int secp256k1_ecdsa_pubkey_tweak_mul(unsigned char *pubkey, int pubkeylen, const unsigned char *tweak) {
int ret = 1;
secp256k1_num_t factor;
secp256k1_num_init(&factor);
secp256k1_num_set_bin(&factor, tweak, 32);
if (secp256k1_num_is_zero(&factor))
ret = 0;
if (secp256k1_num_cmp(&factor, &secp256k1_ge_consts->order) >= 0)
ret = 0;
secp256k1_ge_t p;
if (ret) {
if (!secp256k1_ecdsa_pubkey_parse(&p, pubkey, pubkeylen))
ret = 0;
}
if (ret) {
secp256k1_num_t zero;
secp256k1_num_init(&zero);
secp256k1_num_set_int(&zero, 0);
secp256k1_gej_t pt;
secp256k1_gej_set_ge(&pt, &p);
secp256k1_ecmult(&pt, &pt, &factor, &zero);
secp256k1_num_free(&zero);
secp256k1_ge_set_gej(&p, &pt);
int oldlen = pubkeylen;
secp256k1_ecdsa_pubkey_serialize(&p, pubkey, &pubkeylen, oldlen <= 33);
assert(pubkeylen == oldlen);
}
secp256k1_num_free(&factor);
return ret;
}
int secp256k1_ecdsa_privkey_tweak_add(unsigned char *seckey, const unsigned char *tweak) {
DEBUG_CHECK(seckey != NULL);
DEBUG_CHECK(tweak != NULL);
int ret = 1;
secp256k1_num_t term;
secp256k1_num_init(&term);
secp256k1_num_set_bin(&term, tweak, 32);
if (secp256k1_num_cmp(&term, &secp256k1_ge_consts->order) >= 0)
ret = 0;
secp256k1_num_t sec;
secp256k1_num_init(&sec);
if (ret) {
secp256k1_num_set_bin(&sec, seckey, 32);
secp256k1_num_add(&sec, &sec, &term);
secp256k1_num_mod(&sec, &secp256k1_ge_consts->order);
if (secp256k1_num_is_zero(&sec))
ret = 0;
}
if (ret)
secp256k1_num_get_bin(seckey, 32, &sec);
secp256k1_num_clear(&sec);
secp256k1_num_clear(&term);
secp256k1_num_free(&sec);
secp256k1_num_free(&term);
return ret;
}
void test_wnaf(const secp256k1_num_t *number, int w) {
secp256k1_num_t x, two, t;
secp256k1_num_init(&x);
secp256k1_num_init(&two);
secp256k1_num_init(&t);
secp256k1_num_set_int(&x, 0);
secp256k1_num_set_int(&two, 2);
int wnaf[257];
int bits = secp256k1_ecmult_wnaf(wnaf, number, w);
int zeroes = -1;
for (int i=bits-1; i>=0; i--) {
secp256k1_num_mul(&x, &x, &two);
int v = wnaf[i];
if (v) {
assert(zeroes == -1 || zeroes >= w-1); // check that distance between non-zero elements is at least w-1
zeroes=0;
assert((v & 1) == 1); // check non-zero elements are odd
assert(v <= (1 << (w-1)) - 1); // check range below
assert(v >= -(1 << (w-1)) - 1); // check range above
} else {
assert(zeroes != -1); // check that no unnecessary zero padding exists
zeroes++;
}
secp256k1_num_set_int(&t, v);
secp256k1_num_add(&x, &x, &t);
}
assert(secp256k1_num_cmp(&x, number) == 0); // check that wnaf represents number
secp256k1_num_free(&x);
secp256k1_num_free(&two);
secp256k1_num_free(&t);
}
int secp256k1_ecdsa_sign(const unsigned char *message, int messagelen, unsigned char *signature, int *signaturelen, const unsigned char *seckey, const unsigned char *nonce) {
secp256k1_num_t sec, non, msg;
secp256k1_num_init(&sec);
secp256k1_num_init(&non);
secp256k1_num_init(&msg);
secp256k1_num_set_bin(&sec, seckey, 32);
secp256k1_num_set_bin(&non, nonce, 32);
secp256k1_num_set_bin(&msg, message, messagelen);
int ret = !secp256k1_num_is_zero(&non) &&
(secp256k1_num_cmp(&non, &secp256k1_ge_consts->order) < 0);
secp256k1_ecdsa_sig_t sig;
secp256k1_ecdsa_sig_init(&sig);
if (ret) {
ret = secp256k1_ecdsa_sig_sign(&sig, &sec, &msg, &non, NULL);
}
if (ret) {
secp256k1_ecdsa_sig_serialize(signature, signaturelen, &sig);
}
secp256k1_ecdsa_sig_free(&sig);
secp256k1_num_clear(&msg);
secp256k1_num_clear(&non);
secp256k1_num_clear(&sec);
secp256k1_num_free(&msg);
secp256k1_num_free(&non);
secp256k1_num_free(&sec);
return ret;
}
int secp256k1_ecdsa_pubkey_tweak_add(unsigned char *pubkey, int pubkeylen, const unsigned char *tweak) {
DEBUG_CHECK(secp256k1_ecmult_consts != NULL);
DEBUG_CHECK(pubkey != NULL);
DEBUG_CHECK(tweak != NULL);
int ret = 1;
secp256k1_num_t term;
secp256k1_num_init(&term);
secp256k1_num_set_bin(&term, tweak, 32);
if (secp256k1_num_cmp(&term, &secp256k1_ge_consts->order) >= 0)
ret = 0;
secp256k1_ge_t p;
if (ret) {
if (!secp256k1_ecdsa_pubkey_parse(&p, pubkey, pubkeylen))
ret = 0;
}
if (ret) {
secp256k1_gej_t pt;
secp256k1_gej_set_ge(&pt, &p);
secp256k1_num_t one;
secp256k1_num_init(&one);
secp256k1_num_set_int(&one, 1);
secp256k1_ecmult(&pt, &pt, &one, &term);
secp256k1_num_free(&one);
if (secp256k1_gej_is_infinity(&pt))
ret = 0;
secp256k1_ge_set_gej(&p, &pt);
int oldlen = pubkeylen;
secp256k1_ecdsa_pubkey_serialize(&p, pubkey, &pubkeylen, oldlen <= 33);
VERIFY_CHECK(pubkeylen == oldlen);
}
secp256k1_num_free(&term);
return ret;
}
int secp256k1_ecdsa_sign_compact(const unsigned char *message, int messagelen, unsigned char *sig64, const unsigned char *seckey, const unsigned char *nonce, int *recid) {
secp256k1_num_t sec, non, msg;
secp256k1_num_init(&sec);
secp256k1_num_init(&non);
secp256k1_num_init(&msg);
secp256k1_num_set_bin(&sec, seckey, 32);
secp256k1_num_set_bin(&non, nonce, 32);
secp256k1_num_set_bin(&msg, message, messagelen);
int ret = !secp256k1_num_is_zero(&non) &&
(secp256k1_num_cmp(&non, &secp256k1_ge_consts->order) < 0);
secp256k1_ecdsa_sig_t sig;
secp256k1_ecdsa_sig_init(&sig);
if (ret) {
ret = secp256k1_ecdsa_sig_sign(&sig, &sec, &msg, &non, recid);
}
if (ret) {
secp256k1_num_get_bin(sig64, 32, &sig.r);
secp256k1_num_get_bin(sig64 + 32, 32, &sig.s);
}
secp256k1_ecdsa_sig_free(&sig);
secp256k1_num_clear(&msg);
secp256k1_num_clear(&non);
secp256k1_num_clear(&sec);
secp256k1_num_free(&msg);
secp256k1_num_free(&non);
secp256k1_num_free(&sec);
return ret;
}
void test_ecdsa_openssl() {
const secp256k1_ge_consts_t *c = secp256k1_ge_consts;
secp256k1_num_t key, msg;
secp256k1_num_init(&msg);
unsigned char message[32];
secp256k1_rand256_test(message);
secp256k1_num_set_bin(&msg, message, 32);
secp256k1_num_init(&key);
random_num_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);
assert(ec_key);
unsigned char signature[80];
int sigsize = 80;
assert(ECDSA_sign(0, message, sizeof(message), signature, &sigsize, ec_key));
secp256k1_ecdsa_sig_t sig;
secp256k1_ecdsa_sig_init(&sig);
assert(secp256k1_ecdsa_sig_parse(&sig, signature, sigsize));
assert(secp256k1_ecdsa_sig_verify(&sig, &q, &msg));
secp256k1_num_inc(&sig.r);
assert(!secp256k1_ecdsa_sig_verify(&sig, &q, &msg));
random_sign(&sig, &key, &msg, NULL);
sigsize = 80;
assert(secp256k1_ecdsa_sig_serialize(signature, &sigsize, &sig));
assert(ECDSA_verify(0, message, sizeof(message), signature, sigsize, ec_key) == 1);
secp256k1_ecdsa_sig_free(&sig);
EC_KEY_free(ec_key);
secp256k1_num_free(&key);
secp256k1_num_free(&msg);
}
void test_num_copy_inc_cmp() {
secp256k1_num_t n1,n2;
secp256k1_num_init(&n1);
secp256k1_num_init(&n2);
random_num_order(&n1);
secp256k1_num_copy(&n2, &n1);
assert(secp256k1_num_cmp(&n1, &n2) == 0);
assert(secp256k1_num_cmp(&n2, &n1) == 0);
secp256k1_num_inc(&n2);
assert(secp256k1_num_cmp(&n1, &n2) != 0);
assert(secp256k1_num_cmp(&n2, &n1) != 0);
secp256k1_num_free(&n1);
secp256k1_num_free(&n2);
}
int secp256k1_ecdsa_verify(const unsigned char *msg, int msglen, const unsigned char *sig, int siglen, const unsigned char *pubkey, int pubkeylen) {
int ret = -3;
secp256k1_num_t m;
secp256k1_num_init(&m);
secp256k1_ecdsa_sig_t s;
secp256k1_ecdsa_sig_init(&s);
secp256k1_ge_t q;
secp256k1_num_set_bin(&m, msg, msglen);
if (!secp256k1_ecdsa_pubkey_parse(&q, pubkey, pubkeylen)) {
ret = -1;
goto end;
}
if (!secp256k1_ecdsa_sig_parse(&s, sig, siglen)) {
ret = -2;
goto end;
}
if (!secp256k1_ecdsa_sig_verify(&s, &q, &m)) {
ret = 0;
goto end;
}
ret = 1;
end:
secp256k1_ecdsa_sig_free(&s);
secp256k1_num_free(&m);
return ret;
}
int secp256k1_ecdsa_pubkey_tweak_add(unsigned char *pubkey, int pubkeylen, const unsigned char *tweak) {
int ret = 1;
secp256k1_num_t term;
secp256k1_num_init(&term);
secp256k1_num_set_bin(&term, tweak, 32);
if (secp256k1_num_cmp(&term, &secp256k1_ge_consts->order) >= 0)
ret = 0;
secp256k1_ge_t p;
if (ret) {
if (!secp256k1_ecdsa_pubkey_parse(&p, pubkey, pubkeylen))
ret = 0;
}
if (ret) {
secp256k1_gej_t pt;
secp256k1_ecmult_gen(&pt, &term);
secp256k1_gej_add_ge(&pt, &pt, &p);
if (secp256k1_gej_is_infinity(&pt))
ret = 0;
secp256k1_ge_set_gej(&p, &pt);
int oldlen = pubkeylen;
secp256k1_ecdsa_pubkey_serialize(&p, pubkey, &pubkeylen, oldlen <= 33);
assert(pubkeylen == oldlen);
}
secp256k1_num_free(&term);
return ret;
}
int secp256k1_ecdsa_recover_compact(const unsigned char *msg, int msglen, const unsigned char *sig64, unsigned char *pubkey, int *pubkeylen, int compressed, int recid) {
DEBUG_CHECK(secp256k1_ecmult_consts != NULL);
DEBUG_CHECK(msg != NULL);
DEBUG_CHECK(msglen <= 32);
DEBUG_CHECK(sig64 != NULL);
DEBUG_CHECK(pubkey != NULL);
DEBUG_CHECK(pubkeylen != NULL);
DEBUG_CHECK(recid >= 0 && recid <= 3);
int ret = 0;
secp256k1_num_t m;
secp256k1_num_init(&m);
secp256k1_ecdsa_sig_t sig;
secp256k1_ecdsa_sig_init(&sig);
secp256k1_num_set_bin(&sig.r, sig64, 32);
secp256k1_num_set_bin(&sig.s, sig64 + 32, 32);
secp256k1_num_set_bin(&m, msg, msglen);
secp256k1_ge_t q;
if (secp256k1_ecdsa_sig_recover(&sig, &q, &m, recid)) {
secp256k1_ecdsa_pubkey_serialize(&q, pubkey, pubkeylen, compressed);
ret = 1;
}
secp256k1_ecdsa_sig_free(&sig);
secp256k1_num_free(&m);
return ret;
}
void random_sign(secp256k1_ecdsa_sig_t *sig, const secp256k1_num_t *key, const secp256k1_num_t *msg, int *recid) {
secp256k1_num_t nonce;
secp256k1_num_init(&nonce);
do {
random_num_order_test(&nonce);
} while(!secp256k1_ecdsa_sig_sign(sig, key, msg, &nonce, recid));
secp256k1_num_free(&nonce);
}
int secp256k1_ecdsa_privkey_export(const unsigned char *seckey, unsigned char *privkey, int *privkeylen, int compressed) {
secp256k1_num_t key;
secp256k1_num_init(&key);
secp256k1_num_set_bin(&key, seckey, 32);
int ret = secp256k1_ecdsa_privkey_serialize(privkey, privkeylen, &key, compressed);
secp256k1_num_free(&key);
return ret;
}
int secp256k1_ecdsa_seckey_verify(const unsigned char *seckey) {
secp256k1_num_t sec;
secp256k1_num_init(&sec);
secp256k1_num_set_bin(&sec, seckey, 32);
int ret = !secp256k1_num_is_zero(&sec) &&
(secp256k1_num_cmp(&sec, &secp256k1_ge_consts->order) < 0);
secp256k1_num_free(&sec);
return ret;
}
int secp256k1_ecdsa_privkey_import(unsigned char *seckey, const unsigned char *privkey, int privkeylen) {
secp256k1_num_t key;
secp256k1_num_init(&key);
int ret = secp256k1_ecdsa_privkey_parse(&key, privkey, privkeylen);
if (ret)
secp256k1_num_get_bin(seckey, 32, &key);
secp256k1_num_free(&key);
return ret;
}
void test_ecdsa_sign_verify() {
const secp256k1_ge_consts_t *c = secp256k1_ge_consts;
secp256k1_num_t msg, key;
secp256k1_num_init(&msg);
random_num_order_test(&msg);
secp256k1_num_init(&key);
random_num_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;
secp256k1_ecdsa_sig_init(&sig);
random_sign(&sig, &key, &msg, NULL);
assert(secp256k1_ecdsa_sig_verify(&sig, &pub, &msg));
secp256k1_num_inc(&msg);
assert(!secp256k1_ecdsa_sig_verify(&sig, &pub, &msg));
secp256k1_ecdsa_sig_free(&sig);
secp256k1_num_free(&msg);
secp256k1_num_free(&key);
}
void test_point_times_order(const secp256k1_gej_t *point) {
// multiplying a point by the order results in O
const secp256k1_num_t *order = &secp256k1_ge_consts->order;
secp256k1_num_t zero;
secp256k1_num_init(&zero);
secp256k1_num_set_int(&zero, 0);
secp256k1_gej_t res;
secp256k1_ecmult(&res, point, order, order); // calc res = order * point + order * G;
assert(secp256k1_gej_is_infinity(&res));
secp256k1_num_free(&zero);
}
void run_wnaf() {
secp256k1_num_t n;
secp256k1_num_init(&n);
for (int i=0; i<count; i++) {
random_num_order(&n);
if (i % 1)
secp256k1_num_negate(&n);
test_wnaf(&n, 4+(i%10));
}
secp256k1_num_free(&n);
}
int secp256k1_ecdsa_privkey_tweak_mul(unsigned char *seckey, const unsigned char *tweak) {
int ret = 1;
secp256k1_num_t factor;
secp256k1_num_init(&factor);
secp256k1_num_set_bin(&factor, tweak, 32);
if (secp256k1_num_is_zero(&factor))
ret = 0;
if (secp256k1_num_cmp(&factor, &secp256k1_ge_consts->order) >= 0)
ret = 0;
secp256k1_num_t sec;
secp256k1_num_init(&sec);
if (ret) {
secp256k1_num_set_bin(&sec, seckey, 32);
secp256k1_num_mod_mul(&sec, &sec, &factor, &secp256k1_ge_consts->order);
}
if (ret)
secp256k1_num_get_bin(seckey, 32, &sec);
secp256k1_num_free(&sec);
secp256k1_num_free(&factor);
return ret;
}
void test_num_add_sub() {
secp256k1_num_t n1;
secp256k1_num_t n2;
secp256k1_num_init(&n1);
secp256k1_num_init(&n2);
random_num_order_test(&n1); // n1 = R1
random_num_negate(&n1);
random_num_order_test(&n2); // n2 = R2
random_num_negate(&n2);
secp256k1_num_t n1p2, n2p1, n1m2, n2m1;
secp256k1_num_init(&n1p2);
secp256k1_num_init(&n2p1);
secp256k1_num_init(&n1m2);
secp256k1_num_init(&n2m1);
secp256k1_num_add(&n1p2, &n1, &n2); // n1p2 = R1 + R2
secp256k1_num_add(&n2p1, &n2, &n1); // n2p1 = R2 + R1
secp256k1_num_sub(&n1m2, &n1, &n2); // n1m2 = R1 - R2
secp256k1_num_sub(&n2m1, &n2, &n1); // n2m1 = R2 - R1
assert(secp256k1_num_cmp(&n1p2, &n2p1) == 0);
assert(secp256k1_num_cmp(&n1p2, &n1m2) != 0);
secp256k1_num_negate(&n2m1); // n2m1 = -R2 + R1
assert(secp256k1_num_cmp(&n2m1, &n1m2) == 0);
assert(secp256k1_num_cmp(&n2m1, &n1) != 0);
secp256k1_num_add(&n2m1, &n2m1, &n2); // n2m1 = -R2 + R1 + R2 = R1
assert(secp256k1_num_cmp(&n2m1, &n1) == 0);
assert(secp256k1_num_cmp(&n2p1, &n1) != 0);
secp256k1_num_sub(&n2p1, &n2p1, &n2); // n2p1 = R2 + R1 - R2 = R1
assert(secp256k1_num_cmp(&n2p1, &n1) == 0);
secp256k1_num_free(&n2m1);
secp256k1_num_free(&n1m2);
secp256k1_num_free(&n2p1);
secp256k1_num_free(&n1p2);
secp256k1_num_free(&n2);
secp256k1_num_free(&n1);
}
int secp256k1_ecdsa_pubkey_create(unsigned char *pubkey, int *pubkeylen, const unsigned char *seckey, int compressed) {
secp256k1_num_t sec;
secp256k1_num_init(&sec);
secp256k1_num_set_bin(&sec, seckey, 32);
secp256k1_gej_t pj;
secp256k1_ecmult_gen(&pj, &sec);
secp256k1_num_clear(&sec);
secp256k1_num_free(&sec);
secp256k1_ge_t p;
secp256k1_ge_set_gej(&p, &pj);
secp256k1_ecdsa_pubkey_serialize(&p, pubkey, pubkeylen, compressed);
return 1;
}
void run_num_int() {
secp256k1_num_t n1;
secp256k1_num_init(&n1);
for (int i=-255; i<256; i++) {
unsigned char c1[3] = {};
c1[2] = abs(i);
unsigned char c2[3] = {0x11,0x22,0x33};
secp256k1_num_set_int(&n1, i);
secp256k1_num_get_bin(c2, 3, &n1);
assert(memcmp(c1, c2, 3) == 0);
}
secp256k1_num_free(&n1);
}
int main() {
secp256k1_fe_start();
secp256k1_ge_start();
secp256k1_ecmult_start();
secp256k1_fe_t x;
const secp256k1_num_t *order = &secp256k1_ge_consts->order;
secp256k1_num_t r, s, m;
secp256k1_num_init(&r);
secp256k1_num_init(&s);
secp256k1_num_init(&m);
secp256k1_ecdsa_sig_t sig;
secp256k1_ecdsa_sig_init(&sig);
secp256k1_fe_set_hex(&x, "a357ae915c4a65281309edf20504740f0eb3343990216b4f81063cb65f2f7e0f", 64);
int cnt = 0;
int good = 0;
for (int i=0; i<1000000; i++) {
random_num_order(&r);
random_num_order(&s);
random_num_order(&m);
secp256k1_ecdsa_sig_set_rs(&sig, &r, &s);
secp256k1_ge_t pubkey; secp256k1_ge_set_xo(&pubkey, &x, 1);
if (secp256k1_ge_is_valid(&pubkey)) {
cnt++;
good += secp256k1_ecdsa_sig_verify(&sig, &pubkey, &m);
}
}
printf("%i/%i\n", good, cnt);
secp256k1_num_free(&r);
secp256k1_num_free(&s);
secp256k1_num_free(&m);
secp256k1_ecdsa_sig_free(&sig);
secp256k1_ecmult_stop();
secp256k1_ge_stop();
secp256k1_fe_stop();
return 0;
}
void test_num_get_set_bin() {
secp256k1_num_t n1,n2;
secp256k1_num_init(&n1);
secp256k1_num_init(&n2);
random_num_order_test(&n1);
unsigned char c[32];
secp256k1_num_get_bin(c, 32, &n1);
secp256k1_num_set_bin(&n2, c, 32);
assert(secp256k1_num_cmp(&n1, &n2) == 0);
for (int i=0; i<32; i++) {
// check whether the lower 8 bits correspond to the last byte
int low1 = secp256k1_num_shift(&n1, 8);
int low2 = c[31];
assert(low1 == low2);
// shift bits off the byte representation, and compare
memmove(c+1, c, 31);
c[0] = 0;
secp256k1_num_set_bin(&n2, c, 32);
assert(secp256k1_num_cmp(&n1, &n2) == 0);
}
secp256k1_num_free(&n2);
secp256k1_num_free(&n1);
}
void test_num_negate() {
secp256k1_num_t n1;
secp256k1_num_t n2;
secp256k1_num_init(&n1);
secp256k1_num_init(&n2);
random_num_order_test(&n1); // n1 = R
random_num_negate(&n1);
secp256k1_num_copy(&n2, &n1); // n2 = R
secp256k1_num_sub(&n1, &n2, &n1); // n1 = n2-n1 = 0
assert(secp256k1_num_is_zero(&n1));
secp256k1_num_copy(&n1, &n2); // n1 = R
secp256k1_num_negate(&n1); // n1 = -R
assert(!secp256k1_num_is_zero(&n1));
secp256k1_num_add(&n1, &n2, &n1); // n1 = n2+n1 = 0
assert(secp256k1_num_is_zero(&n1));
secp256k1_num_copy(&n1, &n2); // n1 = R
secp256k1_num_negate(&n1); // n1 = -R
assert(secp256k1_num_is_neg(&n1) != secp256k1_num_is_neg(&n2));
secp256k1_num_negate(&n1); // n1 = R
assert(secp256k1_num_cmp(&n1, &n2) == 0);
assert(secp256k1_num_is_neg(&n1) == secp256k1_num_is_neg(&n2));
secp256k1_num_free(&n2);
secp256k1_num_free(&n1);
}
void test_num_get_set_hex() {
secp256k1_num_t n1,n2;
secp256k1_num_init(&n1);
secp256k1_num_init(&n2);
random_num_order_test(&n1);
char c[64];
secp256k1_num_get_hex(c, 64, &n1);
secp256k1_num_set_hex(&n2, c, 64);
assert(secp256k1_num_cmp(&n1, &n2) == 0);
for (int i=0; i<64; i++) {
// check whether the lower 4 bits correspond to the last hex character
int low1 = secp256k1_num_shift(&n1, 4);
int lowh = c[63];
int low2 = (lowh>>6)*9+(lowh-'0')&15;
assert(low1 == low2);
// shift bits off the hex representation, and compare
memmove(c+1, c, 63);
c[0] = '0';
secp256k1_num_set_hex(&n2, c, 64);
assert(secp256k1_num_cmp(&n1, &n2) == 0);
}
secp256k1_num_free(&n2);
secp256k1_num_free(&n1);
}
int secp256k1_ecdsa_recover_compact(const unsigned char *msg, int msglen, const unsigned char *sig64, unsigned char *pubkey, int *pubkeylen, int compressed, int recid) {
int ret = 0;
secp256k1_num_t m;
secp256k1_num_init(&m);
secp256k1_ecdsa_sig_t sig;
secp256k1_ecdsa_sig_init(&sig);
secp256k1_num_set_bin(&sig.r, sig64, 32);
secp256k1_num_set_bin(&sig.s, sig64 + 32, 32);
secp256k1_num_set_bin(&m, msg, msglen);
secp256k1_ge_t q;
if (secp256k1_ecdsa_sig_recover(&sig, &q, &m, recid)) {
secp256k1_ecdsa_pubkey_serialize(&q, pubkey, pubkeylen, compressed);
ret = 1;
}
secp256k1_ecdsa_sig_free(&sig);
secp256k1_num_free(&m);
return ret;
}
void run_ecmult_chain() {
// random starting point A (on the curve)
secp256k1_fe_t ax; secp256k1_fe_set_hex(&ax, "8b30bbe9ae2a990696b22f670709dff3727fd8bc04d3362c6c7bf458e2846004", 64);
secp256k1_fe_t ay; secp256k1_fe_set_hex(&ay, "a357ae915c4a65281309edf20504740f0eb3343990216b4f81063cb65f2f7e0f", 64);
secp256k1_gej_t a; secp256k1_gej_set_xy(&a, &ax, &ay);
// two random initial factors xn and gn
secp256k1_num_t xn;
secp256k1_num_init(&xn);
secp256k1_num_set_hex(&xn, "84cc5452f7fde1edb4d38a8ce9b1b84ccef31f146e569be9705d357a42985407", 64);
secp256k1_num_t gn;
secp256k1_num_init(&gn);
secp256k1_num_set_hex(&gn, "a1e58d22553dcd42b23980625d4c57a96e9323d42b3152e5ca2c3990edc7c9de", 64);
// two small multipliers to be applied to xn and gn in every iteration:
secp256k1_num_t xf;
secp256k1_num_init(&xf);
secp256k1_num_set_hex(&xf, "1337", 4);
secp256k1_num_t gf;
secp256k1_num_init(&gf);
secp256k1_num_set_hex(&gf, "7113", 4);
// accumulators with the resulting coefficients to A and G
secp256k1_num_t ae;
secp256k1_num_init(&ae);
secp256k1_num_set_int(&ae, 1);
secp256k1_num_t ge;
secp256k1_num_init(&ge);
secp256k1_num_set_int(&ge, 0);
// the point being computed
secp256k1_gej_t x = a;
const secp256k1_num_t *order = &secp256k1_ge_consts->order;
for (int i=0; i<200*count; i++) {
// in each iteration, compute X = xn*X + gn*G;
secp256k1_ecmult(&x, &x, &xn, &gn);
// also compute ae and ge: the actual accumulated factors for A and G
// if X was (ae*A+ge*G), xn*X + gn*G results in (xn*ae*A + (xn*ge+gn)*G)
secp256k1_num_mod_mul(&ae, &ae, &xn, order);
secp256k1_num_mod_mul(&ge, &ge, &xn, order);
secp256k1_num_add(&ge, &ge, &gn);
secp256k1_num_mod(&ge, order);
// modify xn and gn
secp256k1_num_mod_mul(&xn, &xn, &xf, order);
secp256k1_num_mod_mul(&gn, &gn, &gf, order);
// verify
if (i == 19999) {
char res[132]; int resl = 132;
secp256k1_gej_get_hex(res, &resl, &x);
assert(strcmp(res, "(D6E96687F9B10D092A6F35439D86CEBEA4535D0D409F53586440BD74B933E830,B95CBCA2C77DA786539BE8FD53354D2D3B4F566AE658045407ED6015EE1B2A88)") == 0);
}
}
// redo the computation, but directly with the resulting ae and ge coefficients:
secp256k1_gej_t x2; secp256k1_ecmult(&x2, &a, &ae, &ge);
char res[132]; int resl = 132;
char res2[132]; int resl2 = 132;
secp256k1_gej_get_hex(res, &resl, &x);
secp256k1_gej_get_hex(res2, &resl2, &x2);
assert(strcmp(res, res2) == 0);
assert(strlen(res) == 131);
secp256k1_num_free(&xn);
secp256k1_num_free(&gn);
secp256k1_num_free(&xf);
secp256k1_num_free(&gf);
secp256k1_num_free(&ae);
secp256k1_num_free(&ge);
}