ct: Use volatile "trick" in all fe/scalar cmov implementations

Apparently clang 15 is able to compile our cmov code into a branch,
at least for fe_cmov and fe_storage_cmov. This commit makes the
condition volatile in all cmov implementations (except ge but that
one only calls into the fe impls).

This is just a quick fix. We should still look into other methods,
e.g., asm and bitcoin#457. We should also consider not caring about
constant-time in scalar_low_impl.h

We should also consider testing on very new compilers in nightly CI,
see bitcoin-core/secp256k1#864 (comment)

Author: real-or-random

src/field_10x26_impl.h

@@ -1147,8 +1147,9 @@ static void secp256k1_fe_sqr(secp256k1_fe *r, const secp256k1_fe *a) {
 
 static SECP256K1_INLINE void secp256k1_fe_cmov(secp256k1_fe *r, const secp256k1_fe *a, int flag) {
     uint32_t mask0, mask1;
+    volatile int vflag = flag;
     SECP256K1_CHECKMEM_CHECK_VERIFY(r->n, sizeof(r->n));
-    mask0 = flag + ~((uint32_t)0);
+    mask0 = vflag + ~((uint32_t)0);
     mask1 = ~mask0;
     r->n[0] = (r->n[0] & mask0) | (a->n[0] & mask1);
     r->n[1] = (r->n[1] & mask0) | (a->n[1] & mask1);
@@ -1246,8 +1247,9 @@ static SECP256K1_INLINE void secp256k1_fe_half(secp256k1_fe *r) {
 
 static SECP256K1_INLINE void secp256k1_fe_storage_cmov(secp256k1_fe_storage *r, const secp256k1_fe_storage *a, int flag) {
     uint32_t mask0, mask1;
+    volatile int vflag = flag;
     SECP256K1_CHECKMEM_CHECK_VERIFY(r->n, sizeof(r->n));
-    mask0 = flag + ~((uint32_t)0);
+    mask0 = vflag + ~((uint32_t)0);
     mask1 = ~mask0;
     r->n[0] = (r->n[0] & mask0) | (a->n[0] & mask1);
     r->n[1] = (r->n[1] & mask0) | (a->n[1] & mask1);

src/field_5x52_impl.h

@@ -487,8 +487,9 @@ static void secp256k1_fe_sqr(secp256k1_fe *r, const secp256k1_fe *a) {
 
 static SECP256K1_INLINE void secp256k1_fe_cmov(secp256k1_fe *r, const secp256k1_fe *a, int flag) {
     uint64_t mask0, mask1;
+    volatile int vflag = flag;
     SECP256K1_CHECKMEM_CHECK_VERIFY(r->n, sizeof(r->n));
-    mask0 = flag + ~((uint64_t)0);
+    mask0 = vflag + ~((uint64_t)0);
     mask1 = ~mask0;
     r->n[0] = (r->n[0] & mask0) | (a->n[0] & mask1);
     r->n[1] = (r->n[1] & mask0) | (a->n[1] & mask1);
@@ -570,8 +571,9 @@ static SECP256K1_INLINE void secp256k1_fe_half(secp256k1_fe *r) {
 
 static SECP256K1_INLINE void secp256k1_fe_storage_cmov(secp256k1_fe_storage *r, const secp256k1_fe_storage *a, int flag) {
     uint64_t mask0, mask1;
+    volatile int vflag = flag;
     SECP256K1_CHECKMEM_CHECK_VERIFY(r->n, sizeof(r->n));
-    mask0 = flag + ~((uint64_t)0);
+    mask0 = vflag + ~((uint64_t)0);
     mask1 = ~mask0;
     r->n[0] = (r->n[0] & mask0) | (a->n[0] & mask1);
     r->n[1] = (r->n[1] & mask0) | (a->n[1] & mask1);

src/scalar_4x64_impl.h

@@ -811,8 +811,9 @@ SECP256K1_INLINE static void secp256k1_scalar_mul_shift_var(secp256k1_scalar *r,
 
 static SECP256K1_INLINE void secp256k1_scalar_cmov(secp256k1_scalar *r, const secp256k1_scalar *a, int flag) {
     uint64_t mask0, mask1;
+    volatile int vflag = flag;
     SECP256K1_CHECKMEM_CHECK_VERIFY(r->d, sizeof(r->d));
-    mask0 = flag + ~((uint64_t)0);
+    mask0 = vflag + ~((uint64_t)0);
     mask1 = ~mask0;
     r->d[0] = (r->d[0] & mask0) | (a->d[0] & mask1);
     r->d[1] = (r->d[1] & mask0) | (a->d[1] & mask1);

src/scalar_8x32_impl.h

@@ -632,8 +632,9 @@ SECP256K1_INLINE static void secp256k1_scalar_mul_shift_var(secp256k1_scalar *r,
 
 static SECP256K1_INLINE void secp256k1_scalar_cmov(secp256k1_scalar *r, const secp256k1_scalar *a, int flag) {
     uint32_t mask0, mask1;
+    volatile int vflag = flag;
     SECP256K1_CHECKMEM_CHECK_VERIFY(r->d, sizeof(r->d));
-    mask0 = flag + ~((uint32_t)0);
+    mask0 = vflag + ~((uint32_t)0);
     mask1 = ~mask0;
     r->d[0] = (r->d[0] & mask0) | (a->d[0] & mask1);
     r->d[1] = (r->d[1] & mask0) | (a->d[1] & mask1);

src/scalar_low_impl.h

@@ -116,8 +116,9 @@ SECP256K1_INLINE static int secp256k1_scalar_eq(const secp256k1_scalar *a, const
 
 static SECP256K1_INLINE void secp256k1_scalar_cmov(secp256k1_scalar *r, const secp256k1_scalar *a, int flag) {
     uint32_t mask0, mask1;
+    volatile int vflag = flag;
     SECP256K1_CHECKMEM_CHECK_VERIFY(r, sizeof(*r));
-    mask0 = flag + ~((uint32_t)0);
+    mask0 = vflag + ~((uint32_t)0);
     mask1 = ~mask0;
     *r = (*r & mask0) | (*a & mask1);
 }