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 #include <string.h> 75 #include <time.h> 76 77 #include <openssl/ec.h> 78 #ifndef OPENSSL_NO_ENGINE 79 #include <openssl/engine.h> 80 #endif 81 #include <openssl/err.h> 82 #include <openssl/obj_mac.h> 83 #include <openssl/objects.h> 84 #include <openssl/rand.h> 85 #include <openssl/bn.h> 86 #include <openssl/opensslconf.h> 87 88 #define ABORT do { \ 89 fflush(stdout); \ 90 fprintf(stderr, "%s:%d: ABORT\n", __FILE__, __LINE__); \ 91 ERR_print_errors_fp(stderr); \ 92 exit(1); \ 93 } while (0) 94 95 #define TIMING_BASE_PT 0 96 #define TIMING_RAND_PT 1 97 #define TIMING_SIMUL 2 98 99 /* test multiplication with group order, long and negative scalars */ 100 static void group_order_tests(EC_GROUP *group) 101 { 102 BIGNUM *n1, *n2, *order; 103 EC_POINT *P = EC_POINT_new(group); 104 EC_POINT *Q = EC_POINT_new(group); 105 BN_CTX *ctx = BN_CTX_new(); 106 107 n1 = BN_new(); n2 = BN_new(); order = BN_new(); 108 fprintf(stdout, "verify group order ..."); 109 fflush(stdout); 110 if (!EC_GROUP_get_order(group, order, ctx)) ABORT; 111 if (!EC_POINT_mul(group, Q, order, NULL, NULL, ctx)) ABORT; 112 if (!EC_POINT_is_at_infinity(group, Q)) ABORT; 113 fprintf(stdout, "."); 114 fflush(stdout); 115 if (!EC_GROUP_precompute_mult(group, ctx)) ABORT; 116 if (!EC_POINT_mul(group, Q, order, NULL, NULL, ctx)) ABORT; 117 if (!EC_POINT_is_at_infinity(group, Q)) ABORT; 118 fprintf(stdout, " ok\n"); 119 fprintf(stdout, "long/negative scalar tests ... "); 120 if (!BN_one(n1)) ABORT; 121 /* n1 = 1 - order */ 122 if (!BN_sub(n1, n1, order)) ABORT; 123 if(!EC_POINT_mul(group, Q, NULL, P, n1, ctx)) ABORT; 124 if (0 != EC_POINT_cmp(group, Q, P, ctx)) ABORT; 125 /* n2 = 1 + order */ 126 if (!BN_add(n2, order, BN_value_one())) ABORT; 127 if(!EC_POINT_mul(group, Q, NULL, P, n2, ctx)) ABORT; 128 if (0 != EC_POINT_cmp(group, Q, P, ctx)) ABORT; 129 /* n2 = (1 - order) * (1 + order) */ 130 if (!BN_mul(n2, n1, n2, ctx)) ABORT; 131 if(!EC_POINT_mul(group, Q, NULL, P, n2, ctx)) ABORT; 132 if (0 != EC_POINT_cmp(group, Q, P, ctx)) ABORT; 133 fprintf(stdout, "ok\n"); 134 EC_POINT_free(P); 135 EC_POINT_free(Q); 136 BN_free(n1); 137 BN_free(n2); 138 BN_free(order); 139 BN_CTX_free(ctx); 140 } 141 142 static void prime_field_tests(void) 143 { 144 BN_CTX *ctx = NULL; 145 BIGNUM *p, *a, *b; 146 EC_GROUP *group; 147 EC_GROUP *P_160 = NULL, *P_192 = NULL, *P_224 = NULL, *P_256 = NULL, *P_384 = NULL, *P_521 = NULL; 148 EC_POINT *P, *Q, *R; 149 BIGNUM *x, *y, *z; 150 unsigned char buf[100]; 151 size_t i, len; 152 int k; 153 154 #if 1 /* optional */ 155 ctx = BN_CTX_new(); 156 if (!ctx) ABORT; 157 #endif 158 159 p = BN_new(); 160 a = BN_new(); 161 b = BN_new(); 162 if (!p || !a || !b) ABORT; 163 164 if (!BN_hex2bn(&p, "17")) ABORT; 165 if (!BN_hex2bn(&a, "1")) ABORT; 166 if (!BN_hex2bn(&b, "1")) ABORT; 167 168 group = EC_GROUP_new(EC_GFp_mont_method()); /* applications should use EC_GROUP_new_curve_GFp 169 * so that the library gets to choose the EC_METHOD */ 170 if (!group) ABORT; 171 172 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT; 173 174 { 175 EC_GROUP *tmp; 176 tmp = EC_GROUP_new(EC_GROUP_method_of(group)); 177 if (!tmp) ABORT; 178 if (!EC_GROUP_copy(tmp, group)) ABORT; 179 EC_GROUP_free(group); 180 group = tmp; 181 } 182 183 if (!EC_GROUP_get_curve_GFp(group, p, a, b, ctx)) ABORT; 184 185 fprintf(stdout, "Curve defined by Weierstrass equation\n y^2 = x^3 + a*x + b (mod 0x"); 186 BN_print_fp(stdout, p); 187 fprintf(stdout, ")\n a = 0x"); 188 BN_print_fp(stdout, a); 189 fprintf(stdout, "\n b = 0x"); 190 BN_print_fp(stdout, b); 191 fprintf(stdout, "\n"); 192 193 P = EC_POINT_new(group); 194 Q = EC_POINT_new(group); 195 R = EC_POINT_new(group); 196 if (!P || !Q || !R) ABORT; 197 198 if (!EC_POINT_set_to_infinity(group, P)) ABORT; 199 if (!EC_POINT_is_at_infinity(group, P)) ABORT; 200 201 buf[0] = 0; 202 if (!EC_POINT_oct2point(group, Q, buf, 1, ctx)) ABORT; 203 204 if (!EC_POINT_add(group, P, P, Q, ctx)) ABORT; 205 if (!EC_POINT_is_at_infinity(group, P)) ABORT; 206 207 x = BN_new(); 208 y = BN_new(); 209 z = BN_new(); 210 if (!x || !y || !z) ABORT; 211 212 if (!BN_hex2bn(&x, "D")) ABORT; 213 if (!EC_POINT_set_compressed_coordinates_GFp(group, Q, x, 1, ctx)) ABORT; 214 if (!EC_POINT_is_on_curve(group, Q, ctx)) 215 { 216 if (!EC_POINT_get_affine_coordinates_GFp(group, Q, x, y, ctx)) ABORT; 217 fprintf(stderr, "Point is not on curve: x = 0x"); 218 BN_print_fp(stderr, x); 219 fprintf(stderr, ", y = 0x"); 220 BN_print_fp(stderr, y); 221 fprintf(stderr, "\n"); 222 ABORT; 223 } 224 225 fprintf(stdout, "A cyclic subgroup:\n"); 226 k = 100; 227 do 228 { 229 if (k-- == 0) ABORT; 230 231 if (EC_POINT_is_at_infinity(group, P)) 232 fprintf(stdout, " point at infinity\n"); 233 else 234 { 235 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT; 236 237 fprintf(stdout, " x = 0x"); 238 BN_print_fp(stdout, x); 239 fprintf(stdout, ", y = 0x"); 240 BN_print_fp(stdout, y); 241 fprintf(stdout, "\n"); 242 } 243 244 if (!EC_POINT_copy(R, P)) ABORT; 245 if (!EC_POINT_add(group, P, P, Q, ctx)) ABORT; 246 247 #if 0 /* optional */ 248 { 249 EC_POINT *points[3]; 250 251 points[0] = R; 252 points[1] = Q; 253 points[2] = P; 254 if (!EC_POINTs_make_affine(group, 2, points, ctx)) ABORT; 255 } 256 #endif 257 258 } 259 while (!EC_POINT_is_at_infinity(group, P)); 260 261 if (!EC_POINT_add(group, P, Q, R, ctx)) ABORT; 262 if (!EC_POINT_is_at_infinity(group, P)) ABORT; 263 264 len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_COMPRESSED, buf, sizeof buf, ctx); 265 if (len == 0) ABORT; 266 if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT; 267 if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT; 268 fprintf(stdout, "Generator as octet string, compressed form:\n "); 269 for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]); 270 271 len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_UNCOMPRESSED, buf, sizeof buf, ctx); 272 if (len == 0) ABORT; 273 if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT; 274 if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT; 275 fprintf(stdout, "\nGenerator as octet string, uncompressed form:\n "); 276 for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]); 277 278 len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_HYBRID, buf, sizeof buf, ctx); 279 if (len == 0) ABORT; 280 if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT; 281 if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT; 282 fprintf(stdout, "\nGenerator as octet string, hybrid form:\n "); 283 for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]); 284 285 if (!EC_POINT_get_Jprojective_coordinates_GFp(group, R, x, y, z, ctx)) ABORT; 286 fprintf(stdout, "\nA representation of the inverse of that generator in\nJacobian projective coordinates:\n X = 0x"); 287 BN_print_fp(stdout, x); 288 fprintf(stdout, ", Y = 0x"); 289 BN_print_fp(stdout, y); 290 fprintf(stdout, ", Z = 0x"); 291 BN_print_fp(stdout, z); 292 fprintf(stdout, "\n"); 293 294 if (!EC_POINT_invert(group, P, ctx)) ABORT; 295 if (0 != EC_POINT_cmp(group, P, R, ctx)) ABORT; 296 297 298 /* Curve secp160r1 (Certicom Research SEC 2 Version 1.0, section 2.4.2, 2000) 299 * -- not a NIST curve, but commonly used */ 300 301 if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFF")) ABORT; 302 if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT; 303 if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFC")) ABORT; 304 if (!BN_hex2bn(&b, "1C97BEFC54BD7A8B65ACF89F81D4D4ADC565FA45")) ABORT; 305 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT; 306 307 if (!BN_hex2bn(&x, "4A96B5688EF573284664698968C38BB913CBFC82")) ABORT; 308 if (!BN_hex2bn(&y, "23a628553168947d59dcc912042351377ac5fb32")) ABORT; 309 if (!EC_POINT_set_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT; 310 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT; 311 if (!BN_hex2bn(&z, "0100000000000000000001F4C8F927AED3CA752257")) ABORT; 312 if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT; 313 314 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT; 315 fprintf(stdout, "\nSEC2 curve secp160r1 -- Generator:\n x = 0x"); 316 BN_print_fp(stdout, x); 317 fprintf(stdout, "\n y = 0x"); 318 BN_print_fp(stdout, y); 319 fprintf(stdout, "\n"); 320 /* G_y value taken from the standard: */ 321 if (!BN_hex2bn(&z, "23a628553168947d59dcc912042351377ac5fb32")) ABORT; 322 if (0 != BN_cmp(y, z)) ABORT; 323 324 fprintf(stdout, "verify degree ..."); 325 if (EC_GROUP_get_degree(group) != 160) ABORT; 326 fprintf(stdout, " ok\n"); 327 328 group_order_tests(group); 329 330 if (!(P_160 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT; 331 if (!EC_GROUP_copy(P_160, group)) ABORT; 332 333 334 /* Curve P-192 (FIPS PUB 186-2, App. 6) */ 335 336 if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF")) ABORT; 337 if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT; 338 if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC")) ABORT; 339 if (!BN_hex2bn(&b, "64210519E59C80E70FA7E9AB72243049FEB8DEECC146B9B1")) ABORT; 340 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT; 341 342 if (!BN_hex2bn(&x, "188DA80EB03090F67CBF20EB43A18800F4FF0AFD82FF1012")) ABORT; 343 if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 1, ctx)) ABORT; 344 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT; 345 if (!BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22831")) ABORT; 346 if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT; 347 348 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT; 349 fprintf(stdout, "\nNIST curve P-192 -- Generator:\n x = 0x"); 350 BN_print_fp(stdout, x); 351 fprintf(stdout, "\n y = 0x"); 352 BN_print_fp(stdout, y); 353 fprintf(stdout, "\n"); 354 /* G_y value taken from the standard: */ 355 if (!BN_hex2bn(&z, "07192B95FFC8DA78631011ED6B24CDD573F977A11E794811")) ABORT; 356 if (0 != BN_cmp(y, z)) ABORT; 357 358 fprintf(stdout, "verify degree ..."); 359 if (EC_GROUP_get_degree(group) != 192) ABORT; 360 fprintf(stdout, " ok\n"); 361 362 group_order_tests(group); 363 364 if (!(P_192 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT; 365 if (!EC_GROUP_copy(P_192, group)) ABORT; 366 367 368 /* Curve P-224 (FIPS PUB 186-2, App. 6) */ 369 370 if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001")) ABORT; 371 if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT; 372 if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE")) ABORT; 373 if (!BN_hex2bn(&b, "B4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4")) ABORT; 374 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT; 375 376 if (!BN_hex2bn(&x, "B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21")) ABORT; 377 if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 0, ctx)) ABORT; 378 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT; 379 if (!BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D")) ABORT; 380 if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT; 381 382 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT; 383 fprintf(stdout, "\nNIST curve P-224 -- Generator:\n x = 0x"); 384 BN_print_fp(stdout, x); 385 fprintf(stdout, "\n y = 0x"); 386 BN_print_fp(stdout, y); 387 fprintf(stdout, "\n"); 388 /* G_y value taken from the standard: */ 389 if (!BN_hex2bn(&z, "BD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34")) ABORT; 390 if (0 != BN_cmp(y, z)) ABORT; 391 392 fprintf(stdout, "verify degree ..."); 393 if (EC_GROUP_get_degree(group) != 224) ABORT; 394 fprintf(stdout, " ok\n"); 395 396 group_order_tests(group); 397 398 if (!(P_224 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT; 399 if (!EC_GROUP_copy(P_224, group)) ABORT; 400 401 402 /* Curve P-256 (FIPS PUB 186-2, App. 6) */ 403 404 if (!BN_hex2bn(&p, "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF")) ABORT; 405 if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT; 406 if (!BN_hex2bn(&a, "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFC")) ABORT; 407 if (!BN_hex2bn(&b, "5AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B")) ABORT; 408 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT; 409 410 if (!BN_hex2bn(&x, "6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296")) ABORT; 411 if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 1, ctx)) ABORT; 412 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT; 413 if (!BN_hex2bn(&z, "FFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E" 414 "84F3B9CAC2FC632551")) ABORT; 415 if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT; 416 417 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT; 418 fprintf(stdout, "\nNIST curve P-256 -- Generator:\n x = 0x"); 419 BN_print_fp(stdout, x); 420 fprintf(stdout, "\n y = 0x"); 421 BN_print_fp(stdout, y); 422 fprintf(stdout, "\n"); 423 /* G_y value taken from the standard: */ 424 if (!BN_hex2bn(&z, "4FE342E2FE1A7F9B8EE7EB4A7C0F9E162BCE33576B315ECECBB6406837BF51F5")) ABORT; 425 if (0 != BN_cmp(y, z)) ABORT; 426 427 fprintf(stdout, "verify degree ..."); 428 if (EC_GROUP_get_degree(group) != 256) ABORT; 429 fprintf(stdout, " ok\n"); 430 431 group_order_tests(group); 432 433 if (!(P_256 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT; 434 if (!EC_GROUP_copy(P_256, group)) ABORT; 435 436 437 /* Curve P-384 (FIPS PUB 186-2, App. 6) */ 438 439 if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" 440 "FFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFF")) ABORT; 441 if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT; 442 if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" 443 "FFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFC")) ABORT; 444 if (!BN_hex2bn(&b, "B3312FA7E23EE7E4988E056BE3F82D19181D9C6EFE8141" 445 "120314088F5013875AC656398D8A2ED19D2A85C8EDD3EC2AEF")) ABORT; 446 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT; 447 448 if (!BN_hex2bn(&x, "AA87CA22BE8B05378EB1C71EF320AD746E1D3B628BA79B" 449 "9859F741E082542A385502F25DBF55296C3A545E3872760AB7")) ABORT; 450 if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 1, ctx)) ABORT; 451 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT; 452 if (!BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" 453 "FFC7634D81F4372DDF581A0DB248B0A77AECEC196ACCC52973")) ABORT; 454 if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT; 455 456 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT; 457 fprintf(stdout, "\nNIST curve P-384 -- Generator:\n x = 0x"); 458 BN_print_fp(stdout, x); 459 fprintf(stdout, "\n y = 0x"); 460 BN_print_fp(stdout, y); 461 fprintf(stdout, "\n"); 462 /* G_y value taken from the standard: */ 463 if (!BN_hex2bn(&z, "3617DE4A96262C6F5D9E98BF9292DC29F8F41DBD289A14" 464 "7CE9DA3113B5F0B8C00A60B1CE1D7E819D7A431D7C90EA0E5F")) ABORT; 465 if (0 != BN_cmp(y, z)) ABORT; 466 467 fprintf(stdout, "verify degree ..."); 468 if (EC_GROUP_get_degree(group) != 384) ABORT; 469 fprintf(stdout, " ok\n"); 470 471 group_order_tests(group); 472 473 if (!(P_384 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT; 474 if (!EC_GROUP_copy(P_384, group)) ABORT; 475 476 477 /* Curve P-521 (FIPS PUB 186-2, App. 6) */ 478 479 if (!BN_hex2bn(&p, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" 480 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" 481 "FFFFFFFFFFFFFFFFFFFFFFFFFFFF")) ABORT; 482 if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT; 483 if (!BN_hex2bn(&a, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" 484 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" 485 "FFFFFFFFFFFFFFFFFFFFFFFFFFFC")) ABORT; 486 if (!BN_hex2bn(&b, "051953EB9618E1C9A1F929A21A0B68540EEA2DA725B99B" 487 "315F3B8B489918EF109E156193951EC7E937B1652C0BD3BB1BF073573" 488 "DF883D2C34F1EF451FD46B503F00")) ABORT; 489 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT; 490 491 if (!BN_hex2bn(&x, "C6858E06B70404E9CD9E3ECB662395B4429C648139053F" 492 "B521F828AF606B4D3DBAA14B5E77EFE75928FE1DC127A2FFA8DE3348B" 493 "3C1856A429BF97E7E31C2E5BD66")) ABORT; 494 if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 0, ctx)) ABORT; 495 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT; 496 if (!BN_hex2bn(&z, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" 497 "FFFFFFFFFFFFFFFFFFFFA51868783BF2F966B7FCC0148F709A5D03BB5" 498 "C9B8899C47AEBB6FB71E91386409")) ABORT; 499 if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT; 500 501 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT; 502 fprintf(stdout, "\nNIST curve P-521 -- Generator:\n x = 0x"); 503 BN_print_fp(stdout, x); 504 fprintf(stdout, "\n y = 0x"); 505 BN_print_fp(stdout, y); 506 fprintf(stdout, "\n"); 507 /* G_y value taken from the standard: */ 508 if (!BN_hex2bn(&z, "11839296A789A3BC0045C8A5FB42C7D1BD998F54449579" 509 "B446817AFBD17273E662C97EE72995EF42640C550B9013FAD0761353C" 510 "7086A272C24088BE94769FD16650")) ABORT; 511 if (0 != BN_cmp(y, z)) ABORT; 512 513 fprintf(stdout, "verify degree ..."); 514 if (EC_GROUP_get_degree(group) != 521) ABORT; 515 fprintf(stdout, " ok\n"); 516 517 group_order_tests(group); 518 519 if (!(P_521 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT; 520 if (!EC_GROUP_copy(P_521, group)) ABORT; 521 522 523 /* more tests using the last curve */ 524 525 if (!EC_POINT_copy(Q, P)) ABORT; 526 if (EC_POINT_is_at_infinity(group, Q)) ABORT; 527 if (!EC_POINT_dbl(group, P, P, ctx)) ABORT; 528 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT; 529 if (!EC_POINT_invert(group, Q, ctx)) ABORT; /* P = -2Q */ 530 531 if (!EC_POINT_add(group, R, P, Q, ctx)) ABORT; 532 if (!EC_POINT_add(group, R, R, Q, ctx)) ABORT; 533 if (!EC_POINT_is_at_infinity(group, R)) ABORT; /* R = P + 2Q */ 534 535 { 536 const EC_POINT *points[4]; 537 const BIGNUM *scalars[4]; 538 BIGNUM scalar3; 539 540 if (EC_POINT_is_at_infinity(group, Q)) ABORT; 541 points[0] = Q; 542 points[1] = Q; 543 points[2] = Q; 544 points[3] = Q; 545 546 if (!EC_GROUP_get_order(group, z, ctx)) ABORT; 547 if (!BN_add(y, z, BN_value_one())) ABORT; 548 if (BN_is_odd(y)) ABORT; 549 if (!BN_rshift1(y, y)) ABORT; 550 scalars[0] = y; /* (group order + 1)/2, so y*Q + y*Q = Q */ 551 scalars[1] = y; 552 553 fprintf(stdout, "combined multiplication ..."); 554 fflush(stdout); 555 556 /* z is still the group order */ 557 if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) ABORT; 558 if (!EC_POINTs_mul(group, R, z, 2, points, scalars, ctx)) ABORT; 559 if (0 != EC_POINT_cmp(group, P, R, ctx)) ABORT; 560 if (0 != EC_POINT_cmp(group, R, Q, ctx)) ABORT; 561 562 fprintf(stdout, "."); 563 fflush(stdout); 564 565 if (!BN_pseudo_rand(y, BN_num_bits(y), 0, 0)) ABORT; 566 if (!BN_add(z, z, y)) ABORT; 567 BN_set_negative(z, 1); 568 scalars[0] = y; 569 scalars[1] = z; /* z = -(order + y) */ 570 571 if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) ABORT; 572 if (!EC_POINT_is_at_infinity(group, P)) ABORT; 573 574 fprintf(stdout, "."); 575 fflush(stdout); 576 577 if (!BN_pseudo_rand(x, BN_num_bits(y) - 1, 0, 0)) ABORT; 578 if (!BN_add(z, x, y)) ABORT; 579 BN_set_negative(z, 1); 580 scalars[0] = x; 581 scalars[1] = y; 582 scalars[2] = z; /* z = -(x+y) */ 583 584 BN_init(&scalar3); 585 BN_zero(&scalar3); 586 scalars[3] = &scalar3; 587 588 if (!EC_POINTs_mul(group, P, NULL, 4, points, scalars, ctx)) ABORT; 589 if (!EC_POINT_is_at_infinity(group, P)) ABORT; 590 591 fprintf(stdout, " ok\n\n"); 592 593 BN_free(&scalar3); 594 } 595 596 597 if (ctx) 598 BN_CTX_free(ctx); 599 BN_free(p); BN_free(a); BN_free(b); 600 EC_GROUP_free(group); 601 EC_POINT_free(P); 602 EC_POINT_free(Q); 603 EC_POINT_free(R); 604 BN_free(x); BN_free(y); BN_free(z); 605 606 if (P_160) EC_GROUP_free(P_160); 607 if (P_192) EC_GROUP_free(P_192); 608 if (P_224) EC_GROUP_free(P_224); 609 if (P_256) EC_GROUP_free(P_256); 610 if (P_384) EC_GROUP_free(P_384); 611 if (P_521) EC_GROUP_free(P_521); 612 613 } 614 615 /* Change test based on whether binary point compression is enabled or not. */ 616 #ifdef OPENSSL_EC_BIN_PT_COMP 617 #define CHAR2_CURVE_TEST_INTERNAL(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \ 618 if (!BN_hex2bn(&x, _x)) ABORT; \ 619 if (!EC_POINT_set_compressed_coordinates_GF2m(group, P, x, _y_bit, ctx)) ABORT; \ 620 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT; \ 621 if (!BN_hex2bn(&z, _order)) ABORT; \ 622 if (!BN_hex2bn(&cof, _cof)) ABORT; \ 623 if (!EC_GROUP_set_generator(group, P, z, cof)) ABORT; \ 624 if (!EC_POINT_get_affine_coordinates_GF2m(group, P, x, y, ctx)) ABORT; \ 625 fprintf(stdout, "\n%s -- Generator:\n x = 0x", _name); \ 626 BN_print_fp(stdout, x); \ 627 fprintf(stdout, "\n y = 0x"); \ 628 BN_print_fp(stdout, y); \ 629 fprintf(stdout, "\n"); \ 630 /* G_y value taken from the standard: */ \ 631 if (!BN_hex2bn(&z, _y)) ABORT; \ 632 if (0 != BN_cmp(y, z)) ABORT; 633 #else 634 #define CHAR2_CURVE_TEST_INTERNAL(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \ 635 if (!BN_hex2bn(&x, _x)) ABORT; \ 636 if (!BN_hex2bn(&y, _y)) ABORT; \ 637 if (!EC_POINT_set_affine_coordinates_GF2m(group, P, x, y, ctx)) ABORT; \ 638 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT; \ 639 if (!BN_hex2bn(&z, _order)) ABORT; \ 640 if (!BN_hex2bn(&cof, _cof)) ABORT; \ 641 if (!EC_GROUP_set_generator(group, P, z, cof)) ABORT; \ 642 fprintf(stdout, "\n%s -- Generator:\n x = 0x", _name); \ 643 BN_print_fp(stdout, x); \ 644 fprintf(stdout, "\n y = 0x"); \ 645 BN_print_fp(stdout, y); \ 646 fprintf(stdout, "\n"); 647 #endif 648 649 #define CHAR2_CURVE_TEST(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \ 650 if (!BN_hex2bn(&p, _p)) ABORT; \ 651 if (!BN_hex2bn(&a, _a)) ABORT; \ 652 if (!BN_hex2bn(&b, _b)) ABORT; \ 653 if (!EC_GROUP_set_curve_GF2m(group, p, a, b, ctx)) ABORT; \ 654 CHAR2_CURVE_TEST_INTERNAL(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \ 655 fprintf(stdout, "verify degree ..."); \ 656 if (EC_GROUP_get_degree(group) != _degree) ABORT; \ 657 fprintf(stdout, " ok\n"); \ 658 group_order_tests(group); \ 659 if (!(_variable = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT; \ 660 if (!EC_GROUP_copy(_variable, group)) ABORT; \ 661 662 #ifndef OPENSSL_NO_EC2M 663 664 static void char2_field_tests(void) 665 { 666 BN_CTX *ctx = NULL; 667 BIGNUM *p, *a, *b; 668 EC_GROUP *group; 669 EC_GROUP *C2_K163 = NULL, *C2_K233 = NULL, *C2_K283 = NULL, *C2_K409 = NULL, *C2_K571 = NULL; 670 EC_GROUP *C2_B163 = NULL, *C2_B233 = NULL, *C2_B283 = NULL, *C2_B409 = NULL, *C2_B571 = NULL; 671 EC_POINT *P, *Q, *R; 672 BIGNUM *x, *y, *z, *cof; 673 unsigned char buf[100]; 674 size_t i, len; 675 int k; 676 677 #if 1 /* optional */ 678 ctx = BN_CTX_new(); 679 if (!ctx) ABORT; 680 #endif 681 682 p = BN_new(); 683 a = BN_new(); 684 b = BN_new(); 685 if (!p || !a || !b) ABORT; 686 687 if (!BN_hex2bn(&p, "13")) ABORT; 688 if (!BN_hex2bn(&a, "3")) ABORT; 689 if (!BN_hex2bn(&b, "1")) ABORT; 690 691 group = EC_GROUP_new(EC_GF2m_simple_method()); /* applications should use EC_GROUP_new_curve_GF2m 692 * so that the library gets to choose the EC_METHOD */ 693 if (!group) ABORT; 694 if (!EC_GROUP_set_curve_GF2m(group, p, a, b, ctx)) ABORT; 695 696 { 697 EC_GROUP *tmp; 698 tmp = EC_GROUP_new(EC_GROUP_method_of(group)); 699 if (!tmp) ABORT; 700 if (!EC_GROUP_copy(tmp, group)) ABORT; 701 EC_GROUP_free(group); 702 group = tmp; 703 } 704 705 if (!EC_GROUP_get_curve_GF2m(group, p, a, b, ctx)) ABORT; 706 707 fprintf(stdout, "Curve defined by Weierstrass equation\n y^2 + x*y = x^3 + a*x^2 + b (mod 0x"); 708 BN_print_fp(stdout, p); 709 fprintf(stdout, ")\n a = 0x"); 710 BN_print_fp(stdout, a); 711 fprintf(stdout, "\n b = 0x"); 712 BN_print_fp(stdout, b); 713 fprintf(stdout, "\n(0x... means binary polynomial)\n"); 714 715 P = EC_POINT_new(group); 716 Q = EC_POINT_new(group); 717 R = EC_POINT_new(group); 718 if (!P || !Q || !R) ABORT; 719 720 if (!EC_POINT_set_to_infinity(group, P)) ABORT; 721 if (!EC_POINT_is_at_infinity(group, P)) ABORT; 722 723 buf[0] = 0; 724 if (!EC_POINT_oct2point(group, Q, buf, 1, ctx)) ABORT; 725 726 if (!EC_POINT_add(group, P, P, Q, ctx)) ABORT; 727 if (!EC_POINT_is_at_infinity(group, P)) ABORT; 728 729 x = BN_new(); 730 y = BN_new(); 731 z = BN_new(); 732 cof = BN_new(); 733 if (!x || !y || !z || !cof) ABORT; 734 735 if (!BN_hex2bn(&x, "6")) ABORT; 736 /* Change test based on whether binary point compression is enabled or not. */ 737 #ifdef OPENSSL_EC_BIN_PT_COMP 738 if (!EC_POINT_set_compressed_coordinates_GF2m(group, Q, x, 1, ctx)) ABORT; 739 #else 740 if (!BN_hex2bn(&y, "8")) ABORT; 741 if (!EC_POINT_set_affine_coordinates_GF2m(group, Q, x, y, ctx)) ABORT; 742 #endif 743 if (!EC_POINT_is_on_curve(group, Q, ctx)) 744 { 745 /* Change test based on whether binary point compression is enabled or not. */ 746 #ifdef OPENSSL_EC_BIN_PT_COMP 747 if (!EC_POINT_get_affine_coordinates_GF2m(group, Q, x, y, ctx)) ABORT; 748 #endif 749 fprintf(stderr, "Point is not on curve: x = 0x"); 750 BN_print_fp(stderr, x); 751 fprintf(stderr, ", y = 0x"); 752 BN_print_fp(stderr, y); 753 fprintf(stderr, "\n"); 754 ABORT; 755 } 756 757 fprintf(stdout, "A cyclic subgroup:\n"); 758 k = 100; 759 do 760 { 761 if (k-- == 0) ABORT; 762 763 if (EC_POINT_is_at_infinity(group, P)) 764 fprintf(stdout, " point at infinity\n"); 765 else 766 { 767 if (!EC_POINT_get_affine_coordinates_GF2m(group, P, x, y, ctx)) ABORT; 768 769 fprintf(stdout, " x = 0x"); 770 BN_print_fp(stdout, x); 771 fprintf(stdout, ", y = 0x"); 772 BN_print_fp(stdout, y); 773 fprintf(stdout, "\n"); 774 } 775 776 if (!EC_POINT_copy(R, P)) ABORT; 777 if (!EC_POINT_add(group, P, P, Q, ctx)) ABORT; 778 } 779 while (!EC_POINT_is_at_infinity(group, P)); 780 781 if (!EC_POINT_add(group, P, Q, R, ctx)) ABORT; 782 if (!EC_POINT_is_at_infinity(group, P)) ABORT; 783 784 /* Change test based on whether binary point compression is enabled or not. */ 785 #ifdef OPENSSL_EC_BIN_PT_COMP 786 len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_COMPRESSED, buf, sizeof buf, ctx); 787 if (len == 0) ABORT; 788 if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT; 789 if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT; 790 fprintf(stdout, "Generator as octet string, compressed form:\n "); 791 for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]); 792 #endif 793 794 len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_UNCOMPRESSED, buf, sizeof buf, ctx); 795 if (len == 0) ABORT; 796 if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT; 797 if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT; 798 fprintf(stdout, "\nGenerator as octet string, uncompressed form:\n "); 799 for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]); 800 801 /* Change test based on whether binary point compression is enabled or not. */ 802 #ifdef OPENSSL_EC_BIN_PT_COMP 803 len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_HYBRID, buf, sizeof buf, ctx); 804 if (len == 0) ABORT; 805 if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT; 806 if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT; 807 fprintf(stdout, "\nGenerator as octet string, hybrid form:\n "); 808 for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]); 809 #endif 810 811 fprintf(stdout, "\n"); 812 813 if (!EC_POINT_invert(group, P, ctx)) ABORT; 814 if (0 != EC_POINT_cmp(group, P, R, ctx)) ABORT; 815 816 817 /* Curve K-163 (FIPS PUB 186-2, App. 6) */ 818 CHAR2_CURVE_TEST 819 ( 820 "NIST curve K-163", 821 "0800000000000000000000000000000000000000C9", 822 "1", 823 "1", 824 "02FE13C0537BBC11ACAA07D793DE4E6D5E5C94EEE8", 825 "0289070FB05D38FF58321F2E800536D538CCDAA3D9", 826 1, 827 "04000000000000000000020108A2E0CC0D99F8A5EF", 828 "2", 829 163, 830 C2_K163 831 ); 832 833 /* Curve B-163 (FIPS PUB 186-2, App. 6) */ 834 CHAR2_CURVE_TEST 835 ( 836 "NIST curve B-163", 837 "0800000000000000000000000000000000000000C9", 838 "1", 839 "020A601907B8C953CA1481EB10512F78744A3205FD", 840 "03F0EBA16286A2D57EA0991168D4994637E8343E36", 841 "00D51FBC6C71A0094FA2CDD545B11C5C0C797324F1", 842 1, 843 "040000000000000000000292FE77E70C12A4234C33", 844 "2", 845 163, 846 C2_B163 847 ); 848 849 /* Curve K-233 (FIPS PUB 186-2, App. 6) */ 850 CHAR2_CURVE_TEST 851 ( 852 "NIST curve K-233", 853 "020000000000000000000000000000000000000004000000000000000001", 854 "0", 855 "1", 856 "017232BA853A7E731AF129F22FF4149563A419C26BF50A4C9D6EEFAD6126", 857 "01DB537DECE819B7F70F555A67C427A8CD9BF18AEB9B56E0C11056FAE6A3", 858 0, 859 "008000000000000000000000000000069D5BB915BCD46EFB1AD5F173ABDF", 860 "4", 861 233, 862 C2_K233 863 ); 864 865 /* Curve B-233 (FIPS PUB 186-2, App. 6) */ 866 CHAR2_CURVE_TEST 867 ( 868 "NIST curve B-233", 869 "020000000000000000000000000000000000000004000000000000000001", 870 "000000000000000000000000000000000000000000000000000000000001", 871 "0066647EDE6C332C7F8C0923BB58213B333B20E9CE4281FE115F7D8F90AD", 872 "00FAC9DFCBAC8313BB2139F1BB755FEF65BC391F8B36F8F8EB7371FD558B", 873 "01006A08A41903350678E58528BEBF8A0BEFF867A7CA36716F7E01F81052", 874 1, 875 "01000000000000000000000000000013E974E72F8A6922031D2603CFE0D7", 876 "2", 877 233, 878 C2_B233 879 ); 880 881 /* Curve K-283 (FIPS PUB 186-2, App. 6) */ 882 CHAR2_CURVE_TEST 883 ( 884 "NIST curve K-283", 885 "0800000000000000000000000000000000000000000000000000000000000000000010A1", 886 "0", 887 "1", 888 "0503213F78CA44883F1A3B8162F188E553CD265F23C1567A16876913B0C2AC2458492836", 889 "01CCDA380F1C9E318D90F95D07E5426FE87E45C0E8184698E45962364E34116177DD2259", 890 0, 891 "01FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE9AE2ED07577265DFF7F94451E061E163C61", 892 "4", 893 283, 894 C2_K283 895 ); 896 897 /* Curve B-283 (FIPS PUB 186-2, App. 6) */ 898 CHAR2_CURVE_TEST 899 ( 900 "NIST curve B-283", 901 "0800000000000000000000000000000000000000000000000000000000000000000010A1", 902 "000000000000000000000000000000000000000000000000000000000000000000000001", 903 "027B680AC8B8596DA5A4AF8A19A0303FCA97FD7645309FA2A581485AF6263E313B79A2F5", 904 "05F939258DB7DD90E1934F8C70B0DFEC2EED25B8557EAC9C80E2E198F8CDBECD86B12053", 905 "03676854FE24141CB98FE6D4B20D02B4516FF702350EDDB0826779C813F0DF45BE8112F4", 906 1, 907 "03FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEF90399660FC938A90165B042A7CEFADB307", 908 "2", 909 283, 910 C2_B283 911 ); 912 913 /* Curve K-409 (FIPS PUB 186-2, App. 6) */ 914 CHAR2_CURVE_TEST 915 ( 916 "NIST curve K-409", 917 "02000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001", 918 "0", 919 "1", 920 "0060F05F658F49C1AD3AB1890F7184210EFD0987E307C84C27ACCFB8F9F67CC2C460189EB5AAAA62EE222EB1B35540CFE9023746", 921 "01E369050B7C4E42ACBA1DACBF04299C3460782F918EA427E6325165E9EA10E3DA5F6C42E9C55215AA9CA27A5863EC48D8E0286B", 922 1, 923 "007FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE5F83B2D4EA20400EC4557D5ED3E3E7CA5B4B5C83B8E01E5FCF", 924 "4", 925 409, 926 C2_K409 927 ); 928 929 /* Curve B-409 (FIPS PUB 186-2, App. 6) */ 930 CHAR2_CURVE_TEST 931 ( 932 "NIST curve B-409", 933 "02000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001", 934 "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001", 935 "0021A5C2C8EE9FEB5C4B9A753B7B476B7FD6422EF1F3DD674761FA99D6AC27C8A9A197B272822F6CD57A55AA4F50AE317B13545F", 936 "015D4860D088DDB3496B0C6064756260441CDE4AF1771D4DB01FFE5B34E59703DC255A868A1180515603AEAB60794E54BB7996A7", 937 "0061B1CFAB6BE5F32BBFA78324ED106A7636B9C5A7BD198D0158AA4F5488D08F38514F1FDF4B4F40D2181B3681C364BA0273C706", 938 1, 939 "010000000000000000000000000000000000000000000000000001E2AAD6A612F33307BE5FA47C3C9E052F838164CD37D9A21173", 940 "2", 941 409, 942 C2_B409 943 ); 944 945 /* Curve K-571 (FIPS PUB 186-2, App. 6) */ 946 CHAR2_CURVE_TEST 947 ( 948 "NIST curve K-571", 949 "80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425", 950 "0", 951 "1", 952 "026EB7A859923FBC82189631F8103FE4AC9CA2970012D5D46024804801841CA44370958493B205E647DA304DB4CEB08CBBD1BA39494776FB988B47174DCA88C7E2945283A01C8972", 953 "0349DC807F4FBF374F4AEADE3BCA95314DD58CEC9F307A54FFC61EFC006D8A2C9D4979C0AC44AEA74FBEBBB9F772AEDCB620B01A7BA7AF1B320430C8591984F601CD4C143EF1C7A3", 954 0, 955 "020000000000000000000000000000000000000000000000000000000000000000000000131850E1F19A63E4B391A8DB917F4138B630D84BE5D639381E91DEB45CFE778F637C1001", 956 "4", 957 571, 958 C2_K571 959 ); 960 961 /* Curve B-571 (FIPS PUB 186-2, App. 6) */ 962 CHAR2_CURVE_TEST 963 ( 964 "NIST curve B-571", 965 "80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425", 966 "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001", 967 "02F40E7E2221F295DE297117B7F3D62F5C6A97FFCB8CEFF1CD6BA8CE4A9A18AD84FFABBD8EFA59332BE7AD6756A66E294AFD185A78FF12AA520E4DE739BACA0C7FFEFF7F2955727A", 968 "0303001D34B856296C16C0D40D3CD7750A93D1D2955FA80AA5F40FC8DB7B2ABDBDE53950F4C0D293CDD711A35B67FB1499AE60038614F1394ABFA3B4C850D927E1E7769C8EEC2D19", 969 "037BF27342DA639B6DCCFFFEB73D69D78C6C27A6009CBBCA1980F8533921E8A684423E43BAB08A576291AF8F461BB2A8B3531D2F0485C19B16E2F1516E23DD3C1A4827AF1B8AC15B", 970 1, 971 "03FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE661CE18FF55987308059B186823851EC7DD9CA1161DE93D5174D66E8382E9BB2FE84E47", 972 "2", 973 571, 974 C2_B571 975 ); 976 977 /* more tests using the last curve */ 978 979 if (!EC_POINT_copy(Q, P)) ABORT; 980 if (EC_POINT_is_at_infinity(group, Q)) ABORT; 981 if (!EC_POINT_dbl(group, P, P, ctx)) ABORT; 982 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT; 983 if (!EC_POINT_invert(group, Q, ctx)) ABORT; /* P = -2Q */ 984 985 if (!EC_POINT_add(group, R, P, Q, ctx)) ABORT; 986 if (!EC_POINT_add(group, R, R, Q, ctx)) ABORT; 987 if (!EC_POINT_is_at_infinity(group, R)) ABORT; /* R = P + 2Q */ 988 989 { 990 const EC_POINT *points[3]; 991 const BIGNUM *scalars[3]; 992 993 if (EC_POINT_is_at_infinity(group, Q)) ABORT; 994 points[0] = Q; 995 points[1] = Q; 996 points[2] = Q; 997 998 if (!BN_add(y, z, BN_value_one())) ABORT; 999 if (BN_is_odd(y)) ABORT; 1000 if (!BN_rshift1(y, y)) ABORT; 1001 scalars[0] = y; /* (group order + 1)/2, so y*Q + y*Q = Q */ 1002 scalars[1] = y; 1003 1004 fprintf(stdout, "combined multiplication ..."); 1005 fflush(stdout); 1006 1007 /* z is still the group order */ 1008 if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) ABORT; 1009 if (!EC_POINTs_mul(group, R, z, 2, points, scalars, ctx)) ABORT; 1010 if (0 != EC_POINT_cmp(group, P, R, ctx)) ABORT; 1011 if (0 != EC_POINT_cmp(group, R, Q, ctx)) ABORT; 1012 1013 fprintf(stdout, "."); 1014 fflush(stdout); 1015 1016 if (!BN_pseudo_rand(y, BN_num_bits(y), 0, 0)) ABORT; 1017 if (!BN_add(z, z, y)) ABORT; 1018 BN_set_negative(z, 1); 1019 scalars[0] = y; 1020 scalars[1] = z; /* z = -(order + y) */ 1021 1022 if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) ABORT; 1023 if (!EC_POINT_is_at_infinity(group, P)) ABORT; 1024 1025 fprintf(stdout, "."); 1026 fflush(stdout); 1027 1028 if (!BN_pseudo_rand(x, BN_num_bits(y) - 1, 0, 0)) ABORT; 1029 if (!BN_add(z, x, y)) ABORT; 1030 BN_set_negative(z, 1); 1031 scalars[0] = x; 1032 scalars[1] = y; 1033 scalars[2] = z; /* z = -(x+y) */ 1034 1035 if (!EC_POINTs_mul(group, P, NULL, 3, points, scalars, ctx)) ABORT; 1036 if (!EC_POINT_is_at_infinity(group, P)) ABORT; 1037 1038 fprintf(stdout, " ok\n\n"); 1039 } 1040 1041 1042 if (ctx) 1043 BN_CTX_free(ctx); 1044 BN_free(p); BN_free(a); BN_free(b); 1045 EC_GROUP_free(group); 1046 EC_POINT_free(P); 1047 EC_POINT_free(Q); 1048 EC_POINT_free(R); 1049 BN_free(x); BN_free(y); BN_free(z); BN_free(cof); 1050 1051 if (C2_K163) EC_GROUP_free(C2_K163); 1052 if (C2_B163) EC_GROUP_free(C2_B163); 1053 if (C2_K233) EC_GROUP_free(C2_K233); 1054 if (C2_B233) EC_GROUP_free(C2_B233); 1055 if (C2_K283) EC_GROUP_free(C2_K283); 1056 if (C2_B283) EC_GROUP_free(C2_B283); 1057 if (C2_K409) EC_GROUP_free(C2_K409); 1058 if (C2_B409) EC_GROUP_free(C2_B409); 1059 if (C2_K571) EC_GROUP_free(C2_K571); 1060 if (C2_B571) EC_GROUP_free(C2_B571); 1061 1062 } 1063 #endif 1064 1065 static void internal_curve_test(void) 1066 { 1067 EC_builtin_curve *curves = NULL; 1068 size_t crv_len = 0, n = 0; 1069 int ok = 1; 1070 1071 crv_len = EC_get_builtin_curves(NULL, 0); 1072 1073 curves = reallocarray(NULL, sizeof(EC_builtin_curve), crv_len); 1074 1075 if (curves == NULL) 1076 return; 1077 1078 if (!EC_get_builtin_curves(curves, crv_len)) 1079 { 1080 free(curves); 1081 return; 1082 } 1083 1084 fprintf(stdout, "testing internal curves: "); 1085 1086 for (n = 0; n < crv_len; n++) 1087 { 1088 EC_GROUP *group = NULL; 1089 int nid = curves[n].nid; 1090 if ((group = EC_GROUP_new_by_curve_name(nid)) == NULL) 1091 { 1092 ok = 0; 1093 fprintf(stdout, "\nEC_GROUP_new_curve_name() failed with" 1094 " curve %s\n", OBJ_nid2sn(nid)); 1095 /* try next curve */ 1096 continue; 1097 } 1098 if (!EC_GROUP_check(group, NULL)) 1099 { 1100 ok = 0; 1101 fprintf(stdout, "\nEC_GROUP_check() failed with" 1102 " curve %s\n", OBJ_nid2sn(nid)); 1103 EC_GROUP_free(group); 1104 /* try the next curve */ 1105 continue; 1106 } 1107 fprintf(stdout, "."); 1108 fflush(stdout); 1109 EC_GROUP_free(group); 1110 } 1111 if (ok) 1112 fprintf(stdout, " ok\n\n"); 1113 else 1114 { 1115 fprintf(stdout, " failed\n\n"); 1116 ABORT; 1117 } 1118 free(curves); 1119 return; 1120 } 1121 1122 #ifndef OPENSSL_NO_EC_NISTP_64_GCC_128 1123 /* nistp_test_params contains magic numbers for testing our optimized 1124 * implementations of several NIST curves with characteristic > 3. */ 1125 struct nistp_test_params 1126 { 1127 const EC_METHOD* (*meth) (); 1128 int degree; 1129 /* Qx, Qy and D are taken from 1130 * http://csrc.nist.gov/groups/ST/toolkit/documents/Examples/ECDSA_Prime.pdf 1131 * Otherwise, values are standard curve parameters from FIPS 180-3 */ 1132 const char *p, *a, *b, *Qx, *Qy, *Gx, *Gy, *order, *d; 1133 }; 1134 1135 static const struct nistp_test_params nistp_tests_params[] = 1136 { 1137 { 1138 /* P-224 */ 1139 EC_GFp_nistp224_method, 1140 224, 1141 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001", /* p */ 1142 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE", /* a */ 1143 "B4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4", /* b */ 1144 "E84FB0B8E7000CB657D7973CF6B42ED78B301674276DF744AF130B3E", /* Qx */ 1145 "4376675C6FC5612C21A0FF2D2A89D2987DF7A2BC52183B5982298555", /* Qy */ 1146 "B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21", /* Gx */ 1147 "BD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34", /* Gy */ 1148 "FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D", /* order */ 1149 "3F0C488E987C80BE0FEE521F8D90BE6034EC69AE11CA72AA777481E8", /* d */ 1150 }, 1151 { 1152 /* P-256 */ 1153 EC_GFp_nistp256_method, 1154 256, 1155 "ffffffff00000001000000000000000000000000ffffffffffffffffffffffff", /* p */ 1156 "ffffffff00000001000000000000000000000000fffffffffffffffffffffffc", /* a */ 1157 "5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b", /* b */ 1158 "b7e08afdfe94bad3f1dc8c734798ba1c62b3a0ad1e9ea2a38201cd0889bc7a19", /* Qx */ 1159 "3603f747959dbf7a4bb226e41928729063adc7ae43529e61b563bbc606cc5e09", /* Qy */ 1160 "6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296", /* Gx */ 1161 "4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5", /* Gy */ 1162 "ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551", /* order */ 1163 "c477f9f65c22cce20657faa5b2d1d8122336f851a508a1ed04e479c34985bf96", /* d */ 1164 }, 1165 { 1166 /* P-521 */ 1167 EC_GFp_nistp521_method, 1168 521, 1169 "1ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff", /* p */ 1170 "1fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc", /* a */ 1171 "051953eb9618e1c9a1f929a21a0b68540eea2da725b99b315f3b8b489918ef109e156193951ec7e937b1652c0bd3bb1bf073573df883d2c34f1ef451fd46b503f00", /* b */ 1172 "0098e91eef9a68452822309c52fab453f5f117c1da8ed796b255e9ab8f6410cca16e59df403a6bdc6ca467a37056b1e54b3005d8ac030decfeb68df18b171885d5c4", /* Qx */ 1173 "0164350c321aecfc1cca1ba4364c9b15656150b4b78d6a48d7d28e7f31985ef17be8554376b72900712c4b83ad668327231526e313f5f092999a4632fd50d946bc2e", /* Qy */ 1174 "c6858e06b70404e9cd9e3ecb662395b4429c648139053fb521f828af606b4d3dbaa14b5e77efe75928fe1dc127a2ffa8de3348b3c1856a429bf97e7e31c2e5bd66", /* Gx */ 1175 "11839296a789a3bc0045c8a5fb42c7d1bd998f54449579b446817afbd17273e662c97ee72995ef42640c550b9013fad0761353c7086a272c24088be94769fd16650", /* Gy */ 1176 "1fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffa51868783bf2f966b7fcc0148f709a5d03bb5c9b8899c47aebb6fb71e91386409", /* order */ 1177 "0100085f47b8e1b8b11b7eb33028c0b2888e304bfc98501955b45bba1478dc184eeedf09b86a5f7c21994406072787205e69a63709fe35aa93ba333514b24f961722", /* d */ 1178 }, 1179 }; 1180 1181 void nistp_single_test(const struct nistp_test_params *test) 1182 { 1183 BN_CTX *ctx; 1184 BIGNUM *p, *a, *b, *x, *y, *n, *m, *order; 1185 EC_GROUP *NISTP; 1186 EC_POINT *G, *P, *Q, *Q_CHECK; 1187 1188 fprintf(stdout, "\nNIST curve P-%d (optimised implementation):\n", test->degree); 1189 ctx = BN_CTX_new(); 1190 p = BN_new(); 1191 a = BN_new(); 1192 b = BN_new(); 1193 x = BN_new(); y = BN_new(); 1194 m = BN_new(); n = BN_new(); order = BN_new(); 1195 1196 NISTP = EC_GROUP_new(test->meth()); 1197 if(!NISTP) ABORT; 1198 if (!BN_hex2bn(&p, test->p)) ABORT; 1199 if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT; 1200 if (!BN_hex2bn(&a, test->a)) ABORT; 1201 if (!BN_hex2bn(&b, test->b)) ABORT; 1202 if (!EC_GROUP_set_curve_GFp(NISTP, p, a, b, ctx)) ABORT; 1203 G = EC_POINT_new(NISTP); 1204 P = EC_POINT_new(NISTP); 1205 Q = EC_POINT_new(NISTP); 1206 Q_CHECK = EC_POINT_new(NISTP); 1207 if(!BN_hex2bn(&x, test->Qx)) ABORT; 1208 if(!BN_hex2bn(&y, test->Qy)) ABORT; 1209 if(!EC_POINT_set_affine_coordinates_GFp(NISTP, Q_CHECK, x, y, ctx)) ABORT; 1210 if (!BN_hex2bn(&x, test->Gx)) ABORT; 1211 if (!BN_hex2bn(&y, test->Gy)) ABORT; 1212 if (!EC_POINT_set_affine_coordinates_GFp(NISTP, G, x, y, ctx)) ABORT; 1213 if (!BN_hex2bn(&order, test->order)) ABORT; 1214 if (!EC_GROUP_set_generator(NISTP, G, order, BN_value_one())) ABORT; 1215 1216 fprintf(stdout, "verify degree ... "); 1217 if (EC_GROUP_get_degree(NISTP) != test->degree) ABORT; 1218 fprintf(stdout, "ok\n"); 1219 1220 fprintf(stdout, "NIST test vectors ... "); 1221 if (!BN_hex2bn(&n, test->d)) ABORT; 1222 /* fixed point multiplication */ 1223 EC_POINT_mul(NISTP, Q, n, NULL, NULL, ctx); 1224 if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) ABORT; 1225 /* random point multiplication */ 1226 EC_POINT_mul(NISTP, Q, NULL, G, n, ctx); 1227 if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) ABORT; 1228 1229 /* set generator to P = 2*G, where G is the standard generator */ 1230 if (!EC_POINT_dbl(NISTP, P, G, ctx)) ABORT; 1231 if (!EC_GROUP_set_generator(NISTP, P, order, BN_value_one())) ABORT; 1232 /* set the scalar to m=n/2, where n is the NIST test scalar */ 1233 if (!BN_rshift(m, n, 1)) ABORT; 1234 1235 /* test the non-standard generator */ 1236 /* fixed point multiplication */ 1237 EC_POINT_mul(NISTP, Q, m, NULL, NULL, ctx); 1238 if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) ABORT; 1239 /* random point multiplication */ 1240 EC_POINT_mul(NISTP, Q, NULL, P, m, ctx); 1241 if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) ABORT; 1242 1243 /* now repeat all tests with precomputation */ 1244 if (!EC_GROUP_precompute_mult(NISTP, ctx)) ABORT; 1245 1246 /* fixed point multiplication */ 1247 EC_POINT_mul(NISTP, Q, m, NULL, NULL, ctx); 1248 if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) ABORT; 1249 /* random point multiplication */ 1250 EC_POINT_mul(NISTP, Q, NULL, P, m, ctx); 1251 if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) ABORT; 1252 1253 /* reset generator */ 1254 if (!EC_GROUP_set_generator(NISTP, G, order, BN_value_one())) ABORT; 1255 /* fixed point multiplication */ 1256 EC_POINT_mul(NISTP, Q, n, NULL, NULL, ctx); 1257 if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) ABORT; 1258 /* random point multiplication */ 1259 EC_POINT_mul(NISTP, Q, NULL, G, n, ctx); 1260 if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) ABORT; 1261 1262 fprintf(stdout, "ok\n"); 1263 group_order_tests(NISTP); 1264 EC_GROUP_free(NISTP); 1265 EC_POINT_free(G); 1266 EC_POINT_free(P); 1267 EC_POINT_free(Q); 1268 EC_POINT_free(Q_CHECK); 1269 BN_free(n); 1270 BN_free(m); 1271 BN_free(p); 1272 BN_free(a); 1273 BN_free(b); 1274 BN_free(x); 1275 BN_free(y); 1276 BN_free(order); 1277 BN_CTX_free(ctx); 1278 } 1279 1280 void nistp_tests() 1281 { 1282 unsigned i; 1283 1284 for (i = 0; i < sizeof(nistp_tests_params) / sizeof(struct nistp_test_params); i++) 1285 { 1286 nistp_single_test(&nistp_tests_params[i]); 1287 } 1288 } 1289 #endif 1290 1291 int main(int argc, char *argv[]) 1292 { 1293 ERR_load_crypto_strings(); 1294 1295 prime_field_tests(); 1296 puts(""); 1297 #ifndef OPENSSL_NO_EC2M 1298 char2_field_tests(); 1299 #endif 1300 #ifndef OPENSSL_NO_EC_NISTP_64_GCC_128 1301 nistp_tests(); 1302 #endif 1303 /* test the internal curves */ 1304 internal_curve_test(); 1305 1306 #ifndef OPENSSL_NO_ENGINE 1307 ENGINE_cleanup(); 1308 #endif 1309 CRYPTO_cleanup_all_ex_data(); 1310 ERR_free_strings(); 1311 ERR_remove_thread_state(NULL); 1312 CRYPTO_mem_leaks_fp(stderr); 1313 1314 return 0; 1315 } 1316