1/* crypto/ec/ectest.c */ 2/* ==================================================================== 3 * Copyright (c) 1998-2001 The OpenSSL Project. All rights reserved. 4 * 5 * Redistribution and use in source and binary forms, with or without 6 * modification, are permitted provided that the following conditions 7 * are met: 8 * 9 * 1. Redistributions of source code must retain the above copyright 10 * notice, this list of conditions and the following disclaimer. 11 * 12 * 2. Redistributions in binary form must reproduce the above copyright 13 * notice, this list of conditions and the following disclaimer in 14 * the documentation and/or other materials provided with the 15 * distribution. 16 * 17 * 3. All advertising materials mentioning features or use of this 18 * software must display the following acknowledgment: 19 * "This product includes software developed by the OpenSSL Project 20 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" 21 * 22 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to 23 * endorse or promote products derived from this software without 24 * prior written permission. For written permission, please contact 25 * openssl-core@openssl.org. 26 * 27 * 5. Products derived from this software may not be called "OpenSSL" 28 * nor may "OpenSSL" appear in their names without prior written 29 * permission of the OpenSSL Project. 30 * 31 * 6. Redistributions of any form whatsoever must retain the following 32 * acknowledgment: 33 * "This product includes software developed by the OpenSSL Project 34 * for use in the OpenSSL Toolkit (http://www.openssl.org/)" 35 * 36 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY 37 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 38 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR 39 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR 40 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, 41 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT 42 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; 43 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 44 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, 45 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) 46 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED 47 * OF THE POSSIBILITY OF SUCH DAMAGE. 48 * ==================================================================== 49 * 50 * This product includes cryptographic software written by Eric Young 51 * (eay@cryptsoft.com). This product includes software written by Tim 52 * Hudson (tjh@cryptsoft.com). 53 * 54 */ 55 56#include <stdio.h> 57#include <stdlib.h> 58#ifdef FLAT_INC 59#include "e_os.h" 60#else 61#include "../e_os.h" 62#endif 63#include <string.h> 64#include <time.h> 65 66 67#ifdef OPENSSL_NO_EC 68int main(int argc, char * argv[]) { puts("Elliptic curves are disabled."); return 0; } 69#else 70 71 72#include <openssl/ec.h> 73#ifndef OPENSSL_NO_ENGINE 74#include <openssl/engine.h> 75#endif 76#include <openssl/err.h> 77 78#define ABORT do { \ 79 fflush(stdout); \ 80 fprintf(stderr, "%s:%d: ABORT\n", __FILE__, __LINE__); \ 81 ERR_print_errors_fp(stderr); \ 82 EXIT(1); \ 83} while (0) 84 85#if 0 86static void timings(EC_GROUP *group, int multi, BN_CTX *ctx) 87 { 88 clock_t clck; 89 int i, j; 90 BIGNUM *s, *s0; 91 EC_POINT *P; 92 93 s = BN_new(); 94 s0 = BN_new(); 95 if (s == NULL || s0 == NULL) ABORT; 96 97 if (!EC_GROUP_get_curve_GFp(group, s, NULL, NULL, ctx)) ABORT; 98 fprintf(stdout, "Timings for %d bit prime, ", (int)BN_num_bits(s)); 99 if (!EC_GROUP_get_order(group, s, ctx)) ABORT; 100 fprintf(stdout, "%d bit scalars ", (int)BN_num_bits(s)); 101 fflush(stdout); 102 103 P = EC_POINT_new(group); 104 if (P == NULL) ABORT; 105 EC_POINT_copy(P, EC_GROUP_get0_generator(group)); 106 107 clck = clock(); 108 for (i = 0; i < 10; i++) 109 { 110 if (!BN_pseudo_rand(s, BN_num_bits(s), 0, 0)) ABORT; 111 if (multi) 112 { 113 if (!BN_pseudo_rand(s0, BN_num_bits(s), 0, 0)) ABORT; 114 } 115 for (j = 0; j < 10; j++) 116 { 117 if (!EC_POINT_mul(group, P, s, multi ? P : NULL, multi ? s0 : NULL, ctx)) ABORT; 118 } 119 fprintf(stdout, "."); 120 fflush(stdout); 121 } 122 fprintf(stdout, "\n"); 123 124 clck = clock() - clck; 125 126#ifdef CLOCKS_PER_SEC 127 /* "To determine the time in seconds, the value returned 128 * by the clock function should be divided by the value 129 * of the macro CLOCKS_PER_SEC." 130 * -- ISO/IEC 9899 */ 131# define UNIT "s" 132#else 133 /* "`CLOCKS_PER_SEC' undeclared (first use this function)" 134 * -- cc on NeXTstep/OpenStep */ 135# define UNIT "units" 136# define CLOCKS_PER_SEC 1 137#endif 138 139 fprintf(stdout, "%i %s in %.2f " UNIT "\n", i*j, 140 multi ? "s*P+t*Q operations" : "point multiplications", 141 (double)clck/CLOCKS_PER_SEC); 142 fprintf(stdout, "average: %.4f " UNIT "\n", (double)clck/(CLOCKS_PER_SEC*i*j)); 143 144 EC_POINT_free(P); 145 BN_free(s); 146 BN_free(s0); 147 } 148#endif 149 150int main(int argc, char *argv[]) 151 { 152 BN_CTX *ctx = NULL; 153 BIGNUM *p, *a, *b; 154 EC_GROUP *group; 155 EC_GROUP *P_192 = NULL, *P_224 = NULL, *P_256 = NULL, *P_384 = NULL, *P_521 = NULL; 156 EC_POINT *P, *Q, *R; 157 BIGNUM *x, *y, *z; 158 unsigned char buf[100]; 159 size_t i, len; 160 int k; 161 162 /* enable memory leak checking unless explicitly disabled */ 163 if (!((getenv("OPENSSL_DEBUG_MEMORY") != NULL) && (0 == strcmp(getenv("OPENSSL_DEBUG_MEMORY"), "off")))) 164 { 165 CRYPTO_malloc_debug_init(); 166 CRYPTO_set_mem_debug_options(V_CRYPTO_MDEBUG_ALL); 167 } 168 else 169 { 170 /* OPENSSL_DEBUG_MEMORY=off */ 171 CRYPTO_set_mem_debug_functions(0, 0, 0, 0, 0); 172 } 173 CRYPTO_mem_ctrl(CRYPTO_MEM_CHECK_ON); 174 ERR_load_crypto_strings(); 175 176#if 1 /* optional */ 177 ctx = BN_CTX_new(); 178 if (!ctx) ABORT; 179#endif 180 181 p = BN_new(); 182 a = BN_new(); 183 b = BN_new(); 184 if (!p || !a || !b) ABORT; 185 186 if (!BN_hex2bn(&p, "17")) ABORT; 187 if (!BN_hex2bn(&a, "1")) ABORT; 188 if (!BN_hex2bn(&b, "1")) ABORT; 189 190 group = EC_GROUP_new(EC_GFp_mont_method()); /* applications should use EC_GROUP_new_curve_GFp 191 * so that the library gets to choose the EC_METHOD */ 192 if (!group) ABORT; 193 194 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT; 195 196 { 197 EC_GROUP *tmp; 198 tmp = EC_GROUP_new(EC_GROUP_method_of(group)); 199 if (!tmp) ABORT; 200 if (!EC_GROUP_copy(tmp, group)); 201 EC_GROUP_free(group); 202 group = tmp; 203 } 204 205 if (!EC_GROUP_get_curve_GFp(group, p, a, b, ctx)) ABORT; 206 207 fprintf(stdout, "Curve defined by Weierstrass equation\n y^2 = x^3 + a*x + b (mod 0x"); 208 BN_print_fp(stdout, p); 209 fprintf(stdout, ")\n a = 0x"); 210 BN_print_fp(stdout, a); 211 fprintf(stdout, "\n b = 0x"); 212 BN_print_fp(stdout, b); 213 fprintf(stdout, "\n"); 214 215 P = EC_POINT_new(group); 216 Q = EC_POINT_new(group); 217 R = EC_POINT_new(group); 218 if (!P || !Q || !R) ABORT; 219 220 if (!EC_POINT_set_to_infinity(group, P)) ABORT; 221 if (!EC_POINT_is_at_infinity(group, P)) ABORT; 222 223 buf[0] = 0; 224 if (!EC_POINT_oct2point(group, Q, buf, 1, ctx)) ABORT; 225 226 if (!EC_POINT_add(group, P, P, Q, ctx)) ABORT; 227 if (!EC_POINT_is_at_infinity(group, P)) ABORT; 228 229 x = BN_new(); 230 y = BN_new(); 231 z = BN_new(); 232 if (!x || !y || !z) ABORT; 233 234 if (!BN_hex2bn(&x, "D")) ABORT; 235 if (!EC_POINT_set_compressed_coordinates_GFp(group, Q, x, 1, ctx)) ABORT; 236 if (!EC_POINT_is_on_curve(group, Q, ctx)) 237 { 238 if (!EC_POINT_get_affine_coordinates_GFp(group, Q, x, y, ctx)) ABORT; 239 fprintf(stderr, "Point is not on curve: x = 0x"); 240 BN_print_fp(stderr, x); 241 fprintf(stderr, ", y = 0x"); 242 BN_print_fp(stderr, y); 243 fprintf(stderr, "\n"); 244 ABORT; 245 } 246 247 fprintf(stdout, "A cyclic subgroup:\n"); 248 k = 100; 249 do 250 { 251 if (k-- == 0) ABORT; 252 253 if (EC_POINT_is_at_infinity(group, P)) 254 fprintf(stdout, " point at infinity\n"); 255 else 256 { 257 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT; 258 259 fprintf(stdout, " x = 0x"); 260 BN_print_fp(stdout, x); 261 fprintf(stdout, ", y = 0x"); 262 BN_print_fp(stdout, y); 263 fprintf(stdout, "\n"); 264 } 265 266 if (!EC_POINT_copy(R, P)) ABORT; 267 if (!EC_POINT_add(group, P, P, Q, ctx)) ABORT; 268 269#if 0 /* optional */ 270 { 271 EC_POINT *points[3]; 272 273 points[0] = R; 274 points[1] = Q; 275 points[2] = P; 276 if (!EC_POINTs_make_affine(group, 2, points, ctx)) ABORT; 277 } 278#endif 279 280 } 281 while (!EC_POINT_is_at_infinity(group, P)); 282 283 if (!EC_POINT_add(group, P, Q, R, ctx)) ABORT; 284 if (!EC_POINT_is_at_infinity(group, P)) ABORT; 285 286 len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_COMPRESSED, buf, sizeof buf, ctx); 287 if (len == 0) ABORT; 288 if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT; 289 if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT; 290 fprintf(stdout, "Generator as octect string, compressed form:\n "); 291 for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]); 292 293 len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_UNCOMPRESSED, buf, sizeof buf, ctx); 294 if (len == 0) ABORT; 295 if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT; 296 if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT; 297 fprintf(stdout, "\nGenerator as octect string, uncompressed form:\n "); 298 for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]); 299 300 len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_HYBRID, buf, sizeof buf, ctx); 301 if (len == 0) ABORT; 302 if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT; 303 if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT; 304 fprintf(stdout, "\nGenerator as octect string, hybrid form:\n "); 305 for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]); 306 307 if (!EC_POINT_get_Jprojective_coordinates_GFp(group, R, x, y, z, ctx)) ABORT; 308 fprintf(stdout, "\nA representation of the inverse of that generator in\nJacobian projective coordinates:\n X = 0x"); 309 BN_print_fp(stdout, x); 310 fprintf(stdout, ", Y = 0x"); 311 BN_print_fp(stdout, y); 312 fprintf(stdout, ", Z = 0x"); 313 BN_print_fp(stdout, z); 314 fprintf(stdout, "\n"); 315 316 if (!EC_POINT_invert(group, P, ctx)) ABORT; 317 if (0 != EC_POINT_cmp(group, P, R, ctx)) ABORT; 318 319 320 /* Curve P-192 (FIPS PUB 186-2, App. 6) */ 321 322 if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF")) ABORT; 323 if (1 != BN_is_prime(p, BN_prime_checks, 0, ctx, NULL)) ABORT; 324 if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC")) ABORT; 325 if (!BN_hex2bn(&b, "64210519E59C80E70FA7E9AB72243049FEB8DEECC146B9B1")) ABORT; 326 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT; 327 328 if (!BN_hex2bn(&x, "188DA80EB03090F67CBF20EB43A18800F4FF0AFD82FF1012")) ABORT; 329 if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 1, ctx)) ABORT; 330 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT; 331 if (!BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22831")) ABORT; 332 if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT; 333 334 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT; 335 fprintf(stdout, "\nNIST curve P-192 -- Generator:\n x = 0x"); 336 BN_print_fp(stdout, x); 337 fprintf(stdout, "\n y = 0x"); 338 BN_print_fp(stdout, y); 339 fprintf(stdout, "\n"); 340 /* G_y value taken from the standard: */ 341 if (!BN_hex2bn(&z, "07192B95FFC8DA78631011ED6B24CDD573F977A11E794811")) ABORT; 342 if (0 != BN_cmp(y, z)) ABORT; 343 344 fprintf(stdout, "verify group order ..."); 345 fflush(stdout); 346 if (!EC_GROUP_get_order(group, z, ctx)) ABORT; 347 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; 348 if (!EC_POINT_is_at_infinity(group, Q)) ABORT; 349 fprintf(stdout, "."); 350 fflush(stdout); 351 if (!EC_GROUP_precompute_mult(group, ctx)) ABORT; 352 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; 353 if (!EC_POINT_is_at_infinity(group, Q)) ABORT; 354 fprintf(stdout, " ok\n"); 355 356 if (!(P_192 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT; 357 if (!EC_GROUP_copy(P_192, group)) ABORT; 358 359 360 /* Curve P-224 (FIPS PUB 186-2, App. 6) */ 361 362 if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001")) ABORT; 363 if (1 != BN_is_prime(p, BN_prime_checks, 0, ctx, NULL)) ABORT; 364 if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE")) ABORT; 365 if (!BN_hex2bn(&b, "B4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4")) ABORT; 366 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT; 367 368 if (!BN_hex2bn(&x, "B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21")) ABORT; 369 if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 0, ctx)) ABORT; 370 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT; 371 if (!BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D")) ABORT; 372 if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT; 373 374 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT; 375 fprintf(stdout, "\nNIST curve P-224 -- Generator:\n x = 0x"); 376 BN_print_fp(stdout, x); 377 fprintf(stdout, "\n y = 0x"); 378 BN_print_fp(stdout, y); 379 fprintf(stdout, "\n"); 380 /* G_y value taken from the standard: */ 381 if (!BN_hex2bn(&z, "BD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34")) ABORT; 382 if (0 != BN_cmp(y, z)) ABORT; 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_224 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT; 397 if (!EC_GROUP_copy(P_224, group)) ABORT; 398 399 400 /* Curve P-256 (FIPS PUB 186-2, App. 6) */ 401 402 if (!BN_hex2bn(&p, "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF")) ABORT; 403 if (1 != BN_is_prime(p, BN_prime_checks, 0, ctx, NULL)) ABORT; 404 if (!BN_hex2bn(&a, "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFC")) ABORT; 405 if (!BN_hex2bn(&b, "5AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B")) ABORT; 406 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT; 407 408 if (!BN_hex2bn(&x, "6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296")) 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, "FFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E" 412 "84F3B9CAC2FC632551")) ABORT; 413 if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT; 414 415 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT; 416 fprintf(stdout, "\nNIST curve P-256 -- Generator:\n x = 0x"); 417 BN_print_fp(stdout, x); 418 fprintf(stdout, "\n y = 0x"); 419 BN_print_fp(stdout, y); 420 fprintf(stdout, "\n"); 421 /* G_y value taken from the standard: */ 422 if (!BN_hex2bn(&z, "4FE342E2FE1A7F9B8EE7EB4A7C0F9E162BCE33576B315ECECBB6406837BF51F5")) ABORT; 423 if (0 != BN_cmp(y, z)) ABORT; 424 425 fprintf(stdout, "verify group order ..."); 426 fflush(stdout); 427 if (!EC_GROUP_get_order(group, z, ctx)) ABORT; 428 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; 429 if (!EC_POINT_is_at_infinity(group, Q)) ABORT; 430 fprintf(stdout, "."); 431 fflush(stdout); 432 if (!EC_GROUP_precompute_mult(group, ctx)) ABORT; 433 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; 434 if (!EC_POINT_is_at_infinity(group, Q)) ABORT; 435 fprintf(stdout, " ok\n"); 436 437 if (!(P_256 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT; 438 if (!EC_GROUP_copy(P_256, group)) ABORT; 439 440 441 /* Curve P-384 (FIPS PUB 186-2, App. 6) */ 442 443 if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" 444 "FFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFF")) ABORT; 445 if (1 != BN_is_prime(p, BN_prime_checks, 0, ctx, NULL)) ABORT; 446 if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" 447 "FFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFC")) ABORT; 448 if (!BN_hex2bn(&b, "B3312FA7E23EE7E4988E056BE3F82D19181D9C6EFE8141" 449 "120314088F5013875AC656398D8A2ED19D2A85C8EDD3EC2AEF")) ABORT; 450 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT; 451 452 if (!BN_hex2bn(&x, "AA87CA22BE8B05378EB1C71EF320AD746E1D3B628BA79B" 453 "9859F741E082542A385502F25DBF55296C3A545E3872760AB7")) ABORT; 454 if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 1, ctx)) ABORT; 455 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT; 456 if (!BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" 457 "FFC7634D81F4372DDF581A0DB248B0A77AECEC196ACCC52973")) 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-384 -- 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, "3617DE4A96262C6F5D9E98BF9292DC29F8F41DBD289A14" 468 "7CE9DA3113B5F0B8C00A60B1CE1D7E819D7A431D7C90EA0E5F")) ABORT; 469 if (0 != BN_cmp(y, z)) ABORT; 470 471 fprintf(stdout, "verify group order ..."); 472 fflush(stdout); 473 if (!EC_GROUP_get_order(group, z, ctx)) ABORT; 474 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; 475 if (!EC_POINT_is_at_infinity(group, Q)) ABORT; 476 fprintf(stdout, "."); 477 fflush(stdout); 478 if (!EC_GROUP_precompute_mult(group, ctx)) ABORT; 479 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; 480 if (!EC_POINT_is_at_infinity(group, Q)) ABORT; 481 fprintf(stdout, " ok\n"); 482 483 if (!(P_384 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT; 484 if (!EC_GROUP_copy(P_384, group)) ABORT; 485 486 487 /* Curve P-521 (FIPS PUB 186-2, App. 6) */ 488 489 if (!BN_hex2bn(&p, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" 490 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" 491 "FFFFFFFFFFFFFFFFFFFFFFFFFFFF")) ABORT; 492 if (1 != BN_is_prime(p, BN_prime_checks, 0, ctx, NULL)) ABORT; 493 if (!BN_hex2bn(&a, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" 494 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" 495 "FFFFFFFFFFFFFFFFFFFFFFFFFFFC")) ABORT; 496 if (!BN_hex2bn(&b, "051953EB9618E1C9A1F929A21A0B68540EEA2DA725B99B" 497 "315F3B8B489918EF109E156193951EC7E937B1652C0BD3BB1BF073573" 498 "DF883D2C34F1EF451FD46B503F00")) ABORT; 499 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT; 500 501 if (!BN_hex2bn(&x, "C6858E06B70404E9CD9E3ECB662395B4429C648139053F" 502 "B521F828AF606B4D3DBAA14B5E77EFE75928FE1DC127A2FFA8DE3348B" 503 "3C1856A429BF97E7E31C2E5BD66")) ABORT; 504 if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 0, ctx)) ABORT; 505 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT; 506 if (!BN_hex2bn(&z, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" 507 "FFFFFFFFFFFFFFFFFFFFA51868783BF2F966B7FCC0148F709A5D03BB5" 508 "C9B8899C47AEBB6FB71E91386409")) ABORT; 509 if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT; 510 511 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT; 512 fprintf(stdout, "\nNIST curve P-521 -- Generator:\n x = 0x"); 513 BN_print_fp(stdout, x); 514 fprintf(stdout, "\n y = 0x"); 515 BN_print_fp(stdout, y); 516 fprintf(stdout, "\n"); 517 /* G_y value taken from the standard: */ 518 if (!BN_hex2bn(&z, "11839296A789A3BC0045C8A5FB42C7D1BD998F54449579" 519 "B446817AFBD17273E662C97EE72995EF42640C550B9013FAD0761353C" 520 "7086A272C24088BE94769FD16650")) ABORT; 521 if (0 != BN_cmp(y, z)) ABORT; 522 523 fprintf(stdout, "verify group order ..."); 524 fflush(stdout); 525 if (!EC_GROUP_get_order(group, z, ctx)) ABORT; 526 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; 527 if (!EC_POINT_is_at_infinity(group, Q)) ABORT; 528 fprintf(stdout, "."); 529 fflush(stdout); 530 if (!EC_GROUP_precompute_mult(group, ctx)) ABORT; 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_521 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT; 536 if (!EC_GROUP_copy(P_521, group)) ABORT; 537 538 539 /* more tests using the last curve */ 540 541 if (!EC_POINT_copy(Q, P)) ABORT; 542 if (EC_POINT_is_at_infinity(group, Q)) ABORT; 543 if (!EC_POINT_dbl(group, P, P, ctx)) ABORT; 544 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT; 545 if (!EC_POINT_invert(group, Q, ctx)) ABORT; /* P = -2Q */ 546 547 if (!EC_POINT_add(group, R, P, Q, ctx)) ABORT; 548 if (!EC_POINT_add(group, R, R, Q, ctx)) ABORT; 549 if (!EC_POINT_is_at_infinity(group, R)) ABORT; /* R = P + 2Q */ 550 551 { 552 const EC_POINT *points[3]; 553 const BIGNUM *scalars[3]; 554 555 if (EC_POINT_is_at_infinity(group, Q)) ABORT; 556 points[0] = Q; 557 points[1] = Q; 558 points[2] = Q; 559 560 if (!BN_add(y, z, BN_value_one())) ABORT; 561 if (BN_is_odd(y)) ABORT; 562 if (!BN_rshift1(y, y)) ABORT; 563 scalars[0] = y; /* (group order + 1)/2, so y*Q + y*Q = Q */ 564 scalars[1] = y; 565 566 fprintf(stdout, "combined multiplication ..."); 567 fflush(stdout); 568 569 /* z is still the group order */ 570 if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) ABORT; 571 if (!EC_POINTs_mul(group, R, z, 2, points, scalars, ctx)) ABORT; 572 if (0 != EC_POINT_cmp(group, P, R, ctx)) ABORT; 573 if (0 != EC_POINT_cmp(group, R, Q, ctx)) ABORT; 574 575 fprintf(stdout, "."); 576 fflush(stdout); 577 578 if (!BN_pseudo_rand(y, BN_num_bits(y), 0, 0)) ABORT; 579 if (!BN_add(z, z, y)) ABORT; 580 z->neg = 1; 581 scalars[0] = y; 582 scalars[1] = z; /* z = -(order + y) */ 583 584 if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) ABORT; 585 if (!EC_POINT_is_at_infinity(group, P)) ABORT; 586 587 fprintf(stdout, "."); 588 fflush(stdout); 589 590 if (!BN_pseudo_rand(x, BN_num_bits(y) - 1, 0, 0)) ABORT; 591 if (!BN_add(z, x, y)) ABORT; 592 z->neg = 1; 593 scalars[0] = x; 594 scalars[1] = y; 595 scalars[2] = z; /* z = -(x+y) */ 596 597 if (!EC_POINTs_mul(group, P, NULL, 3, points, scalars, ctx)) ABORT; 598 if (!EC_POINT_is_at_infinity(group, P)) ABORT; 599 600 fprintf(stdout, " ok\n\n"); 601 } 602 603 604#if 0 605 timings(P_192, 0, ctx); 606 timings(P_192, 1, ctx); 607 timings(P_224, 0, ctx); 608 timings(P_224, 1, ctx); 609 timings(P_256, 0, ctx); 610 timings(P_256, 1, ctx); 611 timings(P_384, 0, ctx); 612 timings(P_384, 1, ctx); 613 timings(P_521, 0, ctx); 614 timings(P_521, 1, ctx); 615#endif 616 617 618 if (ctx) 619 BN_CTX_free(ctx); 620 BN_free(p); BN_free(a); BN_free(b); 621 EC_GROUP_free(group); 622 EC_POINT_free(P); 623 EC_POINT_free(Q); 624 EC_POINT_free(R); 625 BN_free(x); BN_free(y); BN_free(z); 626 627 if (P_192) EC_GROUP_free(P_192); 628 if (P_224) EC_GROUP_free(P_224); 629 if (P_256) EC_GROUP_free(P_256); 630 if (P_384) EC_GROUP_free(P_384); 631 if (P_521) EC_GROUP_free(P_521); 632 633#ifndef OPENSSL_NO_ENGINE 634 ENGINE_cleanup(); 635#endif 636 CRYPTO_cleanup_all_ex_data(); 637 ERR_free_strings(); 638 ERR_remove_state(0); 639 CRYPTO_mem_leaks_fp(stderr); 640 641 return 0; 642 } 643#endif 644