/* * Copyright 2001-2018 The OpenSSL Project Authors. All Rights Reserved. * Copyright (c) 2002, Oracle and/or its affiliates. All rights reserved * * Licensed under the OpenSSL license (the "License"). You may not use * this file except in compliance with the License. You can obtain a copy * in the file LICENSE in the source distribution or at * https://www.openssl.org/source/license.html */ #include "internal/nelem.h" #include "testutil.h" #ifndef OPENSSL_NO_EC # include # ifndef OPENSSL_NO_ENGINE # include # endif # include # include # include # include # include # include static size_t crv_len = 0; static EC_builtin_curve *curves = NULL; /* test multiplication with group order, long and negative scalars */ static int group_order_tests(EC_GROUP *group) { BIGNUM *n1 = NULL, *n2 = NULL, *order = NULL; EC_POINT *P = NULL, *Q = NULL, *R = NULL, *S = NULL; const EC_POINT *G = NULL; BN_CTX *ctx = NULL; int i = 0, r = 0; if (!TEST_ptr(n1 = BN_new()) || !TEST_ptr(n2 = BN_new()) || !TEST_ptr(order = BN_new()) || !TEST_ptr(ctx = BN_CTX_new()) || !TEST_ptr(G = EC_GROUP_get0_generator(group)) || !TEST_ptr(P = EC_POINT_new(group)) || !TEST_ptr(Q = EC_POINT_new(group)) || !TEST_ptr(R = EC_POINT_new(group)) || !TEST_ptr(S = EC_POINT_new(group))) goto err; if (!TEST_true(EC_GROUP_get_order(group, order, ctx)) || !TEST_true(EC_POINT_mul(group, Q, order, NULL, NULL, ctx)) || !TEST_true(EC_POINT_is_at_infinity(group, Q)) || !TEST_true(EC_GROUP_precompute_mult(group, ctx)) || !TEST_true(EC_POINT_mul(group, Q, order, NULL, NULL, ctx)) || !TEST_true(EC_POINT_is_at_infinity(group, Q)) || !TEST_true(EC_POINT_copy(P, G)) || !TEST_true(BN_one(n1)) || !TEST_true(EC_POINT_mul(group, Q, n1, NULL, NULL, ctx)) || !TEST_int_eq(0, EC_POINT_cmp(group, Q, P, ctx)) || !TEST_true(BN_sub(n1, order, n1)) || !TEST_true(EC_POINT_mul(group, Q, n1, NULL, NULL, ctx)) || !TEST_true(EC_POINT_invert(group, Q, ctx)) || !TEST_int_eq(0, EC_POINT_cmp(group, Q, P, ctx))) goto err; for (i = 1; i <= 2; i++) { const BIGNUM *scalars[6]; const EC_POINT *points[6]; if (!TEST_true(BN_set_word(n1, i)) /* * If i == 1, P will be the predefined generator for which * EC_GROUP_precompute_mult has set up precomputation. */ || !TEST_true(EC_POINT_mul(group, P, n1, NULL, NULL, ctx)) || (i == 1 && !TEST_int_eq(0, EC_POINT_cmp(group, P, G, ctx))) || !TEST_true(BN_one(n1)) /* n1 = 1 - order */ || !TEST_true(BN_sub(n1, n1, order)) || !TEST_true(EC_POINT_mul(group, Q, NULL, P, n1, ctx)) || !TEST_int_eq(0, EC_POINT_cmp(group, Q, P, ctx)) /* n2 = 1 + order */ || !TEST_true(BN_add(n2, order, BN_value_one())) || !TEST_true(EC_POINT_mul(group, Q, NULL, P, n2, ctx)) || !TEST_int_eq(0, EC_POINT_cmp(group, Q, P, ctx)) /* n2 = (1 - order) * (1 + order) = 1 - order^2 */ || !TEST_true(BN_mul(n2, n1, n2, ctx)) || !TEST_true(EC_POINT_mul(group, Q, NULL, P, n2, ctx)) || !TEST_int_eq(0, EC_POINT_cmp(group, Q, P, ctx))) goto err; /* n2 = order^2 - 1 */ BN_set_negative(n2, 0); if (!TEST_true(EC_POINT_mul(group, Q, NULL, P, n2, ctx)) /* Add P to verify the result. */ || !TEST_true(EC_POINT_add(group, Q, Q, P, ctx)) || !TEST_true(EC_POINT_is_at_infinity(group, Q)) /* Exercise EC_POINTs_mul, including corner cases. */ || !TEST_false(EC_POINT_is_at_infinity(group, P))) goto err; scalars[0] = scalars[1] = BN_value_one(); points[0] = points[1] = P; if (!TEST_true(EC_POINTs_mul(group, R, NULL, 2, points, scalars, ctx)) || !TEST_true(EC_POINT_dbl(group, S, points[0], ctx)) || !TEST_int_eq(0, EC_POINT_cmp(group, R, S, ctx))) goto err; 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 (!TEST_true(EC_POINTs_mul(group, P, NULL, 6, points, scalars, ctx)) || !TEST_true(EC_POINT_is_at_infinity(group, P))) goto err; } r = 1; err: if (r == 0 && i != 0) TEST_info(i == 1 ? "allowing precomputation" : "without precomputation"); EC_POINT_free(P); EC_POINT_free(Q); EC_POINT_free(R); EC_POINT_free(S); BN_free(n1); BN_free(n2); BN_free(order); BN_CTX_free(ctx); return r; } static int prime_field_tests(void) { BN_CTX *ctx = NULL; BIGNUM *p = NULL, *a = NULL, *b = NULL, *scalar3 = NULL; EC_GROUP *group = NULL, *tmp = NULL; EC_GROUP *P_160 = NULL, *P_192 = NULL, *P_224 = NULL, *P_256 = NULL, *P_384 = NULL, *P_521 = NULL; EC_POINT *P = NULL, *Q = NULL, *R = NULL; BIGNUM *x = NULL, *y = NULL, *z = NULL, *yplusone = NULL; const EC_POINT *points[4]; const BIGNUM *scalars[4]; unsigned char buf[100]; size_t len, r = 0; int k; if (!TEST_ptr(ctx = BN_CTX_new()) || !TEST_ptr(p = BN_new()) || !TEST_ptr(a = BN_new()) || !TEST_ptr(b = BN_new()) || !TEST_true(BN_hex2bn(&p, "17")) || !TEST_true(BN_hex2bn(&a, "1")) || !TEST_true(BN_hex2bn(&b, "1")) /* * applications should use EC_GROUP_new_curve_GFp so * that the library gets to choose the EC_METHOD */ || !TEST_ptr(group = EC_GROUP_new(EC_GFp_mont_method())) || !TEST_true(EC_GROUP_set_curve(group, p, a, b, ctx)) || !TEST_ptr(tmp = EC_GROUP_new(EC_GROUP_method_of(group))) || !TEST_true(EC_GROUP_copy(tmp, group))) goto err; EC_GROUP_free(group); group = tmp; tmp = NULL; if (!TEST_true(EC_GROUP_get_curve(group, p, a, b, ctx))) goto err; TEST_info("Curve defined by Weierstrass equation"); TEST_note(" y^2 = x^3 + a*x + b (mod p)"); test_output_bignum("a", a); test_output_bignum("b", b); test_output_bignum("p", p); buf[0] = 0; if (!TEST_ptr(P = EC_POINT_new(group)) || !TEST_ptr(Q = EC_POINT_new(group)) || !TEST_ptr(R = EC_POINT_new(group)) || !TEST_true(EC_POINT_set_to_infinity(group, P)) || !TEST_true(EC_POINT_is_at_infinity(group, P)) || !TEST_true(EC_POINT_oct2point(group, Q, buf, 1, ctx)) || !TEST_true(EC_POINT_add(group, P, P, Q, ctx)) || !TEST_true(EC_POINT_is_at_infinity(group, P)) || !TEST_ptr(x = BN_new()) || !TEST_ptr(y = BN_new()) || !TEST_ptr(z = BN_new()) || !TEST_ptr(yplusone = BN_new()) || !TEST_true(BN_hex2bn(&x, "D")) || !TEST_true(EC_POINT_set_compressed_coordinates(group, Q, x, 1, ctx))) goto err; if (!TEST_int_gt(EC_POINT_is_on_curve(group, Q, ctx), 0)) { if (!TEST_true(EC_POINT_get_affine_coordinates(group, Q, x, y, ctx))) goto err; TEST_info("Point is not on curve"); test_output_bignum("x", x); test_output_bignum("y", y); goto err; } TEST_note("A cyclic subgroup:"); k = 100; do { if (!TEST_int_ne(k--, 0)) goto err; if (EC_POINT_is_at_infinity(group, P)) { TEST_note(" point at infinity"); } else { if (!TEST_true(EC_POINT_get_affine_coordinates(group, P, x, y, ctx))) goto err; test_output_bignum("x", x); test_output_bignum("y", y); } if (!TEST_true(EC_POINT_copy(R, P)) || !TEST_true(EC_POINT_add(group, P, P, Q, ctx))) goto err; } while (!EC_POINT_is_at_infinity(group, P)); if (!TEST_true(EC_POINT_add(group, P, Q, R, ctx)) || !TEST_true(EC_POINT_is_at_infinity(group, P))) goto err; len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_COMPRESSED, buf, sizeof(buf), ctx); if (!TEST_size_t_ne(len, 0) || !TEST_true(EC_POINT_oct2point(group, P, buf, len, ctx)) || !TEST_int_eq(0, EC_POINT_cmp(group, P, Q, ctx))) goto err; test_output_memory("Generator as octet string, compressed form:", buf, len); len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_UNCOMPRESSED, buf, sizeof(buf), ctx); if (!TEST_size_t_ne(len, 0) || !TEST_true(EC_POINT_oct2point(group, P, buf, len, ctx)) || !TEST_int_eq(0, EC_POINT_cmp(group, P, Q, ctx))) goto err; test_output_memory("Generator as octet string, uncompressed form:", buf, len); len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_HYBRID, buf, sizeof(buf), ctx); if (!TEST_size_t_ne(len, 0) || !TEST_true(EC_POINT_oct2point(group, P, buf, len, ctx)) || !TEST_int_eq(0, EC_POINT_cmp(group, P, Q, ctx))) goto err; test_output_memory("Generator as octet string, hybrid form:", buf, len); if (!TEST_true(EC_POINT_get_Jprojective_coordinates_GFp(group, R, x, y, z, ctx))) goto err; TEST_info("A representation of the inverse of that generator in"); TEST_note("Jacobian projective coordinates"); test_output_bignum("x", x); test_output_bignum("y", y); test_output_bignum("z", z); if (!TEST_true(EC_POINT_invert(group, P, ctx)) || !TEST_int_eq(0, EC_POINT_cmp(group, P, R, ctx)) /* * Curve secp160r1 (Certicom Research SEC 2 Version 1.0, section 2.4.2, * 2000) -- not a NIST curve, but commonly used */ || !TEST_true(BN_hex2bn(&p, "FFFFFFFF" "FFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFF")) || !TEST_int_eq(1, BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) || !TEST_true(BN_hex2bn(&a, "FFFFFFFF" "FFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFC")) || !TEST_true(BN_hex2bn(&b, "1C97BEFC" "54BD7A8B65ACF89F81D4D4ADC565FA45")) || !TEST_true(EC_GROUP_set_curve(group, p, a, b, ctx)) || !TEST_true(BN_hex2bn(&x, "4A96B568" "8EF573284664698968C38BB913CBFC82")) || !TEST_true(BN_hex2bn(&y, "23a62855" "3168947d59dcc912042351377ac5fb32")) || !TEST_true(BN_add(yplusone, y, BN_value_one())) /* * When (x, y) is on the curve, (x, y + 1) is, as it happens, not, * and therefore setting the coordinates should fail. */ || !TEST_false(EC_POINT_set_affine_coordinates(group, P, x, yplusone, ctx)) || !TEST_true(EC_POINT_set_affine_coordinates(group, P, x, y, ctx)) || !TEST_int_gt(EC_POINT_is_on_curve(group, P, ctx), 0) || !TEST_true(BN_hex2bn(&z, "0100000000" "000000000001F4C8F927AED3CA752257")) || !TEST_true(EC_GROUP_set_generator(group, P, z, BN_value_one())) || !TEST_true(EC_POINT_get_affine_coordinates(group, P, x, y, ctx))) goto err; TEST_info("SEC2 curve secp160r1 -- Generator"); test_output_bignum("x", x); test_output_bignum("y", y); /* G_y value taken from the standard: */ if (!TEST_true(BN_hex2bn(&z, "23a62855" "3168947d59dcc912042351377ac5fb32")) || !TEST_BN_eq(y, z) || !TEST_int_eq(EC_GROUP_get_degree(group), 160) || !group_order_tests(group) || !TEST_ptr(P_160 = EC_GROUP_new(EC_GROUP_method_of(group))) || !TEST_true(EC_GROUP_copy(P_160, group)) /* Curve P-192 (FIPS PUB 186-2, App. 6) */ || !TEST_true(BN_hex2bn(&p, "FFFFFFFFFFFFFFFF" "FFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF")) || !TEST_int_eq(1, BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) || !TEST_true(BN_hex2bn(&a, "FFFFFFFFFFFFFFFF" "FFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC")) || !TEST_true(BN_hex2bn(&b, "64210519E59C80E7" "0FA7E9AB72243049FEB8DEECC146B9B1")) || !TEST_true(EC_GROUP_set_curve(group, p, a, b, ctx)) || !TEST_true(BN_hex2bn(&x, "188DA80EB03090F6" "7CBF20EB43A18800F4FF0AFD82FF1012")) || !TEST_true(EC_POINT_set_compressed_coordinates(group, P, x, 1, ctx)) || !TEST_int_gt(EC_POINT_is_on_curve(group, P, ctx), 0) || !TEST_true(BN_hex2bn(&z, "FFFFFFFFFFFFFFFF" "FFFFFFFF99DEF836146BC9B1B4D22831")) || !TEST_true(EC_GROUP_set_generator(group, P, z, BN_value_one())) || !TEST_true(EC_POINT_get_affine_coordinates(group, P, x, y, ctx))) goto err; TEST_info("NIST curve P-192 -- Generator"); test_output_bignum("x", x); test_output_bignum("y", y); /* G_y value taken from the standard: */ if (!TEST_true(BN_hex2bn(&z, "07192B95FFC8DA78" "631011ED6B24CDD573F977A11E794811")) || !TEST_BN_eq(y, z) || !TEST_true(BN_add(yplusone, y, BN_value_one())) /* * When (x, y) is on the curve, (x, y + 1) is, as it happens, not, * and therefore setting the coordinates should fail. */ || !TEST_false(EC_POINT_set_affine_coordinates(group, P, x, yplusone, ctx)) || !TEST_int_eq(EC_GROUP_get_degree(group), 192) || !group_order_tests(group) || !TEST_ptr(P_192 = EC_GROUP_new(EC_GROUP_method_of(group))) || !TEST_true(EC_GROUP_copy(P_192, group)) /* Curve P-224 (FIPS PUB 186-2, App. 6) */ || !TEST_true(BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFF" "FFFFFFFF000000000000000000000001")) || !TEST_int_eq(1, BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) || !TEST_true(BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFF" "FFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE")) || !TEST_true(BN_hex2bn(&b, "B4050A850C04B3ABF5413256" "5044B0B7D7BFD8BA270B39432355FFB4")) || !TEST_true(EC_GROUP_set_curve(group, p, a, b, ctx)) || !TEST_true(BN_hex2bn(&x, "B70E0CBD6BB4BF7F321390B9" "4A03C1D356C21122343280D6115C1D21")) || !TEST_true(EC_POINT_set_compressed_coordinates(group, P, x, 0, ctx)) || !TEST_int_gt(EC_POINT_is_on_curve(group, P, ctx), 0) || !TEST_true(BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFF" "FFFF16A2E0B8F03E13DD29455C5C2A3D")) || !TEST_true(EC_GROUP_set_generator(group, P, z, BN_value_one())) || !TEST_true(EC_POINT_get_affine_coordinates(group, P, x, y, ctx))) goto err; TEST_info("NIST curve P-224 -- Generator"); test_output_bignum("x", x); test_output_bignum("y", y); /* G_y value taken from the standard: */ if (!TEST_true(BN_hex2bn(&z, "BD376388B5F723FB4C22DFE6" "CD4375A05A07476444D5819985007E34")) || !TEST_BN_eq(y, z) || !TEST_true(BN_add(yplusone, y, BN_value_one())) /* * When (x, y) is on the curve, (x, y + 1) is, as it happens, not, * and therefore setting the coordinates should fail. */ || !TEST_false(EC_POINT_set_affine_coordinates(group, P, x, yplusone, ctx)) || !TEST_int_eq(EC_GROUP_get_degree(group), 224) || !group_order_tests(group) || !TEST_ptr(P_224 = EC_GROUP_new(EC_GROUP_method_of(group))) || !TEST_true(EC_GROUP_copy(P_224, group)) /* Curve P-256 (FIPS PUB 186-2, App. 6) */ || !TEST_true(BN_hex2bn(&p, "FFFFFFFF000000010000000000000000" "00000000FFFFFFFFFFFFFFFFFFFFFFFF")) || !TEST_int_eq(1, BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) || !TEST_true(BN_hex2bn(&a, "FFFFFFFF000000010000000000000000" "00000000FFFFFFFFFFFFFFFFFFFFFFFC")) || !TEST_true(BN_hex2bn(&b, "5AC635D8AA3A93E7B3EBBD55769886BC" "651D06B0CC53B0F63BCE3C3E27D2604B")) || !TEST_true(EC_GROUP_set_curve(group, p, a, b, ctx)) || !TEST_true(BN_hex2bn(&x, "6B17D1F2E12C4247F8BCE6E563A440F2" "77037D812DEB33A0F4A13945D898C296")) || !TEST_true(EC_POINT_set_compressed_coordinates(group, P, x, 1, ctx)) || !TEST_int_gt(EC_POINT_is_on_curve(group, P, ctx), 0) || !TEST_true(BN_hex2bn(&z, "FFFFFFFF00000000FFFFFFFFFFFFFFFF" "BCE6FAADA7179E84F3B9CAC2FC632551")) || !TEST_true(EC_GROUP_set_generator(group, P, z, BN_value_one())) || !TEST_true(EC_POINT_get_affine_coordinates(group, P, x, y, ctx))) goto err; TEST_info("NIST curve P-256 -- Generator"); test_output_bignum("x", x); test_output_bignum("y", y); /* G_y value taken from the standard: */ if (!TEST_true(BN_hex2bn(&z, "4FE342E2FE1A7F9B8EE7EB4A7C0F9E16" "2BCE33576B315ECECBB6406837BF51F5")) || !TEST_BN_eq(y, z) || !TEST_true(BN_add(yplusone, y, BN_value_one())) /* * When (x, y) is on the curve, (x, y + 1) is, as it happens, not, * and therefore setting the coordinates should fail. */ || !TEST_false(EC_POINT_set_affine_coordinates(group, P, x, yplusone, ctx)) || !TEST_int_eq(EC_GROUP_get_degree(group), 256) || !group_order_tests(group) || !TEST_ptr(P_256 = EC_GROUP_new(EC_GROUP_method_of(group))) || !TEST_true(EC_GROUP_copy(P_256, group)) /* Curve P-384 (FIPS PUB 186-2, App. 6) */ || !TEST_true(BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE" "FFFFFFFF0000000000000000FFFFFFFF")) || !TEST_int_eq(1, BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) || !TEST_true(BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE" "FFFFFFFF0000000000000000FFFFFFFC")) || !TEST_true(BN_hex2bn(&b, "B3312FA7E23EE7E4988E056BE3F82D19" "181D9C6EFE8141120314088F5013875A" "C656398D8A2ED19D2A85C8EDD3EC2AEF")) || !TEST_true(EC_GROUP_set_curve(group, p, a, b, ctx)) || !TEST_true(BN_hex2bn(&x, "AA87CA22BE8B05378EB1C71EF320AD74" "6E1D3B628BA79B9859F741E082542A38" "5502F25DBF55296C3A545E3872760AB7")) || !TEST_true(EC_POINT_set_compressed_coordinates(group, P, x, 1, ctx)) || !TEST_int_gt(EC_POINT_is_on_curve(group, P, ctx), 0) || !TEST_true(BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" "FFFFFFFFFFFFFFFFC7634D81F4372DDF" "581A0DB248B0A77AECEC196ACCC52973")) || !TEST_true(EC_GROUP_set_generator(group, P, z, BN_value_one())) || !TEST_true(EC_POINT_get_affine_coordinates(group, P, x, y, ctx))) goto err; TEST_info("NIST curve P-384 -- Generator"); test_output_bignum("x", x); test_output_bignum("y", y); /* G_y value taken from the standard: */ if (!TEST_true(BN_hex2bn(&z, "3617DE4A96262C6F5D9E98BF9292DC29" "F8F41DBD289A147CE9DA3113B5F0B8C0" "0A60B1CE1D7E819D7A431D7C90EA0E5F")) || !TEST_BN_eq(y, z) || !TEST_true(BN_add(yplusone, y, BN_value_one())) /* * When (x, y) is on the curve, (x, y + 1) is, as it happens, not, * and therefore setting the coordinates should fail. */ || !TEST_false(EC_POINT_set_affine_coordinates(group, P, x, yplusone, ctx)) || !TEST_int_eq(EC_GROUP_get_degree(group), 384) || !group_order_tests(group) || !TEST_ptr(P_384 = EC_GROUP_new(EC_GROUP_method_of(group))) || !TEST_true(EC_GROUP_copy(P_384, group)) /* Curve P-521 (FIPS PUB 186-2, App. 6) */ || !TEST_true(BN_hex2bn(&p, "1FF" "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF")) || !TEST_int_eq(1, BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) || !TEST_true(BN_hex2bn(&a, "1FF" "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC")) || !TEST_true(BN_hex2bn(&b, "051" "953EB9618E1C9A1F929A21A0B68540EE" "A2DA725B99B315F3B8B489918EF109E1" "56193951EC7E937B1652C0BD3BB1BF07" "3573DF883D2C34F1EF451FD46B503F00")) || !TEST_true(EC_GROUP_set_curve(group, p, a, b, ctx)) || !TEST_true(BN_hex2bn(&x, "C6" "858E06B70404E9CD9E3ECB662395B442" "9C648139053FB521F828AF606B4D3DBA" "A14B5E77EFE75928FE1DC127A2FFA8DE" "3348B3C1856A429BF97E7E31C2E5BD66")) || !TEST_true(EC_POINT_set_compressed_coordinates(group, P, x, 0, ctx)) || !TEST_int_gt(EC_POINT_is_on_curve(group, P, ctx), 0) || !TEST_true(BN_hex2bn(&z, "1FF" "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFA" "51868783BF2F966B7FCC0148F709A5D0" "3BB5C9B8899C47AEBB6FB71E91386409")) || !TEST_true(EC_GROUP_set_generator(group, P, z, BN_value_one())) || !TEST_true(EC_POINT_get_affine_coordinates(group, P, x, y, ctx))) goto err; TEST_info("NIST curve P-521 -- Generator"); test_output_bignum("x", x); test_output_bignum("y", y); /* G_y value taken from the standard: */ if (!TEST_true(BN_hex2bn(&z, "118" "39296A789A3BC0045C8A5FB42C7D1BD9" "98F54449579B446817AFBD17273E662C" "97EE72995EF42640C550B9013FAD0761" "353C7086A272C24088BE94769FD16650")) || !TEST_BN_eq(y, z) || !TEST_true(BN_add(yplusone, y, BN_value_one())) /* * When (x, y) is on the curve, (x, y + 1) is, as it happens, not, * and therefore setting the coordinates should fail. */ || !TEST_false(EC_POINT_set_affine_coordinates(group, P, x, yplusone, ctx)) || !TEST_int_eq(EC_GROUP_get_degree(group), 521) || !group_order_tests(group) || !TEST_ptr(P_521 = EC_GROUP_new(EC_GROUP_method_of(group))) || !TEST_true(EC_GROUP_copy(P_521, group)) /* more tests using the last curve */ /* Restore the point that got mangled in the (x, y + 1) test. */ || !TEST_true(EC_POINT_set_affine_coordinates(group, P, x, y, ctx)) || !TEST_true(EC_POINT_copy(Q, P)) || !TEST_false(EC_POINT_is_at_infinity(group, Q)) || !TEST_true(EC_POINT_dbl(group, P, P, ctx)) || !TEST_int_gt(EC_POINT_is_on_curve(group, P, ctx), 0) || !TEST_true(EC_POINT_invert(group, Q, ctx)) /* P = -2Q */ || !TEST_true(EC_POINT_add(group, R, P, Q, ctx)) || !TEST_true(EC_POINT_add(group, R, R, Q, ctx)) || !TEST_true(EC_POINT_is_at_infinity(group, R)) /* R = P + 2Q */ || !TEST_false(EC_POINT_is_at_infinity(group, Q))) goto err; points[0] = Q; points[1] = Q; points[2] = Q; points[3] = Q; if (!TEST_true(EC_GROUP_get_order(group, z, ctx)) || !TEST_true(BN_add(y, z, BN_value_one())) || !TEST_BN_even(y) || !TEST_true(BN_rshift1(y, y))) goto err; scalars[0] = y; /* (group order + 1)/2, so y*Q + y*Q = Q */ scalars[1] = y; TEST_note("combined multiplication ..."); /* z is still the group order */ if (!TEST_true(EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) || !TEST_true(EC_POINTs_mul(group, R, z, 2, points, scalars, ctx)) || !TEST_int_eq(0, EC_POINT_cmp(group, P, R, ctx)) || !TEST_int_eq(0, EC_POINT_cmp(group, R, Q, ctx)) || !TEST_true(BN_rand(y, BN_num_bits(y), 0, 0)) || !TEST_true(BN_add(z, z, y))) goto err; BN_set_negative(z, 1); scalars[0] = y; scalars[1] = z; /* z = -(order + y) */ if (!TEST_true(EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) || !TEST_true(EC_POINT_is_at_infinity(group, P)) || !TEST_true(BN_rand(x, BN_num_bits(y) - 1, 0, 0)) || !TEST_true(BN_add(z, x, y))) goto err; BN_set_negative(z, 1); scalars[0] = x; scalars[1] = y; scalars[2] = z; /* z = -(x+y) */ if (!TEST_ptr(scalar3 = BN_new())) goto err; BN_zero(scalar3); scalars[3] = scalar3; if (!TEST_true(EC_POINTs_mul(group, P, NULL, 4, points, scalars, ctx)) || !TEST_true(EC_POINT_is_at_infinity(group, P))) goto err; TEST_note(" ok\n"); r = 1; err: BN_CTX_free(ctx); BN_free(p); BN_free(a); BN_free(b); EC_GROUP_free(group); EC_GROUP_free(tmp); EC_POINT_free(P); EC_POINT_free(Q); EC_POINT_free(R); BN_free(x); BN_free(y); BN_free(z); BN_free(yplusone); BN_free(scalar3); EC_GROUP_free(P_160); EC_GROUP_free(P_192); EC_GROUP_free(P_224); EC_GROUP_free(P_256); EC_GROUP_free(P_384); EC_GROUP_free(P_521); return r; } # ifndef OPENSSL_NO_EC2M static struct c2_curve_test { const char *name; const char *p; const char *a; const char *b; const char *x; const char *y; int ybit; const char *order; const char *cof; int degree; } char2_curve_tests[] = { /* Curve K-163 (FIPS PUB 186-2, App. 6) */ { "NIST curve K-163", "0800000000000000000000000000000000000000C9", "1", "1", "02FE13C0537BBC11ACAA07D793DE4E6D5E5C94EEE8", "0289070FB05D38FF58321F2E800536D538CCDAA3D9", 1, "04000000000000000000020108A2E0CC0D99F8A5EF", "2", 163 }, /* Curve B-163 (FIPS PUB 186-2, App. 6) */ { "NIST curve B-163", "0800000000000000000000000000000000000000C9", "1", "020A601907B8C953CA1481EB10512F78744A3205FD", "03F0EBA16286A2D57EA0991168D4994637E8343E36", "00D51FBC6C71A0094FA2CDD545B11C5C0C797324F1", 1, "040000000000000000000292FE77E70C12A4234C33", "2", 163 }, /* Curve K-233 (FIPS PUB 186-2, App. 6) */ { "NIST curve K-233", "020000000000000000000000000000000000000004000000000000000001", "0", "1", "017232BA853A7E731AF129F22FF4149563A419C26BF50A4C9D6EEFAD6126", "01DB537DECE819B7F70F555A67C427A8CD9BF18AEB9B56E0C11056FAE6A3", 0, "008000000000000000000000000000069D5BB915BCD46EFB1AD5F173ABDF", "4", 233 }, /* Curve B-233 (FIPS PUB 186-2, App. 6) */ { "NIST curve B-233", "020000000000000000000000000000000000000004000000000000000001", "000000000000000000000000000000000000000000000000000000000001", "0066647EDE6C332C7F8C0923BB58213B333B20E9CE4281FE115F7D8F90AD", "00FAC9DFCBAC8313BB2139F1BB755FEF65BC391F8B36F8F8EB7371FD558B", "01006A08A41903350678E58528BEBF8A0BEFF867A7CA36716F7E01F81052", 1, "01000000000000000000000000000013E974E72F8A6922031D2603CFE0D7", "2", 233 }, /* Curve K-283 (FIPS PUB 186-2, App. 6) */ { "NIST curve K-283", "08000000" "00000000000000000000000000000000000000000000000000000000000010A1", "0", "1", "0503213F" "78CA44883F1A3B8162F188E553CD265F23C1567A16876913B0C2AC2458492836", "01CCDA38" "0F1C9E318D90F95D07E5426FE87E45C0E8184698E45962364E34116177DD2259", 0, "01FFFFFF" "FFFFFFFFFFFFFFFFFFFFFFFFFFFFE9AE2ED07577265DFF7F94451E061E163C61", "4", 283 }, /* Curve B-283 (FIPS PUB 186-2, App. 6) */ { "NIST curve B-283", "08000000" "00000000000000000000000000000000000000000000000000000000000010A1", "00000000" "0000000000000000000000000000000000000000000000000000000000000001", "027B680A" "C8B8596DA5A4AF8A19A0303FCA97FD7645309FA2A581485AF6263E313B79A2F5", "05F93925" "8DB7DD90E1934F8C70B0DFEC2EED25B8557EAC9C80E2E198F8CDBECD86B12053", "03676854" "FE24141CB98FE6D4B20D02B4516FF702350EDDB0826779C813F0DF45BE8112F4", 1, "03FFFFFF" "FFFFFFFFFFFFFFFFFFFFFFFFFFFFEF90399660FC938A90165B042A7CEFADB307", "2", 283 }, /* Curve K-409 (FIPS PUB 186-2, App. 6) */ { "NIST curve K-409", "0200000000000000000000000000000000000000" "0000000000000000000000000000000000000000008000000000000000000001", "0", "1", "0060F05F658F49C1AD3AB1890F7184210EFD0987" "E307C84C27ACCFB8F9F67CC2C460189EB5AAAA62EE222EB1B35540CFE9023746", "01E369050B7C4E42ACBA1DACBF04299C3460782F" "918EA427E6325165E9EA10E3DA5F6C42E9C55215AA9CA27A5863EC48D8E0286B", 1, "007FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" "FFFFFFFFFFFFFE5F83B2D4EA20400EC4557D5ED3E3E7CA5B4B5C83B8E01E5FCF", "4", 409 }, /* Curve B-409 (FIPS PUB 186-2, App. 6) */ { "NIST curve B-409", "0200000000000000000000000000000000000000" "0000000000000000000000000000000000000000008000000000000000000001", "0000000000000000000000000000000000000000" "0000000000000000000000000000000000000000000000000000000000000001", "0021A5C2C8EE9FEB5C4B9A753B7B476B7FD6422E" "F1F3DD674761FA99D6AC27C8A9A197B272822F6CD57A55AA4F50AE317B13545F", "015D4860D088DDB3496B0C6064756260441CDE4A" "F1771D4DB01FFE5B34E59703DC255A868A1180515603AEAB60794E54BB7996A7", "0061B1CFAB6BE5F32BBFA78324ED106A7636B9C5" "A7BD198D0158AA4F5488D08F38514F1FDF4B4F40D2181B3681C364BA0273C706", 1, "0100000000000000000000000000000000000000" "00000000000001E2AAD6A612F33307BE5FA47C3C9E052F838164CD37D9A21173", "2", 409 }, /* Curve K-571 (FIPS PUB 186-2, App. 6) */ { "NIST curve K-571", "800000000000000" "0000000000000000000000000000000000000000000000000000000000000000" "0000000000000000000000000000000000000000000000000000000000000425", "0", "1", "026EB7A859923FBC" "82189631F8103FE4AC9CA2970012D5D46024804801841CA44370958493B205E6" "47DA304DB4CEB08CBBD1BA39494776FB988B47174DCA88C7E2945283A01C8972", "0349DC807F4FBF37" "4F4AEADE3BCA95314DD58CEC9F307A54FFC61EFC006D8A2C9D4979C0AC44AEA7" "4FBEBBB9F772AEDCB620B01A7BA7AF1B320430C8591984F601CD4C143EF1C7A3", 0, "0200000000000000" "00000000000000000000000000000000000000000000000000000000131850E1" "F19A63E4B391A8DB917F4138B630D84BE5D639381E91DEB45CFE778F637C1001", "4", 571 }, /* Curve B-571 (FIPS PUB 186-2, App. 6) */ { "NIST curve B-571", "800000000000000" "0000000000000000000000000000000000000000000000000000000000000000" "0000000000000000000000000000000000000000000000000000000000000425", "0000000000000000" "0000000000000000000000000000000000000000000000000000000000000000" "0000000000000000000000000000000000000000000000000000000000000001", "02F40E7E2221F295" "DE297117B7F3D62F5C6A97FFCB8CEFF1CD6BA8CE4A9A18AD84FFABBD8EFA5933" "2BE7AD6756A66E294AFD185A78FF12AA520E4DE739BACA0C7FFEFF7F2955727A", "0303001D34B85629" "6C16C0D40D3CD7750A93D1D2955FA80AA5F40FC8DB7B2ABDBDE53950F4C0D293" "CDD711A35B67FB1499AE60038614F1394ABFA3B4C850D927E1E7769C8EEC2D19", "037BF27342DA639B" "6DCCFFFEB73D69D78C6C27A6009CBBCA1980F8533921E8A684423E43BAB08A57" "6291AF8F461BB2A8B3531D2F0485C19B16E2F1516E23DD3C1A4827AF1B8AC15B", 1, "03FFFFFFFFFFFFFF" "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE661CE18" "FF55987308059B186823851EC7DD9CA1161DE93D5174D66E8382E9BB2FE84E47", "2", 571 } }; static int char2_curve_test(int n) { int r = 0; BN_CTX *ctx = NULL; BIGNUM *p = NULL, *a = NULL, *b = NULL; BIGNUM *x = NULL, *y = NULL, *z = NULL, *cof = NULL, *yplusone = NULL; EC_GROUP *group = NULL, *variable = NULL; EC_POINT *P = NULL, *Q = NULL, *R = NULL; const EC_POINT *points[3]; const BIGNUM *scalars[3]; struct c2_curve_test *const test = char2_curve_tests + n; if (!TEST_ptr(ctx = BN_CTX_new()) || !TEST_ptr(p = BN_new()) || !TEST_ptr(a = BN_new()) || !TEST_ptr(b = BN_new()) || !TEST_ptr(x = BN_new()) || !TEST_ptr(y = BN_new()) || !TEST_ptr(z = BN_new()) || !TEST_ptr(yplusone = BN_new()) || !TEST_true(BN_hex2bn(&p, test->p)) || !TEST_true(BN_hex2bn(&a, test->a)) || !TEST_true(BN_hex2bn(&b, test->b)) || !TEST_true(group = EC_GROUP_new(EC_GF2m_simple_method())) || !TEST_true(EC_GROUP_set_curve(group, p, a, b, ctx)) || !TEST_ptr(P = EC_POINT_new(group)) || !TEST_ptr(Q = EC_POINT_new(group)) || !TEST_ptr(R = EC_POINT_new(group)) || !TEST_true(BN_hex2bn(&x, test->x)) || !TEST_true(BN_hex2bn(&y, test->y)) || !TEST_true(BN_add(yplusone, y, BN_value_one()))) goto err; /* Change test based on whether binary point compression is enabled or not. */ # ifdef OPENSSL_EC_BIN_PT_COMP /* * When (x, y) is on the curve, (x, y + 1) is, as it happens, not, * and therefore setting the coordinates should fail. */ if (!TEST_false(EC_POINT_set_affine_coordinates(group, P, x, yplusone, ctx)) || !TEST_true(EC_POINT_set_compressed_coordinates(group, P, x, test->y_bit, ctx)) || !TEST_int_gt(EC_POINT_is_on_curve(group, P, ctx), 0) || !TEST_true(BN_hex2bn(&z, test->order)) || !TEST_true(BN_hex2bn(&cof, test->cof)) || !TEST_true(EC_GROUP_set_generator(group, P, z, cof)) || !TEST_true(EC_POINT_get_affine_coordinates(group, P, x, y, ctx))) goto err; TEST_info("%s -- Generator", test->name); test_output_bignum("x", x); test_output_bignum("y", y); /* G_y value taken from the standard: */ if (!TEST_true(BN_hex2bn(&z, test->y)) || !TEST_BN_eq(y, z)) goto err; # else /* * When (x, y) is on the curve, (x, y + 1) is, as it happens, not, * and therefore setting the coordinates should fail. */ if (!TEST_false(EC_POINT_set_affine_coordinates(group, P, x, yplusone, ctx)) || !TEST_true(EC_POINT_set_affine_coordinates(group, P, x, y, ctx)) || !TEST_int_gt(EC_POINT_is_on_curve(group, P, ctx), 0) || !TEST_true(BN_hex2bn(&z, test->order)) || !TEST_true(BN_hex2bn(&cof, test->cof)) || !TEST_true(EC_GROUP_set_generator(group, P, z, cof))) goto err; TEST_info("%s -- Generator:", test->name); test_output_bignum("x", x); test_output_bignum("y", y); # endif if (!TEST_int_eq(EC_GROUP_get_degree(group), test->degree) || !group_order_tests(group) || !TEST_ptr(variable = EC_GROUP_new(EC_GROUP_method_of(group))) || !TEST_true(EC_GROUP_copy(variable, group))) goto err; /* more tests using the last curve */ if (n == OSSL_NELEM(char2_curve_tests) - 1) { if (!TEST_true(EC_POINT_set_affine_coordinates(group, P, x, y, ctx)) || !TEST_true(EC_POINT_copy(Q, P)) || !TEST_false(EC_POINT_is_at_infinity(group, Q)) || !TEST_true(EC_POINT_dbl(group, P, P, ctx)) || !TEST_int_gt(EC_POINT_is_on_curve(group, P, ctx), 0) || !TEST_true(EC_POINT_invert(group, Q, ctx)) /* P = -2Q */ || !TEST_true(EC_POINT_add(group, R, P, Q, ctx)) || !TEST_true(EC_POINT_add(group, R, R, Q, ctx)) || !TEST_true(EC_POINT_is_at_infinity(group, R)) /* R = P + 2Q */ || !TEST_false(EC_POINT_is_at_infinity(group, Q))) goto err; points[0] = Q; points[1] = Q; points[2] = Q; if (!TEST_true(BN_add(y, z, BN_value_one())) || !TEST_BN_even(y) || !TEST_true(BN_rshift1(y, y))) goto err; scalars[0] = y; /* (group order + 1)/2, so y*Q + y*Q = Q */ scalars[1] = y; TEST_note("combined multiplication ..."); /* z is still the group order */ if (!TEST_true(EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) || !TEST_true(EC_POINTs_mul(group, R, z, 2, points, scalars, ctx)) || !TEST_int_eq(0, EC_POINT_cmp(group, P, R, ctx)) || !TEST_int_eq(0, EC_POINT_cmp(group, R, Q, ctx))) goto err; if (!TEST_true(BN_rand(y, BN_num_bits(y), 0, 0)) || !TEST_true(BN_add(z, z, y))) goto err; BN_set_negative(z, 1); scalars[0] = y; scalars[1] = z; /* z = -(order + y) */ if (!TEST_true(EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) || !TEST_true(EC_POINT_is_at_infinity(group, P))) goto err; if (!TEST_true(BN_rand(x, BN_num_bits(y) - 1, 0, 0)) || !TEST_true(BN_add(z, x, y))) goto err; BN_set_negative(z, 1); scalars[0] = x; scalars[1] = y; scalars[2] = z; /* z = -(x+y) */ if (!TEST_true(EC_POINTs_mul(group, P, NULL, 3, points, scalars, ctx)) || !TEST_true(EC_POINT_is_at_infinity(group, P))) goto err;; } r = 1; err: BN_CTX_free(ctx); BN_free(p); BN_free(a); BN_free(b); BN_free(x); BN_free(y); BN_free(z); BN_free(yplusone); BN_free(cof); EC_POINT_free(P); EC_POINT_free(Q); EC_POINT_free(R); EC_GROUP_free(group); EC_GROUP_free(variable); return r; } static int char2_field_tests(void) { BN_CTX *ctx = NULL; BIGNUM *p = NULL, *a = NULL, *b = NULL; EC_GROUP *group = NULL, *tmp = NULL; EC_POINT *P = NULL, *Q = NULL, *R = NULL; BIGNUM *x = NULL, *y = NULL, *z = NULL, *cof = NULL, *yplusone = NULL; unsigned char buf[100]; size_t len; int k, r = 0; if (!TEST_ptr(ctx = BN_CTX_new()) || !TEST_ptr(p = BN_new()) || !TEST_ptr(a = BN_new()) || !TEST_ptr(b = BN_new()) || !TEST_true(BN_hex2bn(&p, "13")) || !TEST_true(BN_hex2bn(&a, "3")) || !TEST_true(BN_hex2bn(&b, "1"))) goto err; 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 (!TEST_ptr(group) || !TEST_true(EC_GROUP_set_curve(group, p, a, b, ctx)) || !TEST_ptr(tmp = EC_GROUP_new(EC_GROUP_method_of(group))) || !TEST_true(EC_GROUP_copy(tmp, group))) goto err; EC_GROUP_free(group); group = tmp; tmp = NULL; if (!TEST_true(EC_GROUP_get_curve(group, p, a, b, ctx))) goto err; TEST_info("Curve defined by Weierstrass equation"); TEST_note(" y^2 + x*y = x^3 + a*x^2 + b (mod p)"); test_output_bignum("a", a); test_output_bignum("b", b); test_output_bignum("p", p); if (!TEST_ptr(P = EC_POINT_new(group)) || !TEST_ptr(Q = EC_POINT_new(group)) || !TEST_ptr(R = EC_POINT_new(group)) || !TEST_true(EC_POINT_set_to_infinity(group, P)) || !TEST_true(EC_POINT_is_at_infinity(group, P))) goto err; buf[0] = 0; if (!TEST_true(EC_POINT_oct2point(group, Q, buf, 1, ctx)) || !TEST_true(EC_POINT_add(group, P, P, Q, ctx)) || !TEST_true(EC_POINT_is_at_infinity(group, P)) || !TEST_ptr(x = BN_new()) || !TEST_ptr(y = BN_new()) || !TEST_ptr(z = BN_new()) || !TEST_ptr(cof = BN_new()) || !TEST_ptr(yplusone = BN_new()) || !TEST_true(BN_hex2bn(&x, "6")) /* Change test based on whether binary point compression is enabled or not. */ # ifdef OPENSSL_EC_BIN_PT_COMP || !TEST_true(EC_POINT_set_compressed_coordinates(group, Q, x, 1, ctx)) # else || !TEST_true(BN_hex2bn(&y, "8")) || !TEST_true(EC_POINT_set_affine_coordinates(group, Q, x, y, ctx)) # endif ) goto err; if (!TEST_int_gt(EC_POINT_is_on_curve(group, Q, ctx), 0)) { /* Change test based on whether binary point compression is enabled or not. */ # ifdef OPENSSL_EC_BIN_PT_COMP if (!TEST_true(EC_POINT_get_affine_coordinates(group, Q, x, y, ctx))) goto err; # endif TEST_info("Point is not on curve"); test_output_bignum("x", x); test_output_bignum("y", y); goto err; } TEST_note("A cyclic subgroup:"); k = 100; do { if (!TEST_int_ne(k--, 0)) goto err; if (EC_POINT_is_at_infinity(group, P)) TEST_note(" point at infinity"); else { if (!TEST_true(EC_POINT_get_affine_coordinates(group, P, x, y, ctx))) goto err; test_output_bignum("x", x); test_output_bignum("y", y); } if (!TEST_true(EC_POINT_copy(R, P)) || !TEST_true(EC_POINT_add(group, P, P, Q, ctx))) goto err; } while (!EC_POINT_is_at_infinity(group, P)); if (!TEST_true(EC_POINT_add(group, P, Q, R, ctx)) || !TEST_true(EC_POINT_is_at_infinity(group, P))) goto err; /* 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 (!TEST_size_t_ne(len, 0) || !TEST_true(EC_POINT_oct2point(group, P, buf, len, ctx)) || !TEST_int_eq(0, EC_POINT_cmp(group, P, Q, ctx))) goto err; test_output_memory("Generator as octet string, compressed form:", buf, len); # endif len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_UNCOMPRESSED, buf, sizeof(buf), ctx); if (!TEST_size_t_ne(len, 0) || !TEST_true(EC_POINT_oct2point(group, P, buf, len, ctx)) || !TEST_int_eq(0, EC_POINT_cmp(group, P, Q, ctx))) goto err; test_output_memory("Generator as octet string, uncompressed form:", buf, len); /* 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 (!TEST_size_t_ne(len, 0) || !TEST_true(EC_POINT_oct2point(group, P, buf, len, ctx)) || !TEST_int_eq(0, EC_POINT_cmp(group, P, Q, ctx))) goto err; test_output_memory("Generator as octet string, hybrid form:", buf, len); # endif if (!TEST_true(EC_POINT_invert(group, P, ctx)) || !TEST_int_eq(0, EC_POINT_cmp(group, P, R, ctx))) goto err; TEST_note("\n"); r = 1; err: BN_CTX_free(ctx); BN_free(p); BN_free(a); BN_free(b); EC_GROUP_free(group); EC_GROUP_free(tmp); EC_POINT_free(P); EC_POINT_free(Q); EC_POINT_free(R); BN_free(x); BN_free(y); BN_free(z); BN_free(cof); BN_free(yplusone); return r; } # endif static int internal_curve_test(int n) { EC_GROUP *group = NULL; int nid = curves[n].nid; if (!TEST_ptr(group = EC_GROUP_new_by_curve_name(nid))) { TEST_info("EC_GROUP_new_curve_name() failed with curve %s\n", OBJ_nid2sn(nid)); return 0; } if (!TEST_true(EC_GROUP_check(group, NULL))) { TEST_info("EC_GROUP_check() failed with curve %s\n", OBJ_nid2sn(nid)); EC_GROUP_free(group); return 0; } EC_GROUP_free(group); return 1; } static int internal_curve_test_method(int n) { int r, nid = curves[n].nid; EC_GROUP *group; if (!TEST_ptr(group = EC_GROUP_new_by_curve_name(nid))) { TEST_info("Curve %s failed\n", OBJ_nid2sn(nid)); return 0; } r = group_order_tests(group); EC_GROUP_free(group); return r; } # ifndef OPENSSL_NO_EC_NISTP_64_GCC_128 /* * nistp_test_params contains magic numbers for testing our optimized * implementations of several NIST curves with characteristic > 3. */ struct nistp_test_params { const EC_METHOD *(*meth) (void); int degree; /* * Qx, Qy and D are taken from * http://csrc.nist.gov/groups/ST/toolkit/documents/Examples/ECDSA_Prime.pdf * Otherwise, values are standard curve parameters from FIPS 180-3 */ const char *p, *a, *b, *Qx, *Qy, *Gx, *Gy, *order, *d; }; static const struct nistp_test_params nistp_tests_params[] = { { /* P-224 */ EC_GFp_nistp224_method, 224, /* p */ "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001", /* a */ "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE", /* b */ "B4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4", /* Qx */ "E84FB0B8E7000CB657D7973CF6B42ED78B301674276DF744AF130B3E", /* Qy */ "4376675C6FC5612C21A0FF2D2A89D2987DF7A2BC52183B5982298555", /* Gx */ "B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21", /* Gy */ "BD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34", /* order */ "FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D", /* d */ "3F0C488E987C80BE0FEE521F8D90BE6034EC69AE11CA72AA777481E8", }, { /* P-256 */ EC_GFp_nistp256_method, 256, /* p */ "ffffffff00000001000000000000000000000000ffffffffffffffffffffffff", /* a */ "ffffffff00000001000000000000000000000000fffffffffffffffffffffffc", /* b */ "5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b", /* Qx */ "b7e08afdfe94bad3f1dc8c734798ba1c62b3a0ad1e9ea2a38201cd0889bc7a19", /* Qy */ "3603f747959dbf7a4bb226e41928729063adc7ae43529e61b563bbc606cc5e09", /* Gx */ "6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296", /* Gy */ "4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5", /* order */ "ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551", /* d */ "c477f9f65c22cce20657faa5b2d1d8122336f851a508a1ed04e479c34985bf96", }, { /* P-521 */ EC_GFp_nistp521_method, 521, /* p */ "1ff" "ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff" "ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff", /* a */ "1ff" "ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff" "fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc", /* b */ "051" "953eb9618e1c9a1f929a21a0b68540eea2da725b99b315f3b8b489918ef109e1" "56193951ec7e937b1652c0bd3bb1bf073573df883d2c34f1ef451fd46b503f00", /* Qx */ "0098" "e91eef9a68452822309c52fab453f5f117c1da8ed796b255e9ab8f6410cca16e" "59df403a6bdc6ca467a37056b1e54b3005d8ac030decfeb68df18b171885d5c4", /* Qy */ "0164" "350c321aecfc1cca1ba4364c9b15656150b4b78d6a48d7d28e7f31985ef17be8" "554376b72900712c4b83ad668327231526e313f5f092999a4632fd50d946bc2e", /* Gx */ "c6" "858e06b70404e9cd9e3ecb662395b4429c648139053fb521f828af606b4d3dba" "a14b5e77efe75928fe1dc127a2ffa8de3348b3c1856a429bf97e7e31c2e5bd66", /* Gy */ "118" "39296a789a3bc0045c8a5fb42c7d1bd998f54449579b446817afbd17273e662c" "97ee72995ef42640c550b9013fad0761353c7086a272c24088be94769fd16650", /* order */ "1ff" "fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffa" "51868783bf2f966b7fcc0148f709a5d03bb5c9b8899c47aebb6fb71e91386409", /* d */ "0100" "085f47b8e1b8b11b7eb33028c0b2888e304bfc98501955b45bba1478dc184eee" "df09b86a5f7c21994406072787205e69a63709fe35aa93ba333514b24f961722", }, }; static int nistp_single_test(int idx) { const struct nistp_test_params *test = nistp_tests_params + idx; BN_CTX *ctx = NULL; BIGNUM *p = NULL, *a = NULL, *b = NULL, *x = NULL, *y = NULL; BIGNUM *n = NULL, *m = NULL, *order = NULL, *yplusone = NULL; EC_GROUP *NISTP = NULL; EC_POINT *G = NULL, *P = NULL, *Q = NULL, *Q_CHECK = NULL; int r = 0; TEST_note("NIST curve P-%d (optimised implementation):", test->degree); if (!TEST_ptr(ctx = BN_CTX_new()) || !TEST_ptr(p = BN_new()) || !TEST_ptr(a = BN_new()) || !TEST_ptr(b = BN_new()) || !TEST_ptr(x = BN_new()) || !TEST_ptr(y = BN_new()) || !TEST_ptr(m = BN_new()) || !TEST_ptr(n = BN_new()) || !TEST_ptr(order = BN_new()) || !TEST_ptr(yplusone = BN_new()) || !TEST_ptr(NISTP = EC_GROUP_new(test->meth())) || !TEST_true(BN_hex2bn(&p, test->p)) || !TEST_int_eq(1, BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) || !TEST_true(BN_hex2bn(&a, test->a)) || !TEST_true(BN_hex2bn(&b, test->b)) || !TEST_true(EC_GROUP_set_curve(NISTP, p, a, b, ctx)) || !TEST_ptr(G = EC_POINT_new(NISTP)) || !TEST_ptr(P = EC_POINT_new(NISTP)) || !TEST_ptr(Q = EC_POINT_new(NISTP)) || !TEST_ptr(Q_CHECK = EC_POINT_new(NISTP)) || !TEST_true(BN_hex2bn(&x, test->Qx)) || !TEST_true(BN_hex2bn(&y, test->Qy)) || !TEST_true(BN_add(yplusone, y, BN_value_one())) /* * When (x, y) is on the curve, (x, y + 1) is, as it happens, not, * and therefore setting the coordinates should fail. */ || !TEST_false(EC_POINT_set_affine_coordinates(NISTP, Q_CHECK, x, yplusone, ctx)) || !TEST_true(EC_POINT_set_affine_coordinates(NISTP, Q_CHECK, x, y, ctx)) || !TEST_true(BN_hex2bn(&x, test->Gx)) || !TEST_true(BN_hex2bn(&y, test->Gy)) || !TEST_true(EC_POINT_set_affine_coordinates(NISTP, G, x, y, ctx)) || !TEST_true(BN_hex2bn(&order, test->order)) || !TEST_true(EC_GROUP_set_generator(NISTP, G, order, BN_value_one())) || !TEST_int_eq(EC_GROUP_get_degree(NISTP), test->degree)) goto err; TEST_note("NIST test vectors ... "); if (!TEST_true(BN_hex2bn(&n, test->d))) goto err; /* fixed point multiplication */ EC_POINT_mul(NISTP, Q, n, NULL, NULL, ctx); if (!TEST_int_eq(0, EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx))) goto err; /* random point multiplication */ EC_POINT_mul(NISTP, Q, NULL, G, n, ctx); if (!TEST_int_eq(0, EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) /* set generator to P = 2*G, where G is the standard generator */ || !TEST_true(EC_POINT_dbl(NISTP, P, G, ctx)) || !TEST_true(EC_GROUP_set_generator(NISTP, P, order, BN_value_one())) /* set the scalar to m=n/2, where n is the NIST test scalar */ || !TEST_true(BN_rshift(m, n, 1))) goto err; /* test the non-standard generator */ /* fixed point multiplication */ EC_POINT_mul(NISTP, Q, m, NULL, NULL, ctx); if (!TEST_int_eq(0, EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx))) goto err; /* random point multiplication */ EC_POINT_mul(NISTP, Q, NULL, P, m, ctx); if (!TEST_int_eq(0, EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) /* * We have not performed precomputation so have_precompute mult should be * false */ || !TEST_false(EC_GROUP_have_precompute_mult(NISTP)) /* now repeat all tests with precomputation */ || !TEST_true(EC_GROUP_precompute_mult(NISTP, ctx)) || !TEST_true(EC_GROUP_have_precompute_mult(NISTP))) goto err; /* fixed point multiplication */ EC_POINT_mul(NISTP, Q, m, NULL, NULL, ctx); if (!TEST_int_eq(0, EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx))) goto err; /* random point multiplication */ EC_POINT_mul(NISTP, Q, NULL, P, m, ctx); if (!TEST_int_eq(0, EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) /* reset generator */ || !TEST_true(EC_GROUP_set_generator(NISTP, G, order, BN_value_one()))) goto err; /* fixed point multiplication */ EC_POINT_mul(NISTP, Q, n, NULL, NULL, ctx); if (!TEST_int_eq(0, EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx))) goto err; /* random point multiplication */ EC_POINT_mul(NISTP, Q, NULL, G, n, ctx); if (!TEST_int_eq(0, EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx))) goto err; /* regression test for felem_neg bug */ if (!TEST_true(BN_set_word(m, 32)) || !TEST_true(BN_set_word(n, 31)) || !TEST_true(EC_POINT_copy(P, G)) || !TEST_true(EC_POINT_invert(NISTP, P, ctx)) || !TEST_true(EC_POINT_mul(NISTP, Q, m, P, n, ctx)) || !TEST_int_eq(0, EC_POINT_cmp(NISTP, Q, G, ctx))) goto err; r = group_order_tests(NISTP); err: EC_GROUP_free(NISTP); EC_POINT_free(G); EC_POINT_free(P); EC_POINT_free(Q); EC_POINT_free(Q_CHECK); BN_free(n); BN_free(m); BN_free(p); BN_free(a); BN_free(b); BN_free(x); BN_free(y); BN_free(order); BN_free(yplusone); BN_CTX_free(ctx); return r; } /* * Tests a point known to cause an incorrect underflow in an old version of * ecp_nist521.c */ static int underflow_test(void) { BN_CTX *ctx = NULL; EC_GROUP *grp = NULL; EC_POINT *P = NULL, *Q = NULL, *R = NULL; BIGNUM *x1 = NULL, *y1 = NULL, *z1 = NULL, *x2 = NULL, *y2 = NULL; BIGNUM *k = NULL; int testresult = 0; const char *x1str = "1534f0077fffffe87e9adcfe000000000000000000003e05a21d2400002e031b1f4" "b80000c6fafa4f3c1288798d624a247b5e2ffffffffffffffefe099241900004"; const char *p521m1 = "1ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff" "fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe"; ctx = BN_CTX_new(); if (!TEST_ptr(ctx)) return 0; BN_CTX_start(ctx); x1 = BN_CTX_get(ctx); y1 = BN_CTX_get(ctx); z1 = BN_CTX_get(ctx); x2 = BN_CTX_get(ctx); y2 = BN_CTX_get(ctx); k = BN_CTX_get(ctx); if (!TEST_ptr(k)) goto err; grp = EC_GROUP_new_by_curve_name(NID_secp521r1); P = EC_POINT_new(grp); Q = EC_POINT_new(grp); R = EC_POINT_new(grp); if (!TEST_ptr(grp) || !TEST_ptr(P) || !TEST_ptr(Q) || !TEST_ptr(R)) goto err; if (!TEST_int_gt(BN_hex2bn(&x1, x1str), 0) || !TEST_int_gt(BN_hex2bn(&y1, p521m1), 0) || !TEST_int_gt(BN_hex2bn(&z1, p521m1), 0) || !TEST_int_gt(BN_hex2bn(&k, "02"), 0) || !TEST_true(EC_POINT_set_Jprojective_coordinates_GFp(grp, P, x1, y1, z1, ctx)) || !TEST_true(EC_POINT_mul(grp, Q, NULL, P, k, ctx)) || !TEST_true(EC_POINT_get_affine_coordinates(grp, Q, x1, y1, ctx)) || !TEST_true(EC_POINT_dbl(grp, R, P, ctx)) || !TEST_true(EC_POINT_get_affine_coordinates(grp, R, x2, y2, ctx))) goto err; if (!TEST_int_eq(BN_cmp(x1, x2), 0) || !TEST_int_eq(BN_cmp(y1, y2), 0)) goto err; testresult = 1; err: BN_CTX_end(ctx); EC_POINT_free(P); EC_POINT_free(Q); EC_GROUP_free(grp); BN_CTX_free(ctx); return testresult; } # endif static const unsigned char p521_named[] = { 0x06, 0x05, 0x2b, 0x81, 0x04, 0x00, 0x23, }; static const unsigned char p521_explicit[] = { 0x30, 0x82, 0x01, 0xc3, 0x02, 0x01, 0x01, 0x30, 0x4d, 0x06, 0x07, 0x2a, 0x86, 0x48, 0xce, 0x3d, 0x01, 0x01, 0x02, 0x42, 0x01, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x30, 0x81, 0x9f, 0x04, 0x42, 0x01, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfc, 0x04, 0x42, 0x00, 0x51, 0x95, 0x3e, 0xb9, 0x61, 0x8e, 0x1c, 0x9a, 0x1f, 0x92, 0x9a, 0x21, 0xa0, 0xb6, 0x85, 0x40, 0xee, 0xa2, 0xda, 0x72, 0x5b, 0x99, 0xb3, 0x15, 0xf3, 0xb8, 0xb4, 0x89, 0x91, 0x8e, 0xf1, 0x09, 0xe1, 0x56, 0x19, 0x39, 0x51, 0xec, 0x7e, 0x93, 0x7b, 0x16, 0x52, 0xc0, 0xbd, 0x3b, 0xb1, 0xbf, 0x07, 0x35, 0x73, 0xdf, 0x88, 0x3d, 0x2c, 0x34, 0xf1, 0xef, 0x45, 0x1f, 0xd4, 0x6b, 0x50, 0x3f, 0x00, 0x03, 0x15, 0x00, 0xd0, 0x9e, 0x88, 0x00, 0x29, 0x1c, 0xb8, 0x53, 0x96, 0xcc, 0x67, 0x17, 0x39, 0x32, 0x84, 0xaa, 0xa0, 0xda, 0x64, 0xba, 0x04, 0x81, 0x85, 0x04, 0x00, 0xc6, 0x85, 0x8e, 0x06, 0xb7, 0x04, 0x04, 0xe9, 0xcd, 0x9e, 0x3e, 0xcb, 0x66, 0x23, 0x95, 0xb4, 0x42, 0x9c, 0x64, 0x81, 0x39, 0x05, 0x3f, 0xb5, 0x21, 0xf8, 0x28, 0xaf, 0x60, 0x6b, 0x4d, 0x3d, 0xba, 0xa1, 0x4b, 0x5e, 0x77, 0xef, 0xe7, 0x59, 0x28, 0xfe, 0x1d, 0xc1, 0x27, 0xa2, 0xff, 0xa8, 0xde, 0x33, 0x48, 0xb3, 0xc1, 0x85, 0x6a, 0x42, 0x9b, 0xf9, 0x7e, 0x7e, 0x31, 0xc2, 0xe5, 0xbd, 0x66, 0x01, 0x18, 0x39, 0x29, 0x6a, 0x78, 0x9a, 0x3b, 0xc0, 0x04, 0x5c, 0x8a, 0x5f, 0xb4, 0x2c, 0x7d, 0x1b, 0xd9, 0x98, 0xf5, 0x44, 0x49, 0x57, 0x9b, 0x44, 0x68, 0x17, 0xaf, 0xbd, 0x17, 0x27, 0x3e, 0x66, 0x2c, 0x97, 0xee, 0x72, 0x99, 0x5e, 0xf4, 0x26, 0x40, 0xc5, 0x50, 0xb9, 0x01, 0x3f, 0xad, 0x07, 0x61, 0x35, 0x3c, 0x70, 0x86, 0xa2, 0x72, 0xc2, 0x40, 0x88, 0xbe, 0x94, 0x76, 0x9f, 0xd1, 0x66, 0x50, 0x02, 0x42, 0x01, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfa, 0x51, 0x86, 0x87, 0x83, 0xbf, 0x2f, 0x96, 0x6b, 0x7f, 0xcc, 0x01, 0x48, 0xf7, 0x09, 0xa5, 0xd0, 0x3b, 0xb5, 0xc9, 0xb8, 0x89, 0x9c, 0x47, 0xae, 0xbb, 0x6f, 0xb7, 0x1e, 0x91, 0x38, 0x64, 0x09, 0x02, 0x01, 0x01, }; static int parameter_test(void) { EC_GROUP *group = NULL, *group2 = NULL; ECPARAMETERS *ecparameters = NULL; unsigned char *buf = NULL; int r = 0, len; if (!TEST_ptr(group = EC_GROUP_new_by_curve_name(NID_secp112r1)) || !TEST_ptr(ecparameters = EC_GROUP_get_ecparameters(group, NULL)) || !TEST_ptr(group2 = EC_GROUP_new_from_ecparameters(ecparameters)) || !TEST_int_eq(EC_GROUP_cmp(group, group2, NULL), 0)) goto err; EC_GROUP_free(group); group = NULL; /* Test the named curve encoding, which should be default. */ if (!TEST_ptr(group = EC_GROUP_new_by_curve_name(NID_secp521r1)) || !TEST_true((len = i2d_ECPKParameters(group, &buf)) >= 0) || !TEST_mem_eq(buf, len, p521_named, sizeof(p521_named))) goto err; OPENSSL_free(buf); buf = NULL; /* * Test the explicit encoding. P-521 requires correctly zero-padding the * curve coefficients. */ EC_GROUP_set_asn1_flag(group, OPENSSL_EC_EXPLICIT_CURVE); if (!TEST_true((len = i2d_ECPKParameters(group, &buf)) >= 0) || !TEST_mem_eq(buf, len, p521_explicit, sizeof(p521_explicit))) goto err; r = 1; err: EC_GROUP_free(group); EC_GROUP_free(group2); ECPARAMETERS_free(ecparameters); OPENSSL_free(buf); return r; } #endif int setup_tests(void) { #ifndef OPENSSL_NO_EC crv_len = EC_get_builtin_curves(NULL, 0); if (!TEST_ptr(curves = OPENSSL_malloc(sizeof(*curves) * crv_len)) || !TEST_true(EC_get_builtin_curves(curves, crv_len))) return 0; ADD_TEST(parameter_test); ADD_TEST(prime_field_tests); # ifndef OPENSSL_NO_EC2M ADD_TEST(char2_field_tests); ADD_ALL_TESTS(char2_curve_test, OSSL_NELEM(char2_curve_tests)); # endif # ifndef OPENSSL_NO_EC_NISTP_64_GCC_128 ADD_ALL_TESTS(nistp_single_test, OSSL_NELEM(nistp_tests_params)); ADD_TEST(underflow_test); # endif ADD_ALL_TESTS(internal_curve_test, crv_len); ADD_ALL_TESTS(internal_curve_test_method, crv_len); #endif return 1; } void cleanup_tests(void) { #ifndef OPENSSL_NO_EC OPENSSL_free(curves); #endif }