ectest.c revision 296341
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#ifdef OPENSSL_NO_EC 83int main(int argc, char *argv[]) 84{ 85 puts("Elliptic curves are disabled."); 86 return 0; 87} 88#else 89 90# include <openssl/ec.h> 91# ifndef OPENSSL_NO_ENGINE 92# include <openssl/engine.h> 93# endif 94# include <openssl/err.h> 95# include <openssl/obj_mac.h> 96# include <openssl/objects.h> 97# include <openssl/rand.h> 98# include <openssl/bn.h> 99# include <openssl/opensslconf.h> 100 101# if defined(_MSC_VER) && defined(_MIPS_) && (_MSC_VER/100==12) 102/* suppress "too big too optimize" warning */ 103# pragma warning(disable:4959) 104# endif 105 106# define ABORT do { \ 107 fflush(stdout); \ 108 fprintf(stderr, "%s:%d: ABORT\n", __FILE__, __LINE__); \ 109 ERR_print_errors_fp(stderr); \ 110 EXIT(1); \ 111} while (0) 112 113# define TIMING_BASE_PT 0 114# define TIMING_RAND_PT 1 115# define TIMING_SIMUL 2 116 117# if 0 118static void timings(EC_GROUP *group, int type, BN_CTX *ctx) 119{ 120 clock_t clck; 121 int i, j; 122 BIGNUM *s; 123 BIGNUM *r[10], *r0[10]; 124 EC_POINT *P; 125 126 s = BN_new(); 127 if (s == NULL) 128 ABORT; 129 130 fprintf(stdout, "Timings for %d-bit field, ", EC_GROUP_get_degree(group)); 131 if (!EC_GROUP_get_order(group, s, ctx)) 132 ABORT; 133 fprintf(stdout, "%d-bit scalars ", (int)BN_num_bits(s)); 134 fflush(stdout); 135 136 P = EC_POINT_new(group); 137 if (P == NULL) 138 ABORT; 139 EC_POINT_copy(P, EC_GROUP_get0_generator(group)); 140 141 for (i = 0; i < 10; i++) { 142 if ((r[i] = BN_new()) == NULL) 143 ABORT; 144 if (!BN_pseudo_rand(r[i], BN_num_bits(s), 0, 0)) 145 ABORT; 146 if (type != TIMING_BASE_PT) { 147 if ((r0[i] = BN_new()) == NULL) 148 ABORT; 149 if (!BN_pseudo_rand(r0[i], BN_num_bits(s), 0, 0)) 150 ABORT; 151 } 152 } 153 154 clck = clock(); 155 for (i = 0; i < 10; i++) { 156 for (j = 0; j < 10; j++) { 157 if (!EC_POINT_mul 158 (group, P, (type != TIMING_RAND_PT) ? r[i] : NULL, 159 (type != TIMING_BASE_PT) ? P : NULL, 160 (type != TIMING_BASE_PT) ? r0[i] : NULL, ctx)) 161 ABORT; 162 } 163 } 164 clck = clock() - clck; 165 166 fprintf(stdout, "\n"); 167 168# ifdef CLOCKS_PER_SEC 169 /* 170 * "To determine the time in seconds, the value returned by the clock 171 * function should be divided by the value of the macro CLOCKS_PER_SEC." 172 * -- ISO/IEC 9899 173 */ 174# define UNIT "s" 175# else 176 /* 177 * "`CLOCKS_PER_SEC' undeclared (first use this function)" -- cc on 178 * NeXTstep/OpenStep 179 */ 180# define UNIT "units" 181# define CLOCKS_PER_SEC 1 182# endif 183 184 if (type == TIMING_BASE_PT) { 185 fprintf(stdout, "%i %s in %.2f " UNIT "\n", i * j, 186 "base point multiplications", (double)clck / CLOCKS_PER_SEC); 187 } else if (type == TIMING_RAND_PT) { 188 fprintf(stdout, "%i %s in %.2f " UNIT "\n", i * j, 189 "random point multiplications", 190 (double)clck / CLOCKS_PER_SEC); 191 } else if (type == TIMING_SIMUL) { 192 fprintf(stdout, "%i %s in %.2f " UNIT "\n", i * j, 193 "s*P+t*Q operations", (double)clck / CLOCKS_PER_SEC); 194 } 195 fprintf(stdout, "average: %.4f " UNIT "\n", 196 (double)clck / (CLOCKS_PER_SEC * i * j)); 197 198 EC_POINT_free(P); 199 BN_free(s); 200 for (i = 0; i < 10; i++) { 201 BN_free(r[i]); 202 if (type != TIMING_BASE_PT) 203 BN_free(r0[i]); 204 } 205} 206# endif 207 208/* test multiplication with group order, long and negative scalars */ 209static void group_order_tests(EC_GROUP *group) 210{ 211 BIGNUM *n1, *n2, *order; 212 EC_POINT *P = EC_POINT_new(group); 213 EC_POINT *Q = EC_POINT_new(group); 214 BN_CTX *ctx = BN_CTX_new(); 215 int i; 216 217 n1 = BN_new(); 218 n2 = BN_new(); 219 order = BN_new(); 220 fprintf(stdout, "verify group order ..."); 221 fflush(stdout); 222 if (!EC_GROUP_get_order(group, order, ctx)) 223 ABORT; 224 if (!EC_POINT_mul(group, Q, order, NULL, NULL, ctx)) 225 ABORT; 226 if (!EC_POINT_is_at_infinity(group, Q)) 227 ABORT; 228 fprintf(stdout, "."); 229 fflush(stdout); 230 if (!EC_GROUP_precompute_mult(group, ctx)) 231 ABORT; 232 if (!EC_POINT_mul(group, Q, order, NULL, NULL, ctx)) 233 ABORT; 234 if (!EC_POINT_is_at_infinity(group, Q)) 235 ABORT; 236 fprintf(stdout, " ok\n"); 237 fprintf(stdout, "long/negative scalar tests "); 238 for (i = 1; i <= 2; i++) { 239 const BIGNUM *scalars[6]; 240 const EC_POINT *points[6]; 241 242 fprintf(stdout, i == 1 ? 243 "allowing precomputation ... " : 244 "without precomputation ... "); 245 if (!BN_set_word(n1, i)) 246 ABORT; 247 /* 248 * If i == 1, P will be the predefined generator for which 249 * EC_GROUP_precompute_mult has set up precomputation. 250 */ 251 if (!EC_POINT_mul(group, P, n1, NULL, NULL, ctx)) 252 ABORT; 253 254 if (!BN_one(n1)) 255 ABORT; 256 /* n1 = 1 - order */ 257 if (!BN_sub(n1, n1, order)) 258 ABORT; 259 if (!EC_POINT_mul(group, Q, NULL, P, n1, ctx)) 260 ABORT; 261 if (0 != EC_POINT_cmp(group, Q, P, ctx)) 262 ABORT; 263 264 /* n2 = 1 + order */ 265 if (!BN_add(n2, order, BN_value_one())) 266 ABORT; 267 if (!EC_POINT_mul(group, Q, NULL, P, n2, ctx)) 268 ABORT; 269 if (0 != EC_POINT_cmp(group, Q, P, ctx)) 270 ABORT; 271 272 /* n2 = (1 - order) * (1 + order) = 1 - order^2 */ 273 if (!BN_mul(n2, n1, n2, ctx)) 274 ABORT; 275 if (!EC_POINT_mul(group, Q, NULL, P, n2, ctx)) 276 ABORT; 277 if (0 != EC_POINT_cmp(group, Q, P, ctx)) 278 ABORT; 279 280 /* n2 = order^2 - 1 */ 281 BN_set_negative(n2, 0); 282 if (!EC_POINT_mul(group, Q, NULL, P, n2, ctx)) 283 ABORT; 284 /* Add P to verify the result. */ 285 if (!EC_POINT_add(group, Q, Q, P, ctx)) 286 ABORT; 287 if (!EC_POINT_is_at_infinity(group, Q)) 288 ABORT; 289 290 /* Exercise EC_POINTs_mul, including corner cases. */ 291 if (EC_POINT_is_at_infinity(group, P)) 292 ABORT; 293 scalars[0] = n1; 294 points[0] = Q; /* => infinity */ 295 scalars[1] = n2; 296 points[1] = P; /* => -P */ 297 scalars[2] = n1; 298 points[2] = Q; /* => infinity */ 299 scalars[3] = n2; 300 points[3] = Q; /* => infinity */ 301 scalars[4] = n1; 302 points[4] = P; /* => P */ 303 scalars[5] = n2; 304 points[5] = Q; /* => infinity */ 305 if (!EC_POINTs_mul(group, P, NULL, 6, points, scalars, ctx)) 306 ABORT; 307 if (!EC_POINT_is_at_infinity(group, P)) 308 ABORT; 309 } 310 fprintf(stdout, "ok\n"); 311 312 EC_POINT_free(P); 313 EC_POINT_free(Q); 314 BN_free(n1); 315 BN_free(n2); 316 BN_free(order); 317 BN_CTX_free(ctx); 318} 319 320static void prime_field_tests(void) 321{ 322 BN_CTX *ctx = NULL; 323 BIGNUM *p, *a, *b; 324 EC_GROUP *group; 325 EC_GROUP *P_160 = NULL, *P_192 = NULL, *P_224 = NULL, *P_256 = 326 NULL, *P_384 = NULL, *P_521 = NULL; 327 EC_POINT *P, *Q, *R; 328 BIGNUM *x, *y, *z; 329 unsigned char buf[100]; 330 size_t i, len; 331 int k; 332 333# if 1 /* optional */ 334 ctx = BN_CTX_new(); 335 if (!ctx) 336 ABORT; 337# endif 338 339 p = BN_new(); 340 a = BN_new(); 341 b = BN_new(); 342 if (!p || !a || !b) 343 ABORT; 344 345 if (!BN_hex2bn(&p, "17")) 346 ABORT; 347 if (!BN_hex2bn(&a, "1")) 348 ABORT; 349 if (!BN_hex2bn(&b, "1")) 350 ABORT; 351 352 group = EC_GROUP_new(EC_GFp_mont_method()); /* applications should use 353 * EC_GROUP_new_curve_GFp so 354 * that the library gets to 355 * choose the EC_METHOD */ 356 if (!group) 357 ABORT; 358 359 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) 360 ABORT; 361 362 { 363 EC_GROUP *tmp; 364 tmp = EC_GROUP_new(EC_GROUP_method_of(group)); 365 if (!tmp) 366 ABORT; 367 if (!EC_GROUP_copy(tmp, group)) 368 ABORT; 369 EC_GROUP_free(group); 370 group = tmp; 371 } 372 373 if (!EC_GROUP_get_curve_GFp(group, p, a, b, ctx)) 374 ABORT; 375 376 fprintf(stdout, 377 "Curve defined by Weierstrass equation\n y^2 = x^3 + a*x + b (mod 0x"); 378 BN_print_fp(stdout, p); 379 fprintf(stdout, ")\n a = 0x"); 380 BN_print_fp(stdout, a); 381 fprintf(stdout, "\n b = 0x"); 382 BN_print_fp(stdout, b); 383 fprintf(stdout, "\n"); 384 385 P = EC_POINT_new(group); 386 Q = EC_POINT_new(group); 387 R = EC_POINT_new(group); 388 if (!P || !Q || !R) 389 ABORT; 390 391 if (!EC_POINT_set_to_infinity(group, P)) 392 ABORT; 393 if (!EC_POINT_is_at_infinity(group, P)) 394 ABORT; 395 396 buf[0] = 0; 397 if (!EC_POINT_oct2point(group, Q, buf, 1, ctx)) 398 ABORT; 399 400 if (!EC_POINT_add(group, P, P, Q, ctx)) 401 ABORT; 402 if (!EC_POINT_is_at_infinity(group, P)) 403 ABORT; 404 405 x = BN_new(); 406 y = BN_new(); 407 z = BN_new(); 408 if (!x || !y || !z) 409 ABORT; 410 411 if (!BN_hex2bn(&x, "D")) 412 ABORT; 413 if (!EC_POINT_set_compressed_coordinates_GFp(group, Q, x, 1, ctx)) 414 ABORT; 415 if (EC_POINT_is_on_curve(group, Q, ctx) <= 0) { 416 if (!EC_POINT_get_affine_coordinates_GFp(group, Q, x, y, ctx)) 417 ABORT; 418 fprintf(stderr, "Point is not on curve: x = 0x"); 419 BN_print_fp(stderr, x); 420 fprintf(stderr, ", y = 0x"); 421 BN_print_fp(stderr, y); 422 fprintf(stderr, "\n"); 423 ABORT; 424 } 425 426 fprintf(stdout, "A cyclic subgroup:\n"); 427 k = 100; 428 do { 429 if (k-- == 0) 430 ABORT; 431 432 if (EC_POINT_is_at_infinity(group, P)) 433 fprintf(stdout, " point at infinity\n"); 434 else { 435 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) 436 ABORT; 437 438 fprintf(stdout, " x = 0x"); 439 BN_print_fp(stdout, x); 440 fprintf(stdout, ", y = 0x"); 441 BN_print_fp(stdout, y); 442 fprintf(stdout, "\n"); 443 } 444 445 if (!EC_POINT_copy(R, P)) 446 ABORT; 447 if (!EC_POINT_add(group, P, P, Q, ctx)) 448 ABORT; 449 450# if 0 /* optional */ 451 { 452 EC_POINT *points[3]; 453 454 points[0] = R; 455 points[1] = Q; 456 points[2] = P; 457 if (!EC_POINTs_make_affine(group, 2, points, ctx)) 458 ABORT; 459 } 460# endif 461 462 } 463 while (!EC_POINT_is_at_infinity(group, P)); 464 465 if (!EC_POINT_add(group, P, Q, R, ctx)) 466 ABORT; 467 if (!EC_POINT_is_at_infinity(group, P)) 468 ABORT; 469 470 len = 471 EC_POINT_point2oct(group, Q, POINT_CONVERSION_COMPRESSED, buf, 472 sizeof buf, ctx); 473 if (len == 0) 474 ABORT; 475 if (!EC_POINT_oct2point(group, P, buf, len, ctx)) 476 ABORT; 477 if (0 != EC_POINT_cmp(group, P, Q, ctx)) 478 ABORT; 479 fprintf(stdout, "Generator as octet string, compressed form:\n "); 480 for (i = 0; i < len; i++) 481 fprintf(stdout, "%02X", buf[i]); 482 483 len = 484 EC_POINT_point2oct(group, Q, POINT_CONVERSION_UNCOMPRESSED, buf, 485 sizeof buf, ctx); 486 if (len == 0) 487 ABORT; 488 if (!EC_POINT_oct2point(group, P, buf, len, ctx)) 489 ABORT; 490 if (0 != EC_POINT_cmp(group, P, Q, ctx)) 491 ABORT; 492 fprintf(stdout, "\nGenerator as octet string, uncompressed form:\n "); 493 for (i = 0; i < len; i++) 494 fprintf(stdout, "%02X", buf[i]); 495 496 len = 497 EC_POINT_point2oct(group, Q, POINT_CONVERSION_HYBRID, buf, sizeof buf, 498 ctx); 499 if (len == 0) 500 ABORT; 501 if (!EC_POINT_oct2point(group, P, buf, len, ctx)) 502 ABORT; 503 if (0 != EC_POINT_cmp(group, P, Q, ctx)) 504 ABORT; 505 fprintf(stdout, "\nGenerator as octet string, hybrid form:\n "); 506 for (i = 0; i < len; i++) 507 fprintf(stdout, "%02X", buf[i]); 508 509 if (!EC_POINT_get_Jprojective_coordinates_GFp(group, R, x, y, z, ctx)) 510 ABORT; 511 fprintf(stdout, 512 "\nA representation of the inverse of that generator in\nJacobian projective coordinates:\n X = 0x"); 513 BN_print_fp(stdout, x); 514 fprintf(stdout, ", Y = 0x"); 515 BN_print_fp(stdout, y); 516 fprintf(stdout, ", Z = 0x"); 517 BN_print_fp(stdout, z); 518 fprintf(stdout, "\n"); 519 520 if (!EC_POINT_invert(group, P, ctx)) 521 ABORT; 522 if (0 != EC_POINT_cmp(group, P, R, ctx)) 523 ABORT; 524 525 /* 526 * Curve secp160r1 (Certicom Research SEC 2 Version 1.0, section 2.4.2, 527 * 2000) -- not a NIST curve, but commonly used 528 */ 529 530 if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFF")) 531 ABORT; 532 if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) 533 ABORT; 534 if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFC")) 535 ABORT; 536 if (!BN_hex2bn(&b, "1C97BEFC54BD7A8B65ACF89F81D4D4ADC565FA45")) 537 ABORT; 538 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) 539 ABORT; 540 541 if (!BN_hex2bn(&x, "4A96B5688EF573284664698968C38BB913CBFC82")) 542 ABORT; 543 if (!BN_hex2bn(&y, "23a628553168947d59dcc912042351377ac5fb32")) 544 ABORT; 545 if (!EC_POINT_set_affine_coordinates_GFp(group, P, x, y, ctx)) 546 ABORT; 547 if (EC_POINT_is_on_curve(group, P, ctx) <= 0) 548 ABORT; 549 if (!BN_hex2bn(&z, "0100000000000000000001F4C8F927AED3CA752257")) 550 ABORT; 551 if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) 552 ABORT; 553 554 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) 555 ABORT; 556 fprintf(stdout, "\nSEC2 curve secp160r1 -- Generator:\n x = 0x"); 557 BN_print_fp(stdout, x); 558 fprintf(stdout, "\n y = 0x"); 559 BN_print_fp(stdout, y); 560 fprintf(stdout, "\n"); 561 /* G_y value taken from the standard: */ 562 if (!BN_hex2bn(&z, "23a628553168947d59dcc912042351377ac5fb32")) 563 ABORT; 564 if (0 != BN_cmp(y, z)) 565 ABORT; 566 567 fprintf(stdout, "verify degree ..."); 568 if (EC_GROUP_get_degree(group) != 160) 569 ABORT; 570 fprintf(stdout, " ok\n"); 571 572 group_order_tests(group); 573 574 if (!(P_160 = EC_GROUP_new(EC_GROUP_method_of(group)))) 575 ABORT; 576 if (!EC_GROUP_copy(P_160, group)) 577 ABORT; 578 579 /* Curve P-192 (FIPS PUB 186-2, App. 6) */ 580 581 if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF")) 582 ABORT; 583 if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) 584 ABORT; 585 if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC")) 586 ABORT; 587 if (!BN_hex2bn(&b, "64210519E59C80E70FA7E9AB72243049FEB8DEECC146B9B1")) 588 ABORT; 589 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) 590 ABORT; 591 592 if (!BN_hex2bn(&x, "188DA80EB03090F67CBF20EB43A18800F4FF0AFD82FF1012")) 593 ABORT; 594 if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 1, ctx)) 595 ABORT; 596 if (EC_POINT_is_on_curve(group, P, ctx) <= 0) 597 ABORT; 598 if (!BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22831")) 599 ABORT; 600 if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) 601 ABORT; 602 603 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) 604 ABORT; 605 fprintf(stdout, "\nNIST curve P-192 -- Generator:\n x = 0x"); 606 BN_print_fp(stdout, x); 607 fprintf(stdout, "\n y = 0x"); 608 BN_print_fp(stdout, y); 609 fprintf(stdout, "\n"); 610 /* G_y value taken from the standard: */ 611 if (!BN_hex2bn(&z, "07192B95FFC8DA78631011ED6B24CDD573F977A11E794811")) 612 ABORT; 613 if (0 != BN_cmp(y, z)) 614 ABORT; 615 616 fprintf(stdout, "verify degree ..."); 617 if (EC_GROUP_get_degree(group) != 192) 618 ABORT; 619 fprintf(stdout, " ok\n"); 620 621 group_order_tests(group); 622 623 if (!(P_192 = EC_GROUP_new(EC_GROUP_method_of(group)))) 624 ABORT; 625 if (!EC_GROUP_copy(P_192, group)) 626 ABORT; 627 628 /* Curve P-224 (FIPS PUB 186-2, App. 6) */ 629 630 if (!BN_hex2bn 631 (&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001")) 632 ABORT; 633 if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) 634 ABORT; 635 if (!BN_hex2bn 636 (&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE")) 637 ABORT; 638 if (!BN_hex2bn 639 (&b, "B4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4")) 640 ABORT; 641 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) 642 ABORT; 643 644 if (!BN_hex2bn 645 (&x, "B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21")) 646 ABORT; 647 if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 0, ctx)) 648 ABORT; 649 if (EC_POINT_is_on_curve(group, P, ctx) <= 0) 650 ABORT; 651 if (!BN_hex2bn 652 (&z, "FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D")) 653 ABORT; 654 if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) 655 ABORT; 656 657 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) 658 ABORT; 659 fprintf(stdout, "\nNIST curve P-224 -- Generator:\n x = 0x"); 660 BN_print_fp(stdout, x); 661 fprintf(stdout, "\n y = 0x"); 662 BN_print_fp(stdout, y); 663 fprintf(stdout, "\n"); 664 /* G_y value taken from the standard: */ 665 if (!BN_hex2bn 666 (&z, "BD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34")) 667 ABORT; 668 if (0 != BN_cmp(y, z)) 669 ABORT; 670 671 fprintf(stdout, "verify degree ..."); 672 if (EC_GROUP_get_degree(group) != 224) 673 ABORT; 674 fprintf(stdout, " ok\n"); 675 676 group_order_tests(group); 677 678 if (!(P_224 = EC_GROUP_new(EC_GROUP_method_of(group)))) 679 ABORT; 680 if (!EC_GROUP_copy(P_224, group)) 681 ABORT; 682 683 /* Curve P-256 (FIPS PUB 186-2, App. 6) */ 684 685 if (!BN_hex2bn 686 (&p, 687 "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF")) 688 ABORT; 689 if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) 690 ABORT; 691 if (!BN_hex2bn 692 (&a, 693 "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFC")) 694 ABORT; 695 if (!BN_hex2bn 696 (&b, 697 "5AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B")) 698 ABORT; 699 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) 700 ABORT; 701 702 if (!BN_hex2bn 703 (&x, 704 "6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296")) 705 ABORT; 706 if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 1, ctx)) 707 ABORT; 708 if (EC_POINT_is_on_curve(group, P, ctx) <= 0) 709 ABORT; 710 if (!BN_hex2bn(&z, "FFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E" 711 "84F3B9CAC2FC632551")) 712 ABORT; 713 if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) 714 ABORT; 715 716 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) 717 ABORT; 718 fprintf(stdout, "\nNIST curve P-256 -- Generator:\n x = 0x"); 719 BN_print_fp(stdout, x); 720 fprintf(stdout, "\n y = 0x"); 721 BN_print_fp(stdout, y); 722 fprintf(stdout, "\n"); 723 /* G_y value taken from the standard: */ 724 if (!BN_hex2bn 725 (&z, 726 "4FE342E2FE1A7F9B8EE7EB4A7C0F9E162BCE33576B315ECECBB6406837BF51F5")) 727 ABORT; 728 if (0 != BN_cmp(y, z)) 729 ABORT; 730 731 fprintf(stdout, "verify degree ..."); 732 if (EC_GROUP_get_degree(group) != 256) 733 ABORT; 734 fprintf(stdout, " ok\n"); 735 736 group_order_tests(group); 737 738 if (!(P_256 = EC_GROUP_new(EC_GROUP_method_of(group)))) 739 ABORT; 740 if (!EC_GROUP_copy(P_256, group)) 741 ABORT; 742 743 /* Curve P-384 (FIPS PUB 186-2, App. 6) */ 744 745 if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" 746 "FFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFF")) 747 ABORT; 748 if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) 749 ABORT; 750 if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" 751 "FFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFC")) 752 ABORT; 753 if (!BN_hex2bn(&b, "B3312FA7E23EE7E4988E056BE3F82D19181D9C6EFE8141" 754 "120314088F5013875AC656398D8A2ED19D2A85C8EDD3EC2AEF")) 755 ABORT; 756 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) 757 ABORT; 758 759 if (!BN_hex2bn(&x, "AA87CA22BE8B05378EB1C71EF320AD746E1D3B628BA79B" 760 "9859F741E082542A385502F25DBF55296C3A545E3872760AB7")) 761 ABORT; 762 if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 1, ctx)) 763 ABORT; 764 if (EC_POINT_is_on_curve(group, P, ctx) <= 0) 765 ABORT; 766 if (!BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" 767 "FFC7634D81F4372DDF581A0DB248B0A77AECEC196ACCC52973")) 768 ABORT; 769 if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) 770 ABORT; 771 772 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) 773 ABORT; 774 fprintf(stdout, "\nNIST curve P-384 -- Generator:\n x = 0x"); 775 BN_print_fp(stdout, x); 776 fprintf(stdout, "\n y = 0x"); 777 BN_print_fp(stdout, y); 778 fprintf(stdout, "\n"); 779 /* G_y value taken from the standard: */ 780 if (!BN_hex2bn(&z, "3617DE4A96262C6F5D9E98BF9292DC29F8F41DBD289A14" 781 "7CE9DA3113B5F0B8C00A60B1CE1D7E819D7A431D7C90EA0E5F")) 782 ABORT; 783 if (0 != BN_cmp(y, z)) 784 ABORT; 785 786 fprintf(stdout, "verify degree ..."); 787 if (EC_GROUP_get_degree(group) != 384) 788 ABORT; 789 fprintf(stdout, " ok\n"); 790 791 group_order_tests(group); 792 793 if (!(P_384 = EC_GROUP_new(EC_GROUP_method_of(group)))) 794 ABORT; 795 if (!EC_GROUP_copy(P_384, group)) 796 ABORT; 797 798 /* Curve P-521 (FIPS PUB 186-2, App. 6) */ 799 800 if (!BN_hex2bn(&p, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" 801 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" 802 "FFFFFFFFFFFFFFFFFFFFFFFFFFFF")) 803 ABORT; 804 if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) 805 ABORT; 806 if (!BN_hex2bn(&a, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" 807 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" 808 "FFFFFFFFFFFFFFFFFFFFFFFFFFFC")) 809 ABORT; 810 if (!BN_hex2bn(&b, "051953EB9618E1C9A1F929A21A0B68540EEA2DA725B99B" 811 "315F3B8B489918EF109E156193951EC7E937B1652C0BD3BB1BF073573" 812 "DF883D2C34F1EF451FD46B503F00")) 813 ABORT; 814 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) 815 ABORT; 816 817 if (!BN_hex2bn(&x, "C6858E06B70404E9CD9E3ECB662395B4429C648139053F" 818 "B521F828AF606B4D3DBAA14B5E77EFE75928FE1DC127A2FFA8DE3348B" 819 "3C1856A429BF97E7E31C2E5BD66")) 820 ABORT; 821 if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 0, ctx)) 822 ABORT; 823 if (EC_POINT_is_on_curve(group, P, ctx) <= 0) 824 ABORT; 825 if (!BN_hex2bn(&z, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" 826 "FFFFFFFFFFFFFFFFFFFFA51868783BF2F966B7FCC0148F709A5D03BB5" 827 "C9B8899C47AEBB6FB71E91386409")) 828 ABORT; 829 if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) 830 ABORT; 831 832 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) 833 ABORT; 834 fprintf(stdout, "\nNIST curve P-521 -- Generator:\n x = 0x"); 835 BN_print_fp(stdout, x); 836 fprintf(stdout, "\n y = 0x"); 837 BN_print_fp(stdout, y); 838 fprintf(stdout, "\n"); 839 /* G_y value taken from the standard: */ 840 if (!BN_hex2bn(&z, "11839296A789A3BC0045C8A5FB42C7D1BD998F54449579" 841 "B446817AFBD17273E662C97EE72995EF42640C550B9013FAD0761353C" 842 "7086A272C24088BE94769FD16650")) 843 ABORT; 844 if (0 != BN_cmp(y, z)) 845 ABORT; 846 847 fprintf(stdout, "verify degree ..."); 848 if (EC_GROUP_get_degree(group) != 521) 849 ABORT; 850 fprintf(stdout, " ok\n"); 851 852 group_order_tests(group); 853 854 if (!(P_521 = EC_GROUP_new(EC_GROUP_method_of(group)))) 855 ABORT; 856 if (!EC_GROUP_copy(P_521, group)) 857 ABORT; 858 859 /* more tests using the last curve */ 860 861 if (!EC_POINT_copy(Q, P)) 862 ABORT; 863 if (EC_POINT_is_at_infinity(group, Q)) 864 ABORT; 865 if (!EC_POINT_dbl(group, P, P, ctx)) 866 ABORT; 867 if (EC_POINT_is_on_curve(group, P, ctx) <= 0) 868 ABORT; 869 if (!EC_POINT_invert(group, Q, ctx)) 870 ABORT; /* P = -2Q */ 871 872 if (!EC_POINT_add(group, R, P, Q, ctx)) 873 ABORT; 874 if (!EC_POINT_add(group, R, R, Q, ctx)) 875 ABORT; 876 if (!EC_POINT_is_at_infinity(group, R)) 877 ABORT; /* R = P + 2Q */ 878 879 { 880 const EC_POINT *points[4]; 881 const BIGNUM *scalars[4]; 882 BIGNUM scalar3; 883 884 if (EC_POINT_is_at_infinity(group, Q)) 885 ABORT; 886 points[0] = Q; 887 points[1] = Q; 888 points[2] = Q; 889 points[3] = Q; 890 891 if (!EC_GROUP_get_order(group, z, ctx)) 892 ABORT; 893 if (!BN_add(y, z, BN_value_one())) 894 ABORT; 895 if (BN_is_odd(y)) 896 ABORT; 897 if (!BN_rshift1(y, y)) 898 ABORT; 899 scalars[0] = y; /* (group order + 1)/2, so y*Q + y*Q = Q */ 900 scalars[1] = y; 901 902 fprintf(stdout, "combined multiplication ..."); 903 fflush(stdout); 904 905 /* z is still the group order */ 906 if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) 907 ABORT; 908 if (!EC_POINTs_mul(group, R, z, 2, points, scalars, ctx)) 909 ABORT; 910 if (0 != EC_POINT_cmp(group, P, R, ctx)) 911 ABORT; 912 if (0 != EC_POINT_cmp(group, R, Q, ctx)) 913 ABORT; 914 915 fprintf(stdout, "."); 916 fflush(stdout); 917 918 if (!BN_pseudo_rand(y, BN_num_bits(y), 0, 0)) 919 ABORT; 920 if (!BN_add(z, z, y)) 921 ABORT; 922 BN_set_negative(z, 1); 923 scalars[0] = y; 924 scalars[1] = z; /* z = -(order + y) */ 925 926 if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) 927 ABORT; 928 if (!EC_POINT_is_at_infinity(group, P)) 929 ABORT; 930 931 fprintf(stdout, "."); 932 fflush(stdout); 933 934 if (!BN_pseudo_rand(x, BN_num_bits(y) - 1, 0, 0)) 935 ABORT; 936 if (!BN_add(z, x, y)) 937 ABORT; 938 BN_set_negative(z, 1); 939 scalars[0] = x; 940 scalars[1] = y; 941 scalars[2] = z; /* z = -(x+y) */ 942 943 BN_init(&scalar3); 944 BN_zero(&scalar3); 945 scalars[3] = &scalar3; 946 947 if (!EC_POINTs_mul(group, P, NULL, 4, points, scalars, ctx)) 948 ABORT; 949 if (!EC_POINT_is_at_infinity(group, P)) 950 ABORT; 951 952 fprintf(stdout, " ok\n\n"); 953 954 BN_free(&scalar3); 955 } 956 957# if 0 958 timings(P_160, TIMING_BASE_PT, ctx); 959 timings(P_160, TIMING_RAND_PT, ctx); 960 timings(P_160, TIMING_SIMUL, ctx); 961 timings(P_192, TIMING_BASE_PT, ctx); 962 timings(P_192, TIMING_RAND_PT, ctx); 963 timings(P_192, TIMING_SIMUL, ctx); 964 timings(P_224, TIMING_BASE_PT, ctx); 965 timings(P_224, TIMING_RAND_PT, ctx); 966 timings(P_224, TIMING_SIMUL, ctx); 967 timings(P_256, TIMING_BASE_PT, ctx); 968 timings(P_256, TIMING_RAND_PT, ctx); 969 timings(P_256, TIMING_SIMUL, ctx); 970 timings(P_384, TIMING_BASE_PT, ctx); 971 timings(P_384, TIMING_RAND_PT, ctx); 972 timings(P_384, TIMING_SIMUL, ctx); 973 timings(P_521, TIMING_BASE_PT, ctx); 974 timings(P_521, TIMING_RAND_PT, ctx); 975 timings(P_521, TIMING_SIMUL, ctx); 976# endif 977 978 if (ctx) 979 BN_CTX_free(ctx); 980 BN_free(p); 981 BN_free(a); 982 BN_free(b); 983 EC_GROUP_free(group); 984 EC_POINT_free(P); 985 EC_POINT_free(Q); 986 EC_POINT_free(R); 987 BN_free(x); 988 BN_free(y); 989 BN_free(z); 990 991 if (P_160) 992 EC_GROUP_free(P_160); 993 if (P_192) 994 EC_GROUP_free(P_192); 995 if (P_224) 996 EC_GROUP_free(P_224); 997 if (P_256) 998 EC_GROUP_free(P_256); 999 if (P_384) 1000 EC_GROUP_free(P_384); 1001 if (P_521) 1002 EC_GROUP_free(P_521); 1003 1004} 1005 1006/* Change test based on whether binary point compression is enabled or not. */ 1007# ifdef OPENSSL_EC_BIN_PT_COMP 1008# define CHAR2_CURVE_TEST_INTERNAL(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \ 1009 if (!BN_hex2bn(&x, _x)) ABORT; \ 1010 if (!EC_POINT_set_compressed_coordinates_GF2m(group, P, x, _y_bit, ctx)) ABORT; \ 1011 if (EC_POINT_is_on_curve(group, P, ctx) <= 0) ABORT; \ 1012 if (!BN_hex2bn(&z, _order)) ABORT; \ 1013 if (!BN_hex2bn(&cof, _cof)) ABORT; \ 1014 if (!EC_GROUP_set_generator(group, P, z, cof)) ABORT; \ 1015 if (!EC_POINT_get_affine_coordinates_GF2m(group, P, x, y, ctx)) ABORT; \ 1016 fprintf(stdout, "\n%s -- Generator:\n x = 0x", _name); \ 1017 BN_print_fp(stdout, x); \ 1018 fprintf(stdout, "\n y = 0x"); \ 1019 BN_print_fp(stdout, y); \ 1020 fprintf(stdout, "\n"); \ 1021 /* G_y value taken from the standard: */ \ 1022 if (!BN_hex2bn(&z, _y)) ABORT; \ 1023 if (0 != BN_cmp(y, z)) ABORT; 1024# else 1025# define CHAR2_CURVE_TEST_INTERNAL(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \ 1026 if (!BN_hex2bn(&x, _x)) ABORT; \ 1027 if (!BN_hex2bn(&y, _y)) ABORT; \ 1028 if (!EC_POINT_set_affine_coordinates_GF2m(group, P, x, y, ctx)) ABORT; \ 1029 if (EC_POINT_is_on_curve(group, P, ctx) <= 0) ABORT; \ 1030 if (!BN_hex2bn(&z, _order)) ABORT; \ 1031 if (!BN_hex2bn(&cof, _cof)) ABORT; \ 1032 if (!EC_GROUP_set_generator(group, P, z, cof)) ABORT; \ 1033 fprintf(stdout, "\n%s -- Generator:\n x = 0x", _name); \ 1034 BN_print_fp(stdout, x); \ 1035 fprintf(stdout, "\n y = 0x"); \ 1036 BN_print_fp(stdout, y); \ 1037 fprintf(stdout, "\n"); 1038# endif 1039 1040# define CHAR2_CURVE_TEST(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \ 1041 if (!BN_hex2bn(&p, _p)) ABORT; \ 1042 if (!BN_hex2bn(&a, _a)) ABORT; \ 1043 if (!BN_hex2bn(&b, _b)) ABORT; \ 1044 if (!EC_GROUP_set_curve_GF2m(group, p, a, b, ctx)) ABORT; \ 1045 CHAR2_CURVE_TEST_INTERNAL(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \ 1046 fprintf(stdout, "verify degree ..."); \ 1047 if (EC_GROUP_get_degree(group) != _degree) ABORT; \ 1048 fprintf(stdout, " ok\n"); \ 1049 group_order_tests(group); \ 1050 if (!(_variable = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT; \ 1051 if (!EC_GROUP_copy(_variable, group)) ABORT; \ 1052 1053# ifndef OPENSSL_NO_EC2M 1054 1055static void char2_field_tests(void) 1056{ 1057 BN_CTX *ctx = NULL; 1058 BIGNUM *p, *a, *b; 1059 EC_GROUP *group; 1060 EC_GROUP *C2_K163 = NULL, *C2_K233 = NULL, *C2_K283 = NULL, *C2_K409 = 1061 NULL, *C2_K571 = NULL; 1062 EC_GROUP *C2_B163 = NULL, *C2_B233 = NULL, *C2_B283 = NULL, *C2_B409 = 1063 NULL, *C2_B571 = NULL; 1064 EC_POINT *P, *Q, *R; 1065 BIGNUM *x, *y, *z, *cof; 1066 unsigned char buf[100]; 1067 size_t i, len; 1068 int k; 1069 1070# if 1 /* optional */ 1071 ctx = BN_CTX_new(); 1072 if (!ctx) 1073 ABORT; 1074# endif 1075 1076 p = BN_new(); 1077 a = BN_new(); 1078 b = BN_new(); 1079 if (!p || !a || !b) 1080 ABORT; 1081 1082 if (!BN_hex2bn(&p, "13")) 1083 ABORT; 1084 if (!BN_hex2bn(&a, "3")) 1085 ABORT; 1086 if (!BN_hex2bn(&b, "1")) 1087 ABORT; 1088 1089 group = EC_GROUP_new(EC_GF2m_simple_method()); /* applications should use 1090 * EC_GROUP_new_curve_GF2m 1091 * so that the library gets 1092 * to choose the EC_METHOD */ 1093 if (!group) 1094 ABORT; 1095 if (!EC_GROUP_set_curve_GF2m(group, p, a, b, ctx)) 1096 ABORT; 1097 1098 { 1099 EC_GROUP *tmp; 1100 tmp = EC_GROUP_new(EC_GROUP_method_of(group)); 1101 if (!tmp) 1102 ABORT; 1103 if (!EC_GROUP_copy(tmp, group)) 1104 ABORT; 1105 EC_GROUP_free(group); 1106 group = tmp; 1107 } 1108 1109 if (!EC_GROUP_get_curve_GF2m(group, p, a, b, ctx)) 1110 ABORT; 1111 1112 fprintf(stdout, 1113 "Curve defined by Weierstrass equation\n y^2 + x*y = x^3 + a*x^2 + b (mod 0x"); 1114 BN_print_fp(stdout, p); 1115 fprintf(stdout, ")\n a = 0x"); 1116 BN_print_fp(stdout, a); 1117 fprintf(stdout, "\n b = 0x"); 1118 BN_print_fp(stdout, b); 1119 fprintf(stdout, "\n(0x... means binary polynomial)\n"); 1120 1121 P = EC_POINT_new(group); 1122 Q = EC_POINT_new(group); 1123 R = EC_POINT_new(group); 1124 if (!P || !Q || !R) 1125 ABORT; 1126 1127 if (!EC_POINT_set_to_infinity(group, P)) 1128 ABORT; 1129 if (!EC_POINT_is_at_infinity(group, P)) 1130 ABORT; 1131 1132 buf[0] = 0; 1133 if (!EC_POINT_oct2point(group, Q, buf, 1, ctx)) 1134 ABORT; 1135 1136 if (!EC_POINT_add(group, P, P, Q, ctx)) 1137 ABORT; 1138 if (!EC_POINT_is_at_infinity(group, P)) 1139 ABORT; 1140 1141 x = BN_new(); 1142 y = BN_new(); 1143 z = BN_new(); 1144 cof = BN_new(); 1145 if (!x || !y || !z || !cof) 1146 ABORT; 1147 1148 if (!BN_hex2bn(&x, "6")) 1149 ABORT; 1150/* Change test based on whether binary point compression is enabled or not. */ 1151# ifdef OPENSSL_EC_BIN_PT_COMP 1152 if (!EC_POINT_set_compressed_coordinates_GF2m(group, Q, x, 1, ctx)) 1153 ABORT; 1154# else 1155 if (!BN_hex2bn(&y, "8")) 1156 ABORT; 1157 if (!EC_POINT_set_affine_coordinates_GF2m(group, Q, x, y, ctx)) 1158 ABORT; 1159# endif 1160 if (EC_POINT_is_on_curve(group, Q, ctx) <= 0) { 1161/* Change test based on whether binary point compression is enabled or not. */ 1162# ifdef OPENSSL_EC_BIN_PT_COMP 1163 if (!EC_POINT_get_affine_coordinates_GF2m(group, Q, x, y, ctx)) 1164 ABORT; 1165# endif 1166 fprintf(stderr, "Point is not on curve: x = 0x"); 1167 BN_print_fp(stderr, x); 1168 fprintf(stderr, ", y = 0x"); 1169 BN_print_fp(stderr, y); 1170 fprintf(stderr, "\n"); 1171 ABORT; 1172 } 1173 1174 fprintf(stdout, "A cyclic subgroup:\n"); 1175 k = 100; 1176 do { 1177 if (k-- == 0) 1178 ABORT; 1179 1180 if (EC_POINT_is_at_infinity(group, P)) 1181 fprintf(stdout, " point at infinity\n"); 1182 else { 1183 if (!EC_POINT_get_affine_coordinates_GF2m(group, P, x, y, ctx)) 1184 ABORT; 1185 1186 fprintf(stdout, " x = 0x"); 1187 BN_print_fp(stdout, x); 1188 fprintf(stdout, ", y = 0x"); 1189 BN_print_fp(stdout, y); 1190 fprintf(stdout, "\n"); 1191 } 1192 1193 if (!EC_POINT_copy(R, P)) 1194 ABORT; 1195 if (!EC_POINT_add(group, P, P, Q, ctx)) 1196 ABORT; 1197 } 1198 while (!EC_POINT_is_at_infinity(group, P)); 1199 1200 if (!EC_POINT_add(group, P, Q, R, ctx)) 1201 ABORT; 1202 if (!EC_POINT_is_at_infinity(group, P)) 1203 ABORT; 1204 1205/* Change test based on whether binary point compression is enabled or not. */ 1206# ifdef OPENSSL_EC_BIN_PT_COMP 1207 len = 1208 EC_POINT_point2oct(group, Q, POINT_CONVERSION_COMPRESSED, buf, 1209 sizeof buf, ctx); 1210 if (len == 0) 1211 ABORT; 1212 if (!EC_POINT_oct2point(group, P, buf, len, ctx)) 1213 ABORT; 1214 if (0 != EC_POINT_cmp(group, P, Q, ctx)) 1215 ABORT; 1216 fprintf(stdout, "Generator as octet string, compressed form:\n "); 1217 for (i = 0; i < len; i++) 1218 fprintf(stdout, "%02X", buf[i]); 1219# endif 1220 1221 len = 1222 EC_POINT_point2oct(group, Q, POINT_CONVERSION_UNCOMPRESSED, buf, 1223 sizeof buf, ctx); 1224 if (len == 0) 1225 ABORT; 1226 if (!EC_POINT_oct2point(group, P, buf, len, ctx)) 1227 ABORT; 1228 if (0 != EC_POINT_cmp(group, P, Q, ctx)) 1229 ABORT; 1230 fprintf(stdout, "\nGenerator as octet string, uncompressed form:\n "); 1231 for (i = 0; i < len; i++) 1232 fprintf(stdout, "%02X", buf[i]); 1233 1234/* Change test based on whether binary point compression is enabled or not. */ 1235# ifdef OPENSSL_EC_BIN_PT_COMP 1236 len = 1237 EC_POINT_point2oct(group, Q, POINT_CONVERSION_HYBRID, buf, sizeof buf, 1238 ctx); 1239 if (len == 0) 1240 ABORT; 1241 if (!EC_POINT_oct2point(group, P, buf, len, ctx)) 1242 ABORT; 1243 if (0 != EC_POINT_cmp(group, P, Q, ctx)) 1244 ABORT; 1245 fprintf(stdout, "\nGenerator as octet string, hybrid form:\n "); 1246 for (i = 0; i < len; i++) 1247 fprintf(stdout, "%02X", buf[i]); 1248# endif 1249 1250 fprintf(stdout, "\n"); 1251 1252 if (!EC_POINT_invert(group, P, ctx)) 1253 ABORT; 1254 if (0 != EC_POINT_cmp(group, P, R, ctx)) 1255 ABORT; 1256 1257 /* Curve K-163 (FIPS PUB 186-2, App. 6) */ 1258 CHAR2_CURVE_TEST 1259 ("NIST curve K-163", 1260 "0800000000000000000000000000000000000000C9", 1261 "1", 1262 "1", 1263 "02FE13C0537BBC11ACAA07D793DE4E6D5E5C94EEE8", 1264 "0289070FB05D38FF58321F2E800536D538CCDAA3D9", 1265 1, "04000000000000000000020108A2E0CC0D99F8A5EF", "2", 163, C2_K163); 1266 1267 /* Curve B-163 (FIPS PUB 186-2, App. 6) */ 1268 CHAR2_CURVE_TEST 1269 ("NIST curve B-163", 1270 "0800000000000000000000000000000000000000C9", 1271 "1", 1272 "020A601907B8C953CA1481EB10512F78744A3205FD", 1273 "03F0EBA16286A2D57EA0991168D4994637E8343E36", 1274 "00D51FBC6C71A0094FA2CDD545B11C5C0C797324F1", 1275 1, "040000000000000000000292FE77E70C12A4234C33", "2", 163, C2_B163); 1276 1277 /* Curve K-233 (FIPS PUB 186-2, App. 6) */ 1278 CHAR2_CURVE_TEST 1279 ("NIST curve K-233", 1280 "020000000000000000000000000000000000000004000000000000000001", 1281 "0", 1282 "1", 1283 "017232BA853A7E731AF129F22FF4149563A419C26BF50A4C9D6EEFAD6126", 1284 "01DB537DECE819B7F70F555A67C427A8CD9BF18AEB9B56E0C11056FAE6A3", 1285 0, 1286 "008000000000000000000000000000069D5BB915BCD46EFB1AD5F173ABDF", 1287 "4", 233, C2_K233); 1288 1289 /* Curve B-233 (FIPS PUB 186-2, App. 6) */ 1290 CHAR2_CURVE_TEST 1291 ("NIST curve B-233", 1292 "020000000000000000000000000000000000000004000000000000000001", 1293 "000000000000000000000000000000000000000000000000000000000001", 1294 "0066647EDE6C332C7F8C0923BB58213B333B20E9CE4281FE115F7D8F90AD", 1295 "00FAC9DFCBAC8313BB2139F1BB755FEF65BC391F8B36F8F8EB7371FD558B", 1296 "01006A08A41903350678E58528BEBF8A0BEFF867A7CA36716F7E01F81052", 1297 1, 1298 "01000000000000000000000000000013E974E72F8A6922031D2603CFE0D7", 1299 "2", 233, C2_B233); 1300 1301 /* Curve K-283 (FIPS PUB 186-2, App. 6) */ 1302 CHAR2_CURVE_TEST 1303 ("NIST curve K-283", 1304 "0800000000000000000000000000000000000000000000000000000000000000000010A1", 1305 "0", 1306 "1", 1307 "0503213F78CA44883F1A3B8162F188E553CD265F23C1567A16876913B0C2AC2458492836", 1308 "01CCDA380F1C9E318D90F95D07E5426FE87E45C0E8184698E45962364E34116177DD2259", 1309 0, 1310 "01FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE9AE2ED07577265DFF7F94451E061E163C61", 1311 "4", 283, C2_K283); 1312 1313 /* Curve B-283 (FIPS PUB 186-2, App. 6) */ 1314 CHAR2_CURVE_TEST 1315 ("NIST curve B-283", 1316 "0800000000000000000000000000000000000000000000000000000000000000000010A1", 1317 "000000000000000000000000000000000000000000000000000000000000000000000001", 1318 "027B680AC8B8596DA5A4AF8A19A0303FCA97FD7645309FA2A581485AF6263E313B79A2F5", 1319 "05F939258DB7DD90E1934F8C70B0DFEC2EED25B8557EAC9C80E2E198F8CDBECD86B12053", 1320 "03676854FE24141CB98FE6D4B20D02B4516FF702350EDDB0826779C813F0DF45BE8112F4", 1321 1, 1322 "03FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEF90399660FC938A90165B042A7CEFADB307", 1323 "2", 283, C2_B283); 1324 1325 /* Curve K-409 (FIPS PUB 186-2, App. 6) */ 1326 CHAR2_CURVE_TEST 1327 ("NIST curve K-409", 1328 "02000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001", 1329 "0", 1330 "1", 1331 "0060F05F658F49C1AD3AB1890F7184210EFD0987E307C84C27ACCFB8F9F67CC2C460189EB5AAAA62EE222EB1B35540CFE9023746", 1332 "01E369050B7C4E42ACBA1DACBF04299C3460782F918EA427E6325165E9EA10E3DA5F6C42E9C55215AA9CA27A5863EC48D8E0286B", 1333 1, 1334 "007FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE5F83B2D4EA20400EC4557D5ED3E3E7CA5B4B5C83B8E01E5FCF", 1335 "4", 409, C2_K409); 1336 1337 /* Curve B-409 (FIPS PUB 186-2, App. 6) */ 1338 CHAR2_CURVE_TEST 1339 ("NIST curve B-409", 1340 "02000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001", 1341 "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001", 1342 "0021A5C2C8EE9FEB5C4B9A753B7B476B7FD6422EF1F3DD674761FA99D6AC27C8A9A197B272822F6CD57A55AA4F50AE317B13545F", 1343 "015D4860D088DDB3496B0C6064756260441CDE4AF1771D4DB01FFE5B34E59703DC255A868A1180515603AEAB60794E54BB7996A7", 1344 "0061B1CFAB6BE5F32BBFA78324ED106A7636B9C5A7BD198D0158AA4F5488D08F38514F1FDF4B4F40D2181B3681C364BA0273C706", 1345 1, 1346 "010000000000000000000000000000000000000000000000000001E2AAD6A612F33307BE5FA47C3C9E052F838164CD37D9A21173", 1347 "2", 409, C2_B409); 1348 1349 /* Curve K-571 (FIPS PUB 186-2, App. 6) */ 1350 CHAR2_CURVE_TEST 1351 ("NIST curve K-571", 1352 "80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425", 1353 "0", 1354 "1", 1355 "026EB7A859923FBC82189631F8103FE4AC9CA2970012D5D46024804801841CA44370958493B205E647DA304DB4CEB08CBBD1BA39494776FB988B47174DCA88C7E2945283A01C8972", 1356 "0349DC807F4FBF374F4AEADE3BCA95314DD58CEC9F307A54FFC61EFC006D8A2C9D4979C0AC44AEA74FBEBBB9F772AEDCB620B01A7BA7AF1B320430C8591984F601CD4C143EF1C7A3", 1357 0, 1358 "020000000000000000000000000000000000000000000000000000000000000000000000131850E1F19A63E4B391A8DB917F4138B630D84BE5D639381E91DEB45CFE778F637C1001", 1359 "4", 571, C2_K571); 1360 1361 /* Curve B-571 (FIPS PUB 186-2, App. 6) */ 1362 CHAR2_CURVE_TEST 1363 ("NIST curve B-571", 1364 "80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425", 1365 "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001", 1366 "02F40E7E2221F295DE297117B7F3D62F5C6A97FFCB8CEFF1CD6BA8CE4A9A18AD84FFABBD8EFA59332BE7AD6756A66E294AFD185A78FF12AA520E4DE739BACA0C7FFEFF7F2955727A", 1367 "0303001D34B856296C16C0D40D3CD7750A93D1D2955FA80AA5F40FC8DB7B2ABDBDE53950F4C0D293CDD711A35B67FB1499AE60038614F1394ABFA3B4C850D927E1E7769C8EEC2D19", 1368 "037BF27342DA639B6DCCFFFEB73D69D78C6C27A6009CBBCA1980F8533921E8A684423E43BAB08A576291AF8F461BB2A8B3531D2F0485C19B16E2F1516E23DD3C1A4827AF1B8AC15B", 1369 1, 1370 "03FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE661CE18FF55987308059B186823851EC7DD9CA1161DE93D5174D66E8382E9BB2FE84E47", 1371 "2", 571, C2_B571); 1372 1373 /* more tests using the last curve */ 1374 1375 if (!EC_POINT_copy(Q, P)) 1376 ABORT; 1377 if (EC_POINT_is_at_infinity(group, Q)) 1378 ABORT; 1379 if (!EC_POINT_dbl(group, P, P, ctx)) 1380 ABORT; 1381 if (EC_POINT_is_on_curve(group, P, ctx) <= 0) 1382 ABORT; 1383 if (!EC_POINT_invert(group, Q, ctx)) 1384 ABORT; /* P = -2Q */ 1385 1386 if (!EC_POINT_add(group, R, P, Q, ctx)) 1387 ABORT; 1388 if (!EC_POINT_add(group, R, R, Q, ctx)) 1389 ABORT; 1390 if (!EC_POINT_is_at_infinity(group, R)) 1391 ABORT; /* R = P + 2Q */ 1392 1393 { 1394 const EC_POINT *points[3]; 1395 const BIGNUM *scalars[3]; 1396 1397 if (EC_POINT_is_at_infinity(group, Q)) 1398 ABORT; 1399 points[0] = Q; 1400 points[1] = Q; 1401 points[2] = Q; 1402 1403 if (!BN_add(y, z, BN_value_one())) 1404 ABORT; 1405 if (BN_is_odd(y)) 1406 ABORT; 1407 if (!BN_rshift1(y, y)) 1408 ABORT; 1409 scalars[0] = y; /* (group order + 1)/2, so y*Q + y*Q = Q */ 1410 scalars[1] = y; 1411 1412 fprintf(stdout, "combined multiplication ..."); 1413 fflush(stdout); 1414 1415 /* z is still the group order */ 1416 if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) 1417 ABORT; 1418 if (!EC_POINTs_mul(group, R, z, 2, points, scalars, ctx)) 1419 ABORT; 1420 if (0 != EC_POINT_cmp(group, P, R, ctx)) 1421 ABORT; 1422 if (0 != EC_POINT_cmp(group, R, Q, ctx)) 1423 ABORT; 1424 1425 fprintf(stdout, "."); 1426 fflush(stdout); 1427 1428 if (!BN_pseudo_rand(y, BN_num_bits(y), 0, 0)) 1429 ABORT; 1430 if (!BN_add(z, z, y)) 1431 ABORT; 1432 BN_set_negative(z, 1); 1433 scalars[0] = y; 1434 scalars[1] = z; /* z = -(order + y) */ 1435 1436 if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) 1437 ABORT; 1438 if (!EC_POINT_is_at_infinity(group, P)) 1439 ABORT; 1440 1441 fprintf(stdout, "."); 1442 fflush(stdout); 1443 1444 if (!BN_pseudo_rand(x, BN_num_bits(y) - 1, 0, 0)) 1445 ABORT; 1446 if (!BN_add(z, x, y)) 1447 ABORT; 1448 BN_set_negative(z, 1); 1449 scalars[0] = x; 1450 scalars[1] = y; 1451 scalars[2] = z; /* z = -(x+y) */ 1452 1453 if (!EC_POINTs_mul(group, P, NULL, 3, points, scalars, ctx)) 1454 ABORT; 1455 if (!EC_POINT_is_at_infinity(group, P)) 1456 ABORT; 1457 1458 fprintf(stdout, " ok\n\n"); 1459 } 1460 1461# if 0 1462 timings(C2_K163, TIMING_BASE_PT, ctx); 1463 timings(C2_K163, TIMING_RAND_PT, ctx); 1464 timings(C2_K163, TIMING_SIMUL, ctx); 1465 timings(C2_B163, TIMING_BASE_PT, ctx); 1466 timings(C2_B163, TIMING_RAND_PT, ctx); 1467 timings(C2_B163, TIMING_SIMUL, ctx); 1468 timings(C2_K233, TIMING_BASE_PT, ctx); 1469 timings(C2_K233, TIMING_RAND_PT, ctx); 1470 timings(C2_K233, TIMING_SIMUL, ctx); 1471 timings(C2_B233, TIMING_BASE_PT, ctx); 1472 timings(C2_B233, TIMING_RAND_PT, ctx); 1473 timings(C2_B233, TIMING_SIMUL, ctx); 1474 timings(C2_K283, TIMING_BASE_PT, ctx); 1475 timings(C2_K283, TIMING_RAND_PT, ctx); 1476 timings(C2_K283, TIMING_SIMUL, ctx); 1477 timings(C2_B283, TIMING_BASE_PT, ctx); 1478 timings(C2_B283, TIMING_RAND_PT, ctx); 1479 timings(C2_B283, TIMING_SIMUL, ctx); 1480 timings(C2_K409, TIMING_BASE_PT, ctx); 1481 timings(C2_K409, TIMING_RAND_PT, ctx); 1482 timings(C2_K409, TIMING_SIMUL, ctx); 1483 timings(C2_B409, TIMING_BASE_PT, ctx); 1484 timings(C2_B409, TIMING_RAND_PT, ctx); 1485 timings(C2_B409, TIMING_SIMUL, ctx); 1486 timings(C2_K571, TIMING_BASE_PT, ctx); 1487 timings(C2_K571, TIMING_RAND_PT, ctx); 1488 timings(C2_K571, TIMING_SIMUL, ctx); 1489 timings(C2_B571, TIMING_BASE_PT, ctx); 1490 timings(C2_B571, TIMING_RAND_PT, ctx); 1491 timings(C2_B571, TIMING_SIMUL, ctx); 1492# endif 1493 1494 if (ctx) 1495 BN_CTX_free(ctx); 1496 BN_free(p); 1497 BN_free(a); 1498 BN_free(b); 1499 EC_GROUP_free(group); 1500 EC_POINT_free(P); 1501 EC_POINT_free(Q); 1502 EC_POINT_free(R); 1503 BN_free(x); 1504 BN_free(y); 1505 BN_free(z); 1506 BN_free(cof); 1507 1508 if (C2_K163) 1509 EC_GROUP_free(C2_K163); 1510 if (C2_B163) 1511 EC_GROUP_free(C2_B163); 1512 if (C2_K233) 1513 EC_GROUP_free(C2_K233); 1514 if (C2_B233) 1515 EC_GROUP_free(C2_B233); 1516 if (C2_K283) 1517 EC_GROUP_free(C2_K283); 1518 if (C2_B283) 1519 EC_GROUP_free(C2_B283); 1520 if (C2_K409) 1521 EC_GROUP_free(C2_K409); 1522 if (C2_B409) 1523 EC_GROUP_free(C2_B409); 1524 if (C2_K571) 1525 EC_GROUP_free(C2_K571); 1526 if (C2_B571) 1527 EC_GROUP_free(C2_B571); 1528 1529} 1530# endif 1531 1532static void internal_curve_test(void) 1533{ 1534 EC_builtin_curve *curves = NULL; 1535 size_t crv_len = 0, n = 0; 1536 int ok = 1; 1537 1538 crv_len = EC_get_builtin_curves(NULL, 0); 1539 1540 curves = OPENSSL_malloc(sizeof(EC_builtin_curve) * crv_len); 1541 1542 if (curves == NULL) 1543 return; 1544 1545 if (!EC_get_builtin_curves(curves, crv_len)) { 1546 OPENSSL_free(curves); 1547 return; 1548 } 1549 1550 fprintf(stdout, "testing internal curves: "); 1551 1552 for (n = 0; n < crv_len; n++) { 1553 EC_GROUP *group = NULL; 1554 int nid = curves[n].nid; 1555 if ((group = EC_GROUP_new_by_curve_name(nid)) == NULL) { 1556 ok = 0; 1557 fprintf(stdout, "\nEC_GROUP_new_curve_name() failed with" 1558 " curve %s\n", OBJ_nid2sn(nid)); 1559 /* try next curve */ 1560 continue; 1561 } 1562 if (!EC_GROUP_check(group, NULL)) { 1563 ok = 0; 1564 fprintf(stdout, "\nEC_GROUP_check() failed with" 1565 " curve %s\n", OBJ_nid2sn(nid)); 1566 EC_GROUP_free(group); 1567 /* try the next curve */ 1568 continue; 1569 } 1570 fprintf(stdout, "."); 1571 fflush(stdout); 1572 EC_GROUP_free(group); 1573 } 1574 if (ok) 1575 fprintf(stdout, " ok\n\n"); 1576 else { 1577 fprintf(stdout, " failed\n\n"); 1578 ABORT; 1579 } 1580 OPENSSL_free(curves); 1581 return; 1582} 1583 1584# ifndef OPENSSL_NO_EC_NISTP_64_GCC_128 1585/* 1586 * nistp_test_params contains magic numbers for testing our optimized 1587 * implementations of several NIST curves with characteristic > 3. 1588 */ 1589struct nistp_test_params { 1590 const EC_METHOD *(*meth) (); 1591 int degree; 1592 /* 1593 * Qx, Qy and D are taken from 1594 * http://csrcdocut.gov/groups/ST/toolkit/documents/Examples/ECDSA_Prime.pdf 1595 * Otherwise, values are standard curve parameters from FIPS 180-3 1596 */ 1597 const char *p, *a, *b, *Qx, *Qy, *Gx, *Gy, *order, *d; 1598}; 1599 1600static const struct nistp_test_params nistp_tests_params[] = { 1601 { 1602 /* P-224 */ 1603 EC_GFp_nistp224_method, 1604 224, 1605 /* p */ 1606 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001", 1607 /* a */ 1608 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE", 1609 /* b */ 1610 "B4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4", 1611 /* Qx */ 1612 "E84FB0B8E7000CB657D7973CF6B42ED78B301674276DF744AF130B3E", 1613 /* Qy */ 1614 "4376675C6FC5612C21A0FF2D2A89D2987DF7A2BC52183B5982298555", 1615 /* Gx */ 1616 "B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21", 1617 /* Gy */ 1618 "BD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34", 1619 /* order */ 1620 "FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D", 1621 /* d */ 1622 "3F0C488E987C80BE0FEE521F8D90BE6034EC69AE11CA72AA777481E8", 1623 }, 1624 { 1625 /* P-256 */ 1626 EC_GFp_nistp256_method, 1627 256, 1628 /* p */ 1629 "ffffffff00000001000000000000000000000000ffffffffffffffffffffffff", 1630 /* a */ 1631 "ffffffff00000001000000000000000000000000fffffffffffffffffffffffc", 1632 /* b */ 1633 "5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b", 1634 /* Qx */ 1635 "b7e08afdfe94bad3f1dc8c734798ba1c62b3a0ad1e9ea2a38201cd0889bc7a19", 1636 /* Qy */ 1637 "3603f747959dbf7a4bb226e41928729063adc7ae43529e61b563bbc606cc5e09", 1638 /* Gx */ 1639 "6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296", 1640 /* Gy */ 1641 "4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5", 1642 /* order */ 1643 "ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551", 1644 /* d */ 1645 "c477f9f65c22cce20657faa5b2d1d8122336f851a508a1ed04e479c34985bf96", 1646 }, 1647 { 1648 /* P-521 */ 1649 EC_GFp_nistp521_method, 1650 521, 1651 /* p */ 1652 "1ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff", 1653 /* a */ 1654 "1fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc", 1655 /* b */ 1656 "051953eb9618e1c9a1f929a21a0b68540eea2da725b99b315f3b8b489918ef109e156193951ec7e937b1652c0bd3bb1bf073573df883d2c34f1ef451fd46b503f00", 1657 /* Qx */ 1658 "0098e91eef9a68452822309c52fab453f5f117c1da8ed796b255e9ab8f6410cca16e59df403a6bdc6ca467a37056b1e54b3005d8ac030decfeb68df18b171885d5c4", 1659 /* Qy */ 1660 "0164350c321aecfc1cca1ba4364c9b15656150b4b78d6a48d7d28e7f31985ef17be8554376b72900712c4b83ad668327231526e313f5f092999a4632fd50d946bc2e", 1661 /* Gx */ 1662 "c6858e06b70404e9cd9e3ecb662395b4429c648139053fb521f828af606b4d3dbaa14b5e77efe75928fe1dc127a2ffa8de3348b3c1856a429bf97e7e31c2e5bd66", 1663 /* Gy */ 1664 "11839296a789a3bc0045c8a5fb42c7d1bd998f54449579b446817afbd17273e662c97ee72995ef42640c550b9013fad0761353c7086a272c24088be94769fd16650", 1665 /* order */ 1666 "1fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffa51868783bf2f966b7fcc0148f709a5d03bb5c9b8899c47aebb6fb71e91386409", 1667 /* d */ 1668 "0100085f47b8e1b8b11b7eb33028c0b2888e304bfc98501955b45bba1478dc184eeedf09b86a5f7c21994406072787205e69a63709fe35aa93ba333514b24f961722", 1669 }, 1670}; 1671 1672static void nistp_single_test(const struct nistp_test_params *test) 1673{ 1674 BN_CTX *ctx; 1675 BIGNUM *p, *a, *b, *x, *y, *n, *m, *order; 1676 EC_GROUP *NISTP; 1677 EC_POINT *G, *P, *Q, *Q_CHECK; 1678 1679 fprintf(stdout, "\nNIST curve P-%d (optimised implementation):\n", 1680 test->degree); 1681 ctx = BN_CTX_new(); 1682 p = BN_new(); 1683 a = BN_new(); 1684 b = BN_new(); 1685 x = BN_new(); 1686 y = BN_new(); 1687 m = BN_new(); 1688 n = BN_new(); 1689 order = BN_new(); 1690 1691 NISTP = EC_GROUP_new(test->meth()); 1692 if (!NISTP) 1693 ABORT; 1694 if (!BN_hex2bn(&p, test->p)) 1695 ABORT; 1696 if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) 1697 ABORT; 1698 if (!BN_hex2bn(&a, test->a)) 1699 ABORT; 1700 if (!BN_hex2bn(&b, test->b)) 1701 ABORT; 1702 if (!EC_GROUP_set_curve_GFp(NISTP, p, a, b, ctx)) 1703 ABORT; 1704 G = EC_POINT_new(NISTP); 1705 P = EC_POINT_new(NISTP); 1706 Q = EC_POINT_new(NISTP); 1707 Q_CHECK = EC_POINT_new(NISTP); 1708 if (!BN_hex2bn(&x, test->Qx)) 1709 ABORT; 1710 if (!BN_hex2bn(&y, test->Qy)) 1711 ABORT; 1712 if (!EC_POINT_set_affine_coordinates_GFp(NISTP, Q_CHECK, x, y, ctx)) 1713 ABORT; 1714 if (!BN_hex2bn(&x, test->Gx)) 1715 ABORT; 1716 if (!BN_hex2bn(&y, test->Gy)) 1717 ABORT; 1718 if (!EC_POINT_set_affine_coordinates_GFp(NISTP, G, x, y, ctx)) 1719 ABORT; 1720 if (!BN_hex2bn(&order, test->order)) 1721 ABORT; 1722 if (!EC_GROUP_set_generator(NISTP, G, order, BN_value_one())) 1723 ABORT; 1724 1725 fprintf(stdout, "verify degree ... "); 1726 if (EC_GROUP_get_degree(NISTP) != test->degree) 1727 ABORT; 1728 fprintf(stdout, "ok\n"); 1729 1730 fprintf(stdout, "NIST test vectors ... "); 1731 if (!BN_hex2bn(&n, test->d)) 1732 ABORT; 1733 /* fixed point multiplication */ 1734 EC_POINT_mul(NISTP, Q, n, NULL, NULL, ctx); 1735 if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) 1736 ABORT; 1737 /* random point multiplication */ 1738 EC_POINT_mul(NISTP, Q, NULL, G, n, ctx); 1739 if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) 1740 ABORT; 1741 1742 /* set generator to P = 2*G, where G is the standard generator */ 1743 if (!EC_POINT_dbl(NISTP, P, G, ctx)) 1744 ABORT; 1745 if (!EC_GROUP_set_generator(NISTP, P, order, BN_value_one())) 1746 ABORT; 1747 /* set the scalar to m=n/2, where n is the NIST test scalar */ 1748 if (!BN_rshift(m, n, 1)) 1749 ABORT; 1750 1751 /* test the non-standard generator */ 1752 /* fixed point multiplication */ 1753 EC_POINT_mul(NISTP, Q, m, NULL, NULL, ctx); 1754 if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) 1755 ABORT; 1756 /* random point multiplication */ 1757 EC_POINT_mul(NISTP, Q, NULL, P, m, ctx); 1758 if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) 1759 ABORT; 1760 1761 /* now repeat all tests with precomputation */ 1762 if (!EC_GROUP_precompute_mult(NISTP, ctx)) 1763 ABORT; 1764 1765 /* fixed point multiplication */ 1766 EC_POINT_mul(NISTP, Q, m, NULL, NULL, ctx); 1767 if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) 1768 ABORT; 1769 /* random point multiplication */ 1770 EC_POINT_mul(NISTP, Q, NULL, P, m, ctx); 1771 if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) 1772 ABORT; 1773 1774 /* reset generator */ 1775 if (!EC_GROUP_set_generator(NISTP, G, order, BN_value_one())) 1776 ABORT; 1777 /* fixed point multiplication */ 1778 EC_POINT_mul(NISTP, Q, n, NULL, NULL, ctx); 1779 if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) 1780 ABORT; 1781 /* random point multiplication */ 1782 EC_POINT_mul(NISTP, Q, NULL, G, n, ctx); 1783 if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) 1784 ABORT; 1785 1786 fprintf(stdout, "ok\n"); 1787 group_order_tests(NISTP); 1788# if 0 1789 timings(NISTP, TIMING_BASE_PT, ctx); 1790 timings(NISTP, TIMING_RAND_PT, ctx); 1791# endif 1792 EC_GROUP_free(NISTP); 1793 EC_POINT_free(G); 1794 EC_POINT_free(P); 1795 EC_POINT_free(Q); 1796 EC_POINT_free(Q_CHECK); 1797 BN_free(n); 1798 BN_free(m); 1799 BN_free(p); 1800 BN_free(a); 1801 BN_free(b); 1802 BN_free(x); 1803 BN_free(y); 1804 BN_free(order); 1805 BN_CTX_free(ctx); 1806} 1807 1808static void nistp_tests() 1809{ 1810 unsigned i; 1811 1812 for (i = 0; 1813 i < sizeof(nistp_tests_params) / sizeof(struct nistp_test_params); 1814 i++) { 1815 nistp_single_test(&nistp_tests_params[i]); 1816 } 1817} 1818# endif 1819 1820static const char rnd_seed[] = 1821 "string to make the random number generator think it has entropy"; 1822 1823int main(int argc, char *argv[]) 1824{ 1825 1826 /* enable memory leak checking unless explicitly disabled */ 1827 if (!((getenv("OPENSSL_DEBUG_MEMORY") != NULL) 1828 && (0 == strcmp(getenv("OPENSSL_DEBUG_MEMORY"), "off")))) { 1829 CRYPTO_malloc_debug_init(); 1830 CRYPTO_set_mem_debug_options(V_CRYPTO_MDEBUG_ALL); 1831 } else { 1832 /* OPENSSL_DEBUG_MEMORY=off */ 1833 CRYPTO_set_mem_debug_functions(0, 0, 0, 0, 0); 1834 } 1835 CRYPTO_mem_ctrl(CRYPTO_MEM_CHECK_ON); 1836 ERR_load_crypto_strings(); 1837 1838 RAND_seed(rnd_seed, sizeof rnd_seed); /* or BN_generate_prime may fail */ 1839 1840 prime_field_tests(); 1841 puts(""); 1842# ifndef OPENSSL_NO_EC2M 1843 char2_field_tests(); 1844# endif 1845# ifndef OPENSSL_NO_EC_NISTP_64_GCC_128 1846 nistp_tests(); 1847# endif 1848 /* test the internal curves */ 1849 internal_curve_test(); 1850 1851# ifndef OPENSSL_NO_ENGINE 1852 ENGINE_cleanup(); 1853# endif 1854 CRYPTO_cleanup_all_ex_data(); 1855 ERR_free_strings(); 1856 ERR_remove_thread_state(NULL); 1857 CRYPTO_mem_leaks_fp(stderr); 1858 1859 return 0; 1860} 1861#endif 1862