| /* crypto/ec/ectest.c */ |
| /* |
| * Originally written by Bodo Moeller for the OpenSSL project. |
| */ |
| /* ==================================================================== |
| * Copyright (c) 1998-2001 The OpenSSL Project. All rights reserved. |
| * |
| * Redistribution and use in source and binary forms, with or without |
| * modification, are permitted provided that the following conditions |
| * are met: |
| * |
| * 1. Redistributions of source code must retain the above copyright |
| * notice, this list of conditions and the following disclaimer. |
| * |
| * 2. Redistributions in binary form must reproduce the above copyright |
| * notice, this list of conditions and the following disclaimer in |
| * the documentation and/or other materials provided with the |
| * distribution. |
| * |
| * 3. All advertising materials mentioning features or use of this |
| * software must display the following acknowledgment: |
| * "This product includes software developed by the OpenSSL Project |
| * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" |
| * |
| * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to |
| * endorse or promote products derived from this software without |
| * prior written permission. For written permission, please contact |
| * openssl-core@openssl.org. |
| * |
| * 5. Products derived from this software may not be called "OpenSSL" |
| * nor may "OpenSSL" appear in their names without prior written |
| * permission of the OpenSSL Project. |
| * |
| * 6. Redistributions of any form whatsoever must retain the following |
| * acknowledgment: |
| * "This product includes software developed by the OpenSSL Project |
| * for use in the OpenSSL Toolkit (http://www.openssl.org/)" |
| * |
| * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY |
| * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE |
| * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR |
| * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR |
| * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, |
| * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT |
| * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; |
| * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) |
| * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, |
| * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) |
| * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED |
| * OF THE POSSIBILITY OF SUCH DAMAGE. |
| * ==================================================================== |
| * |
| * This product includes cryptographic software written by Eric Young |
| * (eay@cryptsoft.com). This product includes software written by Tim |
| * Hudson (tjh@cryptsoft.com). |
| * |
| */ |
| /* ==================================================================== |
| * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. |
| * |
| * Portions of the attached software ("Contribution") are developed by |
| * SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project. |
| * |
| * The Contribution is licensed pursuant to the OpenSSL open source |
| * license provided above. |
| * |
| * The elliptic curve binary polynomial software is originally written by |
| * Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems Laboratories. |
| * |
| */ |
| |
| #include <stdio.h> |
| #include <stdlib.h> |
| #ifdef FLAT_INC |
| # include "e_os.h" |
| #else |
| # include "../e_os.h" |
| #endif |
| #include <string.h> |
| #include <time.h> |
| |
| #ifdef OPENSSL_NO_EC |
| int main(int argc, char *argv[]) |
| { |
| puts("Elliptic curves are disabled."); |
| return 0; |
| } |
| #else |
| |
| # include <openssl/ec.h> |
| # ifndef OPENSSL_NO_ENGINE |
| # include <openssl/engine.h> |
| # endif |
| # include <openssl/err.h> |
| # include <openssl/obj_mac.h> |
| # include <openssl/objects.h> |
| # include <openssl/rand.h> |
| # include <openssl/bn.h> |
| # include <openssl/opensslconf.h> |
| |
| # if defined(_MSC_VER) && defined(_MIPS_) && (_MSC_VER/100==12) |
| /* suppress "too big too optimize" warning */ |
| # pragma warning(disable:4959) |
| # endif |
| |
| # define ABORT do { \ |
| fflush(stdout); \ |
| fprintf(stderr, "%s:%d: ABORT\n", __FILE__, __LINE__); \ |
| ERR_print_errors_fp(stderr); \ |
| EXIT(1); \ |
| } while (0) |
| |
| # 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 |
| |
| /* 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; |
| |
| # 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 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) */ |
| |
| 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); |
| |
| } |
| |
| /* Change test based on whether binary point compression is enabled or not. */ |
| # ifdef OPENSSL_EC_BIN_PT_COMP |
| # define CHAR2_CURVE_TEST_INTERNAL(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \ |
| if (!BN_hex2bn(&x, _x)) ABORT; \ |
| if (!EC_POINT_set_compressed_coordinates_GF2m(group, P, x, _y_bit, ctx)) ABORT; \ |
| if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT; \ |
| if (!BN_hex2bn(&z, _order)) ABORT; \ |
| if (!BN_hex2bn(&cof, _cof)) ABORT; \ |
| if (!EC_GROUP_set_generator(group, P, z, cof)) ABORT; \ |
| if (!EC_POINT_get_affine_coordinates_GF2m(group, P, x, y, ctx)) ABORT; \ |
| fprintf(stdout, "\n%s -- Generator:\n x = 0x", _name); \ |
| 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, _y)) ABORT; \ |
| if (0 != BN_cmp(y, z)) ABORT; |
| # else |
| # define CHAR2_CURVE_TEST_INTERNAL(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \ |
| if (!BN_hex2bn(&x, _x)) ABORT; \ |
| if (!BN_hex2bn(&y, _y)) ABORT; \ |
| if (!EC_POINT_set_affine_coordinates_GF2m(group, P, x, y, ctx)) ABORT; \ |
| if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT; \ |
| if (!BN_hex2bn(&z, _order)) ABORT; \ |
| if (!BN_hex2bn(&cof, _cof)) ABORT; \ |
| if (!EC_GROUP_set_generator(group, P, z, cof)) ABORT; \ |
| fprintf(stdout, "\n%s -- Generator:\n x = 0x", _name); \ |
| BN_print_fp(stdout, x); \ |
| fprintf(stdout, "\n y = 0x"); \ |
| BN_print_fp(stdout, y); \ |
| fprintf(stdout, "\n"); |
| # endif |
| |
| # define CHAR2_CURVE_TEST(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \ |
| if (!BN_hex2bn(&p, _p)) ABORT; \ |
| if (!BN_hex2bn(&a, _a)) ABORT; \ |
| if (!BN_hex2bn(&b, _b)) ABORT; \ |
| if (!EC_GROUP_set_curve_GF2m(group, p, a, b, ctx)) ABORT; \ |
| CHAR2_CURVE_TEST_INTERNAL(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \ |
| fprintf(stdout, "verify degree ..."); \ |
| if (EC_GROUP_get_degree(group) != _degree) ABORT; \ |
| fprintf(stdout, " ok\n"); \ |
| group_order_tests(group); \ |
| if (!(_variable = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT; \ |
| if (!EC_GROUP_copy(_variable, group)) ABORT; \ |
| |
| # ifndef OPENSSL_NO_EC2M |
| |
| static void char2_field_tests(void) |
| { |
| BN_CTX *ctx = NULL; |
| BIGNUM *p, *a, *b; |
| EC_GROUP *group; |
| EC_GROUP *C2_K163 = NULL, *C2_K233 = NULL, *C2_K283 = NULL, *C2_K409 = |
| NULL, *C2_K571 = NULL; |
| EC_GROUP *C2_B163 = NULL, *C2_B233 = NULL, *C2_B283 = NULL, *C2_B409 = |
| NULL, *C2_B571 = NULL; |
| EC_POINT *P, *Q, *R; |
| BIGNUM *x, *y, *z, *cof; |
| unsigned char buf[100]; |
| size_t i, len; |
| int k; |
| |
| # if 1 /* optional */ |
| ctx = BN_CTX_new(); |
| if (!ctx) |
| ABORT; |
| # endif |
| |
| p = BN_new(); |
| a = BN_new(); |
| b = BN_new(); |
| if (!p || !a || !b) |
| ABORT; |
| |
| if (!BN_hex2bn(&p, "13")) |
| ABORT; |
| if (!BN_hex2bn(&a, "3")) |
| ABORT; |
| if (!BN_hex2bn(&b, "1")) |
| ABORT; |
| |
| group = EC_GROUP_new(EC_GF2m_simple_method()); /* applications should use |
| * EC_GROUP_new_curve_GF2m |
| * so that the library gets |
| * to choose the EC_METHOD */ |
| if (!group) |
| ABORT; |
| if (!EC_GROUP_set_curve_GF2m(group, p, a, b, ctx)) |
| ABORT; |
| |
| { |
| EC_GROUP *tmp; |
| tmp = EC_GROUP_new(EC_GROUP_method_of(group)); |
| if (!tmp) |
| ABORT; |
| if (!EC_GROUP_copy(tmp, group)) |
| ABORT; |
| EC_GROUP_free(group); |
| group = tmp; |
| } |
| |
| if (!EC_GROUP_get_curve_GF2m(group, p, a, b, ctx)) |
| ABORT; |
| |
| fprintf(stdout, |
| "Curve defined by Weierstrass equation\n y^2 + x*y = x^3 + a*x^2 + b (mod 0x"); |
| BN_print_fp(stdout, p); |
| fprintf(stdout, ")\n a = 0x"); |
| BN_print_fp(stdout, a); |
| fprintf(stdout, "\n b = 0x"); |
| BN_print_fp(stdout, b); |
| fprintf(stdout, "\n(0x... means binary polynomial)\n"); |
| |
| P = EC_POINT_new(group); |
| Q = EC_POINT_new(group); |
| R = EC_POINT_new(group); |
| if (!P || !Q || !R) |
| ABORT; |
| |
| if (!EC_POINT_set_to_infinity(group, P)) |
| ABORT; |
| if (!EC_POINT_is_at_infinity(group, P)) |
| ABORT; |
| |
| buf[0] = 0; |
| if (!EC_POINT_oct2point(group, Q, buf, 1, ctx)) |
| ABORT; |
| |
| if (!EC_POINT_add(group, P, P, Q, ctx)) |
| ABORT; |
| if (!EC_POINT_is_at_infinity(group, P)) |
| ABORT; |
| |
| x = BN_new(); |
| y = BN_new(); |
| z = BN_new(); |
| cof = BN_new(); |
| if (!x || !y || !z || !cof) |
| ABORT; |
| |
| if (!BN_hex2bn(&x, "6")) |
| ABORT; |
| /* Change test based on whether binary point compression is enabled or not. */ |
| # ifdef OPENSSL_EC_BIN_PT_COMP |
| if (!EC_POINT_set_compressed_coordinates_GF2m(group, Q, x, 1, ctx)) |
| ABORT; |
| # else |
| if (!BN_hex2bn(&y, "8")) |
| ABORT; |
| if (!EC_POINT_set_affine_coordinates_GF2m(group, Q, x, y, ctx)) |
| ABORT; |
| # endif |
| if (!EC_POINT_is_on_curve(group, Q, ctx)) { |
| /* Change test based on whether binary point compression is enabled or not. */ |
| # ifdef OPENSSL_EC_BIN_PT_COMP |
| if (!EC_POINT_get_affine_coordinates_GF2m(group, Q, x, y, ctx)) |
| ABORT; |
| # endif |
| fprintf(stderr, "Point is not on curve: x = 0x"); |
| BN_print_fp(stderr, x); |
| fprintf(stderr, ", y = 0x"); |
| BN_print_fp(stderr, y); |
| fprintf(stderr, "\n"); |
| ABORT; |
| } |
| |
| fprintf(stdout, "A cyclic subgroup:\n"); |
| k = 100; |
| do { |
| if (k-- == 0) |
| ABORT; |
| |
| if (EC_POINT_is_at_infinity(group, P)) |
| fprintf(stdout, " point at infinity\n"); |
| else { |
| if (!EC_POINT_get_affine_coordinates_GF2m(group, P, x, y, ctx)) |
| ABORT; |
| |
| fprintf(stdout, " x = 0x"); |
| BN_print_fp(stdout, x); |
| fprintf(stdout, ", y = 0x"); |
| BN_print_fp(stdout, y); |
| fprintf(stdout, "\n"); |
| } |
| |
| if (!EC_POINT_copy(R, P)) |
| ABORT; |
| if (!EC_POINT_add(group, P, P, Q, ctx)) |
| ABORT; |
| } |
| while (!EC_POINT_is_at_infinity(group, P)); |
| |
| if (!EC_POINT_add(group, P, Q, R, ctx)) |
| ABORT; |
| if (!EC_POINT_is_at_infinity(group, P)) |
| ABORT; |
| |
| /* Change test based on whether binary point compression is enabled or not. */ |
| # ifdef OPENSSL_EC_BIN_PT_COMP |
| len = |
| EC_POINT_point2oct(group, Q, POINT_CONVERSION_COMPRESSED, buf, |
| sizeof buf, ctx); |
| if (len == 0) |
| ABORT; |
| if (!EC_POINT_oct2point(group, P, buf, len, ctx)) |
| ABORT; |
| if (0 != EC_POINT_cmp(group, P, Q, ctx)) |
| ABORT; |
| fprintf(stdout, "Generator as octet string, compressed form:\n "); |
| for (i = 0; i < len; i++) |
| fprintf(stdout, "%02X", buf[i]); |
| # endif |
| |
| len = |
| EC_POINT_point2oct(group, Q, POINT_CONVERSION_UNCOMPRESSED, buf, |
| sizeof buf, ctx); |
| if (len == 0) |
| ABORT; |
| if (!EC_POINT_oct2point(group, P, buf, len, ctx)) |
| ABORT; |
| if (0 != EC_POINT_cmp(group, P, Q, ctx)) |
| ABORT; |
| fprintf(stdout, "\nGenerator as octet string, uncompressed form:\n "); |
| for (i = 0; i < len; i++) |
| fprintf(stdout, "%02X", buf[i]); |
| |
| /* Change test based on whether binary point compression is enabled or not. */ |
| # ifdef OPENSSL_EC_BIN_PT_COMP |
| len = |
| EC_POINT_point2oct(group, Q, POINT_CONVERSION_HYBRID, buf, sizeof buf, |
| ctx); |
| if (len == 0) |
| ABORT; |
| if (!EC_POINT_oct2point(group, P, buf, len, ctx)) |
| ABORT; |
| if (0 != EC_POINT_cmp(group, P, Q, ctx)) |
| ABORT; |
| fprintf(stdout, "\nGenerator as octet string, hybrid form:\n "); |
| for (i = 0; i < len; i++) |
| fprintf(stdout, "%02X", buf[i]); |
| # endif |
| |
| fprintf(stdout, "\n"); |
| |
| if (!EC_POINT_invert(group, P, ctx)) |
| ABORT; |
| if (0 != EC_POINT_cmp(group, P, R, ctx)) |
| ABORT; |
| |
| /* Curve K-163 (FIPS PUB 186-2, App. 6) */ |
| CHAR2_CURVE_TEST |
| ("NIST curve K-163", |
| "0800000000000000000000000000000000000000C9", |
| "1", |
| "1", |
| "02FE13C0537BBC11ACAA07D793DE4E6D5E5C94EEE8", |
| "0289070FB05D38FF58321F2E800536D538CCDAA3D9", |
| 1, "04000000000000000000020108A2E0CC0D99F8A5EF", "2", 163, C2_K163); |
| |
| /* Curve B-163 (FIPS PUB 186-2, App. 6) */ |
| CHAR2_CURVE_TEST |
| ("NIST curve B-163", |
| "0800000000000000000000000000000000000000C9", |
| "1", |
| "020A601907B8C953CA1481EB10512F78744A3205FD", |
| "03F0EBA16286A2D57EA0991168D4994637E8343E36", |
| "00D51FBC6C71A0094FA2CDD545B11C5C0C797324F1", |
| 1, "040000000000000000000292FE77E70C12A4234C33", "2", 163, C2_B163); |
| |
| /* Curve K-233 (FIPS PUB 186-2, App. 6) */ |
| CHAR2_CURVE_TEST |
| ("NIST curve K-233", |
| "020000000000000000000000000000000000000004000000000000000001", |
| "0", |
| "1", |
| "017232BA853A7E731AF129F22FF4149563A419C26BF50A4C9D6EEFAD6126", |
| "01DB537DECE819B7F70F555A67C427A8CD9BF18AEB9B56E0C11056FAE6A3", |
| 0, |
| "008000000000000000000000000000069D5BB915BCD46EFB1AD5F173ABDF", |
| "4", 233, C2_K233); |
| |
| /* Curve B-233 (FIPS PUB 186-2, App. 6) */ |
| CHAR2_CURVE_TEST |
| ("NIST curve B-233", |
| "020000000000000000000000000000000000000004000000000000000001", |
| "000000000000000000000000000000000000000000000000000000000001", |
| "0066647EDE6C332C7F8C0923BB58213B333B20E9CE4281FE115F7D8F90AD", |
| "00FAC9DFCBAC8313BB2139F1BB755FEF65BC391F8B36F8F8EB7371FD558B", |
| "01006A08A41903350678E58528BEBF8A0BEFF867A7CA36716F7E01F81052", |
| 1, |
| "01000000000000000000000000000013E974E72F8A6922031D2603CFE0D7", |
| "2", 233, C2_B233); |
| |
| /* Curve K-283 (FIPS PUB 186-2, App. 6) */ |
| CHAR2_CURVE_TEST |
| ("NIST curve K-283", |
| "0800000000000000000000000000000000000000000000000000000000000000000010A1", |
| "0", |
| "1", |
| "0503213F78CA44883F1A3B8162F188E553CD265F23C1567A16876913B0C2AC2458492836", |
| "01CCDA380F1C9E318D90F95D07E5426FE87E45C0E8184698E45962364E34116177DD2259", |
| 0, |
| "01FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE9AE2ED07577265DFF7F94451E061E163C61", |
| "4", 283, C2_K283); |
| |
| /* Curve B-283 (FIPS PUB 186-2, App. 6) */ |
| CHAR2_CURVE_TEST |
| ("NIST curve B-283", |
| "0800000000000000000000000000000000000000000000000000000000000000000010A1", |
| "000000000000000000000000000000000000000000000000000000000000000000000001", |
| "027B680AC8B8596DA5A4AF8A19A0303FCA97FD7645309FA2A581485AF6263E313B79A2F5", |
| "05F939258DB7DD90E1934F8C70B0DFEC2EED25B8557EAC9C80E2E198F8CDBECD86B12053", |
| "03676854FE24141CB98FE6D4B20D02B4516FF702350EDDB0826779C813F0DF45BE8112F4", |
| 1, |
| "03FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEF90399660FC938A90165B042A7CEFADB307", |
| "2", 283, C2_B283); |
| |
| /* Curve K-409 (FIPS PUB 186-2, App. 6) */ |
| CHAR2_CURVE_TEST |
| ("NIST curve K-409", |
| "02000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001", |
| "0", |
| "1", |
| "0060F05F658F49C1AD3AB1890F7184210EFD0987E307C84C27ACCFB8F9F67CC2C460189EB5AAAA62EE222EB1B35540CFE9023746", |
| "01E369050B7C4E42ACBA1DACBF04299C3460782F918EA427E6325165E9EA10E3DA5F6C42E9C55215AA9CA27A5863EC48D8E0286B", |
| 1, |
| "007FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE5F83B2D4EA20400EC4557D5ED3E3E7CA5B4B5C83B8E01E5FCF", |
| "4", 409, C2_K409); |
| |
| /* Curve B-409 (FIPS PUB 186-2, App. 6) */ |
| CHAR2_CURVE_TEST |
| ("NIST curve B-409", |
| "02000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001", |
| "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001", |
| "0021A5C2C8EE9FEB5C4B9A753B7B476B7FD6422EF1F3DD674761FA99D6AC27C8A9A197B272822F6CD57A55AA4F50AE317B13545F", |
| "015D4860D088DDB3496B0C6064756260441CDE4AF1771D4DB01FFE5B34E59703DC255A868A1180515603AEAB60794E54BB7996A7", |
| "0061B1CFAB6BE5F32BBFA78324ED106A7636B9C5A7BD198D0158AA4F5488D08F38514F1FDF4B4F40D2181B3681C364BA0273C706", |
| 1, |
| "010000000000000000000000000000000000000000000000000001E2AAD6A612F33307BE5FA47C3C9E052F838164CD37D9A21173", |
| "2", 409, C2_B409); |
| |
| /* Curve K-571 (FIPS PUB 186-2, App. 6) */ |
| CHAR2_CURVE_TEST |
| ("NIST curve K-571", |
| "80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425", |
| "0", |
| "1", |
| "026EB7A859923FBC82189631F8103FE4AC9CA2970012D5D46024804801841CA44370958493B205E647DA304DB4CEB08CBBD1BA39494776FB988B47174DCA88C7E2945283A01C8972", |
| "0349DC807F4FBF374F4AEADE3BCA95314DD58CEC9F307A54FFC61EFC006D8A2C9D4979C0AC44AEA74FBEBBB9F772AEDCB620B01A7BA7AF1B320430C8591984F601CD4C143EF1C7A3", |
| 0, |
| "020000000000000000000000000000000000000000000000000000000000000000000000131850E1F19A63E4B391A8DB917F4138B630D84BE5D639381E91DEB45CFE778F637C1001", |
| "4", 571, C2_K571); |
| |
| /* Curve B-571 (FIPS PUB 186-2, App. 6) */ |
| CHAR2_CURVE_TEST |
| ("NIST curve B-571", |
| "80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425", |
| "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001", |
| "02F40E7E2221F295DE297117B7F3D62F5C6A97FFCB8CEFF1CD6BA8CE4A9A18AD84FFABBD8EFA59332BE7AD6756A66E294AFD185A78FF12AA520E4DE739BACA0C7FFEFF7F2955727A", |
| "0303001D34B856296C16C0D40D3CD7750A93D1D2955FA80AA5F40FC8DB7B2ABDBDE53950F4C0D293CDD711A35B67FB1499AE60038614F1394ABFA3B4C850D927E1E7769C8EEC2D19", |
| "037BF27342DA639B6DCCFFFEB73D69D78C6C27A6009CBBCA1980F8533921E8A684423E43BAB08A576291AF8F461BB2A8B3531D2F0485C19B16E2F1516E23DD3C1A4827AF1B8AC15B", |
| 1, |
| "03FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE661CE18FF55987308059B186823851EC7DD9CA1161DE93D5174D66E8382E9BB2FE84E47", |
| "2", 571, C2_B571); |
| |
| /* more tests using the last curve */ |
| |
| if (!EC_POINT_copy(Q, P)) |
| ABORT; |
| if (EC_POINT_is_at_infinity(group, Q)) |
| ABORT; |
| if (!EC_POINT_dbl(group, P, P, ctx)) |
| ABORT; |
| if (!EC_POINT_is_on_curve(group, P, ctx)) |
| ABORT; |
| if (!EC_POINT_invert(group, Q, ctx)) |
| ABORT; /* P = -2Q */ |
| |
| if (!EC_POINT_add(group, R, P, Q, ctx)) |
| ABORT; |
| if (!EC_POINT_add(group, R, R, Q, ctx)) |
| ABORT; |
| if (!EC_POINT_is_at_infinity(group, R)) |
| ABORT; /* R = P + 2Q */ |
| |
| { |
| const EC_POINT *points[3]; |
| const BIGNUM *scalars[3]; |
| |
| if (EC_POINT_is_at_infinity(group, Q)) |
| ABORT; |
| points[0] = Q; |
| points[1] = Q; |
| points[2] = Q; |
| |
| if (!BN_add(y, z, BN_value_one())) |
| ABORT; |
| if (BN_is_odd(y)) |
| ABORT; |
| if (!BN_rshift1(y, y)) |
| ABORT; |
| scalars[0] = y; /* (group order + 1)/2, so y*Q + y*Q = Q */ |
| scalars[1] = y; |
| |
| fprintf(stdout, "combined multiplication ..."); |
| fflush(stdout); |
| |
| /* z is still the group order */ |
| if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) |
| ABORT; |
| if (!EC_POINTs_mul(group, R, z, 2, points, scalars, ctx)) |
| ABORT; |
| if (0 != EC_POINT_cmp(group, P, R, ctx)) |
| ABORT; |
| if (0 != EC_POINT_cmp(group, R, Q, ctx)) |
| ABORT; |
| |
| fprintf(stdout, "."); |
| fflush(stdout); |
| |
| if (!BN_pseudo_rand(y, BN_num_bits(y), 0, 0)) |
| ABORT; |
| if (!BN_add(z, z, y)) |
| ABORT; |
| BN_set_negative(z, 1); |
| scalars[0] = y; |
| scalars[1] = z; /* z = -(order + y) */ |
| |
| if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) |
| ABORT; |
| if (!EC_POINT_is_at_infinity(group, P)) |
| ABORT; |
| |
| fprintf(stdout, "."); |
| fflush(stdout); |
| |
| if (!BN_pseudo_rand(x, BN_num_bits(y) - 1, 0, 0)) |
| ABORT; |
| if (!BN_add(z, x, y)) |
| ABORT; |
| BN_set_negative(z, 1); |
| scalars[0] = x; |
| scalars[1] = y; |
| scalars[2] = z; /* z = -(x+y) */ |
| |
| if (!EC_POINTs_mul(group, P, NULL, 3, points, scalars, ctx)) |
| ABORT; |
| if (!EC_POINT_is_at_infinity(group, P)) |
| ABORT; |
| |
| fprintf(stdout, " ok\n\n"); |
| } |
| |
| # if 0 |
| timings(C2_K163, TIMING_BASE_PT, ctx); |
| timings(C2_K163, TIMING_RAND_PT, ctx); |
| timings(C2_K163, TIMING_SIMUL, ctx); |
| timings(C2_B163, TIMING_BASE_PT, ctx); |
| timings(C2_B163, TIMING_RAND_PT, ctx); |
| timings(C2_B163, TIMING_SIMUL, ctx); |
| timings(C2_K233, TIMING_BASE_PT, ctx); |
| timings(C2_K233, TIMING_RAND_PT, ctx); |
| timings(C2_K233, TIMING_SIMUL, ctx); |
| timings(C2_B233, TIMING_BASE_PT, ctx); |
| timings(C2_B233, TIMING_RAND_PT, ctx); |
| timings(C2_B233, TIMING_SIMUL, ctx); |
| timings(C2_K283, TIMING_BASE_PT, ctx); |
| timings(C2_K283, TIMING_RAND_PT, ctx); |
| timings(C2_K283, TIMING_SIMUL, ctx); |
| timings(C2_B283, TIMING_BASE_PT, ctx); |
| timings(C2_B283, TIMING_RAND_PT, ctx); |
| timings(C2_B283, TIMING_SIMUL, ctx); |
| timings(C2_K409, TIMING_BASE_PT, ctx); |
| timings(C2_K409, TIMING_RAND_PT, ctx); |
| timings(C2_K409, TIMING_SIMUL, ctx); |
| timings(C2_B409, TIMING_BASE_PT, ctx); |
| timings(C2_B409, TIMING_RAND_PT, ctx); |
| timings(C2_B409, TIMING_SIMUL, ctx); |
| timings(C2_K571, TIMING_BASE_PT, ctx); |
| timings(C2_K571, TIMING_RAND_PT, ctx); |
| timings(C2_K571, TIMING_SIMUL, ctx); |
| timings(C2_B571, TIMING_BASE_PT, ctx); |
| timings(C2_B571, TIMING_RAND_PT, ctx); |
| timings(C2_B571, TIMING_SIMUL, ctx); |
| # endif |
| |
| if (ctx) |
| BN_CTX_free(ctx); |
| BN_free(p); |
| BN_free(a); |
| BN_free(b); |
| EC_GROUP_free(group); |
| EC_POINT_free(P); |
| EC_POINT_free(Q); |
| EC_POINT_free(R); |
| BN_free(x); |
| BN_free(y); |
| BN_free(z); |
| BN_free(cof); |
| |
| if (C2_K163) |
| EC_GROUP_free(C2_K163); |
| if (C2_B163) |
| EC_GROUP_free(C2_B163); |
| if (C2_K233) |
| EC_GROUP_free(C2_K233); |
| if (C2_B233) |
| EC_GROUP_free(C2_B233); |
| if (C2_K283) |
| EC_GROUP_free(C2_K283); |
| if (C2_B283) |
| EC_GROUP_free(C2_B283); |
| if (C2_K409) |
| EC_GROUP_free(C2_K409); |
| if (C2_B409) |
| EC_GROUP_free(C2_B409); |
| if (C2_K571) |
| EC_GROUP_free(C2_K571); |
| if (C2_B571) |
| EC_GROUP_free(C2_B571); |
| |
| } |
| # endif |
| |
| static void internal_curve_test(void) |
| { |
| EC_builtin_curve *curves = NULL; |
| size_t crv_len = 0, n = 0; |
| int ok = 1; |
| |
| crv_len = EC_get_builtin_curves(NULL, 0); |
| |
| curves = OPENSSL_malloc(sizeof(EC_builtin_curve) * crv_len); |
| |
| if (curves == NULL) |
| return; |
| |
| if (!EC_get_builtin_curves(curves, crv_len)) { |
| OPENSSL_free(curves); |
| return; |
| } |
| |
| fprintf(stdout, "testing internal curves: "); |
| |
| for (n = 0; n < crv_len; n++) { |
| EC_GROUP *group = NULL; |
| int nid = curves[n].nid; |
| if ((group = EC_GROUP_new_by_curve_name(nid)) == NULL) { |
| ok = 0; |
| fprintf(stdout, "\nEC_GROUP_new_curve_name() failed with" |
| " curve %s\n", OBJ_nid2sn(nid)); |
| /* try next curve */ |
| continue; |
| } |
| if (!EC_GROUP_check(group, NULL)) { |
| ok = 0; |
| fprintf(stdout, "\nEC_GROUP_check() failed with" |
| " curve %s\n", OBJ_nid2sn(nid)); |
| EC_GROUP_free(group); |
| /* try the next curve */ |
| continue; |
| } |
| fprintf(stdout, "."); |
| fflush(stdout); |
| EC_GROUP_free(group); |
| } |
| if (ok) |
| fprintf(stdout, " ok\n\n"); |
| else { |
| fprintf(stdout, " failed\n\n"); |
| ABORT; |
| } |
| OPENSSL_free(curves); |
| return; |
| } |
| |
| # 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) (); |
| int degree; |
| /* |
| * Qx, Qy and D are taken from |
| * http://csrcdocut.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 */ |
| "1ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff", |
| /* a */ |
| "1fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc", |
| /* b */ |
| "051953eb9618e1c9a1f929a21a0b68540eea2da725b99b315f3b8b489918ef109e156193951ec7e937b1652c0bd3bb1bf073573df883d2c34f1ef451fd46b503f00", |
| /* Qx */ |
| "0098e91eef9a68452822309c52fab453f5f117c1da8ed796b255e9ab8f6410cca16e59df403a6bdc6ca467a37056b1e54b3005d8ac030decfeb68df18b171885d5c4", |
| /* Qy */ |
| "0164350c321aecfc1cca1ba4364c9b15656150b4b78d6a48d7d28e7f31985ef17be8554376b72900712c4b83ad668327231526e313f5f092999a4632fd50d946bc2e", |
| /* Gx */ |
| "c6858e06b70404e9cd9e3ecb662395b4429c648139053fb521f828af606b4d3dbaa14b5e77efe75928fe1dc127a2ffa8de3348b3c1856a429bf97e7e31c2e5bd66", |
| /* Gy */ |
| "11839296a789a3bc0045c8a5fb42c7d1bd998f54449579b446817afbd17273e662c97ee72995ef42640c550b9013fad0761353c7086a272c24088be94769fd16650", |
| /* order */ |
| "1fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffa51868783bf2f966b7fcc0148f709a5d03bb5c9b8899c47aebb6fb71e91386409", |
| /* d */ |
| "0100085f47b8e1b8b11b7eb33028c0b2888e304bfc98501955b45bba1478dc184eeedf09b86a5f7c21994406072787205e69a63709fe35aa93ba333514b24f961722", |
| }, |
| }; |
| |
| static void nistp_single_test(const struct nistp_test_params *test) |
| { |
| BN_CTX *ctx; |
| BIGNUM *p, *a, *b, *x, *y, *n, *m, *order; |
| EC_GROUP *NISTP; |
| EC_POINT *G, *P, *Q, *Q_CHECK; |
| |
| fprintf(stdout, "\nNIST curve P-%d (optimised implementation):\n", |
| test->degree); |
| ctx = BN_CTX_new(); |
| p = BN_new(); |
| a = BN_new(); |
| b = BN_new(); |
| x = BN_new(); |
| y = BN_new(); |
| m = BN_new(); |
| n = BN_new(); |
| order = BN_new(); |
| |
| NISTP = EC_GROUP_new(test->meth()); |
| if (!NISTP) |
| ABORT; |
| if (!BN_hex2bn(&p, test->p)) |
| ABORT; |
| if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) |
| ABORT; |
| if (!BN_hex2bn(&a, test->a)) |
| ABORT; |
| if (!BN_hex2bn(&b, test->b)) |
| ABORT; |
| if (!EC_GROUP_set_curve_GFp(NISTP, p, a, b, ctx)) |
| ABORT; |
| G = EC_POINT_new(NISTP); |
| P = EC_POINT_new(NISTP); |
| Q = EC_POINT_new(NISTP); |
| Q_CHECK = EC_POINT_new(NISTP); |
| if (!BN_hex2bn(&x, test->Qx)) |
| ABORT; |
| if (!BN_hex2bn(&y, test->Qy)) |
| ABORT; |
| if (!EC_POINT_set_affine_coordinates_GFp(NISTP, Q_CHECK, x, y, ctx)) |
| ABORT; |
| if (!BN_hex2bn(&x, test->Gx)) |
| ABORT; |
| if (!BN_hex2bn(&y, test->Gy)) |
| ABORT; |
| if (!EC_POINT_set_affine_coordinates_GFp(NISTP, G, x, y, ctx)) |
| ABORT; |
| if (!BN_hex2bn(&order, test->order)) |
| ABORT; |
| if (!EC_GROUP_set_generator(NISTP, G, order, BN_value_one())) |
| ABORT; |
| |
| fprintf(stdout, "verify degree ... "); |
| if (EC_GROUP_get_degree(NISTP) != test->degree) |
| ABORT; |
| fprintf(stdout, "ok\n"); |
| |
| fprintf(stdout, "NIST test vectors ... "); |
| if (!BN_hex2bn(&n, test->d)) |
| ABORT; |
| /* fixed point multiplication */ |
| EC_POINT_mul(NISTP, Q, n, NULL, NULL, ctx); |
| if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) |
| ABORT; |
| /* random point multiplication */ |
| EC_POINT_mul(NISTP, Q, NULL, G, n, ctx); |
| if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) |
| ABORT; |
| |
| /* set generator to P = 2*G, where G is the standard generator */ |
| if (!EC_POINT_dbl(NISTP, P, G, ctx)) |
| ABORT; |
| if (!EC_GROUP_set_generator(NISTP, P, order, BN_value_one())) |
| ABORT; |
| /* set the scalar to m=n/2, where n is the NIST test scalar */ |
| if (!BN_rshift(m, n, 1)) |
| ABORT; |
| |
| /* test the non-standard generator */ |
| /* fixed point multiplication */ |
| EC_POINT_mul(NISTP, Q, m, NULL, NULL, ctx); |
| if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) |
| ABORT; |
| /* random point multiplication */ |
| EC_POINT_mul(NISTP, Q, NULL, P, m, ctx); |
| if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) |
| ABORT; |
| |
| /* now repeat all tests with precomputation */ |
| if (!EC_GROUP_precompute_mult(NISTP, ctx)) |
| ABORT; |
| |
| /* fixed point multiplication */ |
| EC_POINT_mul(NISTP, Q, m, NULL, NULL, ctx); |
| if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) |
| ABORT; |
| /* random point multiplication */ |
| EC_POINT_mul(NISTP, Q, NULL, P, m, ctx); |
| if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) |
| ABORT; |
| |
| /* reset generator */ |
| if (!EC_GROUP_set_generator(NISTP, G, order, BN_value_one())) |
| ABORT; |
| /* fixed point multiplication */ |
| EC_POINT_mul(NISTP, Q, n, NULL, NULL, ctx); |
| if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) |
| ABORT; |
| /* random point multiplication */ |
| EC_POINT_mul(NISTP, Q, NULL, G, n, ctx); |
| if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) |
| ABORT; |
| |
| fprintf(stdout, "ok\n"); |
| group_order_tests(NISTP); |
| # if 0 |
| timings(NISTP, TIMING_BASE_PT, ctx); |
| timings(NISTP, TIMING_RAND_PT, ctx); |
| # endif |
| 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_CTX_free(ctx); |
| } |
| |
| static void nistp_tests() |
| { |
| unsigned i; |
| |
| for (i = 0; |
| i < sizeof(nistp_tests_params) / sizeof(struct nistp_test_params); |
| i++) { |
| nistp_single_test(&nistp_tests_params[i]); |
| } |
| } |
| # endif |
| |
| static const char rnd_seed[] = |
| "string to make the random number generator think it has entropy"; |
| |
| int main(int argc, char *argv[]) |
| { |
| |
| /* enable memory leak checking unless explicitly disabled */ |
| if (!((getenv("OPENSSL_DEBUG_MEMORY") != NULL) |
| && (0 == strcmp(getenv("OPENSSL_DEBUG_MEMORY"), "off")))) { |
| CRYPTO_malloc_debug_init(); |
| CRYPTO_set_mem_debug_options(V_CRYPTO_MDEBUG_ALL); |
| } else { |
| /* OPENSSL_DEBUG_MEMORY=off */ |
| CRYPTO_set_mem_debug_functions(0, 0, 0, 0, 0); |
| } |
| CRYPTO_mem_ctrl(CRYPTO_MEM_CHECK_ON); |
| ERR_load_crypto_strings(); |
| |
| RAND_seed(rnd_seed, sizeof rnd_seed); /* or BN_generate_prime may fail */ |
| |
| prime_field_tests(); |
| puts(""); |
| # ifndef OPENSSL_NO_EC2M |
| char2_field_tests(); |
| # endif |
| # ifndef OPENSSL_NO_EC_NISTP_64_GCC_128 |
| nistp_tests(); |
| # endif |
| /* test the internal curves */ |
| internal_curve_test(); |
| |
| # ifndef OPENSSL_NO_ENGINE |
| ENGINE_cleanup(); |
| # endif |
| CRYPTO_cleanup_all_ex_data(); |
| ERR_free_strings(); |
| ERR_remove_thread_state(NULL); |
| CRYPTO_mem_leaks_fp(stderr); |
| |
| return 0; |
| } |
| #endif |
