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Merge #230: norm arg: add prove test vectors
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f3126fd norm arg: remove prove edge tests which are now covered by vectors (Jonas Nick)
847ed9e norm arg: add verification to prove vectors (Jonas Nick)
cf797ed norm arg: add prove test vectors (Jonas Nick)
095c1e7 norm arg: add prove_const to tests (Jonas Nick)
bf7bf8a norm arg: split norm_arg_zero into prove_edge and verify_zero_len (Jonas Nick)
a70c4d4 norm arg: add test vector for |n| = 0 (Jonas Nick)
f5e4b16 norm arg: add test vector for sign bit malleability (Jonas Nick)
c0de361 norm arg: allow X and R to be the point at infinity (Jonas Nick)
f22834f norm arg: add verify vector for n = [0], l = [0] (Jonas Nick)
d8e7f37 musig: move ge_{serialize,parse}_ext to module-independent file (Jonas Nick)

Pull request description:

ACKs for top commit:
  Liam-Eagen:
    ACK f3126fd

Tree-SHA512: 1aad86521fce74435beabe7690c7fcc38ad9ae7a884ddcab69ef825b573433f700723a7672d29df1b4465bc33d5957b6a46f657f988cfd2cc73fa94a3472357d
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@jonasnick
jonasnick committed May 9, 2023
2 parents ce18267 + f3126fd commit 4eab2c2
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Showing 7 changed files with 328 additions and 134 deletions.
19 changes: 2 additions & 17 deletions src/modules/bppp/bppp_norm_product_impl.h
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Original file line number Diff line number Diff line change
Expand Up @@ -300,17 +300,8 @@ static int secp256k1_bppp_rangeproof_norm_product_prove(
return 0;
}

/* We only fail here because we cannot serialize points at infinity. */
if (secp256k1_gej_is_infinity(&xj) || secp256k1_gej_is_infinity(&rj)) {
return 0;
}

secp256k1_ge_set_gej_var(&x_ge, &xj);
secp256k1_fe_normalize_var(&x_ge.x);
secp256k1_fe_normalize_var(&x_ge.y);
secp256k1_ge_set_gej_var(&r_ge, &rj);
secp256k1_fe_normalize_var(&r_ge.x);
secp256k1_fe_normalize_var(&r_ge.y);
secp256k1_bppp_serialize_points(&proof[proof_idx], &x_ge, &r_ge);
proof_idx += 65;

Expand Down Expand Up @@ -379,26 +370,20 @@ static int ec_mult_verify_cb1(secp256k1_scalar *sc, secp256k1_ge *pt, size_t idx
}
idx -= 1;
if (idx % 2 == 0) {
unsigned char pk_buf[33];
idx /= 2;
*sc = data->gammas[idx];
pk_buf[0] = 2 | (data->proof[65*idx] >> 1);
memcpy(&pk_buf[1], &data->proof[65*idx + 1], 32);
if (!secp256k1_eckey_pubkey_parse(pt, pk_buf, sizeof(pk_buf))) {
if (!secp256k1_bppp_parse_one_of_points(pt, &data->proof[65*idx], 0)) {
return 0;
}
} else {
unsigned char pk_buf[33];
secp256k1_scalar neg_one;
idx /= 2;
secp256k1_scalar_set_int(&neg_one, 1);
secp256k1_scalar_negate(&neg_one, &neg_one);
*sc = data->gammas[idx];
secp256k1_scalar_sqr(sc, sc);
secp256k1_scalar_add(sc, sc, &neg_one);
pk_buf[0] = 2 | data->proof[65*idx];
memcpy(&pk_buf[1], &data->proof[65*idx + 33], 32);
if (!secp256k1_eckey_pubkey_parse(pt, pk_buf, sizeof(pk_buf))) {
if (!secp256k1_bppp_parse_one_of_points(pt, &data->proof[65*idx], 1)) {
return 0;
}
}
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31 changes: 27 additions & 4 deletions src/modules/bppp/bppp_util.h
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Original file line number Diff line number Diff line change
Expand Up @@ -15,10 +15,33 @@
/* Outputs a pair of points, amortizing the parity byte between them
* Assumes both points' coordinates have been normalized.
*/
static void secp256k1_bppp_serialize_points(unsigned char *output, const secp256k1_ge *lpt, const secp256k1_ge *rpt) {
output[0] = (secp256k1_fe_is_odd(&lpt->y) << 1) + secp256k1_fe_is_odd(&rpt->y);
secp256k1_fe_get_b32(&output[1], &lpt->x);
secp256k1_fe_get_b32(&output[33], &rpt->x);
static void secp256k1_bppp_serialize_points(unsigned char *output, secp256k1_ge *lpt, secp256k1_ge *rpt) {
unsigned char tmp[33];
secp256k1_ge_serialize_ext(tmp, lpt);
output[0] = (tmp[0] & 1) << 1;
memcpy(&output[1], &tmp[1], 32);
secp256k1_ge_serialize_ext(tmp, rpt);
output[0] |= (tmp[0] & 1);
memcpy(&output[33], &tmp[1], 32);
}

static int secp256k1_bppp_parse_one_of_points(secp256k1_ge *pt, const unsigned char *in65, int idx) {
unsigned char tmp[33] = { 0 };
if (in65[0] > 3) {
return 0;
}
/* Check if the input array encodes the point at infinity */
if ((secp256k1_memcmp_var(tmp, &in65[1 + 32*idx], 32)) != 0) {
tmp[0] = 2 | ((in65[0] & (2 - idx)) >> (1 - idx));
memcpy(&tmp[1], &in65[1 + 32*idx], 32);
} else {
/* If we're parsing the point at infinity, enforce that the sign bit is
* 0. */
if ((in65[0] & (2 - idx)) != 0) {
return 0;
}
}
return secp256k1_ge_parse_ext(pt, tmp);
}

/* Outputs a serialized point in compressed form. Returns 0 at point at infinity.
Expand Down
47 changes: 47 additions & 0 deletions src/modules/bppp/test_vectors/prove.h
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Original file line number Diff line number Diff line change
@@ -0,0 +1,47 @@
static const unsigned char prove_vector_gens[264] = { 0x03, 0xAF, 0x2C, 0x40, 0xAD, 0x03, 0xCD, 0xC5, 0x76, 0x8C, 0x07, 0x1E, 0x58, 0xD6, 0x8C, 0x73, 0x45, 0xBA, 0xEB, 0xB5, 0x3F, 0x40, 0xFA, 0x8B, 0xBF, 0x73, 0x6E, 0x7B, 0x4A, 0x54, 0x06, 0xED, 0x32, 0x03, 0xCC, 0x11, 0x19, 0x22, 0x2C, 0xA1, 0x0A, 0x45, 0x23, 0xAF, 0x9B, 0x40, 0x0D, 0xA4, 0x5E, 0x06, 0x24, 0xF4, 0x5F, 0x07, 0x89, 0x88, 0xCD, 0x71, 0xAE, 0x77, 0xC1, 0xF5, 0x87, 0x4E, 0xFC, 0xA5, 0x03, 0xDE, 0x61, 0xB1, 0x8F, 0x2C, 0xAC, 0x18, 0xF5, 0xE4, 0x06, 0x8F, 0x65, 0x55, 0xA1, 0x30, 0x5E, 0xF5, 0xF4, 0x84, 0xED, 0x6B, 0xDD, 0xC2, 0xCC, 0xE8, 0x51, 0x38, 0xB8, 0xA5, 0x4C, 0x43, 0xBD, 0x02, 0xA5, 0xF9, 0x8C, 0x1F, 0x82, 0x2D, 0xC6, 0xF3, 0x0F, 0x53, 0xDB, 0x74, 0x77, 0xC7, 0x91, 0x04, 0xB0, 0xB1, 0xA6, 0x17, 0xB2, 0x91, 0xF4, 0x8B, 0x93, 0x3E, 0xBB, 0x73, 0x15, 0x3E, 0x5A, 0xD1, 0x02, 0x44, 0xF5, 0xC6, 0x4E, 0x77, 0x60, 0x81, 0x83, 0xFF, 0xC2, 0x8E, 0x06, 0xFE, 0x67, 0x0C, 0x9A, 0x4B, 0xF2, 0x34, 0xB9, 0xEA, 0xE9, 0x37, 0xDA, 0x30, 0xE2, 0x32, 0x27, 0xF3, 0x88, 0x5F, 0x2A, 0x02, 0x1D, 0x49, 0x5D, 0x04, 0xED, 0x61, 0x95, 0x37, 0xDD, 0x95, 0xB1, 0x4F, 0x64, 0x0E, 0x1E, 0xFB, 0x47, 0x9F, 0xA7, 0xD7, 0xE0, 0x7A, 0xB1, 0x02, 0x81, 0x95, 0xD1, 0xA5, 0x7E, 0xB2, 0x74, 0x8F, 0x03, 0x26, 0xA5, 0xEC, 0xE9, 0x71, 0x46, 0x37, 0xAC, 0x3D, 0x74, 0x84, 0x26, 0xCB, 0x7C, 0xE8, 0xFE, 0x4E, 0xB0, 0x6D, 0x70, 0x3D, 0x00, 0x10, 0x1A, 0x3A, 0x5B, 0xB8, 0xAA, 0x29, 0x59, 0x93, 0x15, 0x03, 0xE1, 0xA5, 0x39, 0x44, 0x75, 0x16, 0x28, 0x5F, 0xBA, 0x69, 0xA2, 0x4A, 0x2A, 0xC3, 0x5B, 0x63, 0x1F, 0x40, 0x10, 0x36, 0xF9, 0x4C, 0xD2, 0x76, 0x0F, 0xCF, 0x7F, 0x50, 0x30, 0x6E, 0x2B, 0x1D };
static const unsigned char prove_vector_0_n_vec32[1][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, 0x3F } };
static secp256k1_scalar prove_vector_0_n_vec[1];
static const unsigned char prove_vector_0_l_vec32[1][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, 0x3E } };
static secp256k1_scalar prove_vector_0_l_vec[1];
static const unsigned char prove_vector_0_c_vec32[1][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, 0x3C } };
static secp256k1_scalar prove_vector_0_c_vec[1];
static const unsigned char prove_vector_0_r32[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, 0x3A };
static const unsigned char prove_vector_0_proof[] = { 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, 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, 0x3E };
static const int prove_vector_0_result = 1;
static const unsigned char prove_vector_1_n_vec32[2][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, 0x3F }, { 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 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 } };
static secp256k1_scalar prove_vector_1_n_vec[2];
static const unsigned char prove_vector_1_l_vec32[4][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, 0x3E }, { 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 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 }, { 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, 0x34 }, { 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x0B } };
static secp256k1_scalar prove_vector_1_l_vec[4];
static const unsigned char prove_vector_1_c_vec32[4][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, 0x3C }, { 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 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 }, { 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, 0x30 }, { 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x0D } };
static secp256k1_scalar prove_vector_1_c_vec[4];
static const unsigned char prove_vector_1_r32[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, 0x3A };
static const unsigned char prove_vector_1_proof[] = { 0x00, 0xD2, 0xEC, 0xE2, 0x53, 0x97, 0x28, 0x68, 0x22, 0x59, 0x34, 0xEF, 0xE4, 0x7B, 0x87, 0x4D, 0xE9, 0x57, 0xD5, 0xB7, 0xC7, 0x72, 0xF4, 0xC9, 0xEA, 0x66, 0x14, 0x59, 0xE1, 0xA9, 0xD5, 0xB2, 0x10, 0xDF, 0xE2, 0xFF, 0xF5, 0xA4, 0x38, 0x6B, 0xFE, 0x36, 0x89, 0xE4, 0x9D, 0x90, 0x9F, 0x71, 0x19, 0xE6, 0xA3, 0x1E, 0xAA, 0xAA, 0x4E, 0xFE, 0xC2, 0xD3, 0x37, 0xBB, 0xDE, 0xDB, 0x46, 0x43, 0xC2, 0x01, 0x42, 0x5F, 0xFC, 0xC6, 0x25, 0xA0, 0xB4, 0xF0, 0x76, 0x99, 0xF4, 0x7C, 0xE9, 0x83, 0x82, 0xED, 0x7C, 0x95, 0xBA, 0xD0, 0xE6, 0x5B, 0x88, 0xFD, 0x38, 0xEA, 0x23, 0x54, 0xD4, 0xBD, 0xD4, 0x37, 0xB8, 0x2B, 0x49, 0xAF, 0x81, 0xFD, 0xBE, 0x88, 0xB2, 0xE5, 0x3F, 0xF4, 0x30, 0x52, 0x00, 0x63, 0x9D, 0xAE, 0x82, 0x44, 0xE9, 0x62, 0x87, 0x2A, 0x23, 0x89, 0x10, 0xE4, 0x9A, 0x64, 0x9F, 0x71, 0xD9, 0x32, 0x57, 0x3B, 0xCB, 0xAC, 0x30, 0xAE, 0x71, 0x61, 0xE9, 0x50, 0x1F, 0xCB, 0x49, 0x9C, 0x52, 0xBA, 0x0C, 0xC4, 0x00, 0x58, 0x73, 0x63, 0xD3, 0x42, 0xDE, 0x42, 0x5E, 0xC5, 0x97, 0xE5, 0xDA, 0x88, 0x76, 0x49, 0x6C, 0x8B, 0x92, 0x99, 0xEE, 0xD0, 0xA9, 0xEB, 0x6E, 0xCA, 0xE1, 0x93, 0x81, 0x56, 0x2E, 0xCA, 0xF3, 0x8E, 0xF0, 0x04, 0xD2, 0x96, 0xD8, 0xDB, 0xEE, 0xEE, 0x1C, 0x44 };
static const int prove_vector_1_result = 1;
static const unsigned char prove_vector_2_n_vec32[4][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, 0x3F }, { 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 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 }, { 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, 0x34 }, { 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x0B } };
static secp256k1_scalar prove_vector_2_n_vec[4];
static const unsigned char prove_vector_2_l_vec32[1][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, 0x3E } };
static secp256k1_scalar prove_vector_2_l_vec[1];
static const unsigned char prove_vector_2_c_vec32[1][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, 0x3C } };
static secp256k1_scalar prove_vector_2_c_vec[1];
static const unsigned char prove_vector_2_r32[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, 0x34 };
static const unsigned char prove_vector_2_proof[] = { 0x00, 0xBC, 0x4C, 0x42, 0x67, 0x71, 0x69, 0x52, 0x6A, 0x65, 0xFE, 0xA0, 0xCB, 0x3F, 0x58, 0x8B, 0x48, 0x48, 0x6E, 0x59, 0xFC, 0x55, 0x51, 0x10, 0xB9, 0xBF, 0x6A, 0x7D, 0xBF, 0x32, 0x34, 0x4E, 0x7D, 0xBA, 0xD5, 0xCB, 0xCC, 0x19, 0xED, 0xAA, 0x9F, 0x8D, 0x93, 0x26, 0x5E, 0x3F, 0x3E, 0xAA, 0xDF, 0x0B, 0x1C, 0xB3, 0xDC, 0x37, 0xB6, 0xDB, 0xAE, 0x43, 0x63, 0x92, 0xB5, 0xFF, 0x0D, 0x1C, 0x77, 0x02, 0x7E, 0x2B, 0xB8, 0x87, 0x85, 0x81, 0x13, 0x70, 0x1F, 0x03, 0x65, 0x7D, 0xD8, 0x91, 0x83, 0xE5, 0x7E, 0x8B, 0x9E, 0x6F, 0x1C, 0x08, 0x9C, 0x9C, 0x5F, 0xA4, 0x12, 0x5F, 0xD3, 0xEE, 0xE2, 0x74, 0x7A, 0x2C, 0x58, 0x3A, 0x29, 0x4F, 0x64, 0x10, 0xE7, 0x89, 0xBF, 0xB2, 0xE5, 0xD9, 0xD5, 0xC5, 0x62, 0x83, 0x0C, 0xA8, 0xDD, 0x1E, 0x24, 0x6D, 0xD1, 0x58, 0x8D, 0x80, 0x74, 0xF3, 0xD9, 0x3A, 0x68, 0x7B, 0xF5, 0x12, 0xC6, 0xC2, 0x3F, 0x71, 0x47, 0xDF, 0xCF, 0xC8, 0xE2, 0xC4, 0x59, 0xDF, 0x4F, 0xEC, 0x86, 0xE9, 0xF9, 0x31, 0x94, 0x6A, 0x5F, 0xD9, 0x1E, 0x6B, 0x09, 0xCD, 0xCF, 0x5D, 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, 0x3E };
static const int prove_vector_2_result = 1;
static const unsigned char prove_vector_3_n_vec32[1][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 } };
static secp256k1_scalar prove_vector_3_n_vec[1];
static const unsigned char prove_vector_3_l_vec32[1][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 } };
static secp256k1_scalar prove_vector_3_l_vec[1];
static const unsigned char prove_vector_3_c_vec32[1][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, 0x3C } };
static secp256k1_scalar prove_vector_3_c_vec[1];
static const unsigned char prove_vector_3_r32[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, 0x34 };
static const unsigned char prove_vector_3_proof[] = { 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 };
static const int prove_vector_3_result = 1;
static const unsigned char prove_vector_4_n_vec32[2][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 }, { 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 } };
static secp256k1_scalar prove_vector_4_n_vec[2];
static const unsigned char prove_vector_4_l_vec32[1][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, 0x3A } };
static secp256k1_scalar prove_vector_4_l_vec[1];
static const unsigned char prove_vector_4_c_vec32[1][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, 0x3C } };
static secp256k1_scalar prove_vector_4_c_vec[1];
static const unsigned char prove_vector_4_r32[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, 0x34 };
static const unsigned char prove_vector_4_proof[] = { 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 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, 0xFE, 0xBA, 0xAE, 0xDC, 0xE6, 0xAF, 0x48, 0xA0, 0x3B, 0xBF, 0xD2, 0x5E, 0x8C, 0xD0, 0x36, 0x41, 0x3A };
static const int prove_vector_4_result = 1;

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