1/* crypto/ec/ectest.c */ 2/* 3 * Originally written by Bodo Moeller for the OpenSSL project. 4 */ 5/* ==================================================================== 6 * Copyright (c) 1998-2001 The OpenSSL Project. All rights reserved. 7 * 8 * Redistribution and use in source and binary forms, with or without 9 * modification, are permitted provided that the following conditions 10 * are met: 11 * 12 * 1. Redistributions of source code must retain the above copyright 13 * notice, this list of conditions and the following disclaimer. 14 * 15 * 2. Redistributions in binary form must reproduce the above copyright 16 * notice, this list of conditions and the following disclaimer in 17 * the documentation and/or other materials provided with the 18 * distribution. 19 * 20 * 3. All advertising materials mentioning features or use of this 21 * software must display the following acknowledgment: 22 * "This product includes software developed by the OpenSSL Project 23 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" 24 * 25 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to 26 * endorse or promote products derived from this software without 27 * prior written permission. For written permission, please contact 28 * openssl-core@openssl.org. 29 * 30 * 5. Products derived from this software may not be called "OpenSSL" 31 * nor may "OpenSSL" appear in their names without prior written 32 * permission of the OpenSSL Project. 33 * 34 * 6. Redistributions of any form whatsoever must retain the following 35 * acknowledgment: 36 * "This product includes software developed by the OpenSSL Project 37 * for use in the OpenSSL Toolkit (http://www.openssl.org/)" 38 * 39 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY 40 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 41 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR 42 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR 43 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, 44 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT 45 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; 46 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 47 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, 48 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) 49 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED 50 * OF THE POSSIBILITY OF SUCH DAMAGE. 51 * ==================================================================== 52 * 53 * This product includes cryptographic software written by Eric Young 54 * (eay@cryptsoft.com). This product includes software written by Tim 55 * Hudson (tjh@cryptsoft.com). 56 * 57 */ 58/* ==================================================================== 59 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. 60 * 61 * Portions of the attached software ("Contribution") are developed by 62 * SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project. 63 * 64 * The Contribution is licensed pursuant to the OpenSSL open source 65 * license provided above. 66 * 67 * The elliptic curve binary polynomial software is originally written by 68 * Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems Laboratories. 69 * 70 */ 71 72#include <stdio.h> 73#include <stdlib.h> 74#ifdef FLAT_INC 75#include "e_os.h" 76#else 77#include "../e_os.h" 78#endif 79#include <string.h> 80#include <time.h> 81 82 83#ifdef OPENSSL_NO_EC 84int main(int argc, char * argv[]) { puts("Elliptic curves are disabled."); return 0; } 85#else 86 87 88#include <openssl/ec.h> 89#ifndef OPENSSL_NO_ENGINE 90#include <openssl/engine.h> 91#endif 92#include <openssl/err.h> 93#include <openssl/obj_mac.h> 94#include <openssl/objects.h> 95#include <openssl/rand.h> 96#include <openssl/bn.h> 97 98#if defined(_MSC_VER) && defined(_MIPS_) && (_MSC_VER/100==12) 99/* suppress "too big too optimize" warning */ 100#pragma warning(disable:4959) 101#endif 102 103#define ABORT do { \ 104 fflush(stdout); \ 105 fprintf(stderr, "%s:%d: ABORT\n", __FILE__, __LINE__); \ 106 ERR_print_errors_fp(stderr); \ 107 EXIT(1); \ 108} while (0) 109 110void prime_field_tests(void); 111void char2_field_tests(void); 112void internal_curve_test(void); 113 114#define TIMING_BASE_PT 0 115#define TIMING_RAND_PT 1 116#define TIMING_SIMUL 2 117 118#if 0 119static void timings(EC_GROUP *group, int type, BN_CTX *ctx) 120 { 121 clock_t clck; 122 int i, j; 123 BIGNUM *s; 124 BIGNUM *r[10], *r0[10]; 125 EC_POINT *P; 126 127 s = BN_new(); 128 if (s == NULL) ABORT; 129 130 fprintf(stdout, "Timings for %d-bit field, ", EC_GROUP_get_degree(group)); 131 if (!EC_GROUP_get_order(group, s, ctx)) ABORT; 132 fprintf(stdout, "%d-bit scalars ", (int)BN_num_bits(s)); 133 fflush(stdout); 134 135 P = EC_POINT_new(group); 136 if (P == NULL) ABORT; 137 EC_POINT_copy(P, EC_GROUP_get0_generator(group)); 138 139 for (i = 0; i < 10; i++) 140 { 141 if ((r[i] = BN_new()) == NULL) ABORT; 142 if (!BN_pseudo_rand(r[i], BN_num_bits(s), 0, 0)) ABORT; 143 if (type != TIMING_BASE_PT) 144 { 145 if ((r0[i] = BN_new()) == NULL) ABORT; 146 if (!BN_pseudo_rand(r0[i], BN_num_bits(s), 0, 0)) ABORT; 147 } 148 } 149 150 clck = clock(); 151 for (i = 0; i < 10; i++) 152 { 153 for (j = 0; j < 10; j++) 154 { 155 if (!EC_POINT_mul(group, P, (type != TIMING_RAND_PT) ? r[i] : NULL, 156 (type != TIMING_BASE_PT) ? P : NULL, (type != TIMING_BASE_PT) ? r0[i] : NULL, ctx)) ABORT; 157 } 158 } 159 clck = clock() - clck; 160 161 fprintf(stdout, "\n"); 162 163#ifdef CLOCKS_PER_SEC 164 /* "To determine the time in seconds, the value returned 165 * by the clock function should be divided by the value 166 * of the macro CLOCKS_PER_SEC." 167 * -- ISO/IEC 9899 */ 168# define UNIT "s" 169#else 170 /* "`CLOCKS_PER_SEC' undeclared (first use this function)" 171 * -- cc on NeXTstep/OpenStep */ 172# define UNIT "units" 173# define CLOCKS_PER_SEC 1 174#endif 175 176 if (type == TIMING_BASE_PT) { 177 fprintf(stdout, "%i %s in %.2f " UNIT "\n", i*j, 178 "base point multiplications", (double)clck/CLOCKS_PER_SEC); 179 } else if (type == TIMING_RAND_PT) { 180 fprintf(stdout, "%i %s in %.2f " UNIT "\n", i*j, 181 "random point multiplications", (double)clck/CLOCKS_PER_SEC); 182 } else if (type == TIMING_SIMUL) { 183 fprintf(stdout, "%i %s in %.2f " UNIT "\n", i*j, 184 "s*P+t*Q operations", (double)clck/CLOCKS_PER_SEC); 185 } 186 fprintf(stdout, "average: %.4f " UNIT "\n", (double)clck/(CLOCKS_PER_SEC*i*j)); 187 188 EC_POINT_free(P); 189 BN_free(s); 190 for (i = 0; i < 10; i++) 191 { 192 BN_free(r[i]); 193 if (type != TIMING_BASE_PT) BN_free(r0[i]); 194 } 195 } 196#endif 197 198void prime_field_tests() 199 { 200 BN_CTX *ctx = NULL; 201 BIGNUM *p, *a, *b; 202 EC_GROUP *group; 203 EC_GROUP *P_160 = NULL, *P_192 = NULL, *P_224 = NULL, *P_256 = NULL, *P_384 = NULL, *P_521 = NULL; 204 EC_POINT *P, *Q, *R; 205 BIGNUM *x, *y, *z; 206 unsigned char buf[100]; 207 size_t i, len; 208 int k; 209 210#if 1 /* optional */ 211 ctx = BN_CTX_new(); 212 if (!ctx) ABORT; 213#endif 214 215 p = BN_new(); 216 a = BN_new(); 217 b = BN_new(); 218 if (!p || !a || !b) ABORT; 219 220 if (!BN_hex2bn(&p, "17")) ABORT; 221 if (!BN_hex2bn(&a, "1")) ABORT; 222 if (!BN_hex2bn(&b, "1")) ABORT; 223 224 group = EC_GROUP_new(EC_GFp_mont_method()); /* applications should use EC_GROUP_new_curve_GFp 225 * so that the library gets to choose the EC_METHOD */ 226 if (!group) ABORT; 227 228 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT; 229 230 { 231 EC_GROUP *tmp; 232 tmp = EC_GROUP_new(EC_GROUP_method_of(group)); 233 if (!tmp) ABORT; 234 if (!EC_GROUP_copy(tmp, group)) ABORT; 235 EC_GROUP_free(group); 236 group = tmp; 237 } 238 239 if (!EC_GROUP_get_curve_GFp(group, p, a, b, ctx)) ABORT; 240 241 fprintf(stdout, "Curve defined by Weierstrass equation\n y^2 = x^3 + a*x + b (mod 0x"); 242 BN_print_fp(stdout, p); 243 fprintf(stdout, ")\n a = 0x"); 244 BN_print_fp(stdout, a); 245 fprintf(stdout, "\n b = 0x"); 246 BN_print_fp(stdout, b); 247 fprintf(stdout, "\n"); 248 249 P = EC_POINT_new(group); 250 Q = EC_POINT_new(group); 251 R = EC_POINT_new(group); 252 if (!P || !Q || !R) ABORT; 253 254 if (!EC_POINT_set_to_infinity(group, P)) ABORT; 255 if (!EC_POINT_is_at_infinity(group, P)) ABORT; 256 257 buf[0] = 0; 258 if (!EC_POINT_oct2point(group, Q, buf, 1, ctx)) ABORT; 259 260 if (!EC_POINT_add(group, P, P, Q, ctx)) ABORT; 261 if (!EC_POINT_is_at_infinity(group, P)) ABORT; 262 263 x = BN_new(); 264 y = BN_new(); 265 z = BN_new(); 266 if (!x || !y || !z) ABORT; 267 268 if (!BN_hex2bn(&x, "D")) ABORT; 269 if (!EC_POINT_set_compressed_coordinates_GFp(group, Q, x, 1, ctx)) ABORT; 270 if (!EC_POINT_is_on_curve(group, Q, ctx)) 271 { 272 if (!EC_POINT_get_affine_coordinates_GFp(group, Q, x, y, ctx)) ABORT; 273 fprintf(stderr, "Point is not on curve: x = 0x"); 274 BN_print_fp(stderr, x); 275 fprintf(stderr, ", y = 0x"); 276 BN_print_fp(stderr, y); 277 fprintf(stderr, "\n"); 278 ABORT; 279 } 280 281 fprintf(stdout, "A cyclic subgroup:\n"); 282 k = 100; 283 do 284 { 285 if (k-- == 0) ABORT; 286 287 if (EC_POINT_is_at_infinity(group, P)) 288 fprintf(stdout, " point at infinity\n"); 289 else 290 { 291 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT; 292 293 fprintf(stdout, " x = 0x"); 294 BN_print_fp(stdout, x); 295 fprintf(stdout, ", y = 0x"); 296 BN_print_fp(stdout, y); 297 fprintf(stdout, "\n"); 298 } 299 300 if (!EC_POINT_copy(R, P)) ABORT; 301 if (!EC_POINT_add(group, P, P, Q, ctx)) ABORT; 302 303#if 0 /* optional */ 304 { 305 EC_POINT *points[3]; 306 307 points[0] = R; 308 points[1] = Q; 309 points[2] = P; 310 if (!EC_POINTs_make_affine(group, 2, points, ctx)) ABORT; 311 } 312#endif 313 314 } 315 while (!EC_POINT_is_at_infinity(group, P)); 316 317 if (!EC_POINT_add(group, P, Q, R, ctx)) ABORT; 318 if (!EC_POINT_is_at_infinity(group, P)) ABORT; 319 320 len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_COMPRESSED, buf, sizeof buf, ctx); 321 if (len == 0) ABORT; 322 if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT; 323 if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT; 324 fprintf(stdout, "Generator as octect string, compressed form:\n "); 325 for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]); 326 327 len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_UNCOMPRESSED, buf, sizeof buf, ctx); 328 if (len == 0) ABORT; 329 if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT; 330 if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT; 331 fprintf(stdout, "\nGenerator as octect string, uncompressed form:\n "); 332 for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]); 333 334 len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_HYBRID, buf, sizeof buf, ctx); 335 if (len == 0) ABORT; 336 if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT; 337 if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT; 338 fprintf(stdout, "\nGenerator as octect string, hybrid form:\n "); 339 for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]); 340 341 if (!EC_POINT_get_Jprojective_coordinates_GFp(group, R, x, y, z, ctx)) ABORT; 342 fprintf(stdout, "\nA representation of the inverse of that generator in\nJacobian projective coordinates:\n X = 0x"); 343 BN_print_fp(stdout, x); 344 fprintf(stdout, ", Y = 0x"); 345 BN_print_fp(stdout, y); 346 fprintf(stdout, ", Z = 0x"); 347 BN_print_fp(stdout, z); 348 fprintf(stdout, "\n"); 349 350 if (!EC_POINT_invert(group, P, ctx)) ABORT; 351 if (0 != EC_POINT_cmp(group, P, R, ctx)) ABORT; 352 353 354 /* Curve secp160r1 (Certicom Research SEC 2 Version 1.0, section 2.4.2, 2000) 355 * -- not a NIST curve, but commonly used */ 356 357 if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFF")) ABORT; 358 if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT; 359 if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFC")) ABORT; 360 if (!BN_hex2bn(&b, "1C97BEFC54BD7A8B65ACF89F81D4D4ADC565FA45")) ABORT; 361 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT; 362 363 if (!BN_hex2bn(&x, "4A96B5688EF573284664698968C38BB913CBFC82")) ABORT; 364 if (!BN_hex2bn(&y, "23a628553168947d59dcc912042351377ac5fb32")) ABORT; 365 if (!EC_POINT_set_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT; 366 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT; 367 if (!BN_hex2bn(&z, "0100000000000000000001F4C8F927AED3CA752257")) ABORT; 368 if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT; 369 370 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT; 371 fprintf(stdout, "\nSEC2 curve secp160r1 -- Generator:\n x = 0x"); 372 BN_print_fp(stdout, x); 373 fprintf(stdout, "\n y = 0x"); 374 BN_print_fp(stdout, y); 375 fprintf(stdout, "\n"); 376 /* G_y value taken from the standard: */ 377 if (!BN_hex2bn(&z, "23a628553168947d59dcc912042351377ac5fb32")) ABORT; 378 if (0 != BN_cmp(y, z)) ABORT; 379 380 fprintf(stdout, "verify degree ..."); 381 if (EC_GROUP_get_degree(group) != 160) ABORT; 382 fprintf(stdout, " ok\n"); 383 384 fprintf(stdout, "verify group order ..."); 385 fflush(stdout); 386 if (!EC_GROUP_get_order(group, z, ctx)) ABORT; 387 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; 388 if (!EC_POINT_is_at_infinity(group, Q)) ABORT; 389 fprintf(stdout, "."); 390 fflush(stdout); 391 if (!EC_GROUP_precompute_mult(group, ctx)) ABORT; 392 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; 393 if (!EC_POINT_is_at_infinity(group, Q)) ABORT; 394 fprintf(stdout, " ok\n"); 395 396 if (!(P_160 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT; 397 if (!EC_GROUP_copy(P_160, group)) ABORT; 398 399 400 /* Curve P-192 (FIPS PUB 186-2, App. 6) */ 401 402 if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF")) ABORT; 403 if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT; 404 if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC")) ABORT; 405 if (!BN_hex2bn(&b, "64210519E59C80E70FA7E9AB72243049FEB8DEECC146B9B1")) ABORT; 406 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT; 407 408 if (!BN_hex2bn(&x, "188DA80EB03090F67CBF20EB43A18800F4FF0AFD82FF1012")) ABORT; 409 if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 1, ctx)) ABORT; 410 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT; 411 if (!BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22831")) ABORT; 412 if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT; 413 414 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT; 415 fprintf(stdout, "\nNIST curve P-192 -- Generator:\n x = 0x"); 416 BN_print_fp(stdout, x); 417 fprintf(stdout, "\n y = 0x"); 418 BN_print_fp(stdout, y); 419 fprintf(stdout, "\n"); 420 /* G_y value taken from the standard: */ 421 if (!BN_hex2bn(&z, "07192B95FFC8DA78631011ED6B24CDD573F977A11E794811")) ABORT; 422 if (0 != BN_cmp(y, z)) ABORT; 423 424 fprintf(stdout, "verify degree ..."); 425 if (EC_GROUP_get_degree(group) != 192) ABORT; 426 fprintf(stdout, " ok\n"); 427 428 fprintf(stdout, "verify group order ..."); 429 fflush(stdout); 430 if (!EC_GROUP_get_order(group, z, ctx)) ABORT; 431 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; 432 if (!EC_POINT_is_at_infinity(group, Q)) ABORT; 433 fprintf(stdout, "."); 434 fflush(stdout); 435#if 0 436 if (!EC_GROUP_precompute_mult(group, ctx)) ABORT; 437#endif 438 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; 439 if (!EC_POINT_is_at_infinity(group, Q)) ABORT; 440 fprintf(stdout, " ok\n"); 441 442 if (!(P_192 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT; 443 if (!EC_GROUP_copy(P_192, group)) ABORT; 444 445 446 /* Curve P-224 (FIPS PUB 186-2, App. 6) */ 447 448 if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001")) ABORT; 449 if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT; 450 if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE")) ABORT; 451 if (!BN_hex2bn(&b, "B4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4")) ABORT; 452 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT; 453 454 if (!BN_hex2bn(&x, "B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21")) ABORT; 455 if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 0, ctx)) ABORT; 456 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT; 457 if (!BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D")) ABORT; 458 if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT; 459 460 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT; 461 fprintf(stdout, "\nNIST curve P-224 -- Generator:\n x = 0x"); 462 BN_print_fp(stdout, x); 463 fprintf(stdout, "\n y = 0x"); 464 BN_print_fp(stdout, y); 465 fprintf(stdout, "\n"); 466 /* G_y value taken from the standard: */ 467 if (!BN_hex2bn(&z, "BD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34")) ABORT; 468 if (0 != BN_cmp(y, z)) ABORT; 469 470 fprintf(stdout, "verify degree ..."); 471 if (EC_GROUP_get_degree(group) != 224) ABORT; 472 fprintf(stdout, " ok\n"); 473 474 fprintf(stdout, "verify group order ..."); 475 fflush(stdout); 476 if (!EC_GROUP_get_order(group, z, ctx)) ABORT; 477 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; 478 if (!EC_POINT_is_at_infinity(group, Q)) ABORT; 479 fprintf(stdout, "."); 480 fflush(stdout); 481#if 0 482 if (!EC_GROUP_precompute_mult(group, ctx)) ABORT; 483#endif 484 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; 485 if (!EC_POINT_is_at_infinity(group, Q)) ABORT; 486 fprintf(stdout, " ok\n"); 487 488 if (!(P_224 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT; 489 if (!EC_GROUP_copy(P_224, group)) ABORT; 490 491 492 /* Curve P-256 (FIPS PUB 186-2, App. 6) */ 493 494 if (!BN_hex2bn(&p, "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF")) ABORT; 495 if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT; 496 if (!BN_hex2bn(&a, "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFC")) ABORT; 497 if (!BN_hex2bn(&b, "5AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B")) ABORT; 498 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT; 499 500 if (!BN_hex2bn(&x, "6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296")) ABORT; 501 if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 1, ctx)) ABORT; 502 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT; 503 if (!BN_hex2bn(&z, "FFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E" 504 "84F3B9CAC2FC632551")) ABORT; 505 if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT; 506 507 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT; 508 fprintf(stdout, "\nNIST curve P-256 -- Generator:\n x = 0x"); 509 BN_print_fp(stdout, x); 510 fprintf(stdout, "\n y = 0x"); 511 BN_print_fp(stdout, y); 512 fprintf(stdout, "\n"); 513 /* G_y value taken from the standard: */ 514 if (!BN_hex2bn(&z, "4FE342E2FE1A7F9B8EE7EB4A7C0F9E162BCE33576B315ECECBB6406837BF51F5")) ABORT; 515 if (0 != BN_cmp(y, z)) ABORT; 516 517 fprintf(stdout, "verify degree ..."); 518 if (EC_GROUP_get_degree(group) != 256) ABORT; 519 fprintf(stdout, " ok\n"); 520 521 fprintf(stdout, "verify group order ..."); 522 fflush(stdout); 523 if (!EC_GROUP_get_order(group, z, ctx)) ABORT; 524 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; 525 if (!EC_POINT_is_at_infinity(group, Q)) ABORT; 526 fprintf(stdout, "."); 527 fflush(stdout); 528#if 0 529 if (!EC_GROUP_precompute_mult(group, ctx)) ABORT; 530#endif 531 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; 532 if (!EC_POINT_is_at_infinity(group, Q)) ABORT; 533 fprintf(stdout, " ok\n"); 534 535 if (!(P_256 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT; 536 if (!EC_GROUP_copy(P_256, group)) ABORT; 537 538 539 /* Curve P-384 (FIPS PUB 186-2, App. 6) */ 540 541 if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" 542 "FFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFF")) ABORT; 543 if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT; 544 if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" 545 "FFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFC")) ABORT; 546 if (!BN_hex2bn(&b, "B3312FA7E23EE7E4988E056BE3F82D19181D9C6EFE8141" 547 "120314088F5013875AC656398D8A2ED19D2A85C8EDD3EC2AEF")) ABORT; 548 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT; 549 550 if (!BN_hex2bn(&x, "AA87CA22BE8B05378EB1C71EF320AD746E1D3B628BA79B" 551 "9859F741E082542A385502F25DBF55296C3A545E3872760AB7")) ABORT; 552 if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 1, ctx)) ABORT; 553 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT; 554 if (!BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" 555 "FFC7634D81F4372DDF581A0DB248B0A77AECEC196ACCC52973")) ABORT; 556 if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT; 557 558 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT; 559 fprintf(stdout, "\nNIST curve P-384 -- Generator:\n x = 0x"); 560 BN_print_fp(stdout, x); 561 fprintf(stdout, "\n y = 0x"); 562 BN_print_fp(stdout, y); 563 fprintf(stdout, "\n"); 564 /* G_y value taken from the standard: */ 565 if (!BN_hex2bn(&z, "3617DE4A96262C6F5D9E98BF9292DC29F8F41DBD289A14" 566 "7CE9DA3113B5F0B8C00A60B1CE1D7E819D7A431D7C90EA0E5F")) ABORT; 567 if (0 != BN_cmp(y, z)) ABORT; 568 569 fprintf(stdout, "verify degree ..."); 570 if (EC_GROUP_get_degree(group) != 384) ABORT; 571 fprintf(stdout, " ok\n"); 572 573 fprintf(stdout, "verify group order ..."); 574 fflush(stdout); 575 if (!EC_GROUP_get_order(group, z, ctx)) ABORT; 576 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; 577 if (!EC_POINT_is_at_infinity(group, Q)) ABORT; 578 fprintf(stdout, "."); 579 fflush(stdout); 580#if 0 581 if (!EC_GROUP_precompute_mult(group, ctx)) ABORT; 582#endif 583 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; 584 if (!EC_POINT_is_at_infinity(group, Q)) ABORT; 585 fprintf(stdout, " ok\n"); 586 587 if (!(P_384 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT; 588 if (!EC_GROUP_copy(P_384, group)) ABORT; 589 590 591 /* Curve P-521 (FIPS PUB 186-2, App. 6) */ 592 593 if (!BN_hex2bn(&p, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" 594 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" 595 "FFFFFFFFFFFFFFFFFFFFFFFFFFFF")) ABORT; 596 if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT; 597 if (!BN_hex2bn(&a, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" 598 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" 599 "FFFFFFFFFFFFFFFFFFFFFFFFFFFC")) ABORT; 600 if (!BN_hex2bn(&b, "051953EB9618E1C9A1F929A21A0B68540EEA2DA725B99B" 601 "315F3B8B489918EF109E156193951EC7E937B1652C0BD3BB1BF073573" 602 "DF883D2C34F1EF451FD46B503F00")) ABORT; 603 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT; 604 605 if (!BN_hex2bn(&x, "C6858E06B70404E9CD9E3ECB662395B4429C648139053F" 606 "B521F828AF606B4D3DBAA14B5E77EFE75928FE1DC127A2FFA8DE3348B" 607 "3C1856A429BF97E7E31C2E5BD66")) ABORT; 608 if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 0, ctx)) ABORT; 609 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT; 610 if (!BN_hex2bn(&z, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" 611 "FFFFFFFFFFFFFFFFFFFFA51868783BF2F966B7FCC0148F709A5D03BB5" 612 "C9B8899C47AEBB6FB71E91386409")) ABORT; 613 if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT; 614 615 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT; 616 fprintf(stdout, "\nNIST curve P-521 -- Generator:\n x = 0x"); 617 BN_print_fp(stdout, x); 618 fprintf(stdout, "\n y = 0x"); 619 BN_print_fp(stdout, y); 620 fprintf(stdout, "\n"); 621 /* G_y value taken from the standard: */ 622 if (!BN_hex2bn(&z, "11839296A789A3BC0045C8A5FB42C7D1BD998F54449579" 623 "B446817AFBD17273E662C97EE72995EF42640C550B9013FAD0761353C" 624 "7086A272C24088BE94769FD16650")) ABORT; 625 if (0 != BN_cmp(y, z)) ABORT; 626 627 fprintf(stdout, "verify degree ..."); 628 if (EC_GROUP_get_degree(group) != 521) ABORT; 629 fprintf(stdout, " ok\n"); 630 631 fprintf(stdout, "verify group order ..."); 632 fflush(stdout); 633 if (!EC_GROUP_get_order(group, z, ctx)) ABORT; 634 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; 635 if (!EC_POINT_is_at_infinity(group, Q)) ABORT; 636 fprintf(stdout, "."); 637 fflush(stdout); 638#if 0 639 if (!EC_GROUP_precompute_mult(group, ctx)) ABORT; 640#endif 641 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; 642 if (!EC_POINT_is_at_infinity(group, Q)) ABORT; 643 fprintf(stdout, " ok\n"); 644 645 if (!(P_521 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT; 646 if (!EC_GROUP_copy(P_521, group)) ABORT; 647 648 649 /* more tests using the last curve */ 650 651 if (!EC_POINT_copy(Q, P)) ABORT; 652 if (EC_POINT_is_at_infinity(group, Q)) ABORT; 653 if (!EC_POINT_dbl(group, P, P, ctx)) ABORT; 654 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT; 655 if (!EC_POINT_invert(group, Q, ctx)) ABORT; /* P = -2Q */ 656 657 if (!EC_POINT_add(group, R, P, Q, ctx)) ABORT; 658 if (!EC_POINT_add(group, R, R, Q, ctx)) ABORT; 659 if (!EC_POINT_is_at_infinity(group, R)) ABORT; /* R = P + 2Q */ 660 661 { 662 const EC_POINT *points[3]; 663 const BIGNUM *scalars[3]; 664 665 if (EC_POINT_is_at_infinity(group, Q)) ABORT; 666 points[0] = Q; 667 points[1] = Q; 668 points[2] = Q; 669 670 if (!BN_add(y, z, BN_value_one())) ABORT; 671 if (BN_is_odd(y)) ABORT; 672 if (!BN_rshift1(y, y)) ABORT; 673 scalars[0] = y; /* (group order + 1)/2, so y*Q + y*Q = Q */ 674 scalars[1] = y; 675 676 fprintf(stdout, "combined multiplication ..."); 677 fflush(stdout); 678 679 /* z is still the group order */ 680 if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) ABORT; 681 if (!EC_POINTs_mul(group, R, z, 2, points, scalars, ctx)) ABORT; 682 if (0 != EC_POINT_cmp(group, P, R, ctx)) ABORT; 683 if (0 != EC_POINT_cmp(group, R, Q, ctx)) ABORT; 684 685 fprintf(stdout, "."); 686 fflush(stdout); 687 688 if (!BN_pseudo_rand(y, BN_num_bits(y), 0, 0)) ABORT; 689 if (!BN_add(z, z, y)) ABORT; 690 BN_set_negative(z, 1); 691 scalars[0] = y; 692 scalars[1] = z; /* z = -(order + y) */ 693 694 if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) ABORT; 695 if (!EC_POINT_is_at_infinity(group, P)) ABORT; 696 697 fprintf(stdout, "."); 698 fflush(stdout); 699 700 if (!BN_pseudo_rand(x, BN_num_bits(y) - 1, 0, 0)) ABORT; 701 if (!BN_add(z, x, y)) ABORT; 702 BN_set_negative(z, 1); 703 scalars[0] = x; 704 scalars[1] = y; 705 scalars[2] = z; /* z = -(x+y) */ 706 707 if (!EC_POINTs_mul(group, P, NULL, 3, points, scalars, ctx)) ABORT; 708 if (!EC_POINT_is_at_infinity(group, P)) ABORT; 709 710 fprintf(stdout, " ok\n\n"); 711 } 712 713 714#if 0 715 timings(P_160, TIMING_BASE_PT, ctx); 716 timings(P_160, TIMING_RAND_PT, ctx); 717 timings(P_160, TIMING_SIMUL, ctx); 718 timings(P_192, TIMING_BASE_PT, ctx); 719 timings(P_192, TIMING_RAND_PT, ctx); 720 timings(P_192, TIMING_SIMUL, ctx); 721 timings(P_224, TIMING_BASE_PT, ctx); 722 timings(P_224, TIMING_RAND_PT, ctx); 723 timings(P_224, TIMING_SIMUL, ctx); 724 timings(P_256, TIMING_BASE_PT, ctx); 725 timings(P_256, TIMING_RAND_PT, ctx); 726 timings(P_256, TIMING_SIMUL, ctx); 727 timings(P_384, TIMING_BASE_PT, ctx); 728 timings(P_384, TIMING_RAND_PT, ctx); 729 timings(P_384, TIMING_SIMUL, ctx); 730 timings(P_521, TIMING_BASE_PT, ctx); 731 timings(P_521, TIMING_RAND_PT, ctx); 732 timings(P_521, TIMING_SIMUL, ctx); 733#endif 734 735 736 if (ctx) 737 BN_CTX_free(ctx); 738 BN_free(p); BN_free(a); BN_free(b); 739 EC_GROUP_free(group); 740 EC_POINT_free(P); 741 EC_POINT_free(Q); 742 EC_POINT_free(R); 743 BN_free(x); BN_free(y); BN_free(z); 744 745 if (P_160) EC_GROUP_free(P_160); 746 if (P_192) EC_GROUP_free(P_192); 747 if (P_224) EC_GROUP_free(P_224); 748 if (P_256) EC_GROUP_free(P_256); 749 if (P_384) EC_GROUP_free(P_384); 750 if (P_521) EC_GROUP_free(P_521); 751 752 } 753 754/* Change test based on whether binary point compression is enabled or not. */ 755#ifdef OPENSSL_EC_BIN_PT_COMP 756#define CHAR2_CURVE_TEST_INTERNAL(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \ 757 if (!BN_hex2bn(&x, _x)) ABORT; \ 758 if (!EC_POINT_set_compressed_coordinates_GF2m(group, P, x, _y_bit, ctx)) ABORT; \ 759 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT; \ 760 if (!BN_hex2bn(&z, _order)) ABORT; \ 761 if (!BN_hex2bn(&cof, _cof)) ABORT; \ 762 if (!EC_GROUP_set_generator(group, P, z, cof)) ABORT; \ 763 if (!EC_POINT_get_affine_coordinates_GF2m(group, P, x, y, ctx)) ABORT; \ 764 fprintf(stdout, "\n%s -- Generator:\n x = 0x", _name); \ 765 BN_print_fp(stdout, x); \ 766 fprintf(stdout, "\n y = 0x"); \ 767 BN_print_fp(stdout, y); \ 768 fprintf(stdout, "\n"); \ 769 /* G_y value taken from the standard: */ \ 770 if (!BN_hex2bn(&z, _y)) ABORT; \ 771 if (0 != BN_cmp(y, z)) ABORT; 772#else 773#define CHAR2_CURVE_TEST_INTERNAL(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \ 774 if (!BN_hex2bn(&x, _x)) ABORT; \ 775 if (!BN_hex2bn(&y, _y)) ABORT; \ 776 if (!EC_POINT_set_affine_coordinates_GF2m(group, P, x, y, ctx)) ABORT; \ 777 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT; \ 778 if (!BN_hex2bn(&z, _order)) ABORT; \ 779 if (!BN_hex2bn(&cof, _cof)) ABORT; \ 780 if (!EC_GROUP_set_generator(group, P, z, cof)) ABORT; \ 781 fprintf(stdout, "\n%s -- Generator:\n x = 0x", _name); \ 782 BN_print_fp(stdout, x); \ 783 fprintf(stdout, "\n y = 0x"); \ 784 BN_print_fp(stdout, y); \ 785 fprintf(stdout, "\n"); 786#endif 787 788#define CHAR2_CURVE_TEST(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \ 789 if (!BN_hex2bn(&p, _p)) ABORT; \ 790 if (!BN_hex2bn(&a, _a)) ABORT; \ 791 if (!BN_hex2bn(&b, _b)) ABORT; \ 792 if (!EC_GROUP_set_curve_GF2m(group, p, a, b, ctx)) ABORT; \ 793 CHAR2_CURVE_TEST_INTERNAL(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \ 794 fprintf(stdout, "verify degree ..."); \ 795 if (EC_GROUP_get_degree(group) != _degree) ABORT; \ 796 fprintf(stdout, " ok\n"); \ 797 fprintf(stdout, "verify group order ..."); \ 798 fflush(stdout); \ 799 if (!EC_GROUP_get_order(group, z, ctx)) ABORT; \ 800 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; \ 801 if (!EC_POINT_is_at_infinity(group, Q)) ABORT; \ 802 fprintf(stdout, "."); \ 803 fflush(stdout); \ 804 /* if (!EC_GROUP_precompute_mult(group, ctx)) ABORT; */ \ 805 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; \ 806 if (!EC_POINT_is_at_infinity(group, Q)) ABORT; \ 807 fprintf(stdout, " ok\n"); \ 808 if (!(_variable = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT; \ 809 if (!EC_GROUP_copy(_variable, group)) ABORT; 810 811void char2_field_tests() 812 { 813 BN_CTX *ctx = NULL; 814 BIGNUM *p, *a, *b; 815 EC_GROUP *group; 816 EC_GROUP *C2_K163 = NULL, *C2_K233 = NULL, *C2_K283 = NULL, *C2_K409 = NULL, *C2_K571 = NULL; 817 EC_GROUP *C2_B163 = NULL, *C2_B233 = NULL, *C2_B283 = NULL, *C2_B409 = NULL, *C2_B571 = NULL; 818 EC_POINT *P, *Q, *R; 819 BIGNUM *x, *y, *z, *cof; 820 unsigned char buf[100]; 821 size_t i, len; 822 int k; 823 824#if 1 /* optional */ 825 ctx = BN_CTX_new(); 826 if (!ctx) ABORT; 827#endif 828 829 p = BN_new(); 830 a = BN_new(); 831 b = BN_new(); 832 if (!p || !a || !b) ABORT; 833 834 if (!BN_hex2bn(&p, "13")) ABORT; 835 if (!BN_hex2bn(&a, "3")) ABORT; 836 if (!BN_hex2bn(&b, "1")) ABORT; 837 838 group = EC_GROUP_new(EC_GF2m_simple_method()); /* applications should use EC_GROUP_new_curve_GF2m 839 * so that the library gets to choose the EC_METHOD */ 840 if (!group) ABORT; 841 if (!EC_GROUP_set_curve_GF2m(group, p, a, b, ctx)) ABORT; 842 843 { 844 EC_GROUP *tmp; 845 tmp = EC_GROUP_new(EC_GROUP_method_of(group)); 846 if (!tmp) ABORT; 847 if (!EC_GROUP_copy(tmp, group)) ABORT; 848 EC_GROUP_free(group); 849 group = tmp; 850 } 851 852 if (!EC_GROUP_get_curve_GF2m(group, p, a, b, ctx)) ABORT; 853 854 fprintf(stdout, "Curve defined by Weierstrass equation\n y^2 + x*y = x^3 + a*x^2 + b (mod 0x"); 855 BN_print_fp(stdout, p); 856 fprintf(stdout, ")\n a = 0x"); 857 BN_print_fp(stdout, a); 858 fprintf(stdout, "\n b = 0x"); 859 BN_print_fp(stdout, b); 860 fprintf(stdout, "\n(0x... means binary polynomial)\n"); 861 862 P = EC_POINT_new(group); 863 Q = EC_POINT_new(group); 864 R = EC_POINT_new(group); 865 if (!P || !Q || !R) ABORT; 866 867 if (!EC_POINT_set_to_infinity(group, P)) ABORT; 868 if (!EC_POINT_is_at_infinity(group, P)) ABORT; 869 870 buf[0] = 0; 871 if (!EC_POINT_oct2point(group, Q, buf, 1, ctx)) ABORT; 872 873 if (!EC_POINT_add(group, P, P, Q, ctx)) ABORT; 874 if (!EC_POINT_is_at_infinity(group, P)) ABORT; 875 876 x = BN_new(); 877 y = BN_new(); 878 z = BN_new(); 879 cof = BN_new(); 880 if (!x || !y || !z || !cof) ABORT; 881 882 if (!BN_hex2bn(&x, "6")) ABORT; 883/* Change test based on whether binary point compression is enabled or not. */ 884#ifdef OPENSSL_EC_BIN_PT_COMP 885 if (!EC_POINT_set_compressed_coordinates_GF2m(group, Q, x, 1, ctx)) ABORT; 886#else 887 if (!BN_hex2bn(&y, "8")) ABORT; 888 if (!EC_POINT_set_affine_coordinates_GF2m(group, Q, x, y, ctx)) ABORT; 889#endif 890 if (!EC_POINT_is_on_curve(group, Q, ctx)) 891 { 892/* Change test based on whether binary point compression is enabled or not. */ 893#ifdef OPENSSL_EC_BIN_PT_COMP 894 if (!EC_POINT_get_affine_coordinates_GF2m(group, Q, x, y, ctx)) ABORT; 895#endif 896 fprintf(stderr, "Point is not on curve: x = 0x"); 897 BN_print_fp(stderr, x); 898 fprintf(stderr, ", y = 0x"); 899 BN_print_fp(stderr, y); 900 fprintf(stderr, "\n"); 901 ABORT; 902 } 903 904 fprintf(stdout, "A cyclic subgroup:\n"); 905 k = 100; 906 do 907 { 908 if (k-- == 0) ABORT; 909 910 if (EC_POINT_is_at_infinity(group, P)) 911 fprintf(stdout, " point at infinity\n"); 912 else 913 { 914 if (!EC_POINT_get_affine_coordinates_GF2m(group, P, x, y, ctx)) ABORT; 915 916 fprintf(stdout, " x = 0x"); 917 BN_print_fp(stdout, x); 918 fprintf(stdout, ", y = 0x"); 919 BN_print_fp(stdout, y); 920 fprintf(stdout, "\n"); 921 } 922 923 if (!EC_POINT_copy(R, P)) ABORT; 924 if (!EC_POINT_add(group, P, P, Q, ctx)) ABORT; 925 } 926 while (!EC_POINT_is_at_infinity(group, P)); 927 928 if (!EC_POINT_add(group, P, Q, R, ctx)) ABORT; 929 if (!EC_POINT_is_at_infinity(group, P)) ABORT; 930 931/* Change test based on whether binary point compression is enabled or not. */ 932#ifdef OPENSSL_EC_BIN_PT_COMP 933 len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_COMPRESSED, buf, sizeof buf, ctx); 934 if (len == 0) ABORT; 935 if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT; 936 if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT; 937 fprintf(stdout, "Generator as octet string, compressed form:\n "); 938 for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]); 939#endif 940 941 len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_UNCOMPRESSED, buf, sizeof buf, ctx); 942 if (len == 0) ABORT; 943 if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT; 944 if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT; 945 fprintf(stdout, "\nGenerator as octet string, uncompressed form:\n "); 946 for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]); 947 948/* Change test based on whether binary point compression is enabled or not. */ 949#ifdef OPENSSL_EC_BIN_PT_COMP 950 len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_HYBRID, buf, sizeof buf, ctx); 951 if (len == 0) ABORT; 952 if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT; 953 if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT; 954 fprintf(stdout, "\nGenerator as octet string, hybrid form:\n "); 955 for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]); 956#endif 957 958 fprintf(stdout, "\n"); 959 960 if (!EC_POINT_invert(group, P, ctx)) ABORT; 961 if (0 != EC_POINT_cmp(group, P, R, ctx)) ABORT; 962 963 964 /* Curve K-163 (FIPS PUB 186-2, App. 6) */ 965 CHAR2_CURVE_TEST 966 ( 967 "NIST curve K-163", 968 "0800000000000000000000000000000000000000C9", 969 "1", 970 "1", 971 "02FE13C0537BBC11ACAA07D793DE4E6D5E5C94EEE8", 972 "0289070FB05D38FF58321F2E800536D538CCDAA3D9", 973 1, 974 "04000000000000000000020108A2E0CC0D99F8A5EF", 975 "2", 976 163, 977 C2_K163 978 ); 979 980 /* Curve B-163 (FIPS PUB 186-2, App. 6) */ 981 CHAR2_CURVE_TEST 982 ( 983 "NIST curve B-163", 984 "0800000000000000000000000000000000000000C9", 985 "1", 986 "020A601907B8C953CA1481EB10512F78744A3205FD", 987 "03F0EBA16286A2D57EA0991168D4994637E8343E36", 988 "00D51FBC6C71A0094FA2CDD545B11C5C0C797324F1", 989 1, 990 "040000000000000000000292FE77E70C12A4234C33", 991 "2", 992 163, 993 C2_B163 994 ); 995 996 /* Curve K-233 (FIPS PUB 186-2, App. 6) */ 997 CHAR2_CURVE_TEST 998 ( 999 "NIST curve K-233", 1000 "020000000000000000000000000000000000000004000000000000000001", 1001 "0", 1002 "1", 1003 "017232BA853A7E731AF129F22FF4149563A419C26BF50A4C9D6EEFAD6126", 1004 "01DB537DECE819B7F70F555A67C427A8CD9BF18AEB9B56E0C11056FAE6A3", 1005 0, 1006 "008000000000000000000000000000069D5BB915BCD46EFB1AD5F173ABDF", 1007 "4", 1008 233, 1009 C2_K233 1010 ); 1011 1012 /* Curve B-233 (FIPS PUB 186-2, App. 6) */ 1013 CHAR2_CURVE_TEST 1014 ( 1015 "NIST curve B-233", 1016 "020000000000000000000000000000000000000004000000000000000001", 1017 "000000000000000000000000000000000000000000000000000000000001", 1018 "0066647EDE6C332C7F8C0923BB58213B333B20E9CE4281FE115F7D8F90AD", 1019 "00FAC9DFCBAC8313BB2139F1BB755FEF65BC391F8B36F8F8EB7371FD558B", 1020 "01006A08A41903350678E58528BEBF8A0BEFF867A7CA36716F7E01F81052", 1021 1, 1022 "01000000000000000000000000000013E974E72F8A6922031D2603CFE0D7", 1023 "2", 1024 233, 1025 C2_B233 1026 ); 1027 1028 /* Curve K-283 (FIPS PUB 186-2, App. 6) */ 1029 CHAR2_CURVE_TEST 1030 ( 1031 "NIST curve K-283", 1032 "0800000000000000000000000000000000000000000000000000000000000000000010A1", 1033 "0", 1034 "1", 1035 "0503213F78CA44883F1A3B8162F188E553CD265F23C1567A16876913B0C2AC2458492836", 1036 "01CCDA380F1C9E318D90F95D07E5426FE87E45C0E8184698E45962364E34116177DD2259", 1037 0, 1038 "01FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE9AE2ED07577265DFF7F94451E061E163C61", 1039 "4", 1040 283, 1041 C2_K283 1042 ); 1043 1044 /* Curve B-283 (FIPS PUB 186-2, App. 6) */ 1045 CHAR2_CURVE_TEST 1046 ( 1047 "NIST curve B-283", 1048 "0800000000000000000000000000000000000000000000000000000000000000000010A1", 1049 "000000000000000000000000000000000000000000000000000000000000000000000001", 1050 "027B680AC8B8596DA5A4AF8A19A0303FCA97FD7645309FA2A581485AF6263E313B79A2F5", 1051 "05F939258DB7DD90E1934F8C70B0DFEC2EED25B8557EAC9C80E2E198F8CDBECD86B12053", 1052 "03676854FE24141CB98FE6D4B20D02B4516FF702350EDDB0826779C813F0DF45BE8112F4", 1053 1, 1054 "03FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEF90399660FC938A90165B042A7CEFADB307", 1055 "2", 1056 283, 1057 C2_B283 1058 ); 1059 1060 /* Curve K-409 (FIPS PUB 186-2, App. 6) */ 1061 CHAR2_CURVE_TEST 1062 ( 1063 "NIST curve K-409", 1064 "02000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001", 1065 "0", 1066 "1", 1067 "0060F05F658F49C1AD3AB1890F7184210EFD0987E307C84C27ACCFB8F9F67CC2C460189EB5AAAA62EE222EB1B35540CFE9023746", 1068 "01E369050B7C4E42ACBA1DACBF04299C3460782F918EA427E6325165E9EA10E3DA5F6C42E9C55215AA9CA27A5863EC48D8E0286B", 1069 1, 1070 "007FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE5F83B2D4EA20400EC4557D5ED3E3E7CA5B4B5C83B8E01E5FCF", 1071 "4", 1072 409, 1073 C2_K409 1074 ); 1075 1076 /* Curve B-409 (FIPS PUB 186-2, App. 6) */ 1077 CHAR2_CURVE_TEST 1078 ( 1079 "NIST curve B-409", 1080 "02000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001", 1081 "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001", 1082 "0021A5C2C8EE9FEB5C4B9A753B7B476B7FD6422EF1F3DD674761FA99D6AC27C8A9A197B272822F6CD57A55AA4F50AE317B13545F", 1083 "015D4860D088DDB3496B0C6064756260441CDE4AF1771D4DB01FFE5B34E59703DC255A868A1180515603AEAB60794E54BB7996A7", 1084 "0061B1CFAB6BE5F32BBFA78324ED106A7636B9C5A7BD198D0158AA4F5488D08F38514F1FDF4B4F40D2181B3681C364BA0273C706", 1085 1, 1086 "010000000000000000000000000000000000000000000000000001E2AAD6A612F33307BE5FA47C3C9E052F838164CD37D9A21173", 1087 "2", 1088 409, 1089 C2_B409 1090 ); 1091 1092 /* Curve K-571 (FIPS PUB 186-2, App. 6) */ 1093 CHAR2_CURVE_TEST 1094 ( 1095 "NIST curve K-571", 1096 "80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425", 1097 "0", 1098 "1", 1099 "026EB7A859923FBC82189631F8103FE4AC9CA2970012D5D46024804801841CA44370958493B205E647DA304DB4CEB08CBBD1BA39494776FB988B47174DCA88C7E2945283A01C8972", 1100 "0349DC807F4FBF374F4AEADE3BCA95314DD58CEC9F307A54FFC61EFC006D8A2C9D4979C0AC44AEA74FBEBBB9F772AEDCB620B01A7BA7AF1B320430C8591984F601CD4C143EF1C7A3", 1101 0, 1102 "020000000000000000000000000000000000000000000000000000000000000000000000131850E1F19A63E4B391A8DB917F4138B630D84BE5D639381E91DEB45CFE778F637C1001", 1103 "4", 1104 571, 1105 C2_K571 1106 ); 1107 1108 /* Curve B-571 (FIPS PUB 186-2, App. 6) */ 1109 CHAR2_CURVE_TEST 1110 ( 1111 "NIST curve B-571", 1112 "80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425", 1113 "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001", 1114 "02F40E7E2221F295DE297117B7F3D62F5C6A97FFCB8CEFF1CD6BA8CE4A9A18AD84FFABBD8EFA59332BE7AD6756A66E294AFD185A78FF12AA520E4DE739BACA0C7FFEFF7F2955727A", 1115 "0303001D34B856296C16C0D40D3CD7750A93D1D2955FA80AA5F40FC8DB7B2ABDBDE53950F4C0D293CDD711A35B67FB1499AE60038614F1394ABFA3B4C850D927E1E7769C8EEC2D19", 1116 "037BF27342DA639B6DCCFFFEB73D69D78C6C27A6009CBBCA1980F8533921E8A684423E43BAB08A576291AF8F461BB2A8B3531D2F0485C19B16E2F1516E23DD3C1A4827AF1B8AC15B", 1117 1, 1118 "03FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE661CE18FF55987308059B186823851EC7DD9CA1161DE93D5174D66E8382E9BB2FE84E47", 1119 "2", 1120 571, 1121 C2_B571 1122 ); 1123 1124 /* more tests using the last curve */ 1125 1126 if (!EC_POINT_copy(Q, P)) ABORT; 1127 if (EC_POINT_is_at_infinity(group, Q)) ABORT; 1128 if (!EC_POINT_dbl(group, P, P, ctx)) ABORT; 1129 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT; 1130 if (!EC_POINT_invert(group, Q, ctx)) ABORT; /* P = -2Q */ 1131 1132 if (!EC_POINT_add(group, R, P, Q, ctx)) ABORT; 1133 if (!EC_POINT_add(group, R, R, Q, ctx)) ABORT; 1134 if (!EC_POINT_is_at_infinity(group, R)) ABORT; /* R = P + 2Q */ 1135 1136 { 1137 const EC_POINT *points[3]; 1138 const BIGNUM *scalars[3]; 1139 1140 if (EC_POINT_is_at_infinity(group, Q)) ABORT; 1141 points[0] = Q; 1142 points[1] = Q; 1143 points[2] = Q; 1144 1145 if (!BN_add(y, z, BN_value_one())) ABORT; 1146 if (BN_is_odd(y)) ABORT; 1147 if (!BN_rshift1(y, y)) ABORT; 1148 scalars[0] = y; /* (group order + 1)/2, so y*Q + y*Q = Q */ 1149 scalars[1] = y; 1150 1151 fprintf(stdout, "combined multiplication ..."); 1152 fflush(stdout); 1153 1154 /* z is still the group order */ 1155 if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) ABORT; 1156 if (!EC_POINTs_mul(group, R, z, 2, points, scalars, ctx)) ABORT; 1157 if (0 != EC_POINT_cmp(group, P, R, ctx)) ABORT; 1158 if (0 != EC_POINT_cmp(group, R, Q, ctx)) ABORT; 1159 1160 fprintf(stdout, "."); 1161 fflush(stdout); 1162 1163 if (!BN_pseudo_rand(y, BN_num_bits(y), 0, 0)) ABORT; 1164 if (!BN_add(z, z, y)) ABORT; 1165 BN_set_negative(z, 1); 1166 scalars[0] = y; 1167 scalars[1] = z; /* z = -(order + y) */ 1168 1169 if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) ABORT; 1170 if (!EC_POINT_is_at_infinity(group, P)) ABORT; 1171 1172 fprintf(stdout, "."); 1173 fflush(stdout); 1174 1175 if (!BN_pseudo_rand(x, BN_num_bits(y) - 1, 0, 0)) ABORT; 1176 if (!BN_add(z, x, y)) ABORT; 1177 BN_set_negative(z, 1); 1178 scalars[0] = x; 1179 scalars[1] = y; 1180 scalars[2] = z; /* z = -(x+y) */ 1181 1182 if (!EC_POINTs_mul(group, P, NULL, 3, points, scalars, ctx)) ABORT; 1183 if (!EC_POINT_is_at_infinity(group, P)) ABORT; 1184 1185 fprintf(stdout, " ok\n\n"); 1186 } 1187 1188 1189#if 0 1190 timings(C2_K163, TIMING_BASE_PT, ctx); 1191 timings(C2_K163, TIMING_RAND_PT, ctx); 1192 timings(C2_K163, TIMING_SIMUL, ctx); 1193 timings(C2_B163, TIMING_BASE_PT, ctx); 1194 timings(C2_B163, TIMING_RAND_PT, ctx); 1195 timings(C2_B163, TIMING_SIMUL, ctx); 1196 timings(C2_K233, TIMING_BASE_PT, ctx); 1197 timings(C2_K233, TIMING_RAND_PT, ctx); 1198 timings(C2_K233, TIMING_SIMUL, ctx); 1199 timings(C2_B233, TIMING_BASE_PT, ctx); 1200 timings(C2_B233, TIMING_RAND_PT, ctx); 1201 timings(C2_B233, TIMING_SIMUL, ctx); 1202 timings(C2_K283, TIMING_BASE_PT, ctx); 1203 timings(C2_K283, TIMING_RAND_PT, ctx); 1204 timings(C2_K283, TIMING_SIMUL, ctx); 1205 timings(C2_B283, TIMING_BASE_PT, ctx); 1206 timings(C2_B283, TIMING_RAND_PT, ctx); 1207 timings(C2_B283, TIMING_SIMUL, ctx); 1208 timings(C2_K409, TIMING_BASE_PT, ctx); 1209 timings(C2_K409, TIMING_RAND_PT, ctx); 1210 timings(C2_K409, TIMING_SIMUL, ctx); 1211 timings(C2_B409, TIMING_BASE_PT, ctx); 1212 timings(C2_B409, TIMING_RAND_PT, ctx); 1213 timings(C2_B409, TIMING_SIMUL, ctx); 1214 timings(C2_K571, TIMING_BASE_PT, ctx); 1215 timings(C2_K571, TIMING_RAND_PT, ctx); 1216 timings(C2_K571, TIMING_SIMUL, ctx); 1217 timings(C2_B571, TIMING_BASE_PT, ctx); 1218 timings(C2_B571, TIMING_RAND_PT, ctx); 1219 timings(C2_B571, TIMING_SIMUL, ctx); 1220#endif 1221 1222 1223 if (ctx) 1224 BN_CTX_free(ctx); 1225 BN_free(p); BN_free(a); BN_free(b); 1226 EC_GROUP_free(group); 1227 EC_POINT_free(P); 1228 EC_POINT_free(Q); 1229 EC_POINT_free(R); 1230 BN_free(x); BN_free(y); BN_free(z); BN_free(cof); 1231 1232 if (C2_K163) EC_GROUP_free(C2_K163); 1233 if (C2_B163) EC_GROUP_free(C2_B163); 1234 if (C2_K233) EC_GROUP_free(C2_K233); 1235 if (C2_B233) EC_GROUP_free(C2_B233); 1236 if (C2_K283) EC_GROUP_free(C2_K283); 1237 if (C2_B283) EC_GROUP_free(C2_B283); 1238 if (C2_K409) EC_GROUP_free(C2_K409); 1239 if (C2_B409) EC_GROUP_free(C2_B409); 1240 if (C2_K571) EC_GROUP_free(C2_K571); 1241 if (C2_B571) EC_GROUP_free(C2_B571); 1242 1243 } 1244 1245void internal_curve_test(void) 1246 { 1247 EC_builtin_curve *curves = NULL; 1248 size_t crv_len = 0, n = 0; 1249 int ok = 1; 1250 1251 crv_len = EC_get_builtin_curves(NULL, 0); 1252 1253 curves = OPENSSL_malloc(sizeof(EC_builtin_curve) * crv_len); 1254 1255 if (curves == NULL) 1256 return; 1257 1258 if (!EC_get_builtin_curves(curves, crv_len)) 1259 { 1260 OPENSSL_free(curves); 1261 return; 1262 } 1263 1264 fprintf(stdout, "testing internal curves: "); 1265 1266 for (n = 0; n < crv_len; n++) 1267 { 1268 EC_GROUP *group = NULL; 1269 int nid = curves[n].nid; 1270 if ((group = EC_GROUP_new_by_curve_name(nid)) == NULL) 1271 { 1272 ok = 0; 1273 fprintf(stdout, "\nEC_GROUP_new_curve_name() failed with" 1274 " curve %s\n", OBJ_nid2sn(nid)); 1275 /* try next curve */ 1276 continue; 1277 } 1278 if (!EC_GROUP_check(group, NULL)) 1279 { 1280 ok = 0; 1281 fprintf(stdout, "\nEC_GROUP_check() failed with" 1282 " curve %s\n", OBJ_nid2sn(nid)); 1283 EC_GROUP_free(group); 1284 /* try the next curve */ 1285 continue; 1286 } 1287 fprintf(stdout, "."); 1288 fflush(stdout); 1289 EC_GROUP_free(group); 1290 } 1291 if (ok) 1292 fprintf(stdout, " ok\n"); 1293 else 1294 fprintf(stdout, " failed\n"); 1295 OPENSSL_free(curves); 1296 return; 1297 } 1298 1299static const char rnd_seed[] = "string to make the random number generator think it has entropy"; 1300 1301int main(int argc, char *argv[]) 1302 { 1303 1304 /* enable memory leak checking unless explicitly disabled */ 1305 if (!((getenv("OPENSSL_DEBUG_MEMORY") != NULL) && (0 == strcmp(getenv("OPENSSL_DEBUG_MEMORY"), "off")))) 1306 { 1307 CRYPTO_malloc_debug_init(); 1308 CRYPTO_set_mem_debug_options(V_CRYPTO_MDEBUG_ALL); 1309 } 1310 else 1311 { 1312 /* OPENSSL_DEBUG_MEMORY=off */ 1313 CRYPTO_set_mem_debug_functions(0, 0, 0, 0, 0); 1314 } 1315 CRYPTO_mem_ctrl(CRYPTO_MEM_CHECK_ON); 1316 ERR_load_crypto_strings(); 1317 1318 RAND_seed(rnd_seed, sizeof rnd_seed); /* or BN_generate_prime may fail */ 1319 1320 prime_field_tests(); 1321 puts(""); 1322 char2_field_tests(); 1323 /* test the internal curves */ 1324 internal_curve_test(); 1325 1326#ifndef OPENSSL_NO_ENGINE 1327 ENGINE_cleanup(); 1328#endif 1329 CRYPTO_cleanup_all_ex_data(); 1330 ERR_free_strings(); 1331 ERR_remove_state(0); 1332 CRYPTO_mem_leaks_fp(stderr); 1333 1334 return 0; 1335 } 1336#endif 1337