Add support for Schnorr signatures.

Author: sipa

Makefile.am

@@ -38,6 +38,8 @@ noinst_HEADERS += src/hash_impl.h
 noinst_HEADERS += src/field.h
 noinst_HEADERS += src/field_impl.h
 noinst_HEADERS += src/bench.h
+noinst_HEADERS += src/schnorr.h
+noinst_HEADERS += src/schnorr_impl.h
 
 pkgconfigdir = $(libdir)/pkgconfig
 pkgconfig_DATA = libsecp256k1.pc
@@ -49,10 +51,13 @@ libsecp256k1_la_LIBADD = $(SECP_LIBS)
 
 noinst_PROGRAMS =
 if USE_BENCHMARK
-noinst_PROGRAMS += bench_verify bench_recover bench_sign bench_internal
+noinst_PROGRAMS += bench_verify bench_recover bench_sign bench_internal bench_schnorr_verify
 bench_verify_SOURCES = src/bench_verify.c
 bench_verify_LDADD = libsecp256k1.la $(SECP_LIBS)
 bench_verify_LDFLAGS = -static
+bench_schnorr_verify_SOURCES = src/bench_schnorr_verify.c
+bench_schnorr_verify_LDADD = libsecp256k1.la $(SECP_LIBS)
+bench_schnorr_verify_LDFLAGS = -static
 bench_recover_SOURCES = src/bench_recover.c
 bench_recover_LDADD = libsecp256k1.la $(SECP_LIBS)
 bench_recover_LDFLAGS = -static

include/secp256k1.h

@@ -341,6 +341,189 @@ SECP256K1_WARN_UNUSED_RESULT int secp256k1_context_randomize(
   const unsigned char *seed32
 ) SECP256K1_ARG_NONNULL(1);
 
+/** Create a signature using a custom EC-Schnorr-SHA256 construction. It
+ *  produces non-malleable 64-byte signatures which support public key recovery
+ *  batch validation, and multiparty signing.
+ *  Returns: 1: signature created
+ *           0: the nonce generation function failed, or the private key was
+ *              invalid.
+ *  In:      ctx:    pointer to a context object, initialized for signing
+ *                   (cannot be NULL)
+ *           msg32:  the 32-byte message hash being signed (cannot be NULL)
+ *           seckey: pointer to a 32-byte secret key (cannot be NULL)
+ *           noncefp:pointer to a nonce generation function. If NULL,
+ *                   secp256k1_nonce_function_default is used
+ *           ndata:  pointer to arbitrary data used by the nonce generation
+ *                   function (can be NULL)
+ *  Out:     sig64:  pointer to a 64-byte array where the signature will be
+ *                   placed (cannot be NULL)
+ */
+int secp256k1_schnorr_sign(
+  const secp256k1_context_t* ctx,
+  const unsigned char *msg32,
+  unsigned char *sig64,
+  const unsigned char *seckey,
+  secp256k1_nonce_function_t noncefp,
+  const void *ndata
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
+
+/** Verify a signature created by secp256k1_schnorr_sign.
+ *  Returns: 1: public key and signature correct
+ *           0: incorrect signature
+ *           -1: invalid public key
+ *  In:      ctx:       a secp256k1 context object, initialized for verification.
+ *           msg32:     the 32-byte message hash being verified (cannot be NULL)
+ *           sig64:     the 64-byte signature being verified (cannot be NULL)
+ *           pubkey:    the public key to verify with (cannot be NULL)
+ *           pubkeylen: the length of pubkey
+ */
+SECP256K1_WARN_UNUSED_RESULT int secp256k1_schnorr_verify(
+  const secp256k1_context_t* ctx,
+  const unsigned char *msg32,
+  const unsigned char *sig64,
+  const unsigned char *pubkey,
+  int pubkeylen
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
+
+/** Recover an EC public key from a Schnorr signature created using
+ *  secp256k1_schnorr_sign.
+ *  Returns: 1: public key successfully recovered (which guarantees a correct
+ *           signature).
+ *           0: otherwise.
+ *  In:      ctx:        pointer to a context object, initialized for
+ *                       verification (cannot be NULL)
+ *           msg32:      the 32-byte message hash assumed to be signed (cannot
+ *                       be NULL)
+ *           sig64:      signature as 64 byte array (cannot be NULL)
+ *           compressed: whether to recover a compressed or uncompressed pubkey
+ *  Out:     pubkey:     pointer to a 33 or 65 byte array to put the pubkey
+ *                       (cannot be NULL)
+ *           pubkeylen:  pointer to an int that will contain the pubkey length
+ *                       (cannot be NULL)
+ */
+int secp256k1_schnorr_recover(
+  const secp256k1_context_t* ctx,
+  const unsigned char *msg32,
+  const unsigned char *sig64,
+  unsigned char *pubkey,
+  int *pubkeylen,
+  int compressed
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4) SECP256K1_ARG_NONNULL(5);
+
+/** Generate a nonce pair deterministically for use with
+ *  secp256k1_schnorr_partial_sign.
+ *  Returns: 1: valid nonce pair was generated.
+ *           0: otherwise (nonce generation function failed)
+ *  In:      ctx:        pointer to a context object, initialized for signing
+ *                       (cannot be NULL)
+ *           msg32:      the 32-byte message hash assumed to be signed (cannot
+ *                       be NULL)
+ *           sec32:      the 32-byte private key (cannot be NULL)
+ *           noncefp:    pointer to a nonce generation function. If NULL,
+ *                       secp256k1_nonce_function_default is used
+ *           noncedata:  pointer to arbitrary data used by the nonce generation
+ *                       function (can be NULL)
+ *  Out:     pubnonce33: public side of the nonce (represented as a 33-byte
+ *                       compressed public key) (cannot be NULL)
+ *           privnonce32:private side of the nonce (32 byte) (cannot be NULL)
+ *
+ *  Do not use the output as a private/public key pair for signing/validation.
+ */
+int secp256k1_schnorr_generate_nonce_pair(
+  const secp256k1_context_t* ctx,
+  const unsigned char *msg32,
+  const unsigned char *sec32,
+  secp256k1_nonce_function_t noncefp,
+  const void* noncedata,
+  unsigned char *pubnonce33,
+  unsigned char *privnonce32
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(6) SECP256K1_ARG_NONNULL(7);
+
+/** Add a number of public keys together.
+ *  Returns: 1: the sum of the public keys is valid.
+ *           0: the sum of the public keys is not valid.
+ *          -1: one or more of the inputs were invalid.
+ *  In:     ctx:        pointer to a context object
+ *          out:        pointer to 33-byte array for placing the resulting
+ *                      public key (in compressed format) (cannot be NULL)
+ *          n:          the number of public keys to add together (must be at least 1)
+ *          ins:        pointer to array of pointers to public keys in
+ *                      compressed format (cannot be NULL)
+ *  Use secp256k1_ec_pubkey_compress and secp256k1_ec_pubkey_decompress if the
+ *  uncompressed format is needed.
+ */
+SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_combine(
+  const secp256k1_context_t* ctx,
+  unsigned char *out,
+  int n,
+  const unsigned char **ins
+) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(4);
+
+/** Produce a partial Schnorr signature, which can be combined using
+ *  secp256k1_schnorr_partial_combine, to end up with a full signature that is
+ *  verifiable using secp256k1_schnorr_verify.
+ *  Returns: 1: signature created succesfully.
+ *           0: no valid signature exists with this combination of keys, nonces
+ *              and message (chance around 1 in 2^128)
+ *          -1: invalid private key, nonce, or public nonces.
+ *  In:  ctx:        pointer to context object, initialized for signing (cannot
+ *                   be NULL)
+ *       msg32:      pointer to 32-byte message to sign
+ *       sec32:      pointer to 32-byte private key
+ *       secnonce32: pointer to 32-byte array containing our nonce
+ *       pubnonce33: pointer to 33-byte array containing the sum of the other's
+ *                   nonces (see secp256k1_ec_pubkey_combine)
+ *  Out:  sig64:     pointer to 64-byte array to put partial signature in
+ *
+ * The intended procedure for creating a multiparty signature is:
+ * - Each signer S[i] with private key x[i] and public key Q[i] runs
+ *   secp256k1_schnorr_generate_nonce_pair to produce a pair (k[i],R[i]) of
+ *   private/public nonces.
+ * - All signers communicate their public nonces to each other (revealing your
+ *   private nonce can lead to discovery of your private key, so it should be
+ *   considered secret).
+ * - All signers combine all the public nonces they received (excluding their
+ *   own) using secp256k1_ec_pubkey_combine to obtain an
+ *   Rall[i] = sum(R[0..i-1,i+1..n]).
+ * - All signers produce a partial signature using
+ *   secp256k1_schnorr_partial_sign, passing in their own private key x[i],
+ *   their own private nonce k[i], and the sum of the others' public nonces
+ *   Rall[i].
+ * - All signers communicate their partial signatures to each other.
+ * - Someone combines all partial signatures using
+ *   secp256k1_schnorr_partial_combine, to obtain a full signature.
+ * - The resulting signature is validatable using secp256k1_schnorr_verify, with
+ *   public key equal to the result of secp256k1_ec_pubkey_combine of the
+ *   signers' public keys (sum(Q[0..n])).
+ *
+ *  Note that secp256k1_schnorr_partial_combine and secp256k1_ec_pubkey_combine
+ *  function take their arguments in any order, and it is possible to
+ *  pre-combine several inputs already with one call, and add more inputs later
+ *  by calling the function again.
+ */
+SECP256K1_WARN_UNUSED_RESULT int secp256k1_schnorr_partial_sign(
+  const secp256k1_context_t* ctx,
+  const unsigned char *msg32,
+  unsigned char *sig64,
+  const unsigned char *sec32,
+  const unsigned char *secnonce32,
+  const unsigned char *pubnonce33
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4) SECP256K1_ARG_NONNULL(5) SECP256K1_ARG_NONNULL(6);
+
+/** Combine multiple Schnorr partial signatures.
+ * Returns: 1: the passed signatures were succesfully combined.
+ *          0: some signatures cancel eachother out (chance of 1 in 2^128 per
+ *             signature)
+ *         -1: some inputs were invalid, or the signatures were not created
+ *             using the same set of nonces
+ * In:     ctx:      pointer to a context object
+ *         sig64:    pointer to a 64-byte array to place the combined signature
+ *                   (cannot be NULL)
+ *         n:        the number of signatures to combine (at least 1)
+ * Out:    sig64sin: pointer to an array of n pointers to 64-byte input
+ *                   signatures
+ */
+int secp256k1_schnorr_partial_combine(const secp256k1_context_t* ctx, unsigned char *sig64, int n, const unsigned char **sig64sin);
 
 # ifdef __cplusplus
 }

src/bench_schnorr_verify.c

@@ -0,0 +1,64 @@
+/**********************************************************************
+ * Copyright (c) 2014 Pieter Wuille                                   *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#include <stdio.h>
+#include <string.h>
+
+#include "include/secp256k1.h"
+#include "util.h"
+#include "bench.h"
+
+typedef struct {
+    unsigned char key[32];
+    unsigned char sig[64];
+    unsigned char pubkey[33];
+    int pubkeylen;
+} benchmark_schnorr_sig_t;
+
+typedef struct {
+    secp256k1_context_t *ctx;
+    unsigned char msg[32];
+    benchmark_schnorr_sig_t sigs[64];
+    int numsigs;
+} benchmark_schnorr_verify_t;
+
+static void benchmark_schnorr_init(void* arg) {
+    int i, k;
+    benchmark_schnorr_verify_t* data = (benchmark_schnorr_verify_t*)arg;
+
+    for (i = 0; i < 32; i++) data->msg[i] = 1 + i;
+    for (k = 0; k < data->numsigs; k++) {
+        for (i = 0; i < 32; i++) data->sigs[k].key[i] = 33 + i + k;
+        secp256k1_schnorr_sign(data->ctx, data->msg, data->sigs[k].sig, data->sigs[k].key, NULL, NULL);
+        data->sigs[k].pubkeylen = 33;
+        CHECK(secp256k1_ec_pubkey_create(data->ctx, data->sigs[k].pubkey, &data->sigs[k].pubkeylen, data->sigs[k].key, 1));
+    }
+}
+
+static void benchmark_schnorr_verify(void* arg) {
+    int i;
+    benchmark_schnorr_verify_t* data = (benchmark_schnorr_verify_t*)arg;
+
+    for (i = 0; i < 20000 / data->numsigs; i++) {
+        data->sigs[0].sig[(i >> 8) % 64] ^= (i & 0xFF);
+        CHECK(secp256k1_schnorr_verify(data->ctx, data->msg, data->sigs[0].sig, data->sigs[0].pubkey, data->sigs[0].pubkeylen) == ((i & 0xFF) == 0));
+        data->sigs[0].sig[(i >> 8) % 64] ^= (i & 0xFF);
+    }
+}
+
+
+
+int main(void) {
+    benchmark_schnorr_verify_t data;
+
+    data.ctx = secp256k1_context_create(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY);
+
+    data.numsigs = 1;
+    run_benchmark("schnorr_verify", benchmark_schnorr_verify, benchmark_schnorr_init, NULL, &data, 10, 20000);
+
+    secp256k1_context_destroy(data.ctx);
+    return 0;
+}

src/schnorr.h

@@ -0,0 +1,18 @@
+/***********************************************************************
+ * Copyright (c) 2014-2015 Pieter Wuille                               *
+ * Distributed under the MIT software license, see the accompanying    *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php. *
+ ***********************************************************************/
+
+#ifndef _SECP256K1_SCHNORR_
+#define _SECP256K1_SCHNORR_
+
+#include "scalar.h"
+#include "group.h"
+
+typedef void (*secp256k1_schnorr_msghash_t)(unsigned char *h32, const unsigned char *r32, const unsigned char *msg32);
+
+static int secp256k1_schnorr_sig_sign(const secp256k1_ecmult_gen_context_t* ctx, unsigned char *sig64, const secp256k1_scalar_t *key, const secp256k1_scalar_t *nonce, const secp256k1_ge_t *pubnonce, secp256k1_schnorr_msghash_t hash, const unsigned char *msg32);
+static int secp256k1_schnorr_sig_verify(const secp256k1_ecmult_context_t* ctx, const unsigned char *sig64, const secp256k1_ge_t *pubkey, secp256k1_schnorr_msghash_t hash, const unsigned char *msg32);
+
+#endif