a request for the given protocol is received and should return the response // data or nil. func (t *UDPv5) RegisterTalkHandler(protocol string, handler TalkRequestHandler) { - t.trlock.Lock() - defer t.trlock.Unlock() - t.trhandlers[protocol] = handler + t.talk.register(protocol, handler) } -// TalkRequest sends a talk request to n and waits for a response. +// TalkRequest sends a talk request to a node and waits for a response. func (t *UDPv5) TalkRequest(n *enode.Node, protocol string, request []byte) ([]byte, error) { req := &v5wire.TalkRequest{Protocol: protocol, Message: request} - resp := t.call(n, v5wire.TalkResponseMsg, req) + resp := t.callToNode(n, v5wire.TalkResponseMsg, req) + defer t.callDone(resp) + select { + case respMsg := <-resp.ch: + return respMsg.(*v5wire.TalkResponse).Message, nil + case err := <-resp.err: + return nil, err + } +} + +// TalkRequestToID sends a talk request to a node and waits for a response. +func (t *UDPv5) TalkRequestToID(id enode.ID, addr *net.UDPAddr, protocol string, request []byte) ([]byte, error) { + req := &v5wire.TalkRequest{Protocol: protocol, Message: request} + resp := t.callToID(id, addr, v5wire.TalkResponseMsg, req) defer t.callDone(resp) select { case respMsg := <-resp.ch: @@ -324,7 +348,7 @@ func lookupDistances(target, dest enode.ID) (dists []uint) { td := enode.LogDist(target, dest) dists = append(dists, uint(td)) for i := 1; len(dists) < lookupRequestLimit; i++ { - if td+i < 256 { + if td+i <= 256 { dists = append(dists, uint(td+i)) } if td-i > 0 { @@ -337,7 +361,7 @@ func lookupDistances(target, dest enode.ID) (dists []uint) { // ping calls PING on a node and waits for a PONG response. func (t *UDPv5) ping(n *enode.Node) (uint64, error) { req := &v5wire.Ping{ENRSeq: t.localNode.Node().Seq()} - resp := t.call(n, v5wire.PongMsg, req) + resp := t.callToNode(n, v5wire.PongMsg, req) defer t.callDone(resp) select { @@ -362,7 +386,7 @@ func (t *UDPv5) RequestENR(n *enode.Node) (*enode.Node, error) { // findnode calls FINDNODE on a node and waits for responses. func (t *UDPv5) findnode(n *enode.Node, distances []uint) ([]*enode.Node, error) { - resp := t.call(n, v5wire.NodesMsg, &v5wire.Findnode{Distances: distances}) + resp := t.callToNode(n, v5wire.NodesMsg, &v5wire.Findnode{Distances: distances}) return t.waitForNodes(resp, distances) } @@ -382,13 +406,16 @@ func (t *UDPv5) waitForNodes(c *callV5, distances []uint) ([]*enode.Node, error) for _, record := range response.Nodes { node, err := t.verifyResponseNode(c, record, distances, seen) if err != nil { - t.log.Debug("Invalid record in "+response.Name(), "id", c.node.ID(), "err", err) + t.log.Debug("Invalid record in "+response.Name(), + zap.Stringer("id", c.node.ID()), + zap.Error(err), + ) continue } nodes = append(nodes, node) } if total == -1 { - total = min(int(response.Total), totalNodesResponseLimit) + total = min(int(response.RespCount), totalNodesResponseLimit) } if received++; received == total { return nodes, nil @@ -405,17 +432,17 @@ func (t *UDPv5) verifyResponseNode(c *callV5, r *enr.Record, distances []uint, s if err != nil { return nil, err } - if err := netutil.CheckRelayIP(c.node.IP(), node.IP()); err != nil { + if err := netutil.CheckRelayIP(c.addr.IP, node.IP()); err != nil { return nil, err } if t.netrestrict != nil && !t.netrestrict.Contains(node.IP()) { return nil, errors.New("not contained in netrestrict list") } - if c.node.UDP() <= 1024 { + if node.UDP() <= 1024 { return nil, errLowPort } if distances != nil { - nd := enode.LogDist(c.node.ID(), node.ID()) + nd := enode.LogDist(c.id, node.ID()) if !containsUint(uint(nd), distances) { return nil, errors.New("does not match any requested distance") } @@ -436,17 +463,28 @@ func containsUint(x uint, xs []uint) bool { return false } -// call sends the given call and sets up a handler for response packets (of message type -// responseType). Responses are dispatched to the call's response channel. -func (t *UDPv5) call(node *enode.Node, responseType byte, packet v5wire.Packet) *callV5 { - c := &callV5{ - node: node, - packet: packet, - responseType: responseType, - reqid: make([]byte, 8), - ch: make(chan v5wire.Packet, 1), - err: make(chan error, 1), - } +// callToNode sends the given call and sets up a handler for response packets (of message +// type responseType). Responses are dispatched to the call's response channel. +func (t *UDPv5) callToNode(n *enode.Node, responseType byte, req v5wire.Packet) *callV5 { + addr := &net.UDPAddr{IP: n.IP(), Port: n.UDP()} + c := &callV5{id: n.ID(), addr: addr, node: n} + t.initCall(c, responseType, req) + return c +} + +// callToID is like callToNode, but for cases where the node record is not available. +func (t *UDPv5) callToID(id enode.ID, addr *net.UDPAddr, responseType byte, req v5wire.Packet) *callV5 { + c := &callV5{id: id, addr: addr} + t.initCall(c, responseType, req) + return c +} + +func (t *UDPv5) initCall(c *callV5, responseType byte, packet v5wire.Packet) { + c.packet = packet + c.responseType = responseType + c.reqid = make([]byte, 8) + c.ch = make(chan v5wire.Packet, 1) + c.err = make(chan error, 1) // Assign request ID. crand.Read(c.reqid) packet.SetRequestID(c.reqid) @@ -456,7 +494,6 @@ func (t *UDPv5) call(node *enode.Node, responseType byte, packet v5wire.Packet) case <-t.closeCtx.Done(): c.err <- errClosed } - return c } // callDone tells dispatch that the active call is done. @@ -498,26 +535,27 @@ func (t *UDPv5) dispatch() { for { select { case c := <-t.callCh: - id := c.node.ID() - t.callQueue[id] = append(t.callQueue[id], c) - t.sendNextCall(id) + t.callQueue[c.id] = append(t.callQueue[c.id], c) + t.sendNextCall(c.id) case ct := <-t.respTimeoutCh: - active := t.activeCallByNode[ct.c.node.ID()] + active := t.activeCallByNode[ct.c.id] if ct.c == active && ct.timer == active.timeout { ct.c.err <- errTimeout } case c := <-t.callDoneCh: - id := c.node.ID() - active := t.activeCallByNode[id] + active := t.activeCallByNode[c.id] if active != c { panic("BUG: callDone for inactive call") } c.timeout.Stop() delete(t.activeCallByAuth, c.nonce) - delete(t.activeCallByNode, id) - t.sendNextCall(id) + delete(t.activeCallByNode, c.id) + t.sendNextCall(c.id) + + case r := <-t.sendCh: + t.send(r.destID, r.destAddr, r.msg, nil) case p := <-t.packetInCh: t.handlePacket(p.Data, p.Addr) @@ -587,8 +625,7 @@ func (t *UDPv5) sendCall(c *callV5) { delete(t.activeCallByAuth, c.nonce) } - addr := &net.UDPAddr{IP: c.node.IP(), Port: c.node.UDP()} - newNonce, _ := t.send(c.node.ID(), addr, c.packet, c.challenge) + newNonce, _ := t.send(c.id, c.addr, c.packet, c.challenge) c.nonce = newNonce t.activeCallByAuth[newNonce] = c t.startResponseTimeout(c) @@ -601,16 +638,27 @@ func (t *UDPv5) sendResponse(toID enode.ID, toAddr *net.UDPAddr, packet v5wire.P return err } +func (t *UDPv5) sendFromAnotherThread(toID enode.ID, toAddr *net.UDPAddr, packet v5wire.Packet) { + select { + case t.sendCh <- sendRequest{toID, toAddr, packet}: + case <-t.closeCtx.Done(): + } +} + // send sends a packet to the given node. func (t *UDPv5) send(toID enode.ID, toAddr *net.UDPAddr, packet v5wire.Packet, c *v5wire.Whoareyou) (v5wire.Nonce, error) { addr := toAddr.String() + t.logcontext = append(t.logcontext[:0], "id", toID, "addr", addr) + t.logcontext = packet.AppendLogInfo(t.logcontext) + enc, nonce, err := t.codec.Encode(toID, addr, packet, c) if err != nil { - t.log.Warn(">> "+packet.Name(), "id", toID, "addr", addr, "err", err) + t.logcontext = append(t.logcontext, "err", err) + t.log.Warn(">> "+packet.Name(), zap.Any("context", t.logcontext)) return nonce, err } + _, err = t.conn.WriteToUDP(enc, toAddr) - t.log.Trace(">> "+packet.Name(), "id", toID, "addr", addr) return nonce, err } @@ -623,12 +671,12 @@ func (t *UDPv5) readLoop() { nbytes, from, err := t.conn.ReadFromUDP(buf) if netutil.IsTemporaryError(err) { // Ignore temporary read errors. - t.log.Debug("Temporary UDP read error", "err", err) + t.log.Debug("Temporary UDP read error", zap.Error(err)) continue } else if err != nil { // Shut down the loop for permanent errors. if !errors.Is(err, io.EOF) { - t.log.Debug("UDP read error", "err", err) + t.log.Debug("UDP read error", zap.Error(err)) } return } @@ -651,7 +699,14 @@ func (t *UDPv5) handlePacket(rawpacket []byte, fromAddr *net.UDPAddr) error { addr := fromAddr.String() fromID, fromNode, packet, err := t.codec.Decode(rawpacket, addr) if err != nil { - t.log.Debug("Bad discv5 packet", "id", fromID, "addr", addr, "err", err) + if t.unhandled != nil && v5wire.IsInvalidHeader(err) { + // The packet seems unrelated to discv5, send it to the next protocol. + up := ReadPacket{Data: make([]byte, len(rawpacket)), Addr: fromAddr} + copy(up.Data, rawpacket) + t.unhandled <- up + return nil + } + t.log.Debug("Bad discv5 packet", zap.Stringer("id", fromID), zap.Stringer("addr", fromAddr), zap.Error(err)) return err } if fromNode != nil { @@ -660,7 +715,8 @@ func (t *UDPv5) handlePacket(rawpacket []byte, fromAddr *net.UDPAddr) error { } if packet.Kind() != v5wire.WhoareyouPacket { // WHOAREYOU logged separately to report errors. - t.log.Trace("<< "+packet.Name(), "id", fromID, "addr", addr) + t.logcontext = append(t.logcontext[:0], "id", fromID, "addr", addr) + t.logcontext = packet.AppendLogInfo(t.logcontext) } t.handle(packet, fromID, fromAddr) return nil @@ -670,15 +726,15 @@ func (t *UDPv5) handlePacket(rawpacket []byte, fromAddr *net.UDPAddr) error { func (t *UDPv5) handleCallResponse(fromID enode.ID, fromAddr *net.UDPAddr, p v5wire.Packet) bool { ac := t.activeCallByNode[fromID] if ac == nil || !bytes.Equal(p.RequestID(), ac.reqid) { - t.log.Debug(fmt.Sprintf("Unsolicited/late %s response", p.Name()), "id", fromID, "addr", fromAddr) + t.log.Debug(fmt.Sprintf("Unsolicited/late %s response", p.Name()), zap.Stringer("id", fromID), zap.Stringer("addr", fromAddr)) return false } - if !fromAddr.IP.Equal(ac.node.IP()) || fromAddr.Port != ac.node.UDP() { - t.log.Debug(fmt.Sprintf("%s from wrong endpoint", p.Name()), "id", fromID, "addr", fromAddr) + if !fromAddr.IP.Equal(ac.addr.IP) || fromAddr.Port != ac.addr.Port { + t.log.Debug(fmt.Sprintf("%s from wrong endpoint", p.Name()), zap.Stringer("id", fromID), zap.Stringer("addr", fromAddr)) return false } if p.Kind() != ac.responseType { - t.log.Debug(fmt.Sprintf("Wrong discv5 response type %s", p.Name()), "id", fromID, "addr", fromAddr) + t.log.Debug(fmt.Sprintf("Wrong discv5 response type %s", p.Name()), zap.Stringer("id", fromID), zap.Stringer("addr", fromAddr)) return false } t.startResponseTimeout(ac) @@ -708,14 +764,15 @@ func (t *UDPv5) handle(p v5wire.Packet, fromID enode.ID, fromAddr *net.UDPAddr) t.handlePing(p, fromID, fromAddr) case *v5wire.Pong: if t.handleCallResponse(fromID, fromAddr, p) { - t.localNode.UDPEndpointStatement(fromAddr, &net.UDPAddr{IP: p.ToIP, Port: int(p.ToPort)}) + toAddr, _ := netip.AddrFromSlice(p.ToIP) + t.localNode.UDPEndpointStatement(fromAddr.AddrPort(), netip.AddrPortFrom(toAddr, p.ToPort)) } case *v5wire.Findnode: t.handleFindnode(p, fromID, fromAddr) case *v5wire.Nodes: t.handleCallResponse(fromID, fromAddr, p) case *v5wire.TalkRequest: - t.handleTalkRequest(p, fromID, fromAddr) + t.talk.handleRequest(fromID, fromAddr, p) case *v5wire.TalkResponse: t.handleCallResponse(fromID, fromAddr, p) } @@ -741,12 +798,17 @@ var ( func (t *UDPv5) handleWhoareyou(p *v5wire.Whoareyou, fromID enode.ID, fromAddr *net.UDPAddr) { c, err := t.matchWithCall(fromID, p.Nonce) if err != nil { - t.log.Debug("Invalid "+p.Name(), "addr", fromAddr, "err", err) + t.log.Debug("Invalid "+p.Name(), zap.String("addr", fromAddr.String()), zap.Error(err)) return } + if c.node == nil { + // Can't perform handshake because we don't have the ENR. + t.log.Debug("Can't handle "+p.Name(), zap.String("addr", fromAddr.String()), zap.Error(errors.New("call has no ENR"))) + c.err <- errors.New("remote wants handshake, but call has no ENR") + return + } // Resend the call that was answered by WHOAREYOU. - t.log.Trace("<< "+p.Name(), "id", c.node.ID(), "addr", fromAddr) c.handshakeCount++ c.challenge = p p.Node = c.node @@ -830,20 +892,32 @@ func (t *UDPv5) collectTableNodes(rip net.IP, distances []uint, limit int) []*en // packNodes creates NODES response packets for the given node list. func packNodes(reqid []byte, nodes []*enode.Node) []*v5wire.Nodes { if len(nodes) == 0 { - return []*v5wire.Nodes{{ReqID: reqid, Total: 1}} + return []*v5wire.Nodes{{ReqID: reqid, RespCount: 1}} } - total := uint8(math.Ceil(float64(len(nodes)) / 3)) + // This limit represents the available space for nodes in output packets. Maximum + // packet size is 1280, and out of this ~80 bytes will be taken up by the packet + // frame. So limiting to 1000 bytes here leaves 200 bytes for other fields of the + // NODES message, which is a lot. + const sizeLimit = 1000 + var resp []*v5wire.Nodes for len(nodes) > 0 { - p := &v5wire.Nodes{ReqID: reqid, Total: total} - items := min(nodesResponseItemLimit, len(nodes)) - for i := 0; i < items; i++ { - p.Nodes = append(p.Nodes, nodes[i].Record()) + p := &v5wire.Nodes{ReqID: reqid} + size := uint64(0) + for len(nodes) > 0 { + r := nodes[0].Record() + if size += r.Size(); size > sizeLimit { + break + } + p.Nodes = append(p.Nodes, r) + nodes = nodes[1:] } - nodes = nodes[items:] resp = append(resp, p) } + for _, msg := range resp { + msg.RespCount = uint8(len(resp)) + } return resp } @@ -857,17 +931,3 @@ func (t *UDPv5) SetFallbackNodes(nodes []*enode.Node) error { <-refreshDone return nil } - -// handleTalkRequest runs the talk request handler of the requested protocol. -func (t *UDPv5) handleTalkRequest(p *v5wire.TalkRequest, fromID enode.ID, fromAddr *net.UDPAddr) { - t.trlock.Lock() - handler := t.trhandlers[p.Protocol] - t.trlock.Unlock() - - var response []byte - if handler != nil { - response = handler(fromID, fromAddr, p.Message) - } - resp := &v5wire.TalkResponse{ReqID: p.ReqID, Message: response} - t.sendResponse(fromID, fromAddr, resp) -} diff --git a/vendor/github.com/waku-org/go-discover/discover/v5wire/encoding.go b/vendor/github.com/waku-org/go-discover/discover/v5wire/encoding.go index 47e8dcd911a..5108910620e 100644 --- a/vendor/github.com/waku-org/go-discover/discover/v5wire/encoding.go +++ b/vendor/github.com/waku-org/go-discover/discover/v5wire/encoding.go @@ -65,7 +65,7 @@ type ( handshakeAuthData struct { h struct { SrcID enode.ID - SigSize byte // ignature data + SigSize byte // signature data PubkeySize byte // offset of } // Trailing variable-size data. @@ -94,6 +94,8 @@ const ( // Should reject packets smaller than minPacketSize. minPacketSize = 63 + maxPacketSize = 1280 + minMessageSize = 48 // this refers to data after static headers randomPacketMsgSize = 20 ) @@ -122,6 +124,13 @@ var ( ErrInvalidReqID = errors.New("request ID larger than 8 bytes") ) +// IsInvalidHeader reports whether 'err' is related to an invalid packet header. When it +// returns false, it is pretty certain that the packet causing the error does not belong +// to discv5. +func IsInvalidHeader(err error) bool { + return err == errTooShort || err == errInvalidHeader || err == errMsgTooShort +} + // Packet sizes. var ( sizeofStaticHeader = binary.Size(StaticHeader{}) @@ -147,17 +156,22 @@ type Codec struct { msgctbuf []byte // message data ciphertext // decoder buffer + decbuf []byte reader bytes.Reader } // NewCodec creates a wire codec. -func NewCodec(ln *enode.LocalNode, key *ecdsa.PrivateKey, clock mclock.Clock, protocolID [6]byte) *Codec { +func NewCodec(ln *enode.LocalNode, key *ecdsa.PrivateKey, clock mclock.Clock, protocolID *[6]byte) *Codec { c := &Codec{ sha256: sha256.New(), localnode: ln, privkey: key, sc: NewSessionCache(1024, clock), - protocolID: protocolID, + protocolID: DefaultProtocolID, + decbuf: make([]byte, maxPacketSize), + } + if protocolID != nil { + c.protocolID = *protocolID } return c } @@ -421,10 +435,13 @@ func (c *Codec) encryptMessage(s *session, p Packet, head *Header, headerData [] } // Decode decodes a discovery packet. -func (c *Codec) Decode(input []byte, addr string) (src enode.ID, n *enode.Node, p Packet, err error) { - if len(input) < minPacketSize { +func (c *Codec) Decode(inputData []byte, addr string) (src enode.ID, n *enode.Node, p Packet, err error) { + if len(inputData) < minPacketSize { return enode.ID{}, nil, nil, errTooShort } + // Copy the packet to a tmp buffer to avoid modifying it. + c.decbuf = append(c.decbuf[:0], inputData...) + input := c.decbuf // Unmask the static header. var head Header copy(head.IV[:], input[:sizeofMaskingIV]) @@ -531,7 +548,7 @@ func (c *Codec) decodeHandshake(fromAddr string, head *Header) (n *enode.Node, a if err != nil { return nil, auth, nil, errInvalidAuthKey } - // Derive sesssion keys. + // Derive session keys. session := deriveKeys(sha256.New, c.privkey, ephkey, auth.h.SrcID, c.localnode.ID(), cdata) session = session.keysFlipped() return n, auth, session, nil diff --git a/vendor/github.com/waku-org/go-discover/discover/v5wire/msg.go b/vendor/github.com/waku-org/go-discover/discover/v5wire/msg.go index 1316598a472..401db2f6c58 100644 --- a/vendor/github.com/waku-org/go-discover/discover/v5wire/msg.go +++ b/vendor/github.com/waku-org/go-discover/discover/v5wire/msg.go @@ -20,6 +20,7 @@ import ( "fmt" "net" + "github.com/ethereum/go-ethereum/common/hexutil" "github.com/ethereum/go-ethereum/common/mclock" "github.com/ethereum/go-ethereum/p2p/enode" "github.com/ethereum/go-ethereum/p2p/enr" @@ -32,6 +33,10 @@ type Packet interface { Kind() byte // Kind returns the message type. RequestID() []byte // Returns the request ID. SetRequestID([]byte) // Sets the request ID. + + // AppendLogInfo returns its argument 'ctx' with additional fields + // appended for logging purposes. + AppendLogInfo(ctx []interface{}) []interface{} } // Message types. @@ -44,9 +49,6 @@ const ( TalkResponseMsg RequestTicketMsg TicketMsg - RegtopicMsg - RegconfirmationMsg - TopicQueryMsg UnknownPacket = byte(255) // any non-decryptable packet WhoareyouPacket = byte(254) // the WHOAREYOU packet @@ -59,7 +61,7 @@ type ( Nonce Nonce } - // Whoareyou contains the handshake challenge. + // WHOAREYOU contains the handshake challenge. Whoareyou struct { ChallengeData []byte // Encoded challenge Nonce Nonce // Nonce of request packet @@ -73,13 +75,13 @@ type ( sent mclock.AbsTime // for handshake GC. } - // Ping is sent during liveness checks. + // PING is sent during liveness checks. Ping struct { ReqID []byte ENRSeq uint64 } - // Pong is the reply to Ping. + // PONG is the reply to PING. Pong struct { ReqID []byte ENRSeq uint64 @@ -87,62 +89,35 @@ type ( ToPort uint16 // packet, which provides a way to discover the external address (after NAT). } - // Findnode is a query for nodes in the given bucket. + // FINDNODE is a query for nodes in the given bucket. Findnode struct { ReqID []byte Distances []uint + + // OpID is for debugging purposes and is not part of the packet encoding. + // It identifies the 'operation' on behalf of which the request was sent. + OpID uint64 `rlp:"-"` } - // Nodes is the reply to Findnode and Topicquery. + // NODES is a response to FINDNODE. Nodes struct { - ReqID []byte - Total uint8 - Nodes []*enr.Record + ReqID []byte + RespCount uint8 // total number of responses to the request + Nodes []*enr.Record } - // TalkRequest is an application-level request. + // TALKREQ is an application-level request. TalkRequest struct { ReqID []byte Protocol string Message []byte } - // TalkResponse is the reply to TalkRequest. + // TALKRESP is the reply to TALKREQ. TalkResponse struct { ReqID []byte Message []byte } - - // RequestTicket requests a ticket for a topic queue. - RequestTicket struct { - ReqID []byte - Topic []byte - } - - // Ticket is the response to RequestTicket. - Ticket struct { - ReqID []byte - Ticket []byte - } - - // Regtopic registers the sender in a topic queue using a ticket. - Regtopic struct { - ReqID []byte - Ticket []byte - ENR *enr.Record - } - - // Regconfirmation is the reply to Regtopic. - Regconfirmation struct { - ReqID []byte - Registered bool - } - - // TopicQuery asks for nodes with the given topic. - TopicQuery struct { - ReqID []byte - Topic []byte - } ) // DecodeMessage decodes the message body of a packet. @@ -161,16 +136,6 @@ func DecodeMessage(ptype byte, body []byte) (Packet, error) { dec = new(TalkRequest) case TalkResponseMsg: dec = new(TalkResponse) - case RequestTicketMsg: - dec = new(RequestTicket) - case TicketMsg: - dec = new(Ticket) - case RegtopicMsg: - dec = new(Regtopic) - case RegconfirmationMsg: - dec = new(Regconfirmation) - case TopicQueryMsg: - dec = new(TopicQuery) default: return nil, fmt.Errorf("unknown packet type %d", ptype) } @@ -188,62 +153,77 @@ func (*Whoareyou) Kind() byte { return WhoareyouPacket } func (*Whoareyou) RequestID() []byte { return nil } func (*Whoareyou) SetRequestID([]byte) {} +func (*Whoareyou) AppendLogInfo(ctx []interface{}) []interface{} { + return ctx +} + func (*Unknown) Name() string { return "UNKNOWN/v5" } func (*Unknown) Kind() byte { return UnknownPacket } func (*Unknown) RequestID() []byte { return nil } func (*Unknown) SetRequestID([]byte) {} +func (*Unknown) AppendLogInfo(ctx []interface{}) []interface{} { + return ctx +} + func (*Ping) Name() string { return "PING/v5" } func (*Ping) Kind() byte { return PingMsg } func (p *Ping) RequestID() []byte { return p.ReqID } func (p *Ping) SetRequestID(id []byte) { p.ReqID = id } +func (p *Ping) AppendLogInfo(ctx []interface{}) []interface{} { + return append(ctx, "req", hexutil.Bytes(p.ReqID), "enrseq", p.ENRSeq) +} + func (*Pong) Name() string { return "PONG/v5" } func (*Pong) Kind() byte { return PongMsg } func (p *Pong) RequestID() []byte { return p.ReqID } func (p *Pong) SetRequestID(id []byte) { p.ReqID = id } -func (*Findnode) Name() string { return "FINDNODE/v5" } -func (*Findnode) Kind() byte { return FindnodeMsg } +func (p *Pong) AppendLogInfo(ctx []interface{}) []interface{} { + return append(ctx, "req", hexutil.Bytes(p.ReqID), "enrseq", p.ENRSeq) +} + +func (p *Findnode) Name() string { return "FINDNODE/v5" } +func (p *Findnode) Kind() byte { return FindnodeMsg } func (p *Findnode) RequestID() []byte { return p.ReqID } func (p *Findnode) SetRequestID(id []byte) { p.ReqID = id } +func (p *Findnode) AppendLogInfo(ctx []interface{}) []interface{} { + ctx = append(ctx, "req", hexutil.Bytes(p.ReqID)) + if p.OpID != 0 { + ctx = append(ctx, "opid", p.OpID) + } + return ctx +} + func (*Nodes) Name() string { return "NODES/v5" } func (*Nodes) Kind() byte { return NodesMsg } func (p *Nodes) RequestID() []byte { return p.ReqID } func (p *Nodes) SetRequestID(id []byte) { p.ReqID = id } +func (p *Nodes) AppendLogInfo(ctx []interface{}) []interface{} { + return append(ctx, + "req", hexutil.Bytes(p.ReqID), + "tot", p.RespCount, + "n", len(p.Nodes), + ) +} + func (*TalkRequest) Name() string { return "TALKREQ/v5" } func (*TalkRequest) Kind() byte { return TalkRequestMsg } func (p *TalkRequest) RequestID() []byte { return p.ReqID } func (p *TalkRequest) SetRequestID(id []byte) { p.ReqID = id } +func (p *TalkRequest) AppendLogInfo(ctx []interface{}) []interface{} { + return append(ctx, "proto", p.Protocol, "req", hexutil.Bytes(p.ReqID), "len", len(p.Message)) +} + func (*TalkResponse) Name() string { return "TALKRESP/v5" } func (*TalkResponse) Kind() byte { return TalkResponseMsg } func (p *TalkResponse) RequestID() []byte { return p.ReqID } func (p *TalkResponse) SetRequestID(id []byte) { p.ReqID = id } -func (*RequestTicket) Name() string { return "REQTICKET/v5" } -func (*RequestTicket) Kind() byte { return RequestTicketMsg } -func (p *RequestTicket) RequestID() []byte { return p.ReqID } -func (p *RequestTicket) SetRequestID(id []byte) { p.ReqID = id } - -func (*Regtopic) Name() string { return "REGTOPIC/v5" } -func (*Regtopic) Kind() byte { return RegtopicMsg } -func (p *Regtopic) RequestID() []byte { return p.ReqID } -func (p *Regtopic) SetRequestID(id []byte) { p.ReqID = id } - -func (*Ticket) Name() string { return "TICKET/v5" } -func (*Ticket) Kind() byte { return TicketMsg } -func (p *Ticket) RequestID() []byte { return p.ReqID } -func (p *Ticket) SetRequestID(id []byte) { p.ReqID = id } - -func (*Regconfirmation) Name() string { return "REGCONFIRMATION/v5" } -func (*Regconfirmation) Kind() byte { return RegconfirmationMsg } -func (p *Regconfirmation) RequestID() []byte { return p.ReqID } -func (p *Regconfirmation) SetRequestID(id []byte) { p.ReqID = id } - -func (*TopicQuery) Name() string { return "TOPICQUERY/v5" } -func (*TopicQuery) Kind() byte { return TopicQueryMsg } -func (p *TopicQuery) RequestID() []byte { return p.ReqID } -func (p *TopicQuery) SetRequestID(id []byte) { p.ReqID = id } +func (p *TalkResponse) AppendLogInfo(ctx []interface{}) []interface{} { + return append(ctx, "req", hexutil.Bytes(p.ReqID), "len", len(p.Message)) +} diff --git a/vendor/github.com/waku-org/go-discover/discover/v5wire/session.go b/vendor/github.com/waku-org/go-discover/discover/v5wire/session.go index d52b5c11810..862c21fcee9 100644 --- a/vendor/github.com/waku-org/go-discover/discover/v5wire/session.go +++ b/vendor/github.com/waku-org/go-discover/discover/v5wire/session.go @@ -22,10 +22,10 @@ import ( "encoding/binary" "time" + "github.com/ethereum/go-ethereum/common/lru" "github.com/ethereum/go-ethereum/common/mclock" "github.com/ethereum/go-ethereum/crypto" "github.com/ethereum/go-ethereum/p2p/enode" - "github.com/hashicorp/golang-lru/simplelru" ) const handshakeTimeout = time.Second @@ -33,7 +33,7 @@ const handshakeTimeout = time.Second // The SessionCache keeps negotiated encryption keys and // state for in-progress handshakes in the Discovery v5 wire protocol. type SessionCache struct { - sessions *simplelru.LRU + sessions lru.BasicLRU[sessionID, *session] handshakes map[sessionID]*Whoareyou clock mclock.Clock @@ -62,12 +62,8 @@ func (s *session) keysFlipped() *session { } func NewSessionCache(maxItems int, clock mclock.Clock) *SessionCache { - cache, err := simplelru.NewLRU(maxItems, nil) - if err != nil { - panic("can't create session cache") - } return &SessionCache{ - sessions: cache, + sessions: lru.NewBasicLRU[sessionID, *session](maxItems), handshakes: make(map[sessionID]*Whoareyou), clock: clock, nonceGen: generateNonce, @@ -95,11 +91,8 @@ func (sc *SessionCache) nextNonce(s *session) (Nonce, error) { // session returns the current session for the given node, if any. func (sc *SessionCache) session(id enode.ID, addr string) *session { - item, ok := sc.sessions.Get(sessionID{id, addr}) - if !ok { - return nil - } - return item.(*session) + item, _ := sc.sessions.Get(sessionID{id, addr}) + return item } // readKey returns the current read key for the given node. diff --git a/vendor/github.com/waku-org/go-waku/waku/v2/discv5/discover.go b/vendor/github.com/waku-org/go-waku/waku/v2/discv5/discover.go index aeae8e182e5..646e5dbe31d 100644 --- a/vendor/github.com/waku-org/go-waku/waku/v2/discv5/discover.go +++ b/vendor/github.com/waku-org/go-waku/waku/v2/discv5/discover.go @@ -13,12 +13,13 @@ import ( "github.com/multiformats/go-multiaddr" "github.com/prometheus/client_golang/prometheus" "github.com/waku-org/go-discover/discover" + "go.uber.org/zap" + "github.com/waku-org/go-waku/logging" "github.com/waku-org/go-waku/waku/v2/peerstore" wenr "github.com/waku-org/go-waku/waku/v2/protocol/enr" "github.com/waku-org/go-waku/waku/v2/service" "github.com/waku-org/go-waku/waku/v2/utils" - "go.uber.org/zap" "github.com/ethereum/go-ethereum/p2p/enode" "github.com/ethereum/go-ethereum/p2p/nat" @@ -142,11 +143,9 @@ func NewDiscoveryV5(priv *ecdsa.PrivateKey, localnode *enode.LocalNode, peerConn localnode: localnode, metrics: newMetrics(reg), config: discover.Config{ - PrivateKey: priv, - Bootnodes: bootnodes, - V5Config: discover.V5Config{ - ProtocolID: &protocolID, - }, + PrivateKey: priv, + Bootnodes: bootnodes, + V5ProtocolID: &protocolID, }, udpAddr: &net.UDPAddr{ IP: net.IPv4zero, diff --git a/vendor/github.com/waku-org/go-waku/waku/v2/protocol/enr/localnode.go b/vendor/github.com/waku-org/go-waku/waku/v2/protocol/enr/localnode.go index 802a3bcd248..0eb0b6ee36e 100644 --- a/vendor/github.com/waku-org/go-waku/waku/v2/protocol/enr/localnode.go +++ b/vendor/github.com/waku-org/go-waku/waku/v2/protocol/enr/localnode.go @@ -45,11 +45,6 @@ func WithMultiaddress(multiaddrs ...multiaddr.Multiaddr) ENROption { successIdx := -1 for i := len(multiaddrs); i > 0; i-- { cpy := localnode.Node().Record() // Record() creates a copy for the current iteration - // Copy all the entries that might not have been written in the ENR record due to the - // async nature of localnode.Set - for _, entry := range localnode.Entries() { - cpy.Set(entry) - } cpy.Set(enr.WithEntry(MultiaddrENRField, marshalMultiaddress(multiaddrs[0:i]))) cpy.SetSeq(localnode.Seq() + 1) err = enode.SignV4(cpy, privk) diff --git a/vendor/github.com/waku-org/go-waku/waku/v2/protocol/rln/group_manager/dynamic/mock_client.go b/vendor/github.com/waku-org/go-waku/waku/v2/protocol/rln/group_manager/dynamic/mock_client.go index ea13499789b..509cc466767 100644 --- a/vendor/github.com/waku-org/go-waku/waku/v2/protocol/rln/group_manager/dynamic/mock_client.go +++ b/vendor/github.com/waku-org/go-waku/waku/v2/protocol/rln/group_manager/dynamic/mock_client.go @@ -34,7 +34,7 @@ func (c *MockClient) Close() { } func (c *MockClient) BlockByNumber(ctx context.Context, number *big.Int) (*types.Block, error) { - return types.NewBlock(&types.Header{Number: big.NewInt(c.latestBlockNum.Load())}, nil, nil, nil, nil), nil + return types.NewBlock(&types.Header{Number: big.NewInt(c.latestBlockNum.Load())}, nil, nil, nil), nil } func NewMockClient(t *testing.T, blockFile string) *MockClient { blockChain := MockBlockChain{} diff --git a/vendor/modules.txt b/vendor/modules.txt index a26dfc749ff..84383672373 100644 --- a/vendor/modules.txt +++ b/vendor/modules.txt @@ -1285,8 +1285,8 @@ github.com/urfave/cli/v2 # github.com/wadey/gocovmerge v0.0.0-20160331181800-b5bfa59ec0ad ## explicit github.com/wadey/gocovmerge -# github.com/waku-org/go-discover v0.0.0-20240506173252-4912704efdc5 -## explicit; go 1.15 +# github.com/waku-org/go-discover v0.0.0-20251002230139-b9b5a06121c6 +## explicit; go 1.23.0 github.com/waku-org/go-discover/discover github.com/waku-org/go-discover/discover/v4wire github.com/waku-org/go-discover/discover/v5wire @@ -1295,7 +1295,7 @@ github.com/waku-org/go-discover/discover/v5wire github.com/waku-org/go-libp2p-rendezvous github.com/waku-org/go-libp2p-rendezvous/db github.com/waku-org/go-libp2p-rendezvous/pb -# github.com/waku-org/go-waku v0.8.1-0.20250825172353-0c3d6dc0a8cc +# github.com/waku-org/go-waku v0.10.0 ## explicit; go 1.23.0 github.com/waku-org/go-waku/logging github.com/waku-org/go-waku/tests