int ec_GFp_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx) { int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *); int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); const BIGNUM *p; BN_CTX *new_ctx = NULL; BIGNUM *n0, *n1, *n2, *n3, *n4, *n5, *n6; int ret = 0; if (a == b) return EC_POINT_dbl(group, r, a, ctx); if (EC_POINT_is_at_infinity(group, a)) return EC_POINT_copy(r, b); if (EC_POINT_is_at_infinity(group, b)) return EC_POINT_copy(r, a); field_mul = group->meth->field_mul; field_sqr = group->meth->field_sqr; p = group->field; if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) return 0; } BN_CTX_start(ctx); n0 = BN_CTX_get(ctx); n1 = BN_CTX_get(ctx); n2 = BN_CTX_get(ctx); n3 = BN_CTX_get(ctx); n4 = BN_CTX_get(ctx); n5 = BN_CTX_get(ctx); n6 = BN_CTX_get(ctx); if (n6 == NULL) goto end; /* * Note that in this function we must not read components of 'a' or 'b' * once we have written the corresponding components of 'r'. ('r' might * be one of 'a' or 'b'.) */ /* n1, n2 */ if (b->Z_is_one) { if (!BN_copy(n1, a->X)) goto end; if (!BN_copy(n2, a->Y)) goto end; /* n1 = X_a */ /* n2 = Y_a */ } else { if (!field_sqr(group, n0, b->Z, ctx)) goto end; if (!field_mul(group, n1, a->X, n0, ctx)) goto end; /* n1 = X_a * Z_b^2 */ if (!field_mul(group, n0, n0, b->Z, ctx)) goto end; if (!field_mul(group, n2, a->Y, n0, ctx)) goto end; /* n2 = Y_a * Z_b^3 */ } /* n3, n4 */ if (a->Z_is_one) { if (!BN_copy(n3, b->X)) goto end; if (!BN_copy(n4, b->Y)) goto end; /* n3 = X_b */ /* n4 = Y_b */ } else { if (!field_sqr(group, n0, a->Z, ctx)) goto end; if (!field_mul(group, n3, b->X, n0, ctx)) goto end; /* n3 = X_b * Z_a^2 */ if (!field_mul(group, n0, n0, a->Z, ctx)) goto end; if (!field_mul(group, n4, b->Y, n0, ctx)) goto end; /* n4 = Y_b * Z_a^3 */ } /* n5, n6 */ if (!BN_mod_sub_quick(n5, n1, n3, p)) goto end; if (!BN_mod_sub_quick(n6, n2, n4, p)) goto end; /* n5 = n1 - n3 */ /* n6 = n2 - n4 */ if (BN_is_zero(n5)) { if (BN_is_zero(n6)) { /* a is the same point as b */ BN_CTX_end(ctx); ret = EC_POINT_dbl(group, r, a, ctx); ctx = NULL; goto end; } else { /* a is the inverse of b */ BN_zero(r->Z); r->Z_is_one = 0; ret = 1; goto end; } } /* 'n7', 'n8' */ if (!BN_mod_add_quick(n1, n1, n3, p)) goto end; if (!BN_mod_add_quick(n2, n2, n4, p)) goto end; /* 'n7' = n1 + n3 */ /* 'n8' = n2 + n4 */ /* Z_r */ if (a->Z_is_one && b->Z_is_one) { if (!BN_copy(r->Z, n5)) goto end; } else { if (a->Z_is_one) { if (!BN_copy(n0, b->Z)) goto end; } else if (b->Z_is_one) { if (!BN_copy(n0, a->Z)) goto end; } else { if (!field_mul(group, n0, a->Z, b->Z, ctx)) goto end; } if (!field_mul(group, r->Z, n0, n5, ctx)) goto end; } r->Z_is_one = 0; /* Z_r = Z_a * Z_b * n5 */ /* X_r */ if (!field_sqr(group, n0, n6, ctx)) goto end; if (!field_sqr(group, n4, n5, ctx)) goto end; if (!field_mul(group, n3, n1, n4, ctx)) goto end; if (!BN_mod_sub_quick(r->X, n0, n3, p)) goto end; /* X_r = n6^2 - n5^2 * 'n7' */ /* 'n9' */ if (!BN_mod_lshift1_quick(n0, r->X, p)) goto end; if (!BN_mod_sub_quick(n0, n3, n0, p)) goto end; /* n9 = n5^2 * 'n7' - 2 * X_r */ /* Y_r */ if (!field_mul(group, n0, n0, n6, ctx)) goto end; if (!field_mul(group, n5, n4, n5, ctx)) goto end; /* now n5 is n5^3 */ if (!field_mul(group, n1, n2, n5, ctx)) goto end; if (!BN_mod_sub_quick(n0, n0, n1, p)) goto end; if (BN_is_odd(n0)) if (!BN_add(n0, n0, p)) goto end; /* now 0 <= n0 < 2*p, and n0 is even */ if (!BN_rshift1(r->Y, n0)) goto end; /* Y_r = (n6 * 'n9' - 'n8' * 'n5^3') / 2 */ ret = 1; end: if (ctx) /* otherwise we already called BN_CTX_end */ BN_CTX_end(ctx); BN_CTX_free(new_ctx); return ret; }
int ec_GFp_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx) { int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *); int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); const BIGNUM *p; BN_CTX *new_ctx = NULL; BIGNUM *n0, *n1, *n2, *n3, *n4, *n5, *n6; int ret = 0; if (a == b) { return EC_POINT_dbl(group, r, a, ctx); } if (EC_POINT_is_at_infinity(group, a)) { return EC_POINT_copy(r, b); } if (EC_POINT_is_at_infinity(group, b)) { return EC_POINT_copy(r, a); } field_mul = group->meth->field_mul; field_sqr = group->meth->field_sqr; p = &group->field; if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) { return 0; } } BN_CTX_start(ctx); n0 = BN_CTX_get(ctx); n1 = BN_CTX_get(ctx); n2 = BN_CTX_get(ctx); n3 = BN_CTX_get(ctx); n4 = BN_CTX_get(ctx); n5 = BN_CTX_get(ctx); n6 = BN_CTX_get(ctx); if (n6 == NULL) { goto end; } // Note that in this function we must not read components of 'a' or 'b' // once we have written the corresponding components of 'r'. // ('r' might be one of 'a' or 'b'.) // n1, n2 int b_Z_is_one = BN_cmp(&b->Z, &group->one) == 0; if (b_Z_is_one) { if (!BN_copy(n1, &a->X) || !BN_copy(n2, &a->Y)) { goto end; } // n1 = X_a // n2 = Y_a } else { if (!field_sqr(group, n0, &b->Z, ctx) || !field_mul(group, n1, &a->X, n0, ctx)) { goto end; } // n1 = X_a * Z_b^2 if (!field_mul(group, n0, n0, &b->Z, ctx) || !field_mul(group, n2, &a->Y, n0, ctx)) { goto end; } // n2 = Y_a * Z_b^3 } // n3, n4 int a_Z_is_one = BN_cmp(&a->Z, &group->one) == 0; if (a_Z_is_one) { if (!BN_copy(n3, &b->X) || !BN_copy(n4, &b->Y)) { goto end; } // n3 = X_b // n4 = Y_b } else { if (!field_sqr(group, n0, &a->Z, ctx) || !field_mul(group, n3, &b->X, n0, ctx)) { goto end; } // n3 = X_b * Z_a^2 if (!field_mul(group, n0, n0, &a->Z, ctx) || !field_mul(group, n4, &b->Y, n0, ctx)) { goto end; } // n4 = Y_b * Z_a^3 } // n5, n6 if (!bn_mod_sub_consttime(n5, n1, n3, p, ctx) || !bn_mod_sub_consttime(n6, n2, n4, p, ctx)) { goto end; } // n5 = n1 - n3 // n6 = n2 - n4 if (BN_is_zero(n5)) { if (BN_is_zero(n6)) { // a is the same point as b BN_CTX_end(ctx); ret = EC_POINT_dbl(group, r, a, ctx); ctx = NULL; goto end; } else { // a is the inverse of b BN_zero(&r->Z); ret = 1; goto end; } } // 'n7', 'n8' if (!bn_mod_add_consttime(n1, n1, n3, p, ctx) || !bn_mod_add_consttime(n2, n2, n4, p, ctx)) { goto end; } // 'n7' = n1 + n3 // 'n8' = n2 + n4 // Z_r if (a_Z_is_one && b_Z_is_one) { if (!BN_copy(&r->Z, n5)) { goto end; } } else { if (a_Z_is_one) { if (!BN_copy(n0, &b->Z)) { goto end; } } else if (b_Z_is_one) { if (!BN_copy(n0, &a->Z)) { goto end; } } else if (!field_mul(group, n0, &a->Z, &b->Z, ctx)) { goto end; } if (!field_mul(group, &r->Z, n0, n5, ctx)) { goto end; } } // Z_r = Z_a * Z_b * n5 // X_r if (!field_sqr(group, n0, n6, ctx) || !field_sqr(group, n4, n5, ctx) || !field_mul(group, n3, n1, n4, ctx) || !bn_mod_sub_consttime(&r->X, n0, n3, p, ctx)) { goto end; } // X_r = n6^2 - n5^2 * 'n7' // 'n9' if (!bn_mod_lshift1_consttime(n0, &r->X, p, ctx) || !bn_mod_sub_consttime(n0, n3, n0, p, ctx)) { goto end; } // n9 = n5^2 * 'n7' - 2 * X_r // Y_r if (!field_mul(group, n0, n0, n6, ctx) || !field_mul(group, n5, n4, n5, ctx)) { goto end; // now n5 is n5^3 } if (!field_mul(group, n1, n2, n5, ctx) || !bn_mod_sub_consttime(n0, n0, n1, p, ctx)) { goto end; } if (BN_is_odd(n0) && !BN_add(n0, n0, p)) { goto end; } // now 0 <= n0 < 2*p, and n0 is even if (!BN_rshift1(&r->Y, n0)) { goto end; } // Y_r = (n6 * 'n9' - 'n8' * 'n5^3') / 2 ret = 1; end: if (ctx) { // otherwise we already called BN_CTX_end BN_CTX_end(ctx); } BN_CTX_free(new_ctx); return ret; }
int main() { BIGNUM *x, *y, *exp, *m, *order, *cof; BIGNUM t, store[30]; COMPLEX *a, *b, *r; EC_POINT *point, *Q; int i; x = BN_new(); y = BN_new(); order = BN_new(); exp = BN_new(); m = BN_new(); a = COMP_new(); b = COMP_new(); r = COMP_new(); for( i = 0; i < 30; i++ ) BN_init( &(store[i]) ); if ( Context == NULL ) Context = BN_CTX_new(); bi_init( &malloc ); group = EC_GROUP_new( EC_GFp_simple_method() ); if ( group == NULL ) goto err; if(!BN_set_word(m, 43l)) goto err; BN_set_word(x, 1l); BN_set_word(y, 0l); if ( !EC_GROUP_set_curve_GFp( group, m, x, y, Context) ) goto err; BN_set_word(x, 23l); BN_set_word(y, 8l); BN_set_word(order, 11l); point = EC_POINT_new( group ); EC_POINT_set_affine_coordinates_GFp( group, point, x, y, Context ); cof = BN_new(); BN_set_word( cof, 4 ); EC_GROUP_set_generator( group, point, order, cof ); if ( EC_GROUP_check( group, Context ) ) printf(" group set is ok \n"); TSS_DAA_ISSUER_KEY issuer_key; TSS_DAA_ISSUER_PROOF issuer_proof; TSS_DAA_JOIN_issuer_setup(&issuer_key, &issuer_proof); // printf("\n"); // BN_set_word(x, 41l); // BN_mod_inverse(x, x, m, Context); // BN_print_fp(stdout, x); // // printf("\n"); // BN_set_word(x, 11l); // BN_mod_inverse(x, x, m, Context); // BN_print_fp(stdout, x); char *str = "abcdefghijklmnop"; Q = map_to_point( str ); BN_set_word(x, 23l); BN_set_word(y, 8l); BN_set_word(order, 11l); Q = EC_POINT_new( group ); EC_POINT_set_affine_coordinates_GFp( group, Q, x, y, Context ); Tate( point, Q, order, 0, store, a ); printf("tate pair t(p, Q) =:\n a.x: "); BN_print_fp(stdout, &a->x); printf("\na.y: "); BN_print_fp(stdout, &a->y); EC_POINT_dbl( group, point, point, Context); EC_POINT_get_affine_coordinates_GFp( group, point, x, y, Context); printf("2A.x =:\n"); BN_print_fp(stdout, x); printf("2P.y= :\n"); BN_print_fp(stdout, y); Tate( point, Q, order, 0, store, a ); printf("tate pair t(2p, Q) =:\n a.x: "); BN_print_fp(stdout, &a->x); printf("\na.y: "); BN_print_fp(stdout, &a->y); BN_free( x ); BN_free( y ); BN_free( exp ); BN_free( m ); BN_free( order ); BN_free( cof ); COMP_free( a ); COMP_free( b ); COMP_free( r ); return 0; err: BN_free( &t ); BN_free( x ); BN_free( y ); BN_free( exp ); BN_free( m ); BN_free( order ); BN_free( cof ); COMP_free( a ); COMP_free( b ); COMP_free( r ); return 0; }
void char2_field_tests() { BN_CTX *ctx = NULL; BIGNUM *p, *a, *b; EC_GROUP *group; EC_GROUP *C2_K163 = NULL, *C2_K233 = NULL, *C2_K283 = NULL, *C2_K409 = NULL, *C2_K571 = NULL; EC_GROUP *C2_B163 = NULL, *C2_B233 = NULL, *C2_B283 = NULL, *C2_B409 = NULL, *C2_B571 = NULL; EC_POINT *P, *Q, *R; BIGNUM *x, *y, *z, *cof; unsigned char buf[100]; size_t i, len; int k; #if 1 /* optional */ ctx = BN_CTX_new(); if (!ctx) ABORT; #endif p = BN_new(); a = BN_new(); b = BN_new(); if (!p || !a || !b) ABORT; if (!BN_hex2bn(&p, "13")) ABORT; if (!BN_hex2bn(&a, "3")) ABORT; if (!BN_hex2bn(&b, "1")) ABORT; group = EC_GROUP_new(EC_GF2m_simple_method()); /* applications should use EC_GROUP_new_curve_GF2m * so that the library gets to choose the EC_METHOD */ if (!group) ABORT; if (!EC_GROUP_set_curve_GF2m(group, p, a, b, ctx)) ABORT; { EC_GROUP *tmp; tmp = EC_GROUP_new(EC_GROUP_method_of(group)); if (!tmp) ABORT; if (!EC_GROUP_copy(tmp, group)) ABORT; EC_GROUP_free(group); group = tmp; } if (!EC_GROUP_get_curve_GF2m(group, p, a, b, ctx)) ABORT; fprintf(stdout, "Curve defined by Weierstrass equation\n y^2 + x*y = x^3 + a*x^2 + b (mod 0x"); BN_print_fp(stdout, p); fprintf(stdout, ")\n a = 0x"); BN_print_fp(stdout, a); fprintf(stdout, "\n b = 0x"); BN_print_fp(stdout, b); fprintf(stdout, "\n(0x... means binary polynomial)\n"); P = EC_POINT_new(group); Q = EC_POINT_new(group); R = EC_POINT_new(group); if (!P || !Q || !R) ABORT; if (!EC_POINT_set_to_infinity(group, P)) ABORT; if (!EC_POINT_is_at_infinity(group, P)) ABORT; buf[0] = 0; if (!EC_POINT_oct2point(group, Q, buf, 1, ctx)) ABORT; if (!EC_POINT_add(group, P, P, Q, ctx)) ABORT; if (!EC_POINT_is_at_infinity(group, P)) ABORT; x = BN_new(); y = BN_new(); z = BN_new(); cof = BN_new(); if (!x || !y || !z || !cof) ABORT; if (!BN_hex2bn(&x, "6")) ABORT; /* Change test based on whether binary point compression is enabled or not. */ #ifdef OPENSSL_EC_BIN_PT_COMP if (!EC_POINT_set_compressed_coordinates_GF2m(group, Q, x, 1, ctx)) ABORT; #else if (!BN_hex2bn(&y, "8")) ABORT; if (!EC_POINT_set_affine_coordinates_GF2m(group, Q, x, y, ctx)) ABORT; #endif if (!EC_POINT_is_on_curve(group, Q, ctx)) { /* Change test based on whether binary point compression is enabled or not. */ #ifdef OPENSSL_EC_BIN_PT_COMP if (!EC_POINT_get_affine_coordinates_GF2m(group, Q, x, y, ctx)) ABORT; #endif fprintf(stderr, "Point is not on curve: x = 0x"); BN_print_fp(stderr, x); fprintf(stderr, ", y = 0x"); BN_print_fp(stderr, y); fprintf(stderr, "\n"); ABORT; } fprintf(stdout, "A cyclic subgroup:\n"); k = 100; do { if (k-- == 0) ABORT; if (EC_POINT_is_at_infinity(group, P)) fprintf(stdout, " point at infinity\n"); else { if (!EC_POINT_get_affine_coordinates_GF2m(group, P, x, y, ctx)) ABORT; fprintf(stdout, " x = 0x"); BN_print_fp(stdout, x); fprintf(stdout, ", y = 0x"); BN_print_fp(stdout, y); fprintf(stdout, "\n"); } if (!EC_POINT_copy(R, P)) ABORT; if (!EC_POINT_add(group, P, P, Q, ctx)) ABORT; } while (!EC_POINT_is_at_infinity(group, P)); if (!EC_POINT_add(group, P, Q, R, ctx)) ABORT; if (!EC_POINT_is_at_infinity(group, P)) ABORT; /* Change test based on whether binary point compression is enabled or not. */ #ifdef OPENSSL_EC_BIN_PT_COMP len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_COMPRESSED, buf, sizeof buf, ctx); if (len == 0) ABORT; if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT; if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT; fprintf(stdout, "Generator as octet string, compressed form:\n "); for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]); #endif len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_UNCOMPRESSED, buf, sizeof buf, ctx); if (len == 0) ABORT; if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT; if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT; fprintf(stdout, "\nGenerator as octet string, uncompressed form:\n "); for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]); /* Change test based on whether binary point compression is enabled or not. */ #ifdef OPENSSL_EC_BIN_PT_COMP len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_HYBRID, buf, sizeof buf, ctx); if (len == 0) ABORT; if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT; if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT; fprintf(stdout, "\nGenerator as octet string, hybrid form:\n "); for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]); #endif fprintf(stdout, "\n"); if (!EC_POINT_invert(group, P, ctx)) ABORT; if (0 != EC_POINT_cmp(group, P, R, ctx)) ABORT; /* Curve K-163 (FIPS PUB 186-2, App. 6) */ CHAR2_CURVE_TEST ( "NIST curve K-163", "0800000000000000000000000000000000000000C9", "1", "1", "02FE13C0537BBC11ACAA07D793DE4E6D5E5C94EEE8", "0289070FB05D38FF58321F2E800536D538CCDAA3D9", 1, "04000000000000000000020108A2E0CC0D99F8A5EF", "2", 163, C2_K163 ); /* Curve B-163 (FIPS PUB 186-2, App. 6) */ CHAR2_CURVE_TEST ( "NIST curve B-163", "0800000000000000000000000000000000000000C9", "1", "020A601907B8C953CA1481EB10512F78744A3205FD", "03F0EBA16286A2D57EA0991168D4994637E8343E36", "00D51FBC6C71A0094FA2CDD545B11C5C0C797324F1", 1, "040000000000000000000292FE77E70C12A4234C33", "2", 163, C2_B163 ); /* Curve K-233 (FIPS PUB 186-2, App. 6) */ CHAR2_CURVE_TEST ( "NIST curve K-233", "020000000000000000000000000000000000000004000000000000000001", "0", "1", "017232BA853A7E731AF129F22FF4149563A419C26BF50A4C9D6EEFAD6126", "01DB537DECE819B7F70F555A67C427A8CD9BF18AEB9B56E0C11056FAE6A3", 0, "008000000000000000000000000000069D5BB915BCD46EFB1AD5F173ABDF", "4", 233, C2_K233 ); /* Curve B-233 (FIPS PUB 186-2, App. 6) */ CHAR2_CURVE_TEST ( "NIST curve B-233", "020000000000000000000000000000000000000004000000000000000001", "000000000000000000000000000000000000000000000000000000000001", "0066647EDE6C332C7F8C0923BB58213B333B20E9CE4281FE115F7D8F90AD", "00FAC9DFCBAC8313BB2139F1BB755FEF65BC391F8B36F8F8EB7371FD558B", "01006A08A41903350678E58528BEBF8A0BEFF867A7CA36716F7E01F81052", 1, "01000000000000000000000000000013E974E72F8A6922031D2603CFE0D7", "2", 233, C2_B233 ); /* Curve K-283 (FIPS PUB 186-2, App. 6) */ CHAR2_CURVE_TEST ( "NIST curve K-283", "0800000000000000000000000000000000000000000000000000000000000000000010A1", "0", "1", "0503213F78CA44883F1A3B8162F188E553CD265F23C1567A16876913B0C2AC2458492836", "01CCDA380F1C9E318D90F95D07E5426FE87E45C0E8184698E45962364E34116177DD2259", 0, "01FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE9AE2ED07577265DFF7F94451E061E163C61", "4", 283, C2_K283 ); /* Curve B-283 (FIPS PUB 186-2, App. 6) */ CHAR2_CURVE_TEST ( "NIST curve B-283", "0800000000000000000000000000000000000000000000000000000000000000000010A1", "000000000000000000000000000000000000000000000000000000000000000000000001", "027B680AC8B8596DA5A4AF8A19A0303FCA97FD7645309FA2A581485AF6263E313B79A2F5", "05F939258DB7DD90E1934F8C70B0DFEC2EED25B8557EAC9C80E2E198F8CDBECD86B12053", "03676854FE24141CB98FE6D4B20D02B4516FF702350EDDB0826779C813F0DF45BE8112F4", 1, "03FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEF90399660FC938A90165B042A7CEFADB307", "2", 283, C2_B283 ); /* Curve K-409 (FIPS PUB 186-2, App. 6) */ CHAR2_CURVE_TEST ( "NIST curve K-409", "02000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001", "0", "1", "0060F05F658F49C1AD3AB1890F7184210EFD0987E307C84C27ACCFB8F9F67CC2C460189EB5AAAA62EE222EB1B35540CFE9023746", "01E369050B7C4E42ACBA1DACBF04299C3460782F918EA427E6325165E9EA10E3DA5F6C42E9C55215AA9CA27A5863EC48D8E0286B", 1, "007FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE5F83B2D4EA20400EC4557D5ED3E3E7CA5B4B5C83B8E01E5FCF", "4", 409, C2_K409 ); /* Curve B-409 (FIPS PUB 186-2, App. 6) */ CHAR2_CURVE_TEST ( "NIST curve B-409", "02000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001", "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001", "0021A5C2C8EE9FEB5C4B9A753B7B476B7FD6422EF1F3DD674761FA99D6AC27C8A9A197B272822F6CD57A55AA4F50AE317B13545F", "015D4860D088DDB3496B0C6064756260441CDE4AF1771D4DB01FFE5B34E59703DC255A868A1180515603AEAB60794E54BB7996A7", "0061B1CFAB6BE5F32BBFA78324ED106A7636B9C5A7BD198D0158AA4F5488D08F38514F1FDF4B4F40D2181B3681C364BA0273C706", 1, "010000000000000000000000000000000000000000000000000001E2AAD6A612F33307BE5FA47C3C9E052F838164CD37D9A21173", "2", 409, C2_B409 ); /* Curve K-571 (FIPS PUB 186-2, App. 6) */ CHAR2_CURVE_TEST ( "NIST curve K-571", "80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425", "0", "1", "026EB7A859923FBC82189631F8103FE4AC9CA2970012D5D46024804801841CA44370958493B205E647DA304DB4CEB08CBBD1BA39494776FB988B47174DCA88C7E2945283A01C8972", "0349DC807F4FBF374F4AEADE3BCA95314DD58CEC9F307A54FFC61EFC006D8A2C9D4979C0AC44AEA74FBEBBB9F772AEDCB620B01A7BA7AF1B320430C8591984F601CD4C143EF1C7A3", 0, "020000000000000000000000000000000000000000000000000000000000000000000000131850E1F19A63E4B391A8DB917F4138B630D84BE5D639381E91DEB45CFE778F637C1001", "4", 571, C2_K571 ); /* Curve B-571 (FIPS PUB 186-2, App. 6) */ CHAR2_CURVE_TEST ( "NIST curve B-571", "80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425", "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001", "02F40E7E2221F295DE297117B7F3D62F5C6A97FFCB8CEFF1CD6BA8CE4A9A18AD84FFABBD8EFA59332BE7AD6756A66E294AFD185A78FF12AA520E4DE739BACA0C7FFEFF7F2955727A", "0303001D34B856296C16C0D40D3CD7750A93D1D2955FA80AA5F40FC8DB7B2ABDBDE53950F4C0D293CDD711A35B67FB1499AE60038614F1394ABFA3B4C850D927E1E7769C8EEC2D19", "037BF27342DA639B6DCCFFFEB73D69D78C6C27A6009CBBCA1980F8533921E8A684423E43BAB08A576291AF8F461BB2A8B3531D2F0485C19B16E2F1516E23DD3C1A4827AF1B8AC15B", 1, "03FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE661CE18FF55987308059B186823851EC7DD9CA1161DE93D5174D66E8382E9BB2FE84E47", "2", 571, C2_B571 ); /* more tests using the last curve */ if (!EC_POINT_copy(Q, P)) ABORT; if (EC_POINT_is_at_infinity(group, Q)) ABORT; if (!EC_POINT_dbl(group, P, P, ctx)) ABORT; if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT; if (!EC_POINT_invert(group, Q, ctx)) ABORT; /* P = -2Q */ if (!EC_POINT_add(group, R, P, Q, ctx)) ABORT; if (!EC_POINT_add(group, R, R, Q, ctx)) ABORT; if (!EC_POINT_is_at_infinity(group, R)) ABORT; /* R = P + 2Q */ { const EC_POINT *points[3]; const BIGNUM *scalars[3]; if (EC_POINT_is_at_infinity(group, Q)) ABORT; points[0] = Q; points[1] = Q; points[2] = Q; if (!BN_add(y, z, BN_value_one())) ABORT; if (BN_is_odd(y)) ABORT; if (!BN_rshift1(y, y)) ABORT; scalars[0] = y; /* (group order + 1)/2, so y*Q + y*Q = Q */ scalars[1] = y; fprintf(stdout, "combined multiplication ..."); fflush(stdout); /* z is still the group order */ if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) ABORT; if (!EC_POINTs_mul(group, R, z, 2, points, scalars, ctx)) ABORT; if (0 != EC_POINT_cmp(group, P, R, ctx)) ABORT; if (0 != EC_POINT_cmp(group, R, Q, ctx)) ABORT; fprintf(stdout, "."); fflush(stdout); if (!BN_pseudo_rand(y, BN_num_bits(y), 0, 0)) ABORT; if (!BN_add(z, z, y)) ABORT; BN_set_negative(z, 1); scalars[0] = y; scalars[1] = z; /* z = -(order + y) */ if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) ABORT; if (!EC_POINT_is_at_infinity(group, P)) ABORT; fprintf(stdout, "."); fflush(stdout); if (!BN_pseudo_rand(x, BN_num_bits(y) - 1, 0, 0)) ABORT; if (!BN_add(z, x, y)) ABORT; BN_set_negative(z, 1); scalars[0] = x; scalars[1] = y; scalars[2] = z; /* z = -(x+y) */ if (!EC_POINTs_mul(group, P, NULL, 3, points, scalars, ctx)) ABORT; if (!EC_POINT_is_at_infinity(group, P)) ABORT; fprintf(stdout, " ok\n\n"); } #if 0 timings(C2_K163, TIMING_BASE_PT, ctx); timings(C2_K163, TIMING_RAND_PT, ctx); timings(C2_K163, TIMING_SIMUL, ctx); timings(C2_B163, TIMING_BASE_PT, ctx); timings(C2_B163, TIMING_RAND_PT, ctx); timings(C2_B163, TIMING_SIMUL, ctx); timings(C2_K233, TIMING_BASE_PT, ctx); timings(C2_K233, TIMING_RAND_PT, ctx); timings(C2_K233, TIMING_SIMUL, ctx); timings(C2_B233, TIMING_BASE_PT, ctx); timings(C2_B233, TIMING_RAND_PT, ctx); timings(C2_B233, TIMING_SIMUL, ctx); timings(C2_K283, TIMING_BASE_PT, ctx); timings(C2_K283, TIMING_RAND_PT, ctx); timings(C2_K283, TIMING_SIMUL, ctx); timings(C2_B283, TIMING_BASE_PT, ctx); timings(C2_B283, TIMING_RAND_PT, ctx); timings(C2_B283, TIMING_SIMUL, ctx); timings(C2_K409, TIMING_BASE_PT, ctx); timings(C2_K409, TIMING_RAND_PT, ctx); timings(C2_K409, TIMING_SIMUL, ctx); timings(C2_B409, TIMING_BASE_PT, ctx); timings(C2_B409, TIMING_RAND_PT, ctx); timings(C2_B409, TIMING_SIMUL, ctx); timings(C2_K571, TIMING_BASE_PT, ctx); timings(C2_K571, TIMING_RAND_PT, ctx); timings(C2_K571, TIMING_SIMUL, ctx); timings(C2_B571, TIMING_BASE_PT, ctx); timings(C2_B571, TIMING_RAND_PT, ctx); timings(C2_B571, TIMING_SIMUL, ctx); #endif if (ctx) BN_CTX_free(ctx); BN_free(p); BN_free(a); BN_free(b); EC_GROUP_free(group); EC_POINT_free(P); EC_POINT_free(Q); EC_POINT_free(R); BN_free(x); BN_free(y); BN_free(z); BN_free(cof); if (C2_K163) EC_GROUP_free(C2_K163); if (C2_B163) EC_GROUP_free(C2_B163); if (C2_K233) EC_GROUP_free(C2_K233); if (C2_B233) EC_GROUP_free(C2_B233); if (C2_K283) EC_GROUP_free(C2_K283); if (C2_B283) EC_GROUP_free(C2_B283); if (C2_K409) EC_GROUP_free(C2_K409); if (C2_B409) EC_GROUP_free(C2_B409); if (C2_K571) EC_GROUP_free(C2_K571); if (C2_B571) EC_GROUP_free(C2_B571); }
void prime_field_tests() { BN_CTX *ctx = NULL; BIGNUM *p, *a, *b; EC_GROUP *group; EC_GROUP *P_160 = NULL, *P_192 = NULL, *P_224 = NULL, *P_256 = NULL, *P_384 = NULL, *P_521 = NULL; EC_POINT *P, *Q, *R; BIGNUM *x, *y, *z; unsigned char buf[100]; size_t i, len; int k; #if 1 /* optional */ ctx = BN_CTX_new(); if (!ctx) ABORT; #endif p = BN_new(); a = BN_new(); b = BN_new(); if (!p || !a || !b) ABORT; if (!BN_hex2bn(&p, "17")) ABORT; if (!BN_hex2bn(&a, "1")) ABORT; if (!BN_hex2bn(&b, "1")) ABORT; group = EC_GROUP_new(EC_GFp_mont_method()); /* applications should use EC_GROUP_new_curve_GFp * so that the library gets to choose the EC_METHOD */ if (!group) ABORT; if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT; { EC_GROUP *tmp; tmp = EC_GROUP_new(EC_GROUP_method_of(group)); if (!tmp) ABORT; if (!EC_GROUP_copy(tmp, group)) ABORT; EC_GROUP_free(group); group = tmp; } if (!EC_GROUP_get_curve_GFp(group, p, a, b, ctx)) ABORT; fprintf(stdout, "Curve defined by Weierstrass equation\n y^2 = x^3 + a*x + b (mod 0x"); BN_print_fp(stdout, p); fprintf(stdout, ")\n a = 0x"); BN_print_fp(stdout, a); fprintf(stdout, "\n b = 0x"); BN_print_fp(stdout, b); fprintf(stdout, "\n"); P = EC_POINT_new(group); Q = EC_POINT_new(group); R = EC_POINT_new(group); if (!P || !Q || !R) ABORT; if (!EC_POINT_set_to_infinity(group, P)) ABORT; if (!EC_POINT_is_at_infinity(group, P)) ABORT; buf[0] = 0; if (!EC_POINT_oct2point(group, Q, buf, 1, ctx)) ABORT; if (!EC_POINT_add(group, P, P, Q, ctx)) ABORT; if (!EC_POINT_is_at_infinity(group, P)) ABORT; x = BN_new(); y = BN_new(); z = BN_new(); if (!x || !y || !z) ABORT; if (!BN_hex2bn(&x, "D")) ABORT; if (!EC_POINT_set_compressed_coordinates_GFp(group, Q, x, 1, ctx)) ABORT; if (!EC_POINT_is_on_curve(group, Q, ctx)) { if (!EC_POINT_get_affine_coordinates_GFp(group, Q, x, y, ctx)) ABORT; fprintf(stderr, "Point is not on curve: x = 0x"); BN_print_fp(stderr, x); fprintf(stderr, ", y = 0x"); BN_print_fp(stderr, y); fprintf(stderr, "\n"); ABORT; } fprintf(stdout, "A cyclic subgroup:\n"); k = 100; do { if (k-- == 0) ABORT; if (EC_POINT_is_at_infinity(group, P)) fprintf(stdout, " point at infinity\n"); else { if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT; fprintf(stdout, " x = 0x"); BN_print_fp(stdout, x); fprintf(stdout, ", y = 0x"); BN_print_fp(stdout, y); fprintf(stdout, "\n"); } if (!EC_POINT_copy(R, P)) ABORT; if (!EC_POINT_add(group, P, P, Q, ctx)) ABORT; #if 0 /* optional */ { EC_POINT *points[3]; points[0] = R; points[1] = Q; points[2] = P; if (!EC_POINTs_make_affine(group, 2, points, ctx)) ABORT; } #endif } while (!EC_POINT_is_at_infinity(group, P)); if (!EC_POINT_add(group, P, Q, R, ctx)) ABORT; if (!EC_POINT_is_at_infinity(group, P)) ABORT; len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_COMPRESSED, buf, sizeof buf, ctx); if (len == 0) ABORT; if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT; if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT; fprintf(stdout, "Generator as octect string, compressed form:\n "); for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]); len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_UNCOMPRESSED, buf, sizeof buf, ctx); if (len == 0) ABORT; if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT; if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT; fprintf(stdout, "\nGenerator as octect string, uncompressed form:\n "); for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]); len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_HYBRID, buf, sizeof buf, ctx); if (len == 0) ABORT; if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT; if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT; fprintf(stdout, "\nGenerator as octect string, hybrid form:\n "); for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]); if (!EC_POINT_get_Jprojective_coordinates_GFp(group, R, x, y, z, ctx)) ABORT; fprintf(stdout, "\nA representation of the inverse of that generator in\nJacobian projective coordinates:\n X = 0x"); BN_print_fp(stdout, x); fprintf(stdout, ", Y = 0x"); BN_print_fp(stdout, y); fprintf(stdout, ", Z = 0x"); BN_print_fp(stdout, z); fprintf(stdout, "\n"); if (!EC_POINT_invert(group, P, ctx)) ABORT; if (0 != EC_POINT_cmp(group, P, R, ctx)) ABORT; /* Curve secp160r1 (Certicom Research SEC 2 Version 1.0, section 2.4.2, 2000) * -- not a NIST curve, but commonly used */ if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFF")) ABORT; if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT; if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFC")) ABORT; if (!BN_hex2bn(&b, "1C97BEFC54BD7A8B65ACF89F81D4D4ADC565FA45")) ABORT; if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT; if (!BN_hex2bn(&x, "4A96B5688EF573284664698968C38BB913CBFC82")) ABORT; if (!BN_hex2bn(&y, "23a628553168947d59dcc912042351377ac5fb32")) ABORT; if (!EC_POINT_set_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT; if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT; if (!BN_hex2bn(&z, "0100000000000000000001F4C8F927AED3CA752257")) ABORT; if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT; if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT; fprintf(stdout, "\nSEC2 curve secp160r1 -- Generator:\n x = 0x"); BN_print_fp(stdout, x); fprintf(stdout, "\n y = 0x"); BN_print_fp(stdout, y); fprintf(stdout, "\n"); /* G_y value taken from the standard: */ if (!BN_hex2bn(&z, "23a628553168947d59dcc912042351377ac5fb32")) ABORT; if (0 != BN_cmp(y, z)) ABORT; fprintf(stdout, "verify degree ..."); if (EC_GROUP_get_degree(group) != 160) ABORT; fprintf(stdout, " ok\n"); fprintf(stdout, "verify group order ..."); fflush(stdout); if (!EC_GROUP_get_order(group, z, ctx)) ABORT; if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; if (!EC_POINT_is_at_infinity(group, Q)) ABORT; fprintf(stdout, "."); fflush(stdout); if (!EC_GROUP_precompute_mult(group, ctx)) ABORT; if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; if (!EC_POINT_is_at_infinity(group, Q)) ABORT; fprintf(stdout, " ok\n"); if (!(P_160 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT; if (!EC_GROUP_copy(P_160, group)) ABORT; /* Curve P-192 (FIPS PUB 186-2, App. 6) */ if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF")) ABORT; if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT; if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC")) ABORT; if (!BN_hex2bn(&b, "64210519E59C80E70FA7E9AB72243049FEB8DEECC146B9B1")) ABORT; if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT; if (!BN_hex2bn(&x, "188DA80EB03090F67CBF20EB43A18800F4FF0AFD82FF1012")) ABORT; if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 1, ctx)) ABORT; if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT; if (!BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22831")) ABORT; if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT; if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT; fprintf(stdout, "\nNIST curve P-192 -- Generator:\n x = 0x"); BN_print_fp(stdout, x); fprintf(stdout, "\n y = 0x"); BN_print_fp(stdout, y); fprintf(stdout, "\n"); /* G_y value taken from the standard: */ if (!BN_hex2bn(&z, "07192B95FFC8DA78631011ED6B24CDD573F977A11E794811")) ABORT; if (0 != BN_cmp(y, z)) ABORT; fprintf(stdout, "verify degree ..."); if (EC_GROUP_get_degree(group) != 192) ABORT; fprintf(stdout, " ok\n"); fprintf(stdout, "verify group order ..."); fflush(stdout); if (!EC_GROUP_get_order(group, z, ctx)) ABORT; if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; if (!EC_POINT_is_at_infinity(group, Q)) ABORT; fprintf(stdout, "."); fflush(stdout); #if 0 if (!EC_GROUP_precompute_mult(group, ctx)) ABORT; #endif if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; if (!EC_POINT_is_at_infinity(group, Q)) ABORT; fprintf(stdout, " ok\n"); if (!(P_192 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT; if (!EC_GROUP_copy(P_192, group)) ABORT; /* Curve P-224 (FIPS PUB 186-2, App. 6) */ if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001")) ABORT; if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT; if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE")) ABORT; if (!BN_hex2bn(&b, "B4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4")) ABORT; if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT; if (!BN_hex2bn(&x, "B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21")) ABORT; if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 0, ctx)) ABORT; if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT; if (!BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D")) ABORT; if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT; if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT; fprintf(stdout, "\nNIST curve P-224 -- Generator:\n x = 0x"); BN_print_fp(stdout, x); fprintf(stdout, "\n y = 0x"); BN_print_fp(stdout, y); fprintf(stdout, "\n"); /* G_y value taken from the standard: */ if (!BN_hex2bn(&z, "BD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34")) ABORT; if (0 != BN_cmp(y, z)) ABORT; fprintf(stdout, "verify degree ..."); if (EC_GROUP_get_degree(group) != 224) ABORT; fprintf(stdout, " ok\n"); fprintf(stdout, "verify group order ..."); fflush(stdout); if (!EC_GROUP_get_order(group, z, ctx)) ABORT; if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; if (!EC_POINT_is_at_infinity(group, Q)) ABORT; fprintf(stdout, "."); fflush(stdout); #if 0 if (!EC_GROUP_precompute_mult(group, ctx)) ABORT; #endif if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; if (!EC_POINT_is_at_infinity(group, Q)) ABORT; fprintf(stdout, " ok\n"); if (!(P_224 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT; if (!EC_GROUP_copy(P_224, group)) ABORT; /* Curve P-256 (FIPS PUB 186-2, App. 6) */ if (!BN_hex2bn(&p, "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF")) ABORT; if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT; if (!BN_hex2bn(&a, "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFC")) ABORT; if (!BN_hex2bn(&b, "5AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B")) ABORT; if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT; if (!BN_hex2bn(&x, "6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296")) ABORT; if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 1, ctx)) ABORT; if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT; if (!BN_hex2bn(&z, "FFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E" "84F3B9CAC2FC632551")) ABORT; if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT; if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT; fprintf(stdout, "\nNIST curve P-256 -- Generator:\n x = 0x"); BN_print_fp(stdout, x); fprintf(stdout, "\n y = 0x"); BN_print_fp(stdout, y); fprintf(stdout, "\n"); /* G_y value taken from the standard: */ if (!BN_hex2bn(&z, "4FE342E2FE1A7F9B8EE7EB4A7C0F9E162BCE33576B315ECECBB6406837BF51F5")) ABORT; if (0 != BN_cmp(y, z)) ABORT; fprintf(stdout, "verify degree ..."); if (EC_GROUP_get_degree(group) != 256) ABORT; fprintf(stdout, " ok\n"); fprintf(stdout, "verify group order ..."); fflush(stdout); if (!EC_GROUP_get_order(group, z, ctx)) ABORT; if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; if (!EC_POINT_is_at_infinity(group, Q)) ABORT; fprintf(stdout, "."); fflush(stdout); #if 0 if (!EC_GROUP_precompute_mult(group, ctx)) ABORT; #endif if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; if (!EC_POINT_is_at_infinity(group, Q)) ABORT; fprintf(stdout, " ok\n"); if (!(P_256 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT; if (!EC_GROUP_copy(P_256, group)) ABORT; /* Curve P-384 (FIPS PUB 186-2, App. 6) */ if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" "FFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFF")) ABORT; if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT; if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" "FFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFC")) ABORT; if (!BN_hex2bn(&b, "B3312FA7E23EE7E4988E056BE3F82D19181D9C6EFE8141" "120314088F5013875AC656398D8A2ED19D2A85C8EDD3EC2AEF")) ABORT; if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT; if (!BN_hex2bn(&x, "AA87CA22BE8B05378EB1C71EF320AD746E1D3B628BA79B" "9859F741E082542A385502F25DBF55296C3A545E3872760AB7")) ABORT; if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 1, ctx)) ABORT; if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT; if (!BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" "FFC7634D81F4372DDF581A0DB248B0A77AECEC196ACCC52973")) ABORT; if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT; if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT; fprintf(stdout, "\nNIST curve P-384 -- Generator:\n x = 0x"); BN_print_fp(stdout, x); fprintf(stdout, "\n y = 0x"); BN_print_fp(stdout, y); fprintf(stdout, "\n"); /* G_y value taken from the standard: */ if (!BN_hex2bn(&z, "3617DE4A96262C6F5D9E98BF9292DC29F8F41DBD289A14" "7CE9DA3113B5F0B8C00A60B1CE1D7E819D7A431D7C90EA0E5F")) ABORT; if (0 != BN_cmp(y, z)) ABORT; fprintf(stdout, "verify degree ..."); if (EC_GROUP_get_degree(group) != 384) ABORT; fprintf(stdout, " ok\n"); fprintf(stdout, "verify group order ..."); fflush(stdout); if (!EC_GROUP_get_order(group, z, ctx)) ABORT; if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; if (!EC_POINT_is_at_infinity(group, Q)) ABORT; fprintf(stdout, "."); fflush(stdout); #if 0 if (!EC_GROUP_precompute_mult(group, ctx)) ABORT; #endif if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; if (!EC_POINT_is_at_infinity(group, Q)) ABORT; fprintf(stdout, " ok\n"); if (!(P_384 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT; if (!EC_GROUP_copy(P_384, group)) ABORT; /* Curve P-521 (FIPS PUB 186-2, App. 6) */ if (!BN_hex2bn(&p, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" "FFFFFFFFFFFFFFFFFFFFFFFFFFFF")) ABORT; if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT; if (!BN_hex2bn(&a, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" "FFFFFFFFFFFFFFFFFFFFFFFFFFFC")) ABORT; if (!BN_hex2bn(&b, "051953EB9618E1C9A1F929A21A0B68540EEA2DA725B99B" "315F3B8B489918EF109E156193951EC7E937B1652C0BD3BB1BF073573" "DF883D2C34F1EF451FD46B503F00")) ABORT; if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT; if (!BN_hex2bn(&x, "C6858E06B70404E9CD9E3ECB662395B4429C648139053F" "B521F828AF606B4D3DBAA14B5E77EFE75928FE1DC127A2FFA8DE3348B" "3C1856A429BF97E7E31C2E5BD66")) ABORT; if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 0, ctx)) ABORT; if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT; if (!BN_hex2bn(&z, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" "FFFFFFFFFFFFFFFFFFFFA51868783BF2F966B7FCC0148F709A5D03BB5" "C9B8899C47AEBB6FB71E91386409")) ABORT; if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT; if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT; fprintf(stdout, "\nNIST curve P-521 -- Generator:\n x = 0x"); BN_print_fp(stdout, x); fprintf(stdout, "\n y = 0x"); BN_print_fp(stdout, y); fprintf(stdout, "\n"); /* G_y value taken from the standard: */ if (!BN_hex2bn(&z, "11839296A789A3BC0045C8A5FB42C7D1BD998F54449579" "B446817AFBD17273E662C97EE72995EF42640C550B9013FAD0761353C" "7086A272C24088BE94769FD16650")) ABORT; if (0 != BN_cmp(y, z)) ABORT; fprintf(stdout, "verify degree ..."); if (EC_GROUP_get_degree(group) != 521) ABORT; fprintf(stdout, " ok\n"); fprintf(stdout, "verify group order ..."); fflush(stdout); if (!EC_GROUP_get_order(group, z, ctx)) ABORT; if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; if (!EC_POINT_is_at_infinity(group, Q)) ABORT; fprintf(stdout, "."); fflush(stdout); #if 0 if (!EC_GROUP_precompute_mult(group, ctx)) ABORT; #endif if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; if (!EC_POINT_is_at_infinity(group, Q)) ABORT; fprintf(stdout, " ok\n"); if (!(P_521 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT; if (!EC_GROUP_copy(P_521, group)) ABORT; /* more tests using the last curve */ if (!EC_POINT_copy(Q, P)) ABORT; if (EC_POINT_is_at_infinity(group, Q)) ABORT; if (!EC_POINT_dbl(group, P, P, ctx)) ABORT; if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT; if (!EC_POINT_invert(group, Q, ctx)) ABORT; /* P = -2Q */ if (!EC_POINT_add(group, R, P, Q, ctx)) ABORT; if (!EC_POINT_add(group, R, R, Q, ctx)) ABORT; if (!EC_POINT_is_at_infinity(group, R)) ABORT; /* R = P + 2Q */ { const EC_POINT *points[3]; const BIGNUM *scalars[3]; if (EC_POINT_is_at_infinity(group, Q)) ABORT; points[0] = Q; points[1] = Q; points[2] = Q; if (!BN_add(y, z, BN_value_one())) ABORT; if (BN_is_odd(y)) ABORT; if (!BN_rshift1(y, y)) ABORT; scalars[0] = y; /* (group order + 1)/2, so y*Q + y*Q = Q */ scalars[1] = y; fprintf(stdout, "combined multiplication ..."); fflush(stdout); /* z is still the group order */ if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) ABORT; if (!EC_POINTs_mul(group, R, z, 2, points, scalars, ctx)) ABORT; if (0 != EC_POINT_cmp(group, P, R, ctx)) ABORT; if (0 != EC_POINT_cmp(group, R, Q, ctx)) ABORT; fprintf(stdout, "."); fflush(stdout); if (!BN_pseudo_rand(y, BN_num_bits(y), 0, 0)) ABORT; if (!BN_add(z, z, y)) ABORT; BN_set_negative(z, 1); scalars[0] = y; scalars[1] = z; /* z = -(order + y) */ if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) ABORT; if (!EC_POINT_is_at_infinity(group, P)) ABORT; fprintf(stdout, "."); fflush(stdout); if (!BN_pseudo_rand(x, BN_num_bits(y) - 1, 0, 0)) ABORT; if (!BN_add(z, x, y)) ABORT; BN_set_negative(z, 1); scalars[0] = x; scalars[1] = y; scalars[2] = z; /* z = -(x+y) */ if (!EC_POINTs_mul(group, P, NULL, 3, points, scalars, ctx)) ABORT; if (!EC_POINT_is_at_infinity(group, P)) ABORT; fprintf(stdout, " ok\n\n"); } #if 0 timings(P_160, TIMING_BASE_PT, ctx); timings(P_160, TIMING_RAND_PT, ctx); timings(P_160, TIMING_SIMUL, ctx); timings(P_192, TIMING_BASE_PT, ctx); timings(P_192, TIMING_RAND_PT, ctx); timings(P_192, TIMING_SIMUL, ctx); timings(P_224, TIMING_BASE_PT, ctx); timings(P_224, TIMING_RAND_PT, ctx); timings(P_224, TIMING_SIMUL, ctx); timings(P_256, TIMING_BASE_PT, ctx); timings(P_256, TIMING_RAND_PT, ctx); timings(P_256, TIMING_SIMUL, ctx); timings(P_384, TIMING_BASE_PT, ctx); timings(P_384, TIMING_RAND_PT, ctx); timings(P_384, TIMING_SIMUL, ctx); timings(P_521, TIMING_BASE_PT, ctx); timings(P_521, TIMING_RAND_PT, ctx); timings(P_521, TIMING_SIMUL, ctx); #endif if (ctx) BN_CTX_free(ctx); BN_free(p); BN_free(a); BN_free(b); EC_GROUP_free(group); EC_POINT_free(P); EC_POINT_free(Q); EC_POINT_free(R); BN_free(x); BN_free(y); BN_free(z); if (P_160) EC_GROUP_free(P_160); if (P_192) EC_GROUP_free(P_192); if (P_224) EC_GROUP_free(P_224); if (P_256) EC_GROUP_free(P_256); if (P_384) EC_GROUP_free(P_384); if (P_521) EC_GROUP_free(P_521); }
int main(int argc, const char *argv[]) { int r; int ok = 0; char *prog = "ecc"; // libpopt var poptContext popt_ctx; const char **rest; int command = 0; char *curve_name = "secp192k1"; int point_compressed = 0; point_conversion_form_t point_form; struct poptOption options[] = { {"curve-name", 'c', POPT_ARG_STRING, &curve_name, 0, "elliptic curve name", "NAME"}, {"point-compressed", 'z', POPT_ARG_NONE, &point_compressed, 0, "point format, compress or uncompress", NULL}, {"print-curve", 'p', POPT_ARG_VAL, &command, ECC_PRINT, "print elliptic curve parameters", NULL}, {"random-private-key", 0, POPT_ARG_VAL, &command, ECC_RAND_SKEY, "random generate a private key\n", NULL}, {"random-keypair", 0, POPT_ARG_VAL, &command, ECC_RAND_KEYPAIR, "generate a random key pair\n", NULL}, {"check-point", 'e', POPT_ARG_VAL, &command, ECC_CHECK_POINT, "check if point is valid\n", NULL}, {"point-add", 'a', POPT_ARG_VAL, &command, ECC_ADD, "elliptic curve point addition", NULL}, {"point-double", 'b', POPT_ARG_VAL, &command, ECC_DOUBLE, "elliptic curve point double", NULL}, {"point-mul", 'x', POPT_ARG_VAL, &command, ECC_MUL, "k*G", NULL}, {"point-mul-generator", 'X', POPT_ARG_VAL, &command, ECC_MUL_G, "elliptic curve point scalar multiply", NULL}, {"point-invert", 'i', POPT_ARG_VAL, &command, ECC_INVERT, "elliptic curve point inverse", NULL}, {"ecdsa-sign", 's', POPT_ARG_VAL, &command, ECC_SIGN, "ecdsa sign", NULL}, {"ecdsa-verify", 'v', POPT_ARG_VAL, &command, ECC_VERIFY, "ecdsa verify", NULL}, POPT_AUTOHELP POPT_TABLEEND }; // openssl var EC_GROUP *ec_group = NULL; EC_POINT *P = NULL; EC_POINT *Q = NULL; EC_POINT *R = NULL; BIGNUM *k = BN_new(); BN_CTX *bn_ctx = BN_CTX_new(); // argument parsing popt_ctx = poptGetContext(argv[0], argc, argv, options, 0); if ((r = poptGetNextOpt(popt_ctx)) < -1) { fprintf(stderr, "%s: bad argument %s: %s\n", argv[0], poptBadOption(popt_ctx, POPT_BADOPTION_NOALIAS), poptStrerror(r)); goto exit; } rest = poptGetArgs(popt_ctx); // check arguments ec_group = EC_GROUP_new_by_curve_name(OBJ_txt2nid(curve_name)); if (ec_group == NULL) { fprintf(stderr, "%s: unknown curve name\n", prog); goto exit; } P = EC_POINT_new(ec_group); Q = EC_POINT_new(ec_group); R = EC_POINT_new(ec_group); point_form = point_compressed ? POINT_CONVERSION_COMPRESSED : POINT_CONVERSION_UNCOMPRESSED; switch (command) { case ECC_PRINT: { BIGNUM *p = BN_new(); BIGNUM *a = BN_new(); BIGNUM *b = BN_new(); char *generator; BIGNUM *order = BN_new(); BIGNUM *cofactor = BN_new(); EC_GROUP_get_curve_GFp(ec_group, p, a, b, bn_ctx); generator = EC_POINT_point2hex(ec_group, EC_GROUP_get0_generator(ec_group), point_form, bn_ctx); EC_GROUP_get_order(ec_group, order, bn_ctx); EC_GROUP_get_cofactor(ec_group, cofactor, bn_ctx); fprintf(stdout, "Name : %s\n", OBJ_nid2sn(EC_GROUP_get_curve_name(ec_group))); fprintf(stdout, "FieldType : %s\n", "PrimeField"); fprintf(stdout, "Prime : %s\n", BN_bn2hex(p)); fprintf(stdout, "A : %s\n", BN_bn2hex(a)); fprintf(stdout, "B : %s\n", BN_bn2hex(b)); fprintf(stdout, "Generator : %s\n", generator); fprintf(stdout, "Order : %s\n", BN_bn2hex(order)); fprintf(stdout, "Cofactor : %s\n", BN_bn2hex(cofactor)); BN_free(p); BN_free(a); BN_free(b); BN_free(order); BN_free(cofactor); break; } case ECC_CHECK_POINT: { if (!rest) { fprintf(stderr, "%s: short of point\n", prog); goto exit; } if (!rest[0]) { fprintf(stderr, "%s: short of point\n", prog); goto exit; } if (EC_POINT_hex2point(ec_group, rest[0], P, bn_ctx)) fprintf(stdout, "ture\n"); else fprintf(stdout, "false\n"); break; } case ECC_RAND_SKEY: { EC_KEY *ec_key = EC_KEY_new(); EC_KEY_set_group(ec_key, ec_group); EC_KEY_generate_key(ec_key); fprintf(stdout, "%s\n", BN_bn2hex(EC_KEY_get0_private_key(ec_key))); EC_KEY_free(ec_key); break; } case ECC_RAND_KEYPAIR: { EC_KEY *ec_key = EC_KEY_new(); EC_KEY_set_group(ec_key, ec_group); EC_KEY_generate_key(ec_key); fprintf(stdout, "%s\n", BN_bn2hex(EC_KEY_get0_private_key(ec_key))); fprintf(stdout, "%s\n", EC_POINT_point2hex(ec_group, EC_KEY_get0_public_key(ec_key), point_form, bn_ctx)); EC_KEY_free(ec_key); break; } case ECC_ADD: { if (!rest) { fprintf(stderr, "%s: short of point\n", prog); goto exit; } if (!rest[0] || !rest[1]) { fprintf(stderr, "%s: short of point\n", prog); goto exit; } if (!EC_POINT_hex2point(ec_group, rest[1], P, bn_ctx)) { fprintf(stderr, "%s: first point invalid\n", prog); goto exit; } if (!EC_POINT_hex2point(ec_group, rest[1], Q, bn_ctx)) { fprintf(stderr, "%s: second point invalid\n", prog); goto exit; } EC_POINT_add(ec_group, R, P, Q, bn_ctx); fprintf(stdout, "%s\n", EC_POINT_point2hex(ec_group, R, point_form, bn_ctx)); break; } case ECC_DOUBLE: { EC_POINT_dbl(ec_group, R, P, bn_ctx); fprintf(stdout, "%s\n", EC_POINT_point2hex(ec_group, R, point_form, bn_ctx)); break; } case ECC_MUL: { BIGNUM *order = NULL; if (!BN_hex2bn(&k, rest[0])) { fprintf(stderr, "%s: integer invalid\n", prog); goto exit; } order = BN_new(); EC_GROUP_get_order(ec_group, order, bn_ctx); if (BN_cmp(k, order) >= 0) { fprintf(stderr, "%s: integer value invalid\n", prog); BN_free(order); goto exit; } BN_free(order); if (!EC_POINT_hex2point(ec_group, rest[1], P, bn_ctx)) { fprintf(stderr, "%s: point invalid\n", prog); goto exit; } EC_POINT_mul(ec_group, R, k, P, NULL, bn_ctx); fprintf(stdout, "%s\n", EC_POINT_point2hex(ec_group, R, point_form, bn_ctx)); break; } case ECC_MUL_G: { BIGNUM *order = NULL; if (!BN_hex2bn(&k, rest[0])) { fprintf(stderr, "%s: integer format invalid\n", prog); goto exit; } order = BN_new(); EC_GROUP_get_order(ec_group, order, bn_ctx); if (BN_cmp(k, order) >= 0) { fprintf(stderr, "%s: integer value invalid\n", prog); BN_free(order); goto exit; } BN_free(order); EC_POINT_mul(ec_group, R, k, EC_GROUP_get0_generator(ec_group), NULL, bn_ctx); fprintf(stdout, "%s\n", EC_POINT_point2hex(ec_group, R, point_form, bn_ctx)); break; } default: fprintf(stderr, "%s: command is required\n", prog); break; } ok = 1; exit: if (ec_group) EC_GROUP_free(ec_group); if (P) EC_POINT_free(P); if (k) BN_free(k); if (bn_ctx) BN_CTX_free(bn_ctx); return ok ? 0 : -1; }