Make aux_rnd32==NULL behave identical to 0x0000..00.

BIP340's default signing algorithm always requires an aux_rnd argument,
but permits using an all-zero one when no randomness is available.

Make secp256k1_schnorrsig_sign follow this even when aux_rnd32==NULL,
by treating the same as if an all-zero byte array was provided as
input.

include/secp256k1_schnorrsig.h

@@ -111,7 +111,8 @@ typedef struct {
  *  In:    msg32: the 32-byte message being signed.
  *       keypair: pointer to an initialized keypair.
  *    aux_rand32: 32 bytes of fresh randomness. While recommended to provide
- *                this, it is only supplemental to security and can be NULL. See
+ *                this, it is only supplemental to security and can be NULL. A
+ *                NULL argument is treated the same as an all-zero one. See
  *                BIP-340 "Default Signing" for a full explanation of this
  *                argument and for guidance if randomness is expensive.
  */

src/modules/schnorrsig/main_impl.h

@@ -65,6 +65,17 @@ static int nonce_function_bip340(unsigned char *nonce32, const unsigned char *ms
         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
@@ -77,12 +88,8 @@ static int nonce_function_bip340(unsigned char *nonce32, const unsigned char *ms
         secp256k1_sha256_initialize_tagged(&sha, algo, algolen);
     }
 
-    /* Hash (masked-)key||pk||msg using the tagged hash as per the spec */
-    if (data != NULL) {
-        secp256k1_sha256_write(&sha, masked_key, 32);
-    } else {
-        secp256k1_sha256_write(&sha, key32, 32);
-    }
+    /* 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);

src/modules/schnorrsig/tests_impl.h

@@ -38,7 +38,7 @@ void run_nonce_function_bip340_tests(void) {
     size_t algolen = sizeof(algo);
     secp256k1_sha256 sha;
     secp256k1_sha256 sha_optimized;
-    unsigned char nonce[32];
+    unsigned char nonce[32], nonce_z[32];
     unsigned char msg[32];
     size_t msglen = sizeof(msg);
     unsigned char key[32];
@@ -107,8 +107,11 @@ void run_nonce_function_bip340_tests(void) {
         CHECK(secp256k1_memcmp_var(nonce, nonce2, 32) != 0);
     }
 
-    /* NULL aux_rand argument is allowed. */
+    /* 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);
 }
 
 void test_schnorrsig_api(void) {