void test_ecdsa_sign_verify(void) {
secp256k1_scalar_t msg, key;
random_scalar_order_test(&msg);
random_scalar_order_test(&key);
secp256k1_gej_t pubj; secp256k1_ecmult_gen(&pubj, &key);
secp256k1_ge_t pub; secp256k1_ge_set_gej(&pub, &pubj);
secp256k1_ecdsa_sig_t sig;
random_sign(&sig, &key, &msg, NULL);
secp256k1_num_t msg_num;
secp256k1_scalar_get_num(&msg_num, &msg);
CHECK(secp256k1_ecdsa_sig_verify(&sig, &pub, &msg_num));
secp256k1_num_inc(&msg_num);
CHECK(!secp256k1_ecdsa_sig_verify(&sig, &pub, &msg_num));
}
void test_ecdsa_openssl(void) {
secp256k1_scalar_t key, msg;
unsigned char message[32];
secp256k1_rand256_test(message);
secp256k1_scalar_set_b32(&msg, message, NULL);
random_scalar_order_test(&key);
secp256k1_gej_t qj;
secp256k1_ecmult_gen(&qj, &key);
secp256k1_ge_t q;
secp256k1_ge_set_gej(&q, &qj);
EC_KEY *ec_key = get_openssl_key(&key);
CHECK(ec_key);
unsigned char signature[80];
unsigned int sigsize = 80;
CHECK(ECDSA_sign(0, message, sizeof(message), signature, &sigsize, ec_key));
secp256k1_ecdsa_sig_t sig;
CHECK(secp256k1_ecdsa_sig_parse(&sig, signature, sigsize));
CHECK(secp256k1_ecdsa_sig_verify(&sig, &q, &msg));
secp256k1_scalar_t one;
secp256k1_scalar_set_int(&one, 1);
secp256k1_scalar_t msg2;
secp256k1_scalar_add(&msg2, &msg, &one);
CHECK(!secp256k1_ecdsa_sig_verify(&sig, &q, &msg2));
random_sign(&sig, &key, &msg, NULL);
int secp_sigsize = 80;
CHECK(secp256k1_ecdsa_sig_serialize(signature, &secp_sigsize, &sig));
CHECK(ECDSA_verify(0, message, sizeof(message), signature, secp_sigsize, ec_key) == 1);
EC_KEY_free(ec_key);
}
void test_ecdsa_sign_verify(void) {
int recid;
int getrec;
secp256k1_scalar_t msg, key;
random_scalar_order_test(&msg);
random_scalar_order_test(&key);
secp256k1_gej_t pubj; secp256k1_ecmult_gen(&pubj, &key);
secp256k1_ge_t pub; secp256k1_ge_set_gej(&pub, &pubj);
secp256k1_ecdsa_sig_t sig;
getrec = secp256k1_rand32()&1;
random_sign(&sig, &key, &msg, getrec?&recid:NULL);
if (getrec) CHECK(recid >= 0 && recid < 4);
CHECK(secp256k1_ecdsa_sig_verify(&sig, &pub, &msg));
secp256k1_scalar_t one;
secp256k1_scalar_set_int(&one, 1);
secp256k1_scalar_add(&msg, &msg, &one);
CHECK(!secp256k1_ecdsa_sig_verify(&sig, &pub, &msg));
}
void test_point_times_order(const secp256k1_gej_t *point) {
/* X * (point + G) + (order-X) * (pointer + G) = 0 */
secp256k1_scalar_t x;
random_scalar_order_test(&x);
secp256k1_scalar_t nx;
secp256k1_scalar_negate(&nx, &x);
secp256k1_gej_t res1, res2;
secp256k1_ecmult(&res1, point, &x, &x); /* calc res1 = x * point + x * G; */
secp256k1_ecmult(&res2, point, &nx, &nx); /* calc res2 = (order - x) * point + (order - x) * G; */
secp256k1_gej_add_var(&res1, &res1, &res2);
CHECK(secp256k1_gej_is_infinity(&res1));
CHECK(secp256k1_gej_is_valid(&res1) == 0);
secp256k1_ge_t res3;
secp256k1_ge_set_gej(&res3, &res1);
CHECK(secp256k1_ge_is_infinity(&res3));
CHECK(secp256k1_ge_is_valid(&res3) == 0);
}
void random_num_order_test(secp256k1_num_t *num) {
secp256k1_scalar_t sc;
random_scalar_order_test(&sc);
secp256k1_scalar_get_num(num, &sc);
}
void test_ecdsa_end_to_end(void) {
unsigned char privkey[32];
unsigned char message[32];
/* Generate a random key and message. */
{
secp256k1_scalar_t msg, key;
random_scalar_order_test(&msg);
random_scalar_order_test(&key);
secp256k1_scalar_get_b32(privkey, &key);
secp256k1_scalar_get_b32(message, &msg);
}
/* Construct and verify corresponding public key. */
CHECK(secp256k1_ec_seckey_verify(privkey) == 1);
unsigned char pubkey[65]; int pubkeylen = 65;
CHECK(secp256k1_ec_pubkey_create(pubkey, &pubkeylen, privkey, secp256k1_rand32() % 2) == 1);
CHECK(secp256k1_ec_pubkey_verify(pubkey, pubkeylen));
/* Verify private key import and export. */
unsigned char seckey[300]; int seckeylen = 300;
CHECK(secp256k1_ec_privkey_export(privkey, seckey, &seckeylen, secp256k1_rand32() % 2) == 1);
unsigned char privkey2[32];
CHECK(secp256k1_ec_privkey_import(privkey2, seckey, seckeylen) == 1);
CHECK(memcmp(privkey, privkey2, 32) == 0);
/* Optionally tweak the keys using addition. */
if (secp256k1_rand32() % 3 == 0) {
unsigned char rnd[32];
secp256k1_rand256_test(rnd);
int ret1 = secp256k1_ec_privkey_tweak_add(privkey, rnd);
int ret2 = secp256k1_ec_pubkey_tweak_add(pubkey, pubkeylen, rnd);
CHECK(ret1 == ret2);
if (ret1 == 0) return;
unsigned char pubkey2[65]; int pubkeylen2 = 65;
CHECK(secp256k1_ec_pubkey_create(pubkey2, &pubkeylen2, privkey, pubkeylen == 33) == 1);
CHECK(memcmp(pubkey, pubkey2, pubkeylen) == 0);
}
/* Optionally tweak the keys using multiplication. */
if (secp256k1_rand32() % 3 == 0) {
unsigned char rnd[32];
secp256k1_rand256_test(rnd);
int ret1 = secp256k1_ec_privkey_tweak_mul(privkey, rnd);
int ret2 = secp256k1_ec_pubkey_tweak_mul(pubkey, pubkeylen, rnd);
CHECK(ret1 == ret2);
if (ret1 == 0) return;
unsigned char pubkey2[65]; int pubkeylen2 = 65;
CHECK(secp256k1_ec_pubkey_create(pubkey2, &pubkeylen2, privkey, pubkeylen == 33) == 1);
CHECK(memcmp(pubkey, pubkey2, pubkeylen) == 0);
}
/* Sign. */
unsigned char signature[72]; int signaturelen = 72;
while(1) {
unsigned char rnd[32];
secp256k1_rand256_test(rnd);
if (secp256k1_ecdsa_sign(message, 32, signature, &signaturelen, privkey, rnd) == 1) {
break;
}
}
/* Verify. */
CHECK(secp256k1_ecdsa_verify(message, 32, signature, signaturelen, pubkey, pubkeylen) == 1);
/* Destroy signature and verify again. */
signature[signaturelen - 1 - secp256k1_rand32() % 20] += 1 + (secp256k1_rand32() % 255);
CHECK(secp256k1_ecdsa_verify(message, 32, signature, signaturelen, pubkey, pubkeylen) != 1);
/* Compact sign. */
unsigned char csignature[64]; int recid = 0;
while(1) {
unsigned char rnd[32];
secp256k1_rand256_test(rnd);
if (secp256k1_ecdsa_sign_compact(message, 32, csignature, privkey, rnd, &recid) == 1) {
break;
}
}
/* Recover. */
unsigned char recpubkey[65]; int recpubkeylen = 0;
CHECK(secp256k1_ecdsa_recover_compact(message, 32, csignature, recpubkey, &recpubkeylen, pubkeylen == 33, recid) == 1);
CHECK(recpubkeylen == pubkeylen);
CHECK(memcmp(pubkey, recpubkey, pubkeylen) == 0);
/* Destroy signature and verify again. */
csignature[secp256k1_rand32() % 64] += 1 + (secp256k1_rand32() % 255);
CHECK(secp256k1_ecdsa_recover_compact(message, 32, csignature, recpubkey, &recpubkeylen, pubkeylen == 33, recid) != 1 ||
memcmp(pubkey, recpubkey, pubkeylen) != 0);
CHECK(recpubkeylen == pubkeylen);
}
void random_sign(secp256k1_ecdsa_sig_t *sig, const secp256k1_scalar_t *key, const secp256k1_scalar_t *msg, int *recid) {
secp256k1_scalar_t nonce;
do {
random_scalar_order_test(&nonce);
} while(!secp256k1_ecdsa_sig_sign(sig, key, msg, &nonce, recid));
}
void scalar_test(void) {
unsigned char c[32];
/* Set 's' to a random scalar, with value 'snum'. */
secp256k1_scalar_t s;
random_scalar_order_test(&s);
/* Set 's1' to a random scalar, with value 's1num'. */
secp256k1_scalar_t s1;
random_scalar_order_test(&s1);
/* Set 's2' to a random scalar, with value 'snum2', and byte array representation 'c'. */
secp256k1_scalar_t s2;
random_scalar_order_test(&s2);
secp256k1_scalar_get_b32(c, &s2);
#ifndef USE_NUM_NONE
secp256k1_num_t snum, s1num, s2num;
secp256k1_scalar_get_num(&snum, &s);
secp256k1_scalar_get_num(&s1num, &s1);
secp256k1_scalar_get_num(&s2num, &s2);
secp256k1_num_t order;
secp256k1_scalar_order_get_num(&order);
secp256k1_num_t half_order = order;
secp256k1_num_shift(&half_order, 1);
#endif
{
/* Test that fetching groups of 4 bits from a scalar and recursing n(i)=16*n(i-1)+p(i) reconstructs it. */
secp256k1_scalar_t n;
secp256k1_scalar_set_int(&n, 0);
for (int i = 0; i < 256; i += 4) {
secp256k1_scalar_t t;
secp256k1_scalar_set_int(&t, secp256k1_scalar_get_bits(&s, 256 - 4 - i, 4));
for (int j = 0; j < 4; j++) {
secp256k1_scalar_add(&n, &n, &n);
}
secp256k1_scalar_add(&n, &n, &t);
}
CHECK(secp256k1_scalar_eq(&n, &s));
}
{
/* Test that fetching groups of randomly-sized bits from a scalar and recursing n(i)=b*n(i-1)+p(i) reconstructs it. */
secp256k1_scalar_t n;
secp256k1_scalar_set_int(&n, 0);
int i = 0;
while (i < 256) {
int now = (secp256k1_rand32() % 15) + 1;
if (now + i > 256) {
now = 256 - i;
}
secp256k1_scalar_t t;
secp256k1_scalar_set_int(&t, secp256k1_scalar_get_bits_var(&s, 256 - now - i, now));
for (int j = 0; j < now; j++) {
secp256k1_scalar_add(&n, &n, &n);
}
secp256k1_scalar_add(&n, &n, &t);
i += now;
}
CHECK(secp256k1_scalar_eq(&n, &s));
}
#ifndef USE_NUM_NONE
{
/* Test that adding the scalars together is equal to adding their numbers together modulo the order. */
secp256k1_num_t rnum;
secp256k1_num_add(&rnum, &snum, &s2num);
secp256k1_num_mod(&rnum, &order);
secp256k1_scalar_t r;
secp256k1_scalar_add(&r, &s, &s2);
secp256k1_num_t r2num;
secp256k1_scalar_get_num(&r2num, &r);
CHECK(secp256k1_num_eq(&rnum, &r2num));
}
{
/* Test that multipying the scalars is equal to multiplying their numbers modulo the order. */
secp256k1_num_t rnum;
secp256k1_num_mul(&rnum, &snum, &s2num);
secp256k1_num_mod(&rnum, &order);
secp256k1_scalar_t r;
secp256k1_scalar_mul(&r, &s, &s2);
secp256k1_num_t r2num;
secp256k1_scalar_get_num(&r2num, &r);
CHECK(secp256k1_num_eq(&rnum, &r2num));
/* The result can only be zero if at least one of the factors was zero. */
CHECK(secp256k1_scalar_is_zero(&r) == (secp256k1_scalar_is_zero(&s) || secp256k1_scalar_is_zero(&s2)));
/* The results can only be equal to one of the factors if that factor was zero, or the other factor was one. */
CHECK(secp256k1_num_eq(&rnum, &snum) == (secp256k1_scalar_is_zero(&s) || secp256k1_scalar_is_one(&s2)));
CHECK(secp256k1_num_eq(&rnum, &s2num) == (secp256k1_scalar_is_zero(&s2) || secp256k1_scalar_is_one(&s)));
}
{
/* Check that comparison with zero matches comparison with zero on the number. */
CHECK(secp256k1_num_is_zero(&snum) == secp256k1_scalar_is_zero(&s));
/* Check that comparison with the half order is equal to testing for high scalar. */
CHECK(secp256k1_scalar_is_high(&s) == (secp256k1_num_cmp(&snum, &half_order) > 0));
secp256k1_scalar_t neg;
secp256k1_scalar_negate(&neg, &s);
secp256k1_num_t negnum;
secp256k1_num_sub(&negnum, &order, &snum);
secp256k1_num_mod(&negnum, &order);
/* Check that comparison with the half order is equal to testing for high scalar after negation. */
CHECK(secp256k1_scalar_is_high(&neg) == (secp256k1_num_cmp(&negnum, &half_order) > 0));
/* Negating should change the high property, unless the value was already zero. */
CHECK((secp256k1_scalar_is_high(&s) == secp256k1_scalar_is_high(&neg)) == secp256k1_scalar_is_zero(&s));
secp256k1_num_t negnum2;
secp256k1_scalar_get_num(&negnum2, &neg);
/* Negating a scalar should be equal to (order - n) mod order on the number. */
CHECK(secp256k1_num_eq(&negnum, &negnum2));
secp256k1_scalar_add(&neg, &neg, &s);
/* Adding a number to its negation should result in zero. */
CHECK(secp256k1_scalar_is_zero(&neg));
secp256k1_scalar_negate(&neg, &neg);
/* Negating zero should still result in zero. */
CHECK(secp256k1_scalar_is_zero(&neg));
}
{
/* Test secp256k1_scalar_mul_shift_var. */
secp256k1_scalar_t r;
unsigned int shift = 256 + (secp256k1_rand32() % 257);
secp256k1_scalar_mul_shift_var(&r, &s1, &s2, shift);
secp256k1_num_t rnum;
secp256k1_num_mul(&rnum, &s1num, &s2num);
secp256k1_num_shift(&rnum, shift - 1);
secp256k1_num_t one;
unsigned char cone[1] = {0x01};
secp256k1_num_set_bin(&one, cone, 1);
secp256k1_num_add(&rnum, &rnum, &one);
secp256k1_num_shift(&rnum, 1);
secp256k1_num_t rnum2;
secp256k1_scalar_get_num(&rnum2, &r);
CHECK(secp256k1_num_eq(&rnum, &rnum2));
}
#endif
{
/* Test that scalar inverses are equal to the inverse of their number modulo the order. */
if (!secp256k1_scalar_is_zero(&s)) {
secp256k1_scalar_t inv;
secp256k1_scalar_inverse(&inv, &s);
#ifndef USE_NUM_NONE
secp256k1_num_t invnum;
secp256k1_num_mod_inverse(&invnum, &snum, &order);
secp256k1_num_t invnum2;
secp256k1_scalar_get_num(&invnum2, &inv);
CHECK(secp256k1_num_eq(&invnum, &invnum2));
#endif
secp256k1_scalar_mul(&inv, &inv, &s);
/* Multiplying a scalar with its inverse must result in one. */
CHECK(secp256k1_scalar_is_one(&inv));
secp256k1_scalar_inverse(&inv, &inv);
/* Inverting one must result in one. */
CHECK(secp256k1_scalar_is_one(&inv));
}
}
{
/* Test commutativity of add. */
secp256k1_scalar_t r1, r2;
secp256k1_scalar_add(&r1, &s1, &s2);
secp256k1_scalar_add(&r2, &s2, &s1);
CHECK(secp256k1_scalar_eq(&r1, &r2));
}
{
/* Test add_bit. */
int bit = secp256k1_rand32() % 256;
secp256k1_scalar_t b;
secp256k1_scalar_set_int(&b, 1);
CHECK(secp256k1_scalar_is_one(&b));
for (int i = 0; i < bit; i++) {
secp256k1_scalar_add(&b, &b, &b);
}
secp256k1_scalar_t r1 = s1, r2 = s1;
if (!secp256k1_scalar_add(&r1, &r1, &b)) {
/* No overflow happened. */
secp256k1_scalar_add_bit(&r2, bit);
CHECK(secp256k1_scalar_eq(&r1, &r2));
}
}
{
/* Test commutativity of mul. */
secp256k1_scalar_t r1, r2;
secp256k1_scalar_mul(&r1, &s1, &s2);
secp256k1_scalar_mul(&r2, &s2, &s1);
CHECK(secp256k1_scalar_eq(&r1, &r2));
}
{
/* Test associativity of add. */
secp256k1_scalar_t r1, r2;
secp256k1_scalar_add(&r1, &s1, &s2);
secp256k1_scalar_add(&r1, &r1, &s);
secp256k1_scalar_add(&r2, &s2, &s);
secp256k1_scalar_add(&r2, &s1, &r2);
CHECK(secp256k1_scalar_eq(&r1, &r2));
}
{
/* Test associativity of mul. */
secp256k1_scalar_t r1, r2;
secp256k1_scalar_mul(&r1, &s1, &s2);
secp256k1_scalar_mul(&r1, &r1, &s);
secp256k1_scalar_mul(&r2, &s2, &s);
secp256k1_scalar_mul(&r2, &s1, &r2);
CHECK(secp256k1_scalar_eq(&r1, &r2));
}
{
/* Test distributitivity of mul over add. */
secp256k1_scalar_t r1, r2, t;
secp256k1_scalar_add(&r1, &s1, &s2);
secp256k1_scalar_mul(&r1, &r1, &s);
secp256k1_scalar_mul(&r2, &s1, &s);
secp256k1_scalar_mul(&t, &s2, &s);
secp256k1_scalar_add(&r2, &r2, &t);
CHECK(secp256k1_scalar_eq(&r1, &r2));
}
{
/* Test square. */
secp256k1_scalar_t r1, r2;
secp256k1_scalar_sqr(&r1, &s1);
secp256k1_scalar_mul(&r2, &s1, &s1);
CHECK(secp256k1_scalar_eq(&r1, &r2));
}
}
