-void prime_field_tests(void);
-void char2_field_tests(void);
-void internal_curve_test(void);
-
-#define TIMING_BASE_PT 0
-#define TIMING_RAND_PT 1
-#define TIMING_SIMUL 2
-
-#if 0
-static void timings(EC_GROUP *group, int type, BN_CTX *ctx)
- {
- clock_t clck;
- int i, j;
- BIGNUM *s;
- BIGNUM *r[10], *r0[10];
- EC_POINT *P;
-
- s = BN_new();
- if (s == NULL) ABORT;
-
- fprintf(stdout, "Timings for %d-bit field, ", EC_GROUP_get_degree(group));
- if (!EC_GROUP_get_order(group, s, ctx)) ABORT;
- fprintf(stdout, "%d-bit scalars ", (int)BN_num_bits(s));
- fflush(stdout);
-
- P = EC_POINT_new(group);
- if (P == NULL) ABORT;
- EC_POINT_copy(P, EC_GROUP_get0_generator(group));
-
- for (i = 0; i < 10; i++)
- {
- if ((r[i] = BN_new()) == NULL) ABORT;
- if (!BN_pseudo_rand(r[i], BN_num_bits(s), 0, 0)) ABORT;
- if (type != TIMING_BASE_PT)
- {
- if ((r0[i] = BN_new()) == NULL) ABORT;
- if (!BN_pseudo_rand(r0[i], BN_num_bits(s), 0, 0)) ABORT;
- }
- }
-
- clck = clock();
- for (i = 0; i < 10; i++)
- {
- for (j = 0; j < 10; j++)
- {
- if (!EC_POINT_mul(group, P, (type != TIMING_RAND_PT) ? r[i] : NULL,
- (type != TIMING_BASE_PT) ? P : NULL, (type != TIMING_BASE_PT) ? r0[i] : NULL, ctx)) ABORT;
- }
- }
- clck = clock() - clck;
-
- fprintf(stdout, "\n");
-
-#ifdef CLOCKS_PER_SEC
- /* "To determine the time in seconds, the value returned
- * by the clock function should be divided by the value
- * of the macro CLOCKS_PER_SEC."
- * -- ISO/IEC 9899 */
-# define UNIT "s"
-#else
- /* "`CLOCKS_PER_SEC' undeclared (first use this function)"
- * -- cc on NeXTstep/OpenStep */
-# define UNIT "units"
-# define CLOCKS_PER_SEC 1
-#endif
-
- if (type == TIMING_BASE_PT) {
- fprintf(stdout, "%i %s in %.2f " UNIT "\n", i*j,
- "base point multiplications", (double)clck/CLOCKS_PER_SEC);
- } else if (type == TIMING_RAND_PT) {
- fprintf(stdout, "%i %s in %.2f " UNIT "\n", i*j,
- "random point multiplications", (double)clck/CLOCKS_PER_SEC);
- } else if (type == TIMING_SIMUL) {
- fprintf(stdout, "%i %s in %.2f " UNIT "\n", i*j,
- "s*P+t*Q operations", (double)clck/CLOCKS_PER_SEC);
- }
- fprintf(stdout, "average: %.4f " UNIT "\n", (double)clck/(CLOCKS_PER_SEC*i*j));
-
- EC_POINT_free(P);
- BN_free(s);
- for (i = 0; i < 10; i++)
- {
- BN_free(r[i]);
- if (type != TIMING_BASE_PT) BN_free(r0[i]);
- }
- }
-#endif
-
-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 (!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_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 (!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_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 (!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_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 (!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_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 (!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_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[4];
- const BIGNUM *scalars[4];
- BIGNUM scalar3;
-
- if (EC_POINT_is_at_infinity(group, Q)) ABORT;
- points[0] = Q;
- points[1] = Q;
- points[2] = Q;
- points[3] = 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) */
-
- BN_init(&scalar3);
- BN_zero(&scalar3);
- scalars[3] = &scalar3;
-
- if (!EC_POINTs_mul(group, P, NULL, 4, points, scalars, ctx)) ABORT;
- if (!EC_POINT_is_at_infinity(group, P)) ABORT;
-
- fprintf(stdout, " ok\n\n");
-
- BN_free(&scalar3);
- }
-
-
-#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);
-
- }
+# define TIMING_BASE_PT 0
+# define TIMING_RAND_PT 1
+# define TIMING_SIMUL 2
+
+/* test multiplication with group order, long and negative scalars */
+static void group_order_tests(EC_GROUP *group)
+{
+ BIGNUM *n1, *n2, *order;
+ EC_POINT *P = EC_POINT_new(group);
+ EC_POINT *Q = EC_POINT_new(group);
+ BN_CTX *ctx = BN_CTX_new();
+ int i;
+
+ n1 = BN_new();
+ n2 = BN_new();
+ order = BN_new();
+ fprintf(stdout, "verify group order ...");
+ fflush(stdout);
+ if (!EC_GROUP_get_order(group, order, ctx))
+ ABORT;
+ if (!EC_POINT_mul(group, Q, order, 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, order, NULL, NULL, ctx))
+ ABORT;
+ if (!EC_POINT_is_at_infinity(group, Q))
+ ABORT;
+ fprintf(stdout, " ok\n");
+ fprintf(stdout, "long/negative scalar tests ");
+ for (i = 1; i <= 2; i++) {
+ const BIGNUM *scalars[6];
+ const EC_POINT *points[6];
+
+ fprintf(stdout, i == 1 ?
+ "allowing precomputation ... " :
+ "without precomputation ... ");
+ if (!BN_set_word(n1, i))
+ ABORT;
+ /*
+ * If i == 1, P will be the predefined generator for which
+ * EC_GROUP_precompute_mult has set up precomputation.
+ */
+ if (!EC_POINT_mul(group, P, n1, NULL, NULL, ctx))
+ ABORT;
+
+ if (!BN_one(n1))
+ ABORT;
+ /* n1 = 1 - order */
+ if (!BN_sub(n1, n1, order))
+ ABORT;
+ if (!EC_POINT_mul(group, Q, NULL, P, n1, ctx))
+ ABORT;
+ if (0 != EC_POINT_cmp(group, Q, P, ctx))
+ ABORT;
+
+ /* n2 = 1 + order */
+ if (!BN_add(n2, order, BN_value_one()))
+ ABORT;
+ if (!EC_POINT_mul(group, Q, NULL, P, n2, ctx))
+ ABORT;
+ if (0 != EC_POINT_cmp(group, Q, P, ctx))
+ ABORT;
+
+ /* n2 = (1 - order) * (1 + order) = 1 - order^2 */
+ if (!BN_mul(n2, n1, n2, ctx))
+ ABORT;
+ if (!EC_POINT_mul(group, Q, NULL, P, n2, ctx))
+ ABORT;
+ if (0 != EC_POINT_cmp(group, Q, P, ctx))
+ ABORT;
+
+ /* n2 = order^2 - 1 */
+ BN_set_negative(n2, 0);
+ if (!EC_POINT_mul(group, Q, NULL, P, n2, ctx))
+ ABORT;
+ /* Add P to verify the result. */
+ if (!EC_POINT_add(group, Q, Q, P, ctx))
+ ABORT;
+ if (!EC_POINT_is_at_infinity(group, Q))
+ ABORT;
+
+ /* Exercise EC_POINTs_mul, including corner cases. */
+ if (EC_POINT_is_at_infinity(group, P))
+ ABORT;
+ scalars[0] = n1;
+ points[0] = Q; /* => infinity */
+ scalars[1] = n2;
+ points[1] = P; /* => -P */
+ scalars[2] = n1;
+ points[2] = Q; /* => infinity */
+ scalars[3] = n2;
+ points[3] = Q; /* => infinity */
+ scalars[4] = n1;
+ points[4] = P; /* => P */
+ scalars[5] = n2;
+ points[5] = Q; /* => infinity */
+ if (!EC_POINTs_mul(group, P, NULL, 6, points, scalars, ctx))
+ ABORT;
+ if (!EC_POINT_is_at_infinity(group, P))
+ ABORT;
+ }
+ fprintf(stdout, "ok\n");
+
+ EC_POINT_free(P);
+ EC_POINT_free(Q);
+ BN_free(n1);
+ BN_free(n2);
+ BN_free(order);
+ BN_CTX_free(ctx);
+}
+
+static void prime_field_tests(void)
+{
+ 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;
+
+ }
+ 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 octet 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 octet 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 octet 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");
+
+ group_order_tests(group);
+
+ 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");
+
+ group_order_tests(group);
+
+ 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");
+
+ group_order_tests(group);
+
+ 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");
+
+ group_order_tests(group);
+
+ 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");
+
+ group_order_tests(group);
+
+ 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");
+
+ group_order_tests(group);
+
+ 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[4];
+ const BIGNUM *scalars[4];
+ BIGNUM *scalar3;
+
+ if (EC_POINT_is_at_infinity(group, Q))
+ ABORT;
+ points[0] = Q;
+ points[1] = Q;
+ points[2] = Q;
+ points[3] = Q;
+
+ if (!EC_GROUP_get_order(group, z, ctx))
+ ABORT;
+ 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) */
+
+ scalar3 = BN_new();
+ if (!scalar3)
+ ABORT;
+ BN_zero(scalar3);
+ scalars[3] = scalar3;
+
+ if (!EC_POINTs_mul(group, P, NULL, 4, points, scalars, ctx))
+ ABORT;
+ if (!EC_POINT_is_at_infinity(group, P))
+ ABORT;
+
+ fprintf(stdout, " ok\n\n");
+
+ BN_free(scalar3);
+ }
+
+ 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);
+
+}