#include #include "impl/num.h" #include "impl/field.h" #include "impl/group.h" #include "impl/ecmult.h" #include "impl/ecdsa.h" // #define COUNT 2 #define COUNT 100 void test_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, &ge, order); // modify xn and gn secp256k1_num_mod_mul(&xn, &xn, &xf, order); secp256k1_num_mod_mul(&gn, &gn, &gf, order); } char res[132]; int resl = 132; secp256k1_gej_get_hex(res, &resl, &x); if (COUNT == 100) { 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 res2[132]; int resl2 = 132; 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); } void test_point_times_order(const secp256k1_gej_t *point) { // either the point is not on the curve, or multiplying it by the order results in O if (!secp256k1_gej_is_valid(point)) return; 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 test_run_point_times_order() { secp256k1_fe_t x; secp256k1_fe_set_hex(&x, "02", 2); for (int i=0; i<500; i++) { secp256k1_gej_t j; secp256k1_gej_set_xo(&j, &x, 1); test_point_times_order(&j); secp256k1_fe_sqr(&x, &x); } char c[65]; int cl=65; secp256k1_fe_get_hex(c, &cl, &x); assert(strcmp(c, "7603CB59B0EF6C63FE6084792A0C378CDB3233A80F8A9A09A877DEAD31B38C45") == 0); } 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[1024]; 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); } void test_run_wnaf() { secp256k1_num_t range, min, n; secp256k1_num_init(&range); secp256k1_num_init(&min); secp256k1_num_init(&n); secp256k1_num_set_hex(&range, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF", 256); secp256k1_num_copy(&min, &range); secp256k1_num_shift(&min, 1); secp256k1_num_negate(&min); for (int i=0; iorder); secp256k1_num_init(&key); secp256k1_num_set_rand(&key, &c->order); secp256k1_num_init(&nonce); secp256k1_gej_t pub; secp256k1_ecmult_gen(&pub, &key); secp256k1_ecdsa_sig_t sig; secp256k1_ecdsa_sig_init(&sig); do { secp256k1_num_set_rand(&nonce, &c->order); } while(!secp256k1_ecdsa_sig_sign(&sig, &key, &msg, &nonce)); 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); secp256k1_num_free(&nonce); } void test_run_ecdsa_sign_verify() { for (int i=0; i<10*COUNT; i++) { test_ecdsa_sign_verify(); } } int main(void) { secp256k1_num_start(); secp256k1_fe_start(); secp256k1_ge_start(); secp256k1_ecmult_start(); test_run_wnaf(); test_run_point_times_order(); test_run_ecmult_chain(); test_run_ecdsa_sign_verify(); secp256k1_ecmult_stop(); secp256k1_ge_stop(); secp256k1_fe_stop(); secp256k1_num_stop(); return 0; }