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 (at) 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 (at) cryptsoft.com). This product includes software written by Tim 55 * Hudson (tjh (at) 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 84 int 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 #include <openssl/opensslconf.h> 98 99 #if defined(_MSC_VER) && defined(_MIPS_) && (_MSC_VER/100==12) 100 /* suppress "too big too optimize" warning */ 101 #pragma warning(disable:4959) 102 #endif 103 104 #define ABORT do { \ 105 fflush(stdout); \ 106 fprintf(stderr, "%s:%d: ABORT\n", __FILE__, __LINE__); \ 107 ERR_print_errors_fp(stderr); \ 108 EXIT(1); \ 109 } while (0) 110 111 #define TIMING_BASE_PT 0 112 #define TIMING_RAND_PT 1 113 #define TIMING_SIMUL 2 114 115 #if 0 116 static void timings(EC_GROUP *group, int type, BN_CTX *ctx) 117 { 118 clock_t clck; 119 int i, j; 120 BIGNUM *s; 121 BIGNUM *r[10], *r0[10]; 122 EC_POINT *P; 123 124 s = BN_new(); 125 if (s == NULL) ABORT; 126 127 fprintf(stdout, "Timings for %d-bit field, ", EC_GROUP_get_degree(group)); 128 if (!EC_GROUP_get_order(group, s, ctx)) ABORT; 129 fprintf(stdout, "%d-bit scalars ", (int)BN_num_bits(s)); 130 fflush(stdout); 131 132 P = EC_POINT_new(group); 133 if (P == NULL) ABORT; 134 EC_POINT_copy(P, EC_GROUP_get0_generator(group)); 135 136 for (i = 0; i < 10; i++) 137 { 138 if ((r[i] = BN_new()) == NULL) ABORT; 139 if (!BN_pseudo_rand(r[i], BN_num_bits(s), 0, 0)) ABORT; 140 if (type != TIMING_BASE_PT) 141 { 142 if ((r0[i] = BN_new()) == NULL) ABORT; 143 if (!BN_pseudo_rand(r0[i], BN_num_bits(s), 0, 0)) ABORT; 144 } 145 } 146 147 clck = clock(); 148 for (i = 0; i < 10; i++) 149 { 150 for (j = 0; j < 10; j++) 151 { 152 if (!EC_POINT_mul(group, P, (type != TIMING_RAND_PT) ? r[i] : NULL, 153 (type != TIMING_BASE_PT) ? P : NULL, (type != TIMING_BASE_PT) ? r0[i] : NULL, ctx)) ABORT; 154 } 155 } 156 clck = clock() - clck; 157 158 fprintf(stdout, "\n"); 159 160 #ifdef CLOCKS_PER_SEC 161 /* "To determine the time in seconds, the value returned 162 * by the clock function should be divided by the value 163 * of the macro CLOCKS_PER_SEC." 164 * -- ISO/IEC 9899 */ 165 # define UNIT "s" 166 #else 167 /* "`CLOCKS_PER_SEC' undeclared (first use this function)" 168 * -- cc on NeXTstep/OpenStep */ 169 # define UNIT "units" 170 # define CLOCKS_PER_SEC 1 171 #endif 172 173 if (type == TIMING_BASE_PT) { 174 fprintf(stdout, "%i %s in %.2f " UNIT "\n", i*j, 175 "base point multiplications", (double)clck/CLOCKS_PER_SEC); 176 } else if (type == TIMING_RAND_PT) { 177 fprintf(stdout, "%i %s in %.2f " UNIT "\n", i*j, 178 "random point multiplications", (double)clck/CLOCKS_PER_SEC); 179 } else if (type == TIMING_SIMUL) { 180 fprintf(stdout, "%i %s in %.2f " UNIT "\n", i*j, 181 "s*P+t*Q operations", (double)clck/CLOCKS_PER_SEC); 182 } 183 fprintf(stdout, "average: %.4f " UNIT "\n", (double)clck/(CLOCKS_PER_SEC*i*j)); 184 185 EC_POINT_free(P); 186 BN_free(s); 187 for (i = 0; i < 10; i++) 188 { 189 BN_free(r[i]); 190 if (type != TIMING_BASE_PT) BN_free(r0[i]); 191 } 192 } 193 #endif 194 195 /* test multiplication with group order, long and negative scalars */ 196 static void group_order_tests(EC_GROUP *group) 197 { 198 BIGNUM *n1, *n2, *order; 199 EC_POINT *P = EC_POINT_new(group); 200 EC_POINT *Q = EC_POINT_new(group); 201 BN_CTX *ctx = BN_CTX_new(); 202 int i; 203 204 n1 = BN_new(); n2 = BN_new(); order = BN_new(); 205 fprintf(stdout, "verify group order ..."); 206 fflush(stdout); 207 if (!EC_GROUP_get_order(group, order, ctx)) ABORT; 208 if (!EC_POINT_mul(group, Q, order, NULL, NULL, ctx)) ABORT; 209 if (!EC_POINT_is_at_infinity(group, Q)) ABORT; 210 fprintf(stdout, "."); 211 fflush(stdout); 212 if (!EC_GROUP_precompute_mult(group, ctx)) ABORT; 213 if (!EC_POINT_mul(group, Q, order, NULL, NULL, ctx)) ABORT; 214 if (!EC_POINT_is_at_infinity(group, Q)) ABORT; 215 fprintf(stdout, " ok\n"); 216 fprintf(stdout, "long/negative scalar tests "); 217 for (i = 1; i <= 2; i++) 218 { 219 const BIGNUM *scalars[6]; 220 const EC_POINT *points[6]; 221 222 fprintf(stdout, i == 1 ? 223 "allowing precomputation ... " : 224 "without precomputation ... "); 225 if (!BN_set_word(n1, i)) ABORT; 226 /* If i == 1, P will be the predefined generator for which 227 * EC_GROUP_precompute_mult has set up precomputation. */ 228 if (!EC_POINT_mul(group, P, n1, NULL, NULL, ctx)) ABORT; 229 230 if (!BN_one(n1)) ABORT; 231 /* n1 = 1 - order */ 232 if (!BN_sub(n1, n1, order)) ABORT; 233 if (!EC_POINT_mul(group, Q, NULL, P, n1, ctx)) ABORT; 234 if (0 != EC_POINT_cmp(group, Q, P, ctx)) ABORT; 235 236 /* n2 = 1 + order */ 237 if (!BN_add(n2, order, BN_value_one())) ABORT; 238 if (!EC_POINT_mul(group, Q, NULL, P, n2, ctx)) ABORT; 239 if (0 != EC_POINT_cmp(group, Q, P, ctx)) ABORT; 240 241 /* n2 = (1 - order) * (1 + order) = 1 - order^2 */ 242 if (!BN_mul(n2, n1, n2, ctx)) ABORT; 243 if (!EC_POINT_mul(group, Q, NULL, P, n2, ctx)) ABORT; 244 if (0 != EC_POINT_cmp(group, Q, P, ctx)) ABORT; 245 246 /* n2 = order^2 - 1 */ 247 BN_set_negative(n2, 0); 248 if (!EC_POINT_mul(group, Q, NULL, P, n2, ctx)) ABORT; 249 /* Add P to verify the result. */ 250 if (!EC_POINT_add(group, Q, Q, P, ctx)) ABORT; 251 if (!EC_POINT_is_at_infinity(group, Q)) ABORT; 252 253 /* Exercise EC_POINTs_mul, including corner cases. */ 254 if (EC_POINT_is_at_infinity(group, P)) ABORT; 255 scalars[0] = n1; points[0] = Q; /* => infinity */ 256 scalars[1] = n2; points[1] = P; /* => -P */ 257 scalars[2] = n1; points[2] = Q; /* => infinity */ 258 scalars[3] = n2; points[3] = Q; /* => infinity */ 259 scalars[4] = n1; points[4] = P; /* => P */ 260 scalars[5] = n2; points[5] = Q; /* => infinity */ 261 if (!EC_POINTs_mul(group, P, NULL, 6, points, scalars, ctx)) ABORT; 262 if (!EC_POINT_is_at_infinity(group, P)) ABORT; 263 } 264 fprintf(stdout, "ok\n"); 265 266 EC_POINT_free(P); 267 EC_POINT_free(Q); 268 BN_free(n1); 269 BN_free(n2); 270 BN_free(order); 271 BN_CTX_free(ctx); 272 } 273 274 static void prime_field_tests(void) 275 { 276 BN_CTX *ctx = NULL; 277 BIGNUM *p, *a, *b; 278 EC_GROUP *group; 279 EC_GROUP *P_160 = NULL, *P_192 = NULL, *P_224 = NULL, *P_256 = NULL, *P_384 = NULL, *P_521 = NULL; 280 EC_POINT *P, *Q, *R; 281 BIGNUM *x, *y, *z; 282 unsigned char buf[100]; 283 size_t i, len; 284 int k; 285 286 #if 1 /* optional */ 287 ctx = BN_CTX_new(); 288 if (!ctx) ABORT; 289 #endif 290 291 p = BN_new(); 292 a = BN_new(); 293 b = BN_new(); 294 if (!p || !a || !b) ABORT; 295 296 if (!BN_hex2bn(&p, "17")) ABORT; 297 if (!BN_hex2bn(&a, "1")) ABORT; 298 if (!BN_hex2bn(&b, "1")) ABORT; 299 300 group = EC_GROUP_new(EC_GFp_mont_method()); /* applications should use EC_GROUP_new_curve_GFp 301 * so that the library gets to choose the EC_METHOD */ 302 if (!group) ABORT; 303 304 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT; 305 306 { 307 EC_GROUP *tmp; 308 tmp = EC_GROUP_new(EC_GROUP_method_of(group)); 309 if (!tmp) ABORT; 310 if (!EC_GROUP_copy(tmp, group)) ABORT; 311 EC_GROUP_free(group); 312 group = tmp; 313 } 314 315 if (!EC_GROUP_get_curve_GFp(group, p, a, b, ctx)) ABORT; 316 317 fprintf(stdout, "Curve defined by Weierstrass equation\n y^2 = x^3 + a*x + b (mod 0x"); 318 BN_print_fp(stdout, p); 319 fprintf(stdout, ")\n a = 0x"); 320 BN_print_fp(stdout, a); 321 fprintf(stdout, "\n b = 0x"); 322 BN_print_fp(stdout, b); 323 fprintf(stdout, "\n"); 324 325 P = EC_POINT_new(group); 326 Q = EC_POINT_new(group); 327 R = EC_POINT_new(group); 328 if (!P || !Q || !R) ABORT; 329 330 if (!EC_POINT_set_to_infinity(group, P)) ABORT; 331 if (!EC_POINT_is_at_infinity(group, P)) ABORT; 332 333 buf[0] = 0; 334 if (!EC_POINT_oct2point(group, Q, buf, 1, ctx)) ABORT; 335 336 if (!EC_POINT_add(group, P, P, Q, ctx)) ABORT; 337 if (!EC_POINT_is_at_infinity(group, P)) ABORT; 338 339 x = BN_new(); 340 y = BN_new(); 341 z = BN_new(); 342 if (!x || !y || !z) ABORT; 343 344 if (!BN_hex2bn(&x, "D")) ABORT; 345 if (!EC_POINT_set_compressed_coordinates_GFp(group, Q, x, 1, ctx)) ABORT; 346 if (!EC_POINT_is_on_curve(group, Q, ctx)) 347 { 348 if (!EC_POINT_get_affine_coordinates_GFp(group, Q, x, y, ctx)) ABORT; 349 fprintf(stderr, "Point is not on curve: x = 0x"); 350 BN_print_fp(stderr, x); 351 fprintf(stderr, ", y = 0x"); 352 BN_print_fp(stderr, y); 353 fprintf(stderr, "\n"); 354 ABORT; 355 } 356 357 fprintf(stdout, "A cyclic subgroup:\n"); 358 k = 100; 359 do 360 { 361 if (k-- == 0) ABORT; 362 363 if (EC_POINT_is_at_infinity(group, P)) 364 fprintf(stdout, " point at infinity\n"); 365 else 366 { 367 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT; 368 369 fprintf(stdout, " x = 0x"); 370 BN_print_fp(stdout, x); 371 fprintf(stdout, ", y = 0x"); 372 BN_print_fp(stdout, y); 373 fprintf(stdout, "\n"); 374 } 375 376 if (!EC_POINT_copy(R, P)) ABORT; 377 if (!EC_POINT_add(group, P, P, Q, ctx)) ABORT; 378 379 #if 0 /* optional */ 380 { 381 EC_POINT *points[3]; 382 383 points[0] = R; 384 points[1] = Q; 385 points[2] = P; 386 if (!EC_POINTs_make_affine(group, 2, points, ctx)) ABORT; 387 } 388 #endif 389 390 } 391 while (!EC_POINT_is_at_infinity(group, P)); 392 393 if (!EC_POINT_add(group, P, Q, R, ctx)) ABORT; 394 if (!EC_POINT_is_at_infinity(group, P)) ABORT; 395 396 len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_COMPRESSED, buf, sizeof buf, ctx); 397 if (len == 0) ABORT; 398 if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT; 399 if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT; 400 fprintf(stdout, "Generator as octet string, compressed form:\n "); 401 for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]); 402 403 len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_UNCOMPRESSED, buf, sizeof buf, ctx); 404 if (len == 0) ABORT; 405 if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT; 406 if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT; 407 fprintf(stdout, "\nGenerator as octet string, uncompressed form:\n "); 408 for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]); 409 410 len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_HYBRID, buf, sizeof buf, ctx); 411 if (len == 0) ABORT; 412 if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT; 413 if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT; 414 fprintf(stdout, "\nGenerator as octet string, hybrid form:\n "); 415 for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]); 416 417 if (!EC_POINT_get_Jprojective_coordinates_GFp(group, R, x, y, z, ctx)) ABORT; 418 fprintf(stdout, "\nA representation of the inverse of that generator in\nJacobian projective coordinates:\n X = 0x"); 419 BN_print_fp(stdout, x); 420 fprintf(stdout, ", Y = 0x"); 421 BN_print_fp(stdout, y); 422 fprintf(stdout, ", Z = 0x"); 423 BN_print_fp(stdout, z); 424 fprintf(stdout, "\n"); 425 426 if (!EC_POINT_invert(group, P, ctx)) ABORT; 427 if (0 != EC_POINT_cmp(group, P, R, ctx)) ABORT; 428 429 430 /* Curve secp160r1 (Certicom Research SEC 2 Version 1.0, section 2.4.2, 2000) 431 * -- not a NIST curve, but commonly used */ 432 433 if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFF")) ABORT; 434 if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT; 435 if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFC")) ABORT; 436 if (!BN_hex2bn(&b, "1C97BEFC54BD7A8B65ACF89F81D4D4ADC565FA45")) ABORT; 437 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT; 438 439 if (!BN_hex2bn(&x, "4A96B5688EF573284664698968C38BB913CBFC82")) ABORT; 440 if (!BN_hex2bn(&y, "23a628553168947d59dcc912042351377ac5fb32")) ABORT; 441 if (!EC_POINT_set_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT; 442 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT; 443 if (!BN_hex2bn(&z, "0100000000000000000001F4C8F927AED3CA752257")) ABORT; 444 if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT; 445 446 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT; 447 fprintf(stdout, "\nSEC2 curve secp160r1 -- Generator:\n x = 0x"); 448 BN_print_fp(stdout, x); 449 fprintf(stdout, "\n y = 0x"); 450 BN_print_fp(stdout, y); 451 fprintf(stdout, "\n"); 452 /* G_y value taken from the standard: */ 453 if (!BN_hex2bn(&z, "23a628553168947d59dcc912042351377ac5fb32")) ABORT; 454 if (0 != BN_cmp(y, z)) ABORT; 455 456 fprintf(stdout, "verify degree ..."); 457 if (EC_GROUP_get_degree(group) != 160) ABORT; 458 fprintf(stdout, " ok\n"); 459 460 group_order_tests(group); 461 462 if (!(P_160 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT; 463 if (!EC_GROUP_copy(P_160, group)) ABORT; 464 465 466 /* Curve P-192 (FIPS PUB 186-2, App. 6) */ 467 468 if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF")) ABORT; 469 if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT; 470 if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC")) ABORT; 471 if (!BN_hex2bn(&b, "64210519E59C80E70FA7E9AB72243049FEB8DEECC146B9B1")) ABORT; 472 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT; 473 474 if (!BN_hex2bn(&x, "188DA80EB03090F67CBF20EB43A18800F4FF0AFD82FF1012")) ABORT; 475 if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 1, ctx)) ABORT; 476 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT; 477 if (!BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22831")) ABORT; 478 if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT; 479 480 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT; 481 fprintf(stdout, "\nNIST curve P-192 -- Generator:\n x = 0x"); 482 BN_print_fp(stdout, x); 483 fprintf(stdout, "\n y = 0x"); 484 BN_print_fp(stdout, y); 485 fprintf(stdout, "\n"); 486 /* G_y value taken from the standard: */ 487 if (!BN_hex2bn(&z, "07192B95FFC8DA78631011ED6B24CDD573F977A11E794811")) ABORT; 488 if (0 != BN_cmp(y, z)) ABORT; 489 490 fprintf(stdout, "verify degree ..."); 491 if (EC_GROUP_get_degree(group) != 192) ABORT; 492 fprintf(stdout, " ok\n"); 493 494 group_order_tests(group); 495 496 if (!(P_192 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT; 497 if (!EC_GROUP_copy(P_192, group)) ABORT; 498 499 500 /* Curve P-224 (FIPS PUB 186-2, App. 6) */ 501 502 if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001")) ABORT; 503 if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT; 504 if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE")) ABORT; 505 if (!BN_hex2bn(&b, "B4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4")) ABORT; 506 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT; 507 508 if (!BN_hex2bn(&x, "B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21")) ABORT; 509 if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 0, ctx)) ABORT; 510 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT; 511 if (!BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D")) ABORT; 512 if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT; 513 514 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT; 515 fprintf(stdout, "\nNIST curve P-224 -- Generator:\n x = 0x"); 516 BN_print_fp(stdout, x); 517 fprintf(stdout, "\n y = 0x"); 518 BN_print_fp(stdout, y); 519 fprintf(stdout, "\n"); 520 /* G_y value taken from the standard: */ 521 if (!BN_hex2bn(&z, "BD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34")) ABORT; 522 if (0 != BN_cmp(y, z)) ABORT; 523 524 fprintf(stdout, "verify degree ..."); 525 if (EC_GROUP_get_degree(group) != 224) ABORT; 526 fprintf(stdout, " ok\n"); 527 528 group_order_tests(group); 529 530 if (!(P_224 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT; 531 if (!EC_GROUP_copy(P_224, group)) ABORT; 532 533 534 /* Curve P-256 (FIPS PUB 186-2, App. 6) */ 535 536 if (!BN_hex2bn(&p, "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF")) ABORT; 537 if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT; 538 if (!BN_hex2bn(&a, "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFC")) ABORT; 539 if (!BN_hex2bn(&b, "5AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B")) ABORT; 540 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT; 541 542 if (!BN_hex2bn(&x, "6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296")) ABORT; 543 if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 1, ctx)) ABORT; 544 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT; 545 if (!BN_hex2bn(&z, "FFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E" 546 "84F3B9CAC2FC632551")) ABORT; 547 if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT; 548 549 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT; 550 fprintf(stdout, "\nNIST curve P-256 -- Generator:\n x = 0x"); 551 BN_print_fp(stdout, x); 552 fprintf(stdout, "\n y = 0x"); 553 BN_print_fp(stdout, y); 554 fprintf(stdout, "\n"); 555 /* G_y value taken from the standard: */ 556 if (!BN_hex2bn(&z, "4FE342E2FE1A7F9B8EE7EB4A7C0F9E162BCE33576B315ECECBB6406837BF51F5")) ABORT; 557 if (0 != BN_cmp(y, z)) ABORT; 558 559 fprintf(stdout, "verify degree ..."); 560 if (EC_GROUP_get_degree(group) != 256) ABORT; 561 fprintf(stdout, " ok\n"); 562 563 group_order_tests(group); 564 565 if (!(P_256 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT; 566 if (!EC_GROUP_copy(P_256, group)) ABORT; 567 568 569 /* Curve P-384 (FIPS PUB 186-2, App. 6) */ 570 571 if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" 572 "FFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFF")) ABORT; 573 if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT; 574 if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" 575 "FFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFC")) ABORT; 576 if (!BN_hex2bn(&b, "B3312FA7E23EE7E4988E056BE3F82D19181D9C6EFE8141" 577 "120314088F5013875AC656398D8A2ED19D2A85C8EDD3EC2AEF")) ABORT; 578 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT; 579 580 if (!BN_hex2bn(&x, "AA87CA22BE8B05378EB1C71EF320AD746E1D3B628BA79B" 581 "9859F741E082542A385502F25DBF55296C3A545E3872760AB7")) ABORT; 582 if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 1, ctx)) ABORT; 583 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT; 584 if (!BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" 585 "FFC7634D81F4372DDF581A0DB248B0A77AECEC196ACCC52973")) ABORT; 586 if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT; 587 588 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT; 589 fprintf(stdout, "\nNIST curve P-384 -- Generator:\n x = 0x"); 590 BN_print_fp(stdout, x); 591 fprintf(stdout, "\n y = 0x"); 592 BN_print_fp(stdout, y); 593 fprintf(stdout, "\n"); 594 /* G_y value taken from the standard: */ 595 if (!BN_hex2bn(&z, "3617DE4A96262C6F5D9E98BF9292DC29F8F41DBD289A14" 596 "7CE9DA3113B5F0B8C00A60B1CE1D7E819D7A431D7C90EA0E5F")) ABORT; 597 if (0 != BN_cmp(y, z)) ABORT; 598 599 fprintf(stdout, "verify degree ..."); 600 if (EC_GROUP_get_degree(group) != 384) ABORT; 601 fprintf(stdout, " ok\n"); 602 603 group_order_tests(group); 604 605 if (!(P_384 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT; 606 if (!EC_GROUP_copy(P_384, group)) ABORT; 607 608 609 /* Curve P-521 (FIPS PUB 186-2, App. 6) */ 610 611 if (!BN_hex2bn(&p, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" 612 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" 613 "FFFFFFFFFFFFFFFFFFFFFFFFFFFF")) ABORT; 614 if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT; 615 if (!BN_hex2bn(&a, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" 616 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" 617 "FFFFFFFFFFFFFFFFFFFFFFFFFFFC")) ABORT; 618 if (!BN_hex2bn(&b, "051953EB9618E1C9A1F929A21A0B68540EEA2DA725B99B" 619 "315F3B8B489918EF109E156193951EC7E937B1652C0BD3BB1BF073573" 620 "DF883D2C34F1EF451FD46B503F00")) ABORT; 621 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT; 622 623 if (!BN_hex2bn(&x, "C6858E06B70404E9CD9E3ECB662395B4429C648139053F" 624 "B521F828AF606B4D3DBAA14B5E77EFE75928FE1DC127A2FFA8DE3348B" 625 "3C1856A429BF97E7E31C2E5BD66")) ABORT; 626 if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 0, ctx)) ABORT; 627 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT; 628 if (!BN_hex2bn(&z, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" 629 "FFFFFFFFFFFFFFFFFFFFA51868783BF2F966B7FCC0148F709A5D03BB5" 630 "C9B8899C47AEBB6FB71E91386409")) ABORT; 631 if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT; 632 633 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT; 634 fprintf(stdout, "\nNIST curve P-521 -- Generator:\n x = 0x"); 635 BN_print_fp(stdout, x); 636 fprintf(stdout, "\n y = 0x"); 637 BN_print_fp(stdout, y); 638 fprintf(stdout, "\n"); 639 /* G_y value taken from the standard: */ 640 if (!BN_hex2bn(&z, "11839296A789A3BC0045C8A5FB42C7D1BD998F54449579" 641 "B446817AFBD17273E662C97EE72995EF42640C550B9013FAD0761353C" 642 "7086A272C24088BE94769FD16650")) ABORT; 643 if (0 != BN_cmp(y, z)) ABORT; 644 645 fprintf(stdout, "verify degree ..."); 646 if (EC_GROUP_get_degree(group) != 521) ABORT; 647 fprintf(stdout, " ok\n"); 648 649 group_order_tests(group); 650 651 if (!(P_521 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT; 652 if (!EC_GROUP_copy(P_521, group)) ABORT; 653 654 655 /* more tests using the last curve */ 656 657 if (!EC_POINT_copy(Q, P)) ABORT; 658 if (EC_POINT_is_at_infinity(group, Q)) ABORT; 659 if (!EC_POINT_dbl(group, P, P, ctx)) ABORT; 660 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT; 661 if (!EC_POINT_invert(group, Q, ctx)) ABORT; /* P = -2Q */ 662 663 if (!EC_POINT_add(group, R, P, Q, ctx)) ABORT; 664 if (!EC_POINT_add(group, R, R, Q, ctx)) ABORT; 665 if (!EC_POINT_is_at_infinity(group, R)) ABORT; /* R = P + 2Q */ 666 667 { 668 const EC_POINT *points[4]; 669 const BIGNUM *scalars[4]; 670 BIGNUM scalar3; 671 672 if (EC_POINT_is_at_infinity(group, Q)) ABORT; 673 points[0] = Q; 674 points[1] = Q; 675 points[2] = Q; 676 points[3] = Q; 677 678 if (!EC_GROUP_get_order(group, z, ctx)) ABORT; 679 if (!BN_add(y, z, BN_value_one())) ABORT; 680 if (BN_is_odd(y)) ABORT; 681 if (!BN_rshift1(y, y)) ABORT; 682 scalars[0] = y; /* (group order + 1)/2, so y*Q + y*Q = Q */ 683 scalars[1] = y; 684 685 fprintf(stdout, "combined multiplication ..."); 686 fflush(stdout); 687 688 /* z is still the group order */ 689 if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) ABORT; 690 if (!EC_POINTs_mul(group, R, z, 2, points, scalars, ctx)) ABORT; 691 if (0 != EC_POINT_cmp(group, P, R, ctx)) ABORT; 692 if (0 != EC_POINT_cmp(group, R, Q, ctx)) ABORT; 693 694 fprintf(stdout, "."); 695 fflush(stdout); 696 697 if (!BN_pseudo_rand(y, BN_num_bits(y), 0, 0)) ABORT; 698 if (!BN_add(z, z, y)) ABORT; 699 BN_set_negative(z, 1); 700 scalars[0] = y; 701 scalars[1] = z; /* z = -(order + y) */ 702 703 if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) ABORT; 704 if (!EC_POINT_is_at_infinity(group, P)) ABORT; 705 706 fprintf(stdout, "."); 707 fflush(stdout); 708 709 if (!BN_pseudo_rand(x, BN_num_bits(y) - 1, 0, 0)) ABORT; 710 if (!BN_add(z, x, y)) ABORT; 711 BN_set_negative(z, 1); 712 scalars[0] = x; 713 scalars[1] = y; 714 scalars[2] = z; /* z = -(x+y) */ 715 716 BN_init(&scalar3); 717 BN_zero(&scalar3); 718 scalars[3] = &scalar3; 719 720 if (!EC_POINTs_mul(group, P, NULL, 4, points, scalars, ctx)) ABORT; 721 if (!EC_POINT_is_at_infinity(group, P)) ABORT; 722 723 fprintf(stdout, " ok\n\n"); 724 725 BN_free(&scalar3); 726 } 727 728 729 #if 0 730 timings(P_160, TIMING_BASE_PT, ctx); 731 timings(P_160, TIMING_RAND_PT, ctx); 732 timings(P_160, TIMING_SIMUL, ctx); 733 timings(P_192, TIMING_BASE_PT, ctx); 734 timings(P_192, TIMING_RAND_PT, ctx); 735 timings(P_192, TIMING_SIMUL, ctx); 736 timings(P_224, TIMING_BASE_PT, ctx); 737 timings(P_224, TIMING_RAND_PT, ctx); 738 timings(P_224, TIMING_SIMUL, ctx); 739 timings(P_256, TIMING_BASE_PT, ctx); 740 timings(P_256, TIMING_RAND_PT, ctx); 741 timings(P_256, TIMING_SIMUL, ctx); 742 timings(P_384, TIMING_BASE_PT, ctx); 743 timings(P_384, TIMING_RAND_PT, ctx); 744 timings(P_384, TIMING_SIMUL, ctx); 745 timings(P_521, TIMING_BASE_PT, ctx); 746 timings(P_521, TIMING_RAND_PT, ctx); 747 timings(P_521, TIMING_SIMUL, ctx); 748 #endif 749 750 751 if (ctx) 752 BN_CTX_free(ctx); 753 BN_free(p); BN_free(a); BN_free(b); 754 EC_GROUP_free(group); 755 EC_POINT_free(P); 756 EC_POINT_free(Q); 757 EC_POINT_free(R); 758 BN_free(x); BN_free(y); BN_free(z); 759 760 if (P_160) EC_GROUP_free(P_160); 761 if (P_192) EC_GROUP_free(P_192); 762 if (P_224) EC_GROUP_free(P_224); 763 if (P_256) EC_GROUP_free(P_256); 764 if (P_384) EC_GROUP_free(P_384); 765 if (P_521) EC_GROUP_free(P_521); 766 767 } 768 769 /* Change test based on whether binary point compression is enabled or not. */ 770 #ifdef OPENSSL_EC_BIN_PT_COMP 771 #define CHAR2_CURVE_TEST_INTERNAL(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \ 772 if (!BN_hex2bn(&x, _x)) ABORT; \ 773 if (!EC_POINT_set_compressed_coordinates_GF2m(group, P, x, _y_bit, ctx)) ABORT; \ 774 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT; \ 775 if (!BN_hex2bn(&z, _order)) ABORT; \ 776 if (!BN_hex2bn(&cof, _cof)) ABORT; \ 777 if (!EC_GROUP_set_generator(group, P, z, cof)) ABORT; \ 778 if (!EC_POINT_get_affine_coordinates_GF2m(group, P, x, y, ctx)) ABORT; \ 779 fprintf(stdout, "\n%s -- Generator:\n x = 0x", _name); \ 780 BN_print_fp(stdout, x); \ 781 fprintf(stdout, "\n y = 0x"); \ 782 BN_print_fp(stdout, y); \ 783 fprintf(stdout, "\n"); \ 784 /* G_y value taken from the standard: */ \ 785 if (!BN_hex2bn(&z, _y)) ABORT; \ 786 if (0 != BN_cmp(y, z)) ABORT; 787 #else 788 #define CHAR2_CURVE_TEST_INTERNAL(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \ 789 if (!BN_hex2bn(&x, _x)) ABORT; \ 790 if (!BN_hex2bn(&y, _y)) ABORT; \ 791 if (!EC_POINT_set_affine_coordinates_GF2m(group, P, x, y, ctx)) ABORT; \ 792 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT; \ 793 if (!BN_hex2bn(&z, _order)) ABORT; \ 794 if (!BN_hex2bn(&cof, _cof)) ABORT; \ 795 if (!EC_GROUP_set_generator(group, P, z, cof)) ABORT; \ 796 fprintf(stdout, "\n%s -- Generator:\n x = 0x", _name); \ 797 BN_print_fp(stdout, x); \ 798 fprintf(stdout, "\n y = 0x"); \ 799 BN_print_fp(stdout, y); \ 800 fprintf(stdout, "\n"); 801 #endif 802 803 #define CHAR2_CURVE_TEST(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \ 804 if (!BN_hex2bn(&p, _p)) ABORT; \ 805 if (!BN_hex2bn(&a, _a)) ABORT; \ 806 if (!BN_hex2bn(&b, _b)) ABORT; \ 807 if (!EC_GROUP_set_curve_GF2m(group, p, a, b, ctx)) ABORT; \ 808 CHAR2_CURVE_TEST_INTERNAL(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \ 809 fprintf(stdout, "verify degree ..."); \ 810 if (EC_GROUP_get_degree(group) != _degree) ABORT; \ 811 fprintf(stdout, " ok\n"); \ 812 group_order_tests(group); \ 813 if (!(_variable = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT; \ 814 if (!EC_GROUP_copy(_variable, group)) ABORT; \ 815 816 #ifndef OPENSSL_NO_EC2M 817 818 static void char2_field_tests(void) 819 { 820 BN_CTX *ctx = NULL; 821 BIGNUM *p, *a, *b; 822 EC_GROUP *group; 823 EC_GROUP *C2_K163 = NULL, *C2_K233 = NULL, *C2_K283 = NULL, *C2_K409 = NULL, *C2_K571 = NULL; 824 EC_GROUP *C2_B163 = NULL, *C2_B233 = NULL, *C2_B283 = NULL, *C2_B409 = NULL, *C2_B571 = NULL; 825 EC_POINT *P, *Q, *R; 826 BIGNUM *x, *y, *z, *cof; 827 unsigned char buf[100]; 828 size_t i, len; 829 int k; 830 831 #if 1 /* optional */ 832 ctx = BN_CTX_new(); 833 if (!ctx) ABORT; 834 #endif 835 836 p = BN_new(); 837 a = BN_new(); 838 b = BN_new(); 839 if (!p || !a || !b) ABORT; 840 841 if (!BN_hex2bn(&p, "13")) ABORT; 842 if (!BN_hex2bn(&a, "3")) ABORT; 843 if (!BN_hex2bn(&b, "1")) ABORT; 844 845 group = EC_GROUP_new(EC_GF2m_simple_method()); /* applications should use EC_GROUP_new_curve_GF2m 846 * so that the library gets to choose the EC_METHOD */ 847 if (!group) ABORT; 848 if (!EC_GROUP_set_curve_GF2m(group, p, a, b, ctx)) ABORT; 849 850 { 851 EC_GROUP *tmp; 852 tmp = EC_GROUP_new(EC_GROUP_method_of(group)); 853 if (!tmp) ABORT; 854 if (!EC_GROUP_copy(tmp, group)) ABORT; 855 EC_GROUP_free(group); 856 group = tmp; 857 } 858 859 if (!EC_GROUP_get_curve_GF2m(group, p, a, b, ctx)) ABORT; 860 861 fprintf(stdout, "Curve defined by Weierstrass equation\n y^2 + x*y = x^3 + a*x^2 + b (mod 0x"); 862 BN_print_fp(stdout, p); 863 fprintf(stdout, ")\n a = 0x"); 864 BN_print_fp(stdout, a); 865 fprintf(stdout, "\n b = 0x"); 866 BN_print_fp(stdout, b); 867 fprintf(stdout, "\n(0x... means binary polynomial)\n"); 868 869 P = EC_POINT_new(group); 870 Q = EC_POINT_new(group); 871 R = EC_POINT_new(group); 872 if (!P || !Q || !R) ABORT; 873 874 if (!EC_POINT_set_to_infinity(group, P)) ABORT; 875 if (!EC_POINT_is_at_infinity(group, P)) ABORT; 876 877 buf[0] = 0; 878 if (!EC_POINT_oct2point(group, Q, buf, 1, ctx)) ABORT; 879 880 if (!EC_POINT_add(group, P, P, Q, ctx)) ABORT; 881 if (!EC_POINT_is_at_infinity(group, P)) ABORT; 882 883 x = BN_new(); 884 y = BN_new(); 885 z = BN_new(); 886 cof = BN_new(); 887 if (!x || !y || !z || !cof) ABORT; 888 889 if (!BN_hex2bn(&x, "6")) ABORT; 890 /* Change test based on whether binary point compression is enabled or not. */ 891 #ifdef OPENSSL_EC_BIN_PT_COMP 892 if (!EC_POINT_set_compressed_coordinates_GF2m(group, Q, x, 1, ctx)) ABORT; 893 #else 894 if (!BN_hex2bn(&y, "8")) ABORT; 895 if (!EC_POINT_set_affine_coordinates_GF2m(group, Q, x, y, ctx)) ABORT; 896 #endif 897 if (!EC_POINT_is_on_curve(group, Q, ctx)) 898 { 899 /* Change test based on whether binary point compression is enabled or not. */ 900 #ifdef OPENSSL_EC_BIN_PT_COMP 901 if (!EC_POINT_get_affine_coordinates_GF2m(group, Q, x, y, ctx)) ABORT; 902 #endif 903 fprintf(stderr, "Point is not on curve: x = 0x"); 904 BN_print_fp(stderr, x); 905 fprintf(stderr, ", y = 0x"); 906 BN_print_fp(stderr, y); 907 fprintf(stderr, "\n"); 908 ABORT; 909 } 910 911 fprintf(stdout, "A cyclic subgroup:\n"); 912 k = 100; 913 do 914 { 915 if (k-- == 0) ABORT; 916 917 if (EC_POINT_is_at_infinity(group, P)) 918 fprintf(stdout, " point at infinity\n"); 919 else 920 { 921 if (!EC_POINT_get_affine_coordinates_GF2m(group, P, x, y, ctx)) ABORT; 922 923 fprintf(stdout, " x = 0x"); 924 BN_print_fp(stdout, x); 925 fprintf(stdout, ", y = 0x"); 926 BN_print_fp(stdout, y); 927 fprintf(stdout, "\n"); 928 } 929 930 if (!EC_POINT_copy(R, P)) ABORT; 931 if (!EC_POINT_add(group, P, P, Q, ctx)) ABORT; 932 } 933 while (!EC_POINT_is_at_infinity(group, P)); 934 935 if (!EC_POINT_add(group, P, Q, R, ctx)) ABORT; 936 if (!EC_POINT_is_at_infinity(group, P)) ABORT; 937 938 /* Change test based on whether binary point compression is enabled or not. */ 939 #ifdef OPENSSL_EC_BIN_PT_COMP 940 len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_COMPRESSED, buf, sizeof buf, ctx); 941 if (len == 0) ABORT; 942 if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT; 943 if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT; 944 fprintf(stdout, "Generator as octet string, compressed form:\n "); 945 for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]); 946 #endif 947 948 len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_UNCOMPRESSED, buf, sizeof buf, ctx); 949 if (len == 0) ABORT; 950 if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT; 951 if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT; 952 fprintf(stdout, "\nGenerator as octet string, uncompressed form:\n "); 953 for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]); 954 955 /* Change test based on whether binary point compression is enabled or not. */ 956 #ifdef OPENSSL_EC_BIN_PT_COMP 957 len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_HYBRID, buf, sizeof buf, ctx); 958 if (len == 0) ABORT; 959 if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT; 960 if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT; 961 fprintf(stdout, "\nGenerator as octet string, hybrid form:\n "); 962 for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]); 963 #endif 964 965 fprintf(stdout, "\n"); 966 967 if (!EC_POINT_invert(group, P, ctx)) ABORT; 968 if (0 != EC_POINT_cmp(group, P, R, ctx)) ABORT; 969 970 971 /* Curve K-163 (FIPS PUB 186-2, App. 6) */ 972 CHAR2_CURVE_TEST 973 ( 974 "NIST curve K-163", 975 "0800000000000000000000000000000000000000C9", 976 "1", 977 "1", 978 "02FE13C0537BBC11ACAA07D793DE4E6D5E5C94EEE8", 979 "0289070FB05D38FF58321F2E800536D538CCDAA3D9", 980 1, 981 "04000000000000000000020108A2E0CC0D99F8A5EF", 982 "2", 983 163, 984 C2_K163 985 ); 986 987 /* Curve B-163 (FIPS PUB 186-2, App. 6) */ 988 CHAR2_CURVE_TEST 989 ( 990 "NIST curve B-163", 991 "0800000000000000000000000000000000000000C9", 992 "1", 993 "020A601907B8C953CA1481EB10512F78744A3205FD", 994 "03F0EBA16286A2D57EA0991168D4994637E8343E36", 995 "00D51FBC6C71A0094FA2CDD545B11C5C0C797324F1", 996 1, 997 "040000000000000000000292FE77E70C12A4234C33", 998 "2", 999 163, 1000 C2_B163 1001 ); 1002 1003 /* Curve K-233 (FIPS PUB 186-2, App. 6) */ 1004 CHAR2_CURVE_TEST 1005 ( 1006 "NIST curve K-233", 1007 "020000000000000000000000000000000000000004000000000000000001", 1008 "0", 1009 "1", 1010 "017232BA853A7E731AF129F22FF4149563A419C26BF50A4C9D6EEFAD6126", 1011 "01DB537DECE819B7F70F555A67C427A8CD9BF18AEB9B56E0C11056FAE6A3", 1012 0, 1013 "008000000000000000000000000000069D5BB915BCD46EFB1AD5F173ABDF", 1014 "4", 1015 233, 1016 C2_K233 1017 ); 1018 1019 /* Curve B-233 (FIPS PUB 186-2, App. 6) */ 1020 CHAR2_CURVE_TEST 1021 ( 1022 "NIST curve B-233", 1023 "020000000000000000000000000000000000000004000000000000000001", 1024 "000000000000000000000000000000000000000000000000000000000001", 1025 "0066647EDE6C332C7F8C0923BB58213B333B20E9CE4281FE115F7D8F90AD", 1026 "00FAC9DFCBAC8313BB2139F1BB755FEF65BC391F8B36F8F8EB7371FD558B", 1027 "01006A08A41903350678E58528BEBF8A0BEFF867A7CA36716F7E01F81052", 1028 1, 1029 "01000000000000000000000000000013E974E72F8A6922031D2603CFE0D7", 1030 "2", 1031 233, 1032 C2_B233 1033 ); 1034 1035 /* Curve K-283 (FIPS PUB 186-2, App. 6) */ 1036 CHAR2_CURVE_TEST 1037 ( 1038 "NIST curve K-283", 1039 "0800000000000000000000000000000000000000000000000000000000000000000010A1", 1040 "0", 1041 "1", 1042 "0503213F78CA44883F1A3B8162F188E553CD265F23C1567A16876913B0C2AC2458492836", 1043 "01CCDA380F1C9E318D90F95D07E5426FE87E45C0E8184698E45962364E34116177DD2259", 1044 0, 1045 "01FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE9AE2ED07577265DFF7F94451E061E163C61", 1046 "4", 1047 283, 1048 C2_K283 1049 ); 1050 1051 /* Curve B-283 (FIPS PUB 186-2, App. 6) */ 1052 CHAR2_CURVE_TEST 1053 ( 1054 "NIST curve B-283", 1055 "0800000000000000000000000000000000000000000000000000000000000000000010A1", 1056 "000000000000000000000000000000000000000000000000000000000000000000000001", 1057 "027B680AC8B8596DA5A4AF8A19A0303FCA97FD7645309FA2A581485AF6263E313B79A2F5", 1058 "05F939258DB7DD90E1934F8C70B0DFEC2EED25B8557EAC9C80E2E198F8CDBECD86B12053", 1059 "03676854FE24141CB98FE6D4B20D02B4516FF702350EDDB0826779C813F0DF45BE8112F4", 1060 1, 1061 "03FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEF90399660FC938A90165B042A7CEFADB307", 1062 "2", 1063 283, 1064 C2_B283 1065 ); 1066 1067 /* Curve K-409 (FIPS PUB 186-2, App. 6) */ 1068 CHAR2_CURVE_TEST 1069 ( 1070 "NIST curve K-409", 1071 "02000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001", 1072 "0", 1073 "1", 1074 "0060F05F658F49C1AD3AB1890F7184210EFD0987E307C84C27ACCFB8F9F67CC2C460189EB5AAAA62EE222EB1B35540CFE9023746", 1075 "01E369050B7C4E42ACBA1DACBF04299C3460782F918EA427E6325165E9EA10E3DA5F6C42E9C55215AA9CA27A5863EC48D8E0286B", 1076 1, 1077 "007FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE5F83B2D4EA20400EC4557D5ED3E3E7CA5B4B5C83B8E01E5FCF", 1078 "4", 1079 409, 1080 C2_K409 1081 ); 1082 1083 /* Curve B-409 (FIPS PUB 186-2, App. 6) */ 1084 CHAR2_CURVE_TEST 1085 ( 1086 "NIST curve B-409", 1087 "02000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001", 1088 "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001", 1089 "0021A5C2C8EE9FEB5C4B9A753B7B476B7FD6422EF1F3DD674761FA99D6AC27C8A9A197B272822F6CD57A55AA4F50AE317B13545F", 1090 "015D4860D088DDB3496B0C6064756260441CDE4AF1771D4DB01FFE5B34E59703DC255A868A1180515603AEAB60794E54BB7996A7", 1091 "0061B1CFAB6BE5F32BBFA78324ED106A7636B9C5A7BD198D0158AA4F5488D08F38514F1FDF4B4F40D2181B3681C364BA0273C706", 1092 1, 1093 "010000000000000000000000000000000000000000000000000001E2AAD6A612F33307BE5FA47C3C9E052F838164CD37D9A21173", 1094 "2", 1095 409, 1096 C2_B409 1097 ); 1098 1099 /* Curve K-571 (FIPS PUB 186-2, App. 6) */ 1100 CHAR2_CURVE_TEST 1101 ( 1102 "NIST curve K-571", 1103 "80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425", 1104 "0", 1105 "1", 1106 "026EB7A859923FBC82189631F8103FE4AC9CA2970012D5D46024804801841CA44370958493B205E647DA304DB4CEB08CBBD1BA39494776FB988B47174DCA88C7E2945283A01C8972", 1107 "0349DC807F4FBF374F4AEADE3BCA95314DD58CEC9F307A54FFC61EFC006D8A2C9D4979C0AC44AEA74FBEBBB9F772AEDCB620B01A7BA7AF1B320430C8591984F601CD4C143EF1C7A3", 1108 0, 1109 "020000000000000000000000000000000000000000000000000000000000000000000000131850E1F19A63E4B391A8DB917F4138B630D84BE5D639381E91DEB45CFE778F637C1001", 1110 "4", 1111 571, 1112 C2_K571 1113 ); 1114 1115 /* Curve B-571 (FIPS PUB 186-2, App. 6) */ 1116 CHAR2_CURVE_TEST 1117 ( 1118 "NIST curve B-571", 1119 "80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425", 1120 "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001", 1121 "02F40E7E2221F295DE297117B7F3D62F5C6A97FFCB8CEFF1CD6BA8CE4A9A18AD84FFABBD8EFA59332BE7AD6756A66E294AFD185A78FF12AA520E4DE739BACA0C7FFEFF7F2955727A", 1122 "0303001D34B856296C16C0D40D3CD7750A93D1D2955FA80AA5F40FC8DB7B2ABDBDE53950F4C0D293CDD711A35B67FB1499AE60038614F1394ABFA3B4C850D927E1E7769C8EEC2D19", 1123 "037BF27342DA639B6DCCFFFEB73D69D78C6C27A6009CBBCA1980F8533921E8A684423E43BAB08A576291AF8F461BB2A8B3531D2F0485C19B16E2F1516E23DD3C1A4827AF1B8AC15B", 1124 1, 1125 "03FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE661CE18FF55987308059B186823851EC7DD9CA1161DE93D5174D66E8382E9BB2FE84E47", 1126 "2", 1127 571, 1128 C2_B571 1129 ); 1130 1131 /* more tests using the last curve */ 1132 1133 if (!EC_POINT_copy(Q, P)) ABORT; 1134 if (EC_POINT_is_at_infinity(group, Q)) ABORT; 1135 if (!EC_POINT_dbl(group, P, P, ctx)) ABORT; 1136 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT; 1137 if (!EC_POINT_invert(group, Q, ctx)) ABORT; /* P = -2Q */ 1138 1139 if (!EC_POINT_add(group, R, P, Q, ctx)) ABORT; 1140 if (!EC_POINT_add(group, R, R, Q, ctx)) ABORT; 1141 if (!EC_POINT_is_at_infinity(group, R)) ABORT; /* R = P + 2Q */ 1142 1143 { 1144 const EC_POINT *points[3]; 1145 const BIGNUM *scalars[3]; 1146 1147 if (EC_POINT_is_at_infinity(group, Q)) ABORT; 1148 points[0] = Q; 1149 points[1] = Q; 1150 points[2] = Q; 1151 1152 if (!BN_add(y, z, BN_value_one())) ABORT; 1153 if (BN_is_odd(y)) ABORT; 1154 if (!BN_rshift1(y, y)) ABORT; 1155 scalars[0] = y; /* (group order + 1)/2, so y*Q + y*Q = Q */ 1156 scalars[1] = y; 1157 1158 fprintf(stdout, "combined multiplication ..."); 1159 fflush(stdout); 1160 1161 /* z is still the group order */ 1162 if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) ABORT; 1163 if (!EC_POINTs_mul(group, R, z, 2, points, scalars, ctx)) ABORT; 1164 if (0 != EC_POINT_cmp(group, P, R, ctx)) ABORT; 1165 if (0 != EC_POINT_cmp(group, R, Q, ctx)) ABORT; 1166 1167 fprintf(stdout, "."); 1168 fflush(stdout); 1169 1170 if (!BN_pseudo_rand(y, BN_num_bits(y), 0, 0)) ABORT; 1171 if (!BN_add(z, z, y)) ABORT; 1172 BN_set_negative(z, 1); 1173 scalars[0] = y; 1174 scalars[1] = z; /* z = -(order + y) */ 1175 1176 if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) ABORT; 1177 if (!EC_POINT_is_at_infinity(group, P)) ABORT; 1178 1179 fprintf(stdout, "."); 1180 fflush(stdout); 1181 1182 if (!BN_pseudo_rand(x, BN_num_bits(y) - 1, 0, 0)) ABORT; 1183 if (!BN_add(z, x, y)) ABORT; 1184 BN_set_negative(z, 1); 1185 scalars[0] = x; 1186 scalars[1] = y; 1187 scalars[2] = z; /* z = -(x+y) */ 1188 1189 if (!EC_POINTs_mul(group, P, NULL, 3, points, scalars, ctx)) ABORT; 1190 if (!EC_POINT_is_at_infinity(group, P)) ABORT; 1191 1192 fprintf(stdout, " ok\n\n"); 1193 } 1194 1195 1196 #if 0 1197 timings(C2_K163, TIMING_BASE_PT, ctx); 1198 timings(C2_K163, TIMING_RAND_PT, ctx); 1199 timings(C2_K163, TIMING_SIMUL, ctx); 1200 timings(C2_B163, TIMING_BASE_PT, ctx); 1201 timings(C2_B163, TIMING_RAND_PT, ctx); 1202 timings(C2_B163, TIMING_SIMUL, ctx); 1203 timings(C2_K233, TIMING_BASE_PT, ctx); 1204 timings(C2_K233, TIMING_RAND_PT, ctx); 1205 timings(C2_K233, TIMING_SIMUL, ctx); 1206 timings(C2_B233, TIMING_BASE_PT, ctx); 1207 timings(C2_B233, TIMING_RAND_PT, ctx); 1208 timings(C2_B233, TIMING_SIMUL, ctx); 1209 timings(C2_K283, TIMING_BASE_PT, ctx); 1210 timings(C2_K283, TIMING_RAND_PT, ctx); 1211 timings(C2_K283, TIMING_SIMUL, ctx); 1212 timings(C2_B283, TIMING_BASE_PT, ctx); 1213 timings(C2_B283, TIMING_RAND_PT, ctx); 1214 timings(C2_B283, TIMING_SIMUL, ctx); 1215 timings(C2_K409, TIMING_BASE_PT, ctx); 1216 timings(C2_K409, TIMING_RAND_PT, ctx); 1217 timings(C2_K409, TIMING_SIMUL, ctx); 1218 timings(C2_B409, TIMING_BASE_PT, ctx); 1219 timings(C2_B409, TIMING_RAND_PT, ctx); 1220 timings(C2_B409, TIMING_SIMUL, ctx); 1221 timings(C2_K571, TIMING_BASE_PT, ctx); 1222 timings(C2_K571, TIMING_RAND_PT, ctx); 1223 timings(C2_K571, TIMING_SIMUL, ctx); 1224 timings(C2_B571, TIMING_BASE_PT, ctx); 1225 timings(C2_B571, TIMING_RAND_PT, ctx); 1226 timings(C2_B571, TIMING_SIMUL, ctx); 1227 #endif 1228 1229 1230 if (ctx) 1231 BN_CTX_free(ctx); 1232 BN_free(p); BN_free(a); BN_free(b); 1233 EC_GROUP_free(group); 1234 EC_POINT_free(P); 1235 EC_POINT_free(Q); 1236 EC_POINT_free(R); 1237 BN_free(x); BN_free(y); BN_free(z); BN_free(cof); 1238 1239 if (C2_K163) EC_GROUP_free(C2_K163); 1240 if (C2_B163) EC_GROUP_free(C2_B163); 1241 if (C2_K233) EC_GROUP_free(C2_K233); 1242 if (C2_B233) EC_GROUP_free(C2_B233); 1243 if (C2_K283) EC_GROUP_free(C2_K283); 1244 if (C2_B283) EC_GROUP_free(C2_B283); 1245 if (C2_K409) EC_GROUP_free(C2_K409); 1246 if (C2_B409) EC_GROUP_free(C2_B409); 1247 if (C2_K571) EC_GROUP_free(C2_K571); 1248 if (C2_B571) EC_GROUP_free(C2_B571); 1249 1250 } 1251 #endif 1252 1253 static void internal_curve_test(void) 1254 { 1255 EC_builtin_curve *curves = NULL; 1256 size_t crv_len = 0, n = 0; 1257 int ok = 1; 1258 1259 crv_len = EC_get_builtin_curves(NULL, 0); 1260 1261 curves = OPENSSL_malloc(sizeof(EC_builtin_curve) * crv_len); 1262 1263 if (curves == NULL) 1264 return; 1265 1266 if (!EC_get_builtin_curves(curves, crv_len)) 1267 { 1268 OPENSSL_free(curves); 1269 return; 1270 } 1271 1272 fprintf(stdout, "testing internal curves: "); 1273 1274 for (n = 0; n < crv_len; n++) 1275 { 1276 EC_GROUP *group = NULL; 1277 int nid = curves[n].nid; 1278 if ((group = EC_GROUP_new_by_curve_name(nid)) == NULL) 1279 { 1280 ok = 0; 1281 fprintf(stdout, "\nEC_GROUP_new_curve_name() failed with" 1282 " curve %s\n", OBJ_nid2sn(nid)); 1283 /* try next curve */ 1284 continue; 1285 } 1286 if (!EC_GROUP_check(group, NULL)) 1287 { 1288 ok = 0; 1289 fprintf(stdout, "\nEC_GROUP_check() failed with" 1290 " curve %s\n", OBJ_nid2sn(nid)); 1291 EC_GROUP_free(group); 1292 /* try the next curve */ 1293 continue; 1294 } 1295 fprintf(stdout, "."); 1296 fflush(stdout); 1297 EC_GROUP_free(group); 1298 } 1299 if (ok) 1300 fprintf(stdout, " ok\n\n"); 1301 else 1302 { 1303 fprintf(stdout, " failed\n\n"); 1304 ABORT; 1305 } 1306 OPENSSL_free(curves); 1307 return; 1308 } 1309 1310 #ifndef OPENSSL_NO_EC_NISTP_64_GCC_128 1311 /* nistp_test_params contains magic numbers for testing our optimized 1312 * implementations of several NIST curves with characteristic > 3. */ 1313 struct nistp_test_params 1314 { 1315 const EC_METHOD* (*meth) (); 1316 int degree; 1317 /* Qx, Qy and D are taken from 1318 * http://csrc.nist.gov/groups/ST/toolkit/documents/Examples/ECDSA_Prime.pdf 1319 * Otherwise, values are standard curve parameters from FIPS 180-3 */ 1320 const char *p, *a, *b, *Qx, *Qy, *Gx, *Gy, *order, *d; 1321 }; 1322 1323 static const struct nistp_test_params nistp_tests_params[] = 1324 { 1325 { 1326 /* P-224 */ 1327 EC_GFp_nistp224_method, 1328 224, 1329 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001", /* p */ 1330 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE", /* a */ 1331 "B4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4", /* b */ 1332 "E84FB0B8E7000CB657D7973CF6B42ED78B301674276DF744AF130B3E", /* Qx */ 1333 "4376675C6FC5612C21A0FF2D2A89D2987DF7A2BC52183B5982298555", /* Qy */ 1334 "B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21", /* Gx */ 1335 "BD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34", /* Gy */ 1336 "FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D", /* order */ 1337 "3F0C488E987C80BE0FEE521F8D90BE6034EC69AE11CA72AA777481E8", /* d */ 1338 }, 1339 { 1340 /* P-256 */ 1341 EC_GFp_nistp256_method, 1342 256, 1343 "ffffffff00000001000000000000000000000000ffffffffffffffffffffffff", /* p */ 1344 "ffffffff00000001000000000000000000000000fffffffffffffffffffffffc", /* a */ 1345 "5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b", /* b */ 1346 "b7e08afdfe94bad3f1dc8c734798ba1c62b3a0ad1e9ea2a38201cd0889bc7a19", /* Qx */ 1347 "3603f747959dbf7a4bb226e41928729063adc7ae43529e61b563bbc606cc5e09", /* Qy */ 1348 "6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296", /* Gx */ 1349 "4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5", /* Gy */ 1350 "ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551", /* order */ 1351 "c477f9f65c22cce20657faa5b2d1d8122336f851a508a1ed04e479c34985bf96", /* d */ 1352 }, 1353 { 1354 /* P-521 */ 1355 EC_GFp_nistp521_method, 1356 521, 1357 "1ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff", /* p */ 1358 "1fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc", /* a */ 1359 "051953eb9618e1c9a1f929a21a0b68540eea2da725b99b315f3b8b489918ef109e156193951ec7e937b1652c0bd3bb1bf073573df883d2c34f1ef451fd46b503f00", /* b */ 1360 "0098e91eef9a68452822309c52fab453f5f117c1da8ed796b255e9ab8f6410cca16e59df403a6bdc6ca467a37056b1e54b3005d8ac030decfeb68df18b171885d5c4", /* Qx */ 1361 "0164350c321aecfc1cca1ba4364c9b15656150b4b78d6a48d7d28e7f31985ef17be8554376b72900712c4b83ad668327231526e313f5f092999a4632fd50d946bc2e", /* Qy */ 1362 "c6858e06b70404e9cd9e3ecb662395b4429c648139053fb521f828af606b4d3dbaa14b5e77efe75928fe1dc127a2ffa8de3348b3c1856a429bf97e7e31c2e5bd66", /* Gx */ 1363 "11839296a789a3bc0045c8a5fb42c7d1bd998f54449579b446817afbd17273e662c97ee72995ef42640c550b9013fad0761353c7086a272c24088be94769fd16650", /* Gy */ 1364 "1fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffa51868783bf2f966b7fcc0148f709a5d03bb5c9b8899c47aebb6fb71e91386409", /* order */ 1365 "0100085f47b8e1b8b11b7eb33028c0b2888e304bfc98501955b45bba1478dc184eeedf09b86a5f7c21994406072787205e69a63709fe35aa93ba333514b24f961722", /* d */ 1366 }, 1367 }; 1368 1369 void nistp_single_test(const struct nistp_test_params *test) 1370 { 1371 BN_CTX *ctx; 1372 BIGNUM *p, *a, *b, *x, *y, *n, *m, *order; 1373 EC_GROUP *NISTP; 1374 EC_POINT *G, *P, *Q, *Q_CHECK; 1375 1376 fprintf(stdout, "\nNIST curve P-%d (optimised implementation):\n", test->degree); 1377 ctx = BN_CTX_new(); 1378 p = BN_new(); 1379 a = BN_new(); 1380 b = BN_new(); 1381 x = BN_new(); y = BN_new(); 1382 m = BN_new(); n = BN_new(); order = BN_new(); 1383 1384 NISTP = EC_GROUP_new(test->meth()); 1385 if(!NISTP) ABORT; 1386 if (!BN_hex2bn(&p, test->p)) ABORT; 1387 if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT; 1388 if (!BN_hex2bn(&a, test->a)) ABORT; 1389 if (!BN_hex2bn(&b, test->b)) ABORT; 1390 if (!EC_GROUP_set_curve_GFp(NISTP, p, a, b, ctx)) ABORT; 1391 G = EC_POINT_new(NISTP); 1392 P = EC_POINT_new(NISTP); 1393 Q = EC_POINT_new(NISTP); 1394 Q_CHECK = EC_POINT_new(NISTP); 1395 if(!BN_hex2bn(&x, test->Qx)) ABORT; 1396 if(!BN_hex2bn(&y, test->Qy)) ABORT; 1397 if(!EC_POINT_set_affine_coordinates_GFp(NISTP, Q_CHECK, x, y, ctx)) ABORT; 1398 if (!BN_hex2bn(&x, test->Gx)) ABORT; 1399 if (!BN_hex2bn(&y, test->Gy)) ABORT; 1400 if (!EC_POINT_set_affine_coordinates_GFp(NISTP, G, x, y, ctx)) ABORT; 1401 if (!BN_hex2bn(&order, test->order)) ABORT; 1402 if (!EC_GROUP_set_generator(NISTP, G, order, BN_value_one())) ABORT; 1403 1404 fprintf(stdout, "verify degree ... "); 1405 if (EC_GROUP_get_degree(NISTP) != test->degree) ABORT; 1406 fprintf(stdout, "ok\n"); 1407 1408 fprintf(stdout, "NIST test vectors ... "); 1409 if (!BN_hex2bn(&n, test->d)) ABORT; 1410 /* fixed point multiplication */ 1411 EC_POINT_mul(NISTP, Q, n, NULL, NULL, ctx); 1412 if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) ABORT; 1413 /* random point multiplication */ 1414 EC_POINT_mul(NISTP, Q, NULL, G, n, ctx); 1415 if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) ABORT; 1416 1417 /* set generator to P = 2*G, where G is the standard generator */ 1418 if (!EC_POINT_dbl(NISTP, P, G, ctx)) ABORT; 1419 if (!EC_GROUP_set_generator(NISTP, P, order, BN_value_one())) ABORT; 1420 /* set the scalar to m=n/2, where n is the NIST test scalar */ 1421 if (!BN_rshift(m, n, 1)) ABORT; 1422 1423 /* test the non-standard generator */ 1424 /* fixed point multiplication */ 1425 EC_POINT_mul(NISTP, Q, m, NULL, NULL, ctx); 1426 if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) ABORT; 1427 /* random point multiplication */ 1428 EC_POINT_mul(NISTP, Q, NULL, P, m, ctx); 1429 if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) ABORT; 1430 1431 /* now repeat all tests with precomputation */ 1432 if (!EC_GROUP_precompute_mult(NISTP, ctx)) ABORT; 1433 1434 /* fixed point multiplication */ 1435 EC_POINT_mul(NISTP, Q, m, NULL, NULL, ctx); 1436 if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) ABORT; 1437 /* random point multiplication */ 1438 EC_POINT_mul(NISTP, Q, NULL, P, m, ctx); 1439 if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) ABORT; 1440 1441 /* reset generator */ 1442 if (!EC_GROUP_set_generator(NISTP, G, order, BN_value_one())) ABORT; 1443 /* fixed point multiplication */ 1444 EC_POINT_mul(NISTP, Q, n, NULL, NULL, ctx); 1445 if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) ABORT; 1446 /* random point multiplication */ 1447 EC_POINT_mul(NISTP, Q, NULL, G, n, ctx); 1448 if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) ABORT; 1449 1450 fprintf(stdout, "ok\n"); 1451 group_order_tests(NISTP); 1452 #if 0 1453 timings(NISTP, TIMING_BASE_PT, ctx); 1454 timings(NISTP, TIMING_RAND_PT, ctx); 1455 #endif 1456 EC_GROUP_free(NISTP); 1457 EC_POINT_free(G); 1458 EC_POINT_free(P); 1459 EC_POINT_free(Q); 1460 EC_POINT_free(Q_CHECK); 1461 BN_free(n); 1462 BN_free(m); 1463 BN_free(p); 1464 BN_free(a); 1465 BN_free(b); 1466 BN_free(x); 1467 BN_free(y); 1468 BN_free(order); 1469 BN_CTX_free(ctx); 1470 } 1471 1472 void nistp_tests() 1473 { 1474 unsigned i; 1475 1476 for (i = 0; i < sizeof(nistp_tests_params) / sizeof(struct nistp_test_params); i++) 1477 { 1478 nistp_single_test(&nistp_tests_params[i]); 1479 } 1480 } 1481 #endif 1482 1483 static const char rnd_seed[] = "string to make the random number generator think it has entropy"; 1484 1485 int main(int argc, char *argv[]) 1486 { 1487 1488 /* enable memory leak checking unless explicitly disabled */ 1489 if (!((getenv("OPENSSL_DEBUG_MEMORY") != NULL) && (0 == strcmp(getenv("OPENSSL_DEBUG_MEMORY"), "off")))) 1490 { 1491 CRYPTO_malloc_debug_init(); 1492 CRYPTO_set_mem_debug_options(V_CRYPTO_MDEBUG_ALL); 1493 } 1494 else 1495 { 1496 /* OPENSSL_DEBUG_MEMORY=off */ 1497 CRYPTO_set_mem_debug_functions(0, 0, 0, 0, 0); 1498 } 1499 CRYPTO_mem_ctrl(CRYPTO_MEM_CHECK_ON); 1500 ERR_load_crypto_strings(); 1501 1502 RAND_seed(rnd_seed, sizeof rnd_seed); /* or BN_generate_prime may fail */ 1503 1504 prime_field_tests(); 1505 puts(""); 1506 #ifndef OPENSSL_NO_EC2M 1507 char2_field_tests(); 1508 #endif 1509 #ifndef OPENSSL_NO_EC_NISTP_64_GCC_128 1510 nistp_tests(); 1511 #endif 1512 /* test the internal curves */ 1513 internal_curve_test(); 1514 1515 #ifndef OPENSSL_NO_ENGINE 1516 ENGINE_cleanup(); 1517 #endif 1518 CRYPTO_cleanup_all_ex_data(); 1519 ERR_free_strings(); 1520 ERR_remove_thread_state(NULL); 1521 CRYPTO_mem_leaks_fp(stderr); 1522 1523 return 0; 1524 } 1525 #endif 1526
