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| 1 /* crypto/ec/ecp_smpl.c */ | |
| 2 /* Includes code written by Lenka Fibikova <fibikova@exp-math.uni-essen.de> | |
| 3 * for the OpenSSL project. | |
| 4 * Includes code written by Bodo Moeller for the OpenSSL project. | |
| 5 */ | |
| 6 /* ==================================================================== | |
| 7 * Copyright (c) 1998-2002 The OpenSSL Project. All rights reserved. | |
| 8 * | |
| 9 * Redistribution and use in source and binary forms, with or without | |
| 10 * modification, are permitted provided that the following conditions | |
| 11 * are met: | |
| 12 * | |
| 13 * 1. Redistributions of source code must retain the above copyright | |
| 14 * notice, this list of conditions and the following disclaimer. | |
| 15 * | |
| 16 * 2. Redistributions in binary form must reproduce the above copyright | |
| 17 * notice, this list of conditions and the following disclaimer in | |
| 18 * the documentation and/or other materials provided with the | |
| 19 * distribution. | |
| 20 * | |
| 21 * 3. All advertising materials mentioning features or use of this | |
| 22 * software must display the following acknowledgment: | |
| 23 * "This product includes software developed by the OpenSSL Project | |
| 24 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" | |
| 25 * | |
| 26 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to | |
| 27 * endorse or promote products derived from this software without | |
| 28 * prior written permission. For written permission, please contact | |
| 29 * openssl-core@openssl.org. | |
| 30 * | |
| 31 * 5. Products derived from this software may not be called "OpenSSL" | |
| 32 * nor may "OpenSSL" appear in their names without prior written | |
| 33 * permission of the OpenSSL Project. | |
| 34 * | |
| 35 * 6. Redistributions of any form whatsoever must retain the following | |
| 36 * acknowledgment: | |
| 37 * "This product includes software developed by the OpenSSL Project | |
| 38 * for use in the OpenSSL Toolkit (http://www.openssl.org/)" | |
| 39 * | |
| 40 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY | |
| 41 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE | |
| 42 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR | |
| 43 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR | |
| 44 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, | |
| 45 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT | |
| 46 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; | |
| 47 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) | |
| 48 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, | |
| 49 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) | |
| 50 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED | |
| 51 * OF THE POSSIBILITY OF SUCH DAMAGE. | |
| 52 * ==================================================================== | |
| 53 * | |
| 54 * This product includes cryptographic software written by Eric Young | |
| 55 * (eay@cryptsoft.com). This product includes software written by Tim | |
| 56 * Hudson (tjh@cryptsoft.com). | |
| 57 * | |
| 58 */ | |
| 59 /* ==================================================================== | |
| 60 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. | |
| 61 * Portions of this software developed by SUN MICROSYSTEMS, INC., | |
| 62 * and contributed to the OpenSSL project. | |
| 63 */ | |
| 64 | |
| 65 #include <openssl/err.h> | |
| 66 #include <openssl/symhacks.h> | |
| 67 | |
| 68 #ifdef OPENSSL_FIPS | |
| 69 #include <openssl/fips.h> | |
| 70 #endif | |
| 71 | |
| 72 #include "ec_lcl.h" | |
| 73 | |
| 74 const EC_METHOD *EC_GFp_simple_method(void) | |
| 75 { | |
| 76 #ifdef OPENSSL_FIPS | |
| 77 return fips_ec_gfp_simple_method(); | |
| 78 #else | |
| 79 static const EC_METHOD ret = { | |
| 80 EC_FLAGS_DEFAULT_OCT, | |
| 81 NID_X9_62_prime_field, | |
| 82 ec_GFp_simple_group_init, | |
| 83 ec_GFp_simple_group_finish, | |
| 84 ec_GFp_simple_group_clear_finish, | |
| 85 ec_GFp_simple_group_copy, | |
| 86 ec_GFp_simple_group_set_curve, | |
| 87 ec_GFp_simple_group_get_curve, | |
| 88 ec_GFp_simple_group_get_degree, | |
| 89 ec_GFp_simple_group_check_discriminant, | |
| 90 ec_GFp_simple_point_init, | |
| 91 ec_GFp_simple_point_finish, | |
| 92 ec_GFp_simple_point_clear_finish, | |
| 93 ec_GFp_simple_point_copy, | |
| 94 ec_GFp_simple_point_set_to_infinity, | |
| 95 ec_GFp_simple_set_Jprojective_coordinates_GFp, | |
| 96 ec_GFp_simple_get_Jprojective_coordinates_GFp, | |
| 97 ec_GFp_simple_point_set_affine_coordinates, | |
| 98 ec_GFp_simple_point_get_affine_coordinates, | |
| 99 0,0,0, | |
| 100 ec_GFp_simple_add, | |
| 101 ec_GFp_simple_dbl, | |
| 102 ec_GFp_simple_invert, | |
| 103 ec_GFp_simple_is_at_infinity, | |
| 104 ec_GFp_simple_is_on_curve, | |
| 105 ec_GFp_simple_cmp, | |
| 106 ec_GFp_simple_make_affine, | |
| 107 ec_GFp_simple_points_make_affine, | |
| 108 0 /* mul */, | |
| 109 0 /* precompute_mult */, | |
| 110 0 /* have_precompute_mult */, | |
| 111 ec_GFp_simple_field_mul, | |
| 112 ec_GFp_simple_field_sqr, | |
| 113 0 /* field_div */, | |
| 114 0 /* field_encode */, | |
| 115 0 /* field_decode */, | |
| 116 0 /* field_set_to_one */ }; | |
| 117 | |
| 118 return &ret; | |
| 119 #endif | |
| 120 } | |
| 121 | |
| 122 | |
| 123 /* Most method functions in this file are designed to work with | |
| 124 * non-trivial representations of field elements if necessary | |
| 125 * (see ecp_mont.c): while standard modular addition and subtraction | |
| 126 * are used, the field_mul and field_sqr methods will be used for | |
| 127 * multiplication, and field_encode and field_decode (if defined) | |
| 128 * will be used for converting between representations. | |
| 129 | |
| 130 * Functions ec_GFp_simple_points_make_affine() and | |
| 131 * ec_GFp_simple_point_get_affine_coordinates() specifically assume | |
| 132 * that if a non-trivial representation is used, it is a Montgomery | |
| 133 * representation (i.e. 'encoding' means multiplying by some factor R). | |
| 134 */ | |
| 135 | |
| 136 | |
| 137 int ec_GFp_simple_group_init(EC_GROUP *group) | |
| 138 { | |
| 139 BN_init(&group->field); | |
| 140 BN_init(&group->a); | |
| 141 BN_init(&group->b); | |
| 142 group->a_is_minus3 = 0; | |
| 143 return 1; | |
| 144 } | |
| 145 | |
| 146 | |
| 147 void ec_GFp_simple_group_finish(EC_GROUP *group) | |
| 148 { | |
| 149 BN_free(&group->field); | |
| 150 BN_free(&group->a); | |
| 151 BN_free(&group->b); | |
| 152 } | |
| 153 | |
| 154 | |
| 155 void ec_GFp_simple_group_clear_finish(EC_GROUP *group) | |
| 156 { | |
| 157 BN_clear_free(&group->field); | |
| 158 BN_clear_free(&group->a); | |
| 159 BN_clear_free(&group->b); | |
| 160 } | |
| 161 | |
| 162 | |
| 163 int ec_GFp_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src) | |
| 164 { | |
| 165 if (!BN_copy(&dest->field, &src->field)) return 0; | |
| 166 if (!BN_copy(&dest->a, &src->a)) return 0; | |
| 167 if (!BN_copy(&dest->b, &src->b)) return 0; | |
| 168 | |
| 169 dest->a_is_minus3 = src->a_is_minus3; | |
| 170 | |
| 171 return 1; | |
| 172 } | |
| 173 | |
| 174 | |
| 175 int ec_GFp_simple_group_set_curve(EC_GROUP *group, | |
| 176 const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) | |
| 177 { | |
| 178 int ret = 0; | |
| 179 BN_CTX *new_ctx = NULL; | |
| 180 BIGNUM *tmp_a; | |
| 181 | |
| 182 /* p must be a prime > 3 */ | |
| 183 if (BN_num_bits(p) <= 2 || !BN_is_odd(p)) | |
| 184 { | |
| 185 ECerr(EC_F_EC_GFP_SIMPLE_GROUP_SET_CURVE, EC_R_INVALID_FIELD); | |
| 186 return 0; | |
| 187 } | |
| 188 | |
| 189 if (ctx == NULL) | |
| 190 { | |
| 191 ctx = new_ctx = BN_CTX_new(); | |
| 192 if (ctx == NULL) | |
| 193 return 0; | |
| 194 } | |
| 195 | |
| 196 BN_CTX_start(ctx); | |
| 197 tmp_a = BN_CTX_get(ctx); | |
| 198 if (tmp_a == NULL) goto err; | |
| 199 | |
| 200 /* group->field */ | |
| 201 if (!BN_copy(&group->field, p)) goto err; | |
| 202 BN_set_negative(&group->field, 0); | |
| 203 | |
| 204 /* group->a */ | |
| 205 if (!BN_nnmod(tmp_a, a, p, ctx)) goto err; | |
| 206 if (group->meth->field_encode) | |
| 207 { if (!group->meth->field_encode(group, &group->a, tmp_a, ctx))
goto err; } | |
| 208 else | |
| 209 if (!BN_copy(&group->a, tmp_a)) goto err; | |
| 210 | |
| 211 /* group->b */ | |
| 212 if (!BN_nnmod(&group->b, b, p, ctx)) goto err; | |
| 213 if (group->meth->field_encode) | |
| 214 if (!group->meth->field_encode(group, &group->b, &group->b, ctx)
) goto err; | |
| 215 | |
| 216 /* group->a_is_minus3 */ | |
| 217 if (!BN_add_word(tmp_a, 3)) goto err; | |
| 218 group->a_is_minus3 = (0 == BN_cmp(tmp_a, &group->field)); | |
| 219 | |
| 220 ret = 1; | |
| 221 | |
| 222 err: | |
| 223 BN_CTX_end(ctx); | |
| 224 if (new_ctx != NULL) | |
| 225 BN_CTX_free(new_ctx); | |
| 226 return ret; | |
| 227 } | |
| 228 | |
| 229 | |
| 230 int ec_GFp_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, B
IGNUM *b, BN_CTX *ctx) | |
| 231 { | |
| 232 int ret = 0; | |
| 233 BN_CTX *new_ctx = NULL; | |
| 234 | |
| 235 if (p != NULL) | |
| 236 { | |
| 237 if (!BN_copy(p, &group->field)) return 0; | |
| 238 } | |
| 239 | |
| 240 if (a != NULL || b != NULL) | |
| 241 { | |
| 242 if (group->meth->field_decode) | |
| 243 { | |
| 244 if (ctx == NULL) | |
| 245 { | |
| 246 ctx = new_ctx = BN_CTX_new(); | |
| 247 if (ctx == NULL) | |
| 248 return 0; | |
| 249 } | |
| 250 if (a != NULL) | |
| 251 { | |
| 252 if (!group->meth->field_decode(group, a, &group-
>a, ctx)) goto err; | |
| 253 } | |
| 254 if (b != NULL) | |
| 255 { | |
| 256 if (!group->meth->field_decode(group, b, &group-
>b, ctx)) goto err; | |
| 257 } | |
| 258 } | |
| 259 else | |
| 260 { | |
| 261 if (a != NULL) | |
| 262 { | |
| 263 if (!BN_copy(a, &group->a)) goto err; | |
| 264 } | |
| 265 if (b != NULL) | |
| 266 { | |
| 267 if (!BN_copy(b, &group->b)) goto err; | |
| 268 } | |
| 269 } | |
| 270 } | |
| 271 | |
| 272 ret = 1; | |
| 273 | |
| 274 err: | |
| 275 if (new_ctx) | |
| 276 BN_CTX_free(new_ctx); | |
| 277 return ret; | |
| 278 } | |
| 279 | |
| 280 | |
| 281 int ec_GFp_simple_group_get_degree(const EC_GROUP *group) | |
| 282 { | |
| 283 return BN_num_bits(&group->field); | |
| 284 } | |
| 285 | |
| 286 | |
| 287 int ec_GFp_simple_group_check_discriminant(const EC_GROUP *group, BN_CTX *ctx) | |
| 288 { | |
| 289 int ret = 0; | |
| 290 BIGNUM *a,*b,*order,*tmp_1,*tmp_2; | |
| 291 const BIGNUM *p = &group->field; | |
| 292 BN_CTX *new_ctx = NULL; | |
| 293 | |
| 294 if (ctx == NULL) | |
| 295 { | |
| 296 ctx = new_ctx = BN_CTX_new(); | |
| 297 if (ctx == NULL) | |
| 298 { | |
| 299 ECerr(EC_F_EC_GFP_SIMPLE_GROUP_CHECK_DISCRIMINANT, ERR_R
_MALLOC_FAILURE); | |
| 300 goto err; | |
| 301 } | |
| 302 } | |
| 303 BN_CTX_start(ctx); | |
| 304 a = BN_CTX_get(ctx); | |
| 305 b = BN_CTX_get(ctx); | |
| 306 tmp_1 = BN_CTX_get(ctx); | |
| 307 tmp_2 = BN_CTX_get(ctx); | |
| 308 order = BN_CTX_get(ctx); | |
| 309 if (order == NULL) goto err; | |
| 310 | |
| 311 if (group->meth->field_decode) | |
| 312 { | |
| 313 if (!group->meth->field_decode(group, a, &group->a, ctx)) goto e
rr; | |
| 314 if (!group->meth->field_decode(group, b, &group->b, ctx)) goto e
rr; | |
| 315 } | |
| 316 else | |
| 317 { | |
| 318 if (!BN_copy(a, &group->a)) goto err; | |
| 319 if (!BN_copy(b, &group->b)) goto err; | |
| 320 } | |
| 321 | |
| 322 /* check the discriminant: | |
| 323 * y^2 = x^3 + a*x + b is an elliptic curve <=> 4*a^3 + 27*b^2 != 0 (mod
p) | |
| 324 * 0 =< a, b < p */ | |
| 325 if (BN_is_zero(a)) | |
| 326 { | |
| 327 if (BN_is_zero(b)) goto err; | |
| 328 } | |
| 329 else if (!BN_is_zero(b)) | |
| 330 { | |
| 331 if (!BN_mod_sqr(tmp_1, a, p, ctx)) goto err; | |
| 332 if (!BN_mod_mul(tmp_2, tmp_1, a, p, ctx)) goto err; | |
| 333 if (!BN_lshift(tmp_1, tmp_2, 2)) goto err; | |
| 334 /* tmp_1 = 4*a^3 */ | |
| 335 | |
| 336 if (!BN_mod_sqr(tmp_2, b, p, ctx)) goto err; | |
| 337 if (!BN_mul_word(tmp_2, 27)) goto err; | |
| 338 /* tmp_2 = 27*b^2 */ | |
| 339 | |
| 340 if (!BN_mod_add(a, tmp_1, tmp_2, p, ctx)) goto err; | |
| 341 if (BN_is_zero(a)) goto err; | |
| 342 } | |
| 343 ret = 1; | |
| 344 | |
| 345 err: | |
| 346 if (ctx != NULL) | |
| 347 BN_CTX_end(ctx); | |
| 348 if (new_ctx != NULL) | |
| 349 BN_CTX_free(new_ctx); | |
| 350 return ret; | |
| 351 } | |
| 352 | |
| 353 | |
| 354 int ec_GFp_simple_point_init(EC_POINT *point) | |
| 355 { | |
| 356 BN_init(&point->X); | |
| 357 BN_init(&point->Y); | |
| 358 BN_init(&point->Z); | |
| 359 point->Z_is_one = 0; | |
| 360 | |
| 361 return 1; | |
| 362 } | |
| 363 | |
| 364 | |
| 365 void ec_GFp_simple_point_finish(EC_POINT *point) | |
| 366 { | |
| 367 BN_free(&point->X); | |
| 368 BN_free(&point->Y); | |
| 369 BN_free(&point->Z); | |
| 370 } | |
| 371 | |
| 372 | |
| 373 void ec_GFp_simple_point_clear_finish(EC_POINT *point) | |
| 374 { | |
| 375 BN_clear_free(&point->X); | |
| 376 BN_clear_free(&point->Y); | |
| 377 BN_clear_free(&point->Z); | |
| 378 point->Z_is_one = 0; | |
| 379 } | |
| 380 | |
| 381 | |
| 382 int ec_GFp_simple_point_copy(EC_POINT *dest, const EC_POINT *src) | |
| 383 { | |
| 384 if (!BN_copy(&dest->X, &src->X)) return 0; | |
| 385 if (!BN_copy(&dest->Y, &src->Y)) return 0; | |
| 386 if (!BN_copy(&dest->Z, &src->Z)) return 0; | |
| 387 dest->Z_is_one = src->Z_is_one; | |
| 388 | |
| 389 return 1; | |
| 390 } | |
| 391 | |
| 392 | |
| 393 int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *group, EC_POINT *point) | |
| 394 { | |
| 395 point->Z_is_one = 0; | |
| 396 BN_zero(&point->Z); | |
| 397 return 1; | |
| 398 } | |
| 399 | |
| 400 | |
| 401 int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *group, EC_POIN
T *point, | |
| 402 const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *ctx) | |
| 403 { | |
| 404 BN_CTX *new_ctx = NULL; | |
| 405 int ret = 0; | |
| 406 | |
| 407 if (ctx == NULL) | |
| 408 { | |
| 409 ctx = new_ctx = BN_CTX_new(); | |
| 410 if (ctx == NULL) | |
| 411 return 0; | |
| 412 } | |
| 413 | |
| 414 if (x != NULL) | |
| 415 { | |
| 416 if (!BN_nnmod(&point->X, x, &group->field, ctx)) goto err; | |
| 417 if (group->meth->field_encode) | |
| 418 { | |
| 419 if (!group->meth->field_encode(group, &point->X, &point-
>X, ctx)) goto err; | |
| 420 } | |
| 421 } | |
| 422 | |
| 423 if (y != NULL) | |
| 424 { | |
| 425 if (!BN_nnmod(&point->Y, y, &group->field, ctx)) goto err; | |
| 426 if (group->meth->field_encode) | |
| 427 { | |
| 428 if (!group->meth->field_encode(group, &point->Y, &point-
>Y, ctx)) goto err; | |
| 429 } | |
| 430 } | |
| 431 | |
| 432 if (z != NULL) | |
| 433 { | |
| 434 int Z_is_one; | |
| 435 | |
| 436 if (!BN_nnmod(&point->Z, z, &group->field, ctx)) goto err; | |
| 437 Z_is_one = BN_is_one(&point->Z); | |
| 438 if (group->meth->field_encode) | |
| 439 { | |
| 440 if (Z_is_one && (group->meth->field_set_to_one != 0)) | |
| 441 { | |
| 442 if (!group->meth->field_set_to_one(group, &point
->Z, ctx)) goto err; | |
| 443 } | |
| 444 else | |
| 445 { | |
| 446 if (!group->meth->field_encode(group, &point->Z,
&point->Z, ctx)) goto err; | |
| 447 } | |
| 448 } | |
| 449 point->Z_is_one = Z_is_one; | |
| 450 } | |
| 451 | |
| 452 ret = 1; | |
| 453 | |
| 454 err: | |
| 455 if (new_ctx != NULL) | |
| 456 BN_CTX_free(new_ctx); | |
| 457 return ret; | |
| 458 } | |
| 459 | |
| 460 | |
| 461 int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *group, const E
C_POINT *point, | |
| 462 BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *ctx) | |
| 463 { | |
| 464 BN_CTX *new_ctx = NULL; | |
| 465 int ret = 0; | |
| 466 | |
| 467 if (group->meth->field_decode != 0) | |
| 468 { | |
| 469 if (ctx == NULL) | |
| 470 { | |
| 471 ctx = new_ctx = BN_CTX_new(); | |
| 472 if (ctx == NULL) | |
| 473 return 0; | |
| 474 } | |
| 475 | |
| 476 if (x != NULL) | |
| 477 { | |
| 478 if (!group->meth->field_decode(group, x, &point->X, ctx)
) goto err; | |
| 479 } | |
| 480 if (y != NULL) | |
| 481 { | |
| 482 if (!group->meth->field_decode(group, y, &point->Y, ctx)
) goto err; | |
| 483 } | |
| 484 if (z != NULL) | |
| 485 { | |
| 486 if (!group->meth->field_decode(group, z, &point->Z, ctx)
) goto err; | |
| 487 } | |
| 488 } | |
| 489 else | |
| 490 { | |
| 491 if (x != NULL) | |
| 492 { | |
| 493 if (!BN_copy(x, &point->X)) goto err; | |
| 494 } | |
| 495 if (y != NULL) | |
| 496 { | |
| 497 if (!BN_copy(y, &point->Y)) goto err; | |
| 498 } | |
| 499 if (z != NULL) | |
| 500 { | |
| 501 if (!BN_copy(z, &point->Z)) goto err; | |
| 502 } | |
| 503 } | |
| 504 | |
| 505 ret = 1; | |
| 506 | |
| 507 err: | |
| 508 if (new_ctx != NULL) | |
| 509 BN_CTX_free(new_ctx); | |
| 510 return ret; | |
| 511 } | |
| 512 | |
| 513 | |
| 514 int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *group, EC_POINT *
point, | |
| 515 const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx) | |
| 516 { | |
| 517 if (x == NULL || y == NULL) | |
| 518 { | |
| 519 /* unlike for projective coordinates, we do not tolerate this */ | |
| 520 ECerr(EC_F_EC_GFP_SIMPLE_POINT_SET_AFFINE_COORDINATES, ERR_R_PAS
SED_NULL_PARAMETER); | |
| 521 return 0; | |
| 522 } | |
| 523 | |
| 524 return EC_POINT_set_Jprojective_coordinates_GFp(group, point, x, y, BN_v
alue_one(), ctx); | |
| 525 } | |
| 526 | |
| 527 | |
| 528 int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *group, const EC_P
OINT *point, | |
| 529 BIGNUM *x, BIGNUM *y, BN_CTX *ctx) | |
| 530 { | |
| 531 BN_CTX *new_ctx = NULL; | |
| 532 BIGNUM *Z, *Z_1, *Z_2, *Z_3; | |
| 533 const BIGNUM *Z_; | |
| 534 int ret = 0; | |
| 535 | |
| 536 if (EC_POINT_is_at_infinity(group, point)) | |
| 537 { | |
| 538 ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES, EC_R_POIN
T_AT_INFINITY); | |
| 539 return 0; | |
| 540 } | |
| 541 | |
| 542 if (ctx == NULL) | |
| 543 { | |
| 544 ctx = new_ctx = BN_CTX_new(); | |
| 545 if (ctx == NULL) | |
| 546 return 0; | |
| 547 } | |
| 548 | |
| 549 BN_CTX_start(ctx); | |
| 550 Z = BN_CTX_get(ctx); | |
| 551 Z_1 = BN_CTX_get(ctx); | |
| 552 Z_2 = BN_CTX_get(ctx); | |
| 553 Z_3 = BN_CTX_get(ctx); | |
| 554 if (Z_3 == NULL) goto err; | |
| 555 | |
| 556 /* transform (X, Y, Z) into (x, y) := (X/Z^2, Y/Z^3) */ | |
| 557 | |
| 558 if (group->meth->field_decode) | |
| 559 { | |
| 560 if (!group->meth->field_decode(group, Z, &point->Z, ctx)) goto e
rr; | |
| 561 Z_ = Z; | |
| 562 } | |
| 563 else | |
| 564 { | |
| 565 Z_ = &point->Z; | |
| 566 } | |
| 567 | |
| 568 if (BN_is_one(Z_)) | |
| 569 { | |
| 570 if (group->meth->field_decode) | |
| 571 { | |
| 572 if (x != NULL) | |
| 573 { | |
| 574 if (!group->meth->field_decode(group, x, &point-
>X, ctx)) goto err; | |
| 575 } | |
| 576 if (y != NULL) | |
| 577 { | |
| 578 if (!group->meth->field_decode(group, y, &point-
>Y, ctx)) goto err; | |
| 579 } | |
| 580 } | |
| 581 else | |
| 582 { | |
| 583 if (x != NULL) | |
| 584 { | |
| 585 if (!BN_copy(x, &point->X)) goto err; | |
| 586 } | |
| 587 if (y != NULL) | |
| 588 { | |
| 589 if (!BN_copy(y, &point->Y)) goto err; | |
| 590 } | |
| 591 } | |
| 592 } | |
| 593 else | |
| 594 { | |
| 595 if (!BN_mod_inverse(Z_1, Z_, &group->field, ctx)) | |
| 596 { | |
| 597 ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES, E
RR_R_BN_LIB); | |
| 598 goto err; | |
| 599 } | |
| 600 | |
| 601 if (group->meth->field_encode == 0) | |
| 602 { | |
| 603 /* field_sqr works on standard representation */ | |
| 604 if (!group->meth->field_sqr(group, Z_2, Z_1, ctx)) goto
err; | |
| 605 } | |
| 606 else | |
| 607 { | |
| 608 if (!BN_mod_sqr(Z_2, Z_1, &group->field, ctx)) goto err; | |
| 609 } | |
| 610 | |
| 611 if (x != NULL) | |
| 612 { | |
| 613 /* in the Montgomery case, field_mul will cancel out Mon
tgomery factor in X: */ | |
| 614 if (!group->meth->field_mul(group, x, &point->X, Z_2, ct
x)) goto err; | |
| 615 } | |
| 616 | |
| 617 if (y != NULL) | |
| 618 { | |
| 619 if (group->meth->field_encode == 0) | |
| 620 { | |
| 621 /* field_mul works on standard representation */ | |
| 622 if (!group->meth->field_mul(group, Z_3, Z_2, Z_1
, ctx)) goto err; | |
| 623 } | |
| 624 else | |
| 625 { | |
| 626 if (!BN_mod_mul(Z_3, Z_2, Z_1, &group->field, ct
x)) goto err; | |
| 627 } | |
| 628 | |
| 629 /* in the Montgomery case, field_mul will cancel out Mon
tgomery factor in Y: */ | |
| 630 if (!group->meth->field_mul(group, y, &point->Y, Z_3, ct
x)) goto err; | |
| 631 } | |
| 632 } | |
| 633 | |
| 634 ret = 1; | |
| 635 | |
| 636 err: | |
| 637 BN_CTX_end(ctx); | |
| 638 if (new_ctx != NULL) | |
| 639 BN_CTX_free(new_ctx); | |
| 640 return ret; | |
| 641 } | |
| 642 | |
| 643 int ec_GFp_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, con
st EC_POINT *b, BN_CTX *ctx) | |
| 644 { | |
| 645 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNU
M *, BN_CTX *); | |
| 646 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); | |
| 647 const BIGNUM *p; | |
| 648 BN_CTX *new_ctx = NULL; | |
| 649 BIGNUM *n0, *n1, *n2, *n3, *n4, *n5, *n6; | |
| 650 int ret = 0; | |
| 651 | |
| 652 if (a == b) | |
| 653 return EC_POINT_dbl(group, r, a, ctx); | |
| 654 if (EC_POINT_is_at_infinity(group, a)) | |
| 655 return EC_POINT_copy(r, b); | |
| 656 if (EC_POINT_is_at_infinity(group, b)) | |
| 657 return EC_POINT_copy(r, a); | |
| 658 | |
| 659 field_mul = group->meth->field_mul; | |
| 660 field_sqr = group->meth->field_sqr; | |
| 661 p = &group->field; | |
| 662 | |
| 663 if (ctx == NULL) | |
| 664 { | |
| 665 ctx = new_ctx = BN_CTX_new(); | |
| 666 if (ctx == NULL) | |
| 667 return 0; | |
| 668 } | |
| 669 | |
| 670 BN_CTX_start(ctx); | |
| 671 n0 = BN_CTX_get(ctx); | |
| 672 n1 = BN_CTX_get(ctx); | |
| 673 n2 = BN_CTX_get(ctx); | |
| 674 n3 = BN_CTX_get(ctx); | |
| 675 n4 = BN_CTX_get(ctx); | |
| 676 n5 = BN_CTX_get(ctx); | |
| 677 n6 = BN_CTX_get(ctx); | |
| 678 if (n6 == NULL) goto end; | |
| 679 | |
| 680 /* Note that in this function we must not read components of 'a' or 'b' | |
| 681 * once we have written the corresponding components of 'r'. | |
| 682 * ('r' might be one of 'a' or 'b'.) | |
| 683 */ | |
| 684 | |
| 685 /* n1, n2 */ | |
| 686 if (b->Z_is_one) | |
| 687 { | |
| 688 if (!BN_copy(n1, &a->X)) goto end; | |
| 689 if (!BN_copy(n2, &a->Y)) goto end; | |
| 690 /* n1 = X_a */ | |
| 691 /* n2 = Y_a */ | |
| 692 } | |
| 693 else | |
| 694 { | |
| 695 if (!field_sqr(group, n0, &b->Z, ctx)) goto end; | |
| 696 if (!field_mul(group, n1, &a->X, n0, ctx)) goto end; | |
| 697 /* n1 = X_a * Z_b^2 */ | |
| 698 | |
| 699 if (!field_mul(group, n0, n0, &b->Z, ctx)) goto end; | |
| 700 if (!field_mul(group, n2, &a->Y, n0, ctx)) goto end; | |
| 701 /* n2 = Y_a * Z_b^3 */ | |
| 702 } | |
| 703 | |
| 704 /* n3, n4 */ | |
| 705 if (a->Z_is_one) | |
| 706 { | |
| 707 if (!BN_copy(n3, &b->X)) goto end; | |
| 708 if (!BN_copy(n4, &b->Y)) goto end; | |
| 709 /* n3 = X_b */ | |
| 710 /* n4 = Y_b */ | |
| 711 } | |
| 712 else | |
| 713 { | |
| 714 if (!field_sqr(group, n0, &a->Z, ctx)) goto end; | |
| 715 if (!field_mul(group, n3, &b->X, n0, ctx)) goto end; | |
| 716 /* n3 = X_b * Z_a^2 */ | |
| 717 | |
| 718 if (!field_mul(group, n0, n0, &a->Z, ctx)) goto end; | |
| 719 if (!field_mul(group, n4, &b->Y, n0, ctx)) goto end; | |
| 720 /* n4 = Y_b * Z_a^3 */ | |
| 721 } | |
| 722 | |
| 723 /* n5, n6 */ | |
| 724 if (!BN_mod_sub_quick(n5, n1, n3, p)) goto end; | |
| 725 if (!BN_mod_sub_quick(n6, n2, n4, p)) goto end; | |
| 726 /* n5 = n1 - n3 */ | |
| 727 /* n6 = n2 - n4 */ | |
| 728 | |
| 729 if (BN_is_zero(n5)) | |
| 730 { | |
| 731 if (BN_is_zero(n6)) | |
| 732 { | |
| 733 /* a is the same point as b */ | |
| 734 BN_CTX_end(ctx); | |
| 735 ret = EC_POINT_dbl(group, r, a, ctx); | |
| 736 ctx = NULL; | |
| 737 goto end; | |
| 738 } | |
| 739 else | |
| 740 { | |
| 741 /* a is the inverse of b */ | |
| 742 BN_zero(&r->Z); | |
| 743 r->Z_is_one = 0; | |
| 744 ret = 1; | |
| 745 goto end; | |
| 746 } | |
| 747 } | |
| 748 | |
| 749 /* 'n7', 'n8' */ | |
| 750 if (!BN_mod_add_quick(n1, n1, n3, p)) goto end; | |
| 751 if (!BN_mod_add_quick(n2, n2, n4, p)) goto end; | |
| 752 /* 'n7' = n1 + n3 */ | |
| 753 /* 'n8' = n2 + n4 */ | |
| 754 | |
| 755 /* Z_r */ | |
| 756 if (a->Z_is_one && b->Z_is_one) | |
| 757 { | |
| 758 if (!BN_copy(&r->Z, n5)) goto end; | |
| 759 } | |
| 760 else | |
| 761 { | |
| 762 if (a->Z_is_one) | |
| 763 { if (!BN_copy(n0, &b->Z)) goto end; } | |
| 764 else if (b->Z_is_one) | |
| 765 { if (!BN_copy(n0, &a->Z)) goto end; } | |
| 766 else | |
| 767 { if (!field_mul(group, n0, &a->Z, &b->Z, ctx)) goto end
; } | |
| 768 if (!field_mul(group, &r->Z, n0, n5, ctx)) goto end; | |
| 769 } | |
| 770 r->Z_is_one = 0; | |
| 771 /* Z_r = Z_a * Z_b * n5 */ | |
| 772 | |
| 773 /* X_r */ | |
| 774 if (!field_sqr(group, n0, n6, ctx)) goto end; | |
| 775 if (!field_sqr(group, n4, n5, ctx)) goto end; | |
| 776 if (!field_mul(group, n3, n1, n4, ctx)) goto end; | |
| 777 if (!BN_mod_sub_quick(&r->X, n0, n3, p)) goto end; | |
| 778 /* X_r = n6^2 - n5^2 * 'n7' */ | |
| 779 | |
| 780 /* 'n9' */ | |
| 781 if (!BN_mod_lshift1_quick(n0, &r->X, p)) goto end; | |
| 782 if (!BN_mod_sub_quick(n0, n3, n0, p)) goto end; | |
| 783 /* n9 = n5^2 * 'n7' - 2 * X_r */ | |
| 784 | |
| 785 /* Y_r */ | |
| 786 if (!field_mul(group, n0, n0, n6, ctx)) goto end; | |
| 787 if (!field_mul(group, n5, n4, n5, ctx)) goto end; /* now n5 is n5^3 */ | |
| 788 if (!field_mul(group, n1, n2, n5, ctx)) goto end; | |
| 789 if (!BN_mod_sub_quick(n0, n0, n1, p)) goto end; | |
| 790 if (BN_is_odd(n0)) | |
| 791 if (!BN_add(n0, n0, p)) goto end; | |
| 792 /* now 0 <= n0 < 2*p, and n0 is even */ | |
| 793 if (!BN_rshift1(&r->Y, n0)) goto end; | |
| 794 /* Y_r = (n6 * 'n9' - 'n8' * 'n5^3') / 2 */ | |
| 795 | |
| 796 ret = 1; | |
| 797 | |
| 798 end: | |
| 799 if (ctx) /* otherwise we already called BN_CTX_end */ | |
| 800 BN_CTX_end(ctx); | |
| 801 if (new_ctx != NULL) | |
| 802 BN_CTX_free(new_ctx); | |
| 803 return ret; | |
| 804 } | |
| 805 | |
| 806 | |
| 807 int ec_GFp_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_
CTX *ctx) | |
| 808 { | |
| 809 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNU
M *, BN_CTX *); | |
| 810 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); | |
| 811 const BIGNUM *p; | |
| 812 BN_CTX *new_ctx = NULL; | |
| 813 BIGNUM *n0, *n1, *n2, *n3; | |
| 814 int ret = 0; | |
| 815 | |
| 816 if (EC_POINT_is_at_infinity(group, a)) | |
| 817 { | |
| 818 BN_zero(&r->Z); | |
| 819 r->Z_is_one = 0; | |
| 820 return 1; | |
| 821 } | |
| 822 | |
| 823 field_mul = group->meth->field_mul; | |
| 824 field_sqr = group->meth->field_sqr; | |
| 825 p = &group->field; | |
| 826 | |
| 827 if (ctx == NULL) | |
| 828 { | |
| 829 ctx = new_ctx = BN_CTX_new(); | |
| 830 if (ctx == NULL) | |
| 831 return 0; | |
| 832 } | |
| 833 | |
| 834 BN_CTX_start(ctx); | |
| 835 n0 = BN_CTX_get(ctx); | |
| 836 n1 = BN_CTX_get(ctx); | |
| 837 n2 = BN_CTX_get(ctx); | |
| 838 n3 = BN_CTX_get(ctx); | |
| 839 if (n3 == NULL) goto err; | |
| 840 | |
| 841 /* Note that in this function we must not read components of 'a' | |
| 842 * once we have written the corresponding components of 'r'. | |
| 843 * ('r' might the same as 'a'.) | |
| 844 */ | |
| 845 | |
| 846 /* n1 */ | |
| 847 if (a->Z_is_one) | |
| 848 { | |
| 849 if (!field_sqr(group, n0, &a->X, ctx)) goto err; | |
| 850 if (!BN_mod_lshift1_quick(n1, n0, p)) goto err; | |
| 851 if (!BN_mod_add_quick(n0, n0, n1, p)) goto err; | |
| 852 if (!BN_mod_add_quick(n1, n0, &group->a, p)) goto err; | |
| 853 /* n1 = 3 * X_a^2 + a_curve */ | |
| 854 } | |
| 855 else if (group->a_is_minus3) | |
| 856 { | |
| 857 if (!field_sqr(group, n1, &a->Z, ctx)) goto err; | |
| 858 if (!BN_mod_add_quick(n0, &a->X, n1, p)) goto err; | |
| 859 if (!BN_mod_sub_quick(n2, &a->X, n1, p)) goto err; | |
| 860 if (!field_mul(group, n1, n0, n2, ctx)) goto err; | |
| 861 if (!BN_mod_lshift1_quick(n0, n1, p)) goto err; | |
| 862 if (!BN_mod_add_quick(n1, n0, n1, p)) goto err; | |
| 863 /* n1 = 3 * (X_a + Z_a^2) * (X_a - Z_a^2) | |
| 864 * = 3 * X_a^2 - 3 * Z_a^4 */ | |
| 865 } | |
| 866 else | |
| 867 { | |
| 868 if (!field_sqr(group, n0, &a->X, ctx)) goto err; | |
| 869 if (!BN_mod_lshift1_quick(n1, n0, p)) goto err; | |
| 870 if (!BN_mod_add_quick(n0, n0, n1, p)) goto err; | |
| 871 if (!field_sqr(group, n1, &a->Z, ctx)) goto err; | |
| 872 if (!field_sqr(group, n1, n1, ctx)) goto err; | |
| 873 if (!field_mul(group, n1, n1, &group->a, ctx)) goto err; | |
| 874 if (!BN_mod_add_quick(n1, n1, n0, p)) goto err; | |
| 875 /* n1 = 3 * X_a^2 + a_curve * Z_a^4 */ | |
| 876 } | |
| 877 | |
| 878 /* Z_r */ | |
| 879 if (a->Z_is_one) | |
| 880 { | |
| 881 if (!BN_copy(n0, &a->Y)) goto err; | |
| 882 } | |
| 883 else | |
| 884 { | |
| 885 if (!field_mul(group, n0, &a->Y, &a->Z, ctx)) goto err; | |
| 886 } | |
| 887 if (!BN_mod_lshift1_quick(&r->Z, n0, p)) goto err; | |
| 888 r->Z_is_one = 0; | |
| 889 /* Z_r = 2 * Y_a * Z_a */ | |
| 890 | |
| 891 /* n2 */ | |
| 892 if (!field_sqr(group, n3, &a->Y, ctx)) goto err; | |
| 893 if (!field_mul(group, n2, &a->X, n3, ctx)) goto err; | |
| 894 if (!BN_mod_lshift_quick(n2, n2, 2, p)) goto err; | |
| 895 /* n2 = 4 * X_a * Y_a^2 */ | |
| 896 | |
| 897 /* X_r */ | |
| 898 if (!BN_mod_lshift1_quick(n0, n2, p)) goto err; | |
| 899 if (!field_sqr(group, &r->X, n1, ctx)) goto err; | |
| 900 if (!BN_mod_sub_quick(&r->X, &r->X, n0, p)) goto err; | |
| 901 /* X_r = n1^2 - 2 * n2 */ | |
| 902 | |
| 903 /* n3 */ | |
| 904 if (!field_sqr(group, n0, n3, ctx)) goto err; | |
| 905 if (!BN_mod_lshift_quick(n3, n0, 3, p)) goto err; | |
| 906 /* n3 = 8 * Y_a^4 */ | |
| 907 | |
| 908 /* Y_r */ | |
| 909 if (!BN_mod_sub_quick(n0, n2, &r->X, p)) goto err; | |
| 910 if (!field_mul(group, n0, n1, n0, ctx)) goto err; | |
| 911 if (!BN_mod_sub_quick(&r->Y, n0, n3, p)) goto err; | |
| 912 /* Y_r = n1 * (n2 - X_r) - n3 */ | |
| 913 | |
| 914 ret = 1; | |
| 915 | |
| 916 err: | |
| 917 BN_CTX_end(ctx); | |
| 918 if (new_ctx != NULL) | |
| 919 BN_CTX_free(new_ctx); | |
| 920 return ret; | |
| 921 } | |
| 922 | |
| 923 | |
| 924 int ec_GFp_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx) | |
| 925 { | |
| 926 if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(&point->Y)) | |
| 927 /* point is its own inverse */ | |
| 928 return 1; | |
| 929 | |
| 930 return BN_usub(&point->Y, &group->field, &point->Y); | |
| 931 } | |
| 932 | |
| 933 | |
| 934 int ec_GFp_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point) | |
| 935 { | |
| 936 return BN_is_zero(&point->Z); | |
| 937 } | |
| 938 | |
| 939 | |
| 940 int ec_GFp_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_C
TX *ctx) | |
| 941 { | |
| 942 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNU
M *, BN_CTX *); | |
| 943 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); | |
| 944 const BIGNUM *p; | |
| 945 BN_CTX *new_ctx = NULL; | |
| 946 BIGNUM *rh, *tmp, *Z4, *Z6; | |
| 947 int ret = -1; | |
| 948 | |
| 949 if (EC_POINT_is_at_infinity(group, point)) | |
| 950 return 1; | |
| 951 | |
| 952 field_mul = group->meth->field_mul; | |
| 953 field_sqr = group->meth->field_sqr; | |
| 954 p = &group->field; | |
| 955 | |
| 956 if (ctx == NULL) | |
| 957 { | |
| 958 ctx = new_ctx = BN_CTX_new(); | |
| 959 if (ctx == NULL) | |
| 960 return -1; | |
| 961 } | |
| 962 | |
| 963 BN_CTX_start(ctx); | |
| 964 rh = BN_CTX_get(ctx); | |
| 965 tmp = BN_CTX_get(ctx); | |
| 966 Z4 = BN_CTX_get(ctx); | |
| 967 Z6 = BN_CTX_get(ctx); | |
| 968 if (Z6 == NULL) goto err; | |
| 969 | |
| 970 /* We have a curve defined by a Weierstrass equation | |
| 971 * y^2 = x^3 + a*x + b. | |
| 972 * The point to consider is given in Jacobian projective coordinates | |
| 973 * where (X, Y, Z) represents (x, y) = (X/Z^2, Y/Z^3). | |
| 974 * Substituting this and multiplying by Z^6 transforms the above equat
ion into | |
| 975 * Y^2 = X^3 + a*X*Z^4 + b*Z^6. | |
| 976 * To test this, we add up the right-hand side in 'rh'. | |
| 977 */ | |
| 978 | |
| 979 /* rh := X^2 */ | |
| 980 if (!field_sqr(group, rh, &point->X, ctx)) goto err; | |
| 981 | |
| 982 if (!point->Z_is_one) | |
| 983 { | |
| 984 if (!field_sqr(group, tmp, &point->Z, ctx)) goto err; | |
| 985 if (!field_sqr(group, Z4, tmp, ctx)) goto err; | |
| 986 if (!field_mul(group, Z6, Z4, tmp, ctx)) goto err; | |
| 987 | |
| 988 /* rh := (rh + a*Z^4)*X */ | |
| 989 if (group->a_is_minus3) | |
| 990 { | |
| 991 if (!BN_mod_lshift1_quick(tmp, Z4, p)) goto err; | |
| 992 if (!BN_mod_add_quick(tmp, tmp, Z4, p)) goto err; | |
| 993 if (!BN_mod_sub_quick(rh, rh, tmp, p)) goto err; | |
| 994 if (!field_mul(group, rh, rh, &point->X, ctx)) goto err; | |
| 995 } | |
| 996 else | |
| 997 { | |
| 998 if (!field_mul(group, tmp, Z4, &group->a, ctx)) goto err
; | |
| 999 if (!BN_mod_add_quick(rh, rh, tmp, p)) goto err; | |
| 1000 if (!field_mul(group, rh, rh, &point->X, ctx)) goto err; | |
| 1001 } | |
| 1002 | |
| 1003 /* rh := rh + b*Z^6 */ | |
| 1004 if (!field_mul(group, tmp, &group->b, Z6, ctx)) goto err; | |
| 1005 if (!BN_mod_add_quick(rh, rh, tmp, p)) goto err; | |
| 1006 } | |
| 1007 else | |
| 1008 { | |
| 1009 /* point->Z_is_one */ | |
| 1010 | |
| 1011 /* rh := (rh + a)*X */ | |
| 1012 if (!BN_mod_add_quick(rh, rh, &group->a, p)) goto err; | |
| 1013 if (!field_mul(group, rh, rh, &point->X, ctx)) goto err; | |
| 1014 /* rh := rh + b */ | |
| 1015 if (!BN_mod_add_quick(rh, rh, &group->b, p)) goto err; | |
| 1016 } | |
| 1017 | |
| 1018 /* 'lh' := Y^2 */ | |
| 1019 if (!field_sqr(group, tmp, &point->Y, ctx)) goto err; | |
| 1020 | |
| 1021 ret = (0 == BN_ucmp(tmp, rh)); | |
| 1022 | |
| 1023 err: | |
| 1024 BN_CTX_end(ctx); | |
| 1025 if (new_ctx != NULL) | |
| 1026 BN_CTX_free(new_ctx); | |
| 1027 return ret; | |
| 1028 } | |
| 1029 | |
| 1030 | |
| 1031 int ec_GFp_simple_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *
b, BN_CTX *ctx) | |
| 1032 { | |
| 1033 /* return values: | |
| 1034 * -1 error | |
| 1035 * 0 equal (in affine coordinates) | |
| 1036 * 1 not equal | |
| 1037 */ | |
| 1038 | |
| 1039 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNU
M *, BN_CTX *); | |
| 1040 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); | |
| 1041 BN_CTX *new_ctx = NULL; | |
| 1042 BIGNUM *tmp1, *tmp2, *Za23, *Zb23; | |
| 1043 const BIGNUM *tmp1_, *tmp2_; | |
| 1044 int ret = -1; | |
| 1045 | |
| 1046 if (EC_POINT_is_at_infinity(group, a)) | |
| 1047 { | |
| 1048 return EC_POINT_is_at_infinity(group, b) ? 0 : 1; | |
| 1049 } | |
| 1050 | |
| 1051 if (EC_POINT_is_at_infinity(group, b)) | |
| 1052 return 1; | |
| 1053 | |
| 1054 if (a->Z_is_one && b->Z_is_one) | |
| 1055 { | |
| 1056 return ((BN_cmp(&a->X, &b->X) == 0) && BN_cmp(&a->Y, &b->Y) == 0
) ? 0 : 1; | |
| 1057 } | |
| 1058 | |
| 1059 field_mul = group->meth->field_mul; | |
| 1060 field_sqr = group->meth->field_sqr; | |
| 1061 | |
| 1062 if (ctx == NULL) | |
| 1063 { | |
| 1064 ctx = new_ctx = BN_CTX_new(); | |
| 1065 if (ctx == NULL) | |
| 1066 return -1; | |
| 1067 } | |
| 1068 | |
| 1069 BN_CTX_start(ctx); | |
| 1070 tmp1 = BN_CTX_get(ctx); | |
| 1071 tmp2 = BN_CTX_get(ctx); | |
| 1072 Za23 = BN_CTX_get(ctx); | |
| 1073 Zb23 = BN_CTX_get(ctx); | |
| 1074 if (Zb23 == NULL) goto end; | |
| 1075 | |
| 1076 /* We have to decide whether | |
| 1077 * (X_a/Z_a^2, Y_a/Z_a^3) = (X_b/Z_b^2, Y_b/Z_b^3), | |
| 1078 * or equivalently, whether | |
| 1079 * (X_a*Z_b^2, Y_a*Z_b^3) = (X_b*Z_a^2, Y_b*Z_a^3). | |
| 1080 */ | |
| 1081 | |
| 1082 if (!b->Z_is_one) | |
| 1083 { | |
| 1084 if (!field_sqr(group, Zb23, &b->Z, ctx)) goto end; | |
| 1085 if (!field_mul(group, tmp1, &a->X, Zb23, ctx)) goto end; | |
| 1086 tmp1_ = tmp1; | |
| 1087 } | |
| 1088 else | |
| 1089 tmp1_ = &a->X; | |
| 1090 if (!a->Z_is_one) | |
| 1091 { | |
| 1092 if (!field_sqr(group, Za23, &a->Z, ctx)) goto end; | |
| 1093 if (!field_mul(group, tmp2, &b->X, Za23, ctx)) goto end; | |
| 1094 tmp2_ = tmp2; | |
| 1095 } | |
| 1096 else | |
| 1097 tmp2_ = &b->X; | |
| 1098 | |
| 1099 /* compare X_a*Z_b^2 with X_b*Z_a^2 */ | |
| 1100 if (BN_cmp(tmp1_, tmp2_) != 0) | |
| 1101 { | |
| 1102 ret = 1; /* points differ */ | |
| 1103 goto end; | |
| 1104 } | |
| 1105 | |
| 1106 | |
| 1107 if (!b->Z_is_one) | |
| 1108 { | |
| 1109 if (!field_mul(group, Zb23, Zb23, &b->Z, ctx)) goto end; | |
| 1110 if (!field_mul(group, tmp1, &a->Y, Zb23, ctx)) goto end; | |
| 1111 /* tmp1_ = tmp1 */ | |
| 1112 } | |
| 1113 else | |
| 1114 tmp1_ = &a->Y; | |
| 1115 if (!a->Z_is_one) | |
| 1116 { | |
| 1117 if (!field_mul(group, Za23, Za23, &a->Z, ctx)) goto end; | |
| 1118 if (!field_mul(group, tmp2, &b->Y, Za23, ctx)) goto end; | |
| 1119 /* tmp2_ = tmp2 */ | |
| 1120 } | |
| 1121 else | |
| 1122 tmp2_ = &b->Y; | |
| 1123 | |
| 1124 /* compare Y_a*Z_b^3 with Y_b*Z_a^3 */ | |
| 1125 if (BN_cmp(tmp1_, tmp2_) != 0) | |
| 1126 { | |
| 1127 ret = 1; /* points differ */ | |
| 1128 goto end; | |
| 1129 } | |
| 1130 | |
| 1131 /* points are equal */ | |
| 1132 ret = 0; | |
| 1133 | |
| 1134 end: | |
| 1135 BN_CTX_end(ctx); | |
| 1136 if (new_ctx != NULL) | |
| 1137 BN_CTX_free(new_ctx); | |
| 1138 return ret; | |
| 1139 } | |
| 1140 | |
| 1141 | |
| 1142 int ec_GFp_simple_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ct
x) | |
| 1143 { | |
| 1144 BN_CTX *new_ctx = NULL; | |
| 1145 BIGNUM *x, *y; | |
| 1146 int ret = 0; | |
| 1147 | |
| 1148 if (point->Z_is_one || EC_POINT_is_at_infinity(group, point)) | |
| 1149 return 1; | |
| 1150 | |
| 1151 if (ctx == NULL) | |
| 1152 { | |
| 1153 ctx = new_ctx = BN_CTX_new(); | |
| 1154 if (ctx == NULL) | |
| 1155 return 0; | |
| 1156 } | |
| 1157 | |
| 1158 BN_CTX_start(ctx); | |
| 1159 x = BN_CTX_get(ctx); | |
| 1160 y = BN_CTX_get(ctx); | |
| 1161 if (y == NULL) goto err; | |
| 1162 | |
| 1163 if (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx)) goto
err; | |
| 1164 if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) goto
err; | |
| 1165 if (!point->Z_is_one) | |
| 1166 { | |
| 1167 ECerr(EC_F_EC_GFP_SIMPLE_MAKE_AFFINE, ERR_R_INTERNAL_ERROR); | |
| 1168 goto err; | |
| 1169 } | |
| 1170 | |
| 1171 ret = 1; | |
| 1172 | |
| 1173 err: | |
| 1174 BN_CTX_end(ctx); | |
| 1175 if (new_ctx != NULL) | |
| 1176 BN_CTX_free(new_ctx); | |
| 1177 return ret; | |
| 1178 } | |
| 1179 | |
| 1180 | |
| 1181 int ec_GFp_simple_points_make_affine(const EC_GROUP *group, size_t num, EC_POINT
*points[], BN_CTX *ctx) | |
| 1182 { | |
| 1183 BN_CTX *new_ctx = NULL; | |
| 1184 BIGNUM *tmp0, *tmp1; | |
| 1185 size_t pow2 = 0; | |
| 1186 BIGNUM **heap = NULL; | |
| 1187 size_t i; | |
| 1188 int ret = 0; | |
| 1189 | |
| 1190 if (num == 0) | |
| 1191 return 1; | |
| 1192 | |
| 1193 if (ctx == NULL) | |
| 1194 { | |
| 1195 ctx = new_ctx = BN_CTX_new(); | |
| 1196 if (ctx == NULL) | |
| 1197 return 0; | |
| 1198 } | |
| 1199 | |
| 1200 BN_CTX_start(ctx); | |
| 1201 tmp0 = BN_CTX_get(ctx); | |
| 1202 tmp1 = BN_CTX_get(ctx); | |
| 1203 if (tmp0 == NULL || tmp1 == NULL) goto err; | |
| 1204 | |
| 1205 /* Before converting the individual points, compute inverses of all Z va
lues. | |
| 1206 * Modular inversion is rather slow, but luckily we can do with a single | |
| 1207 * explicit inversion, plus about 3 multiplications per input value. | |
| 1208 */ | |
| 1209 | |
| 1210 pow2 = 1; | |
| 1211 while (num > pow2) | |
| 1212 pow2 <<= 1; | |
| 1213 /* Now pow2 is the smallest power of 2 satifsying pow2 >= num. | |
| 1214 * We need twice that. */ | |
| 1215 pow2 <<= 1; | |
| 1216 | |
| 1217 heap = OPENSSL_malloc(pow2 * sizeof heap[0]); | |
| 1218 if (heap == NULL) goto err; | |
| 1219 | |
| 1220 /* The array is used as a binary tree, exactly as in heapsort: | |
| 1221 * | |
| 1222 * heap[1] | |
| 1223 * heap[2] heap[3] | |
| 1224 * heap[4] heap[5] heap[6] heap[7] | |
| 1225 * heap[8]heap[9] heap[10]heap[11] heap[12]heap[13] heap[14] heap[15] | |
| 1226 * | |
| 1227 * We put the Z's in the last line; | |
| 1228 * then we set each other node to the product of its two child-nodes (wh
ere | |
| 1229 * empty or 0 entries are treated as ones); | |
| 1230 * then we invert heap[1]; | |
| 1231 * then we invert each other node by replacing it by the product of its | |
| 1232 * parent (after inversion) and its sibling (before inversion). | |
| 1233 */ | |
| 1234 heap[0] = NULL; | |
| 1235 for (i = pow2/2 - 1; i > 0; i--) | |
| 1236 heap[i] = NULL; | |
| 1237 for (i = 0; i < num; i++) | |
| 1238 heap[pow2/2 + i] = &points[i]->Z; | |
| 1239 for (i = pow2/2 + num; i < pow2; i++) | |
| 1240 heap[i] = NULL; | |
| 1241 | |
| 1242 /* set each node to the product of its children */ | |
| 1243 for (i = pow2/2 - 1; i > 0; i--) | |
| 1244 { | |
| 1245 heap[i] = BN_new(); | |
| 1246 if (heap[i] == NULL) goto err; | |
| 1247 | |
| 1248 if (heap[2*i] != NULL) | |
| 1249 { | |
| 1250 if ((heap[2*i + 1] == NULL) || BN_is_zero(heap[2*i + 1])
) | |
| 1251 { | |
| 1252 if (!BN_copy(heap[i], heap[2*i])) goto err; | |
| 1253 } | |
| 1254 else | |
| 1255 { | |
| 1256 if (BN_is_zero(heap[2*i])) | |
| 1257 { | |
| 1258 if (!BN_copy(heap[i], heap[2*i + 1])) go
to err; | |
| 1259 } | |
| 1260 else | |
| 1261 { | |
| 1262 if (!group->meth->field_mul(group, heap[
i], | |
| 1263 heap[2*i], heap[2*i + 1], ctx))
goto err; | |
| 1264 } | |
| 1265 } | |
| 1266 } | |
| 1267 } | |
| 1268 | |
| 1269 /* invert heap[1] */ | |
| 1270 if (!BN_is_zero(heap[1])) | |
| 1271 { | |
| 1272 if (!BN_mod_inverse(heap[1], heap[1], &group->field, ctx)) | |
| 1273 { | |
| 1274 ECerr(EC_F_EC_GFP_SIMPLE_POINTS_MAKE_AFFINE, ERR_R_BN_LI
B); | |
| 1275 goto err; | |
| 1276 } | |
| 1277 } | |
| 1278 if (group->meth->field_encode != 0) | |
| 1279 { | |
| 1280 /* in the Montgomery case, we just turned R*H (representing H) | |
| 1281 * into 1/(R*H), but we need R*(1/H) (representing 1/H); | |
| 1282 * i.e. we have need to multiply by the Montgomery factor twice
*/ | |
| 1283 if (!group->meth->field_encode(group, heap[1], heap[1], ctx)) go
to err; | |
| 1284 if (!group->meth->field_encode(group, heap[1], heap[1], ctx)) go
to err; | |
| 1285 } | |
| 1286 | |
| 1287 /* set other heap[i]'s to their inverses */ | |
| 1288 for (i = 2; i < pow2/2 + num; i += 2) | |
| 1289 { | |
| 1290 /* i is even */ | |
| 1291 if ((heap[i + 1] != NULL) && !BN_is_zero(heap[i + 1])) | |
| 1292 { | |
| 1293 if (!group->meth->field_mul(group, tmp0, heap[i/2], heap
[i + 1], ctx)) goto err; | |
| 1294 if (!group->meth->field_mul(group, tmp1, heap[i/2], heap
[i], ctx)) goto err; | |
| 1295 if (!BN_copy(heap[i], tmp0)) goto err; | |
| 1296 if (!BN_copy(heap[i + 1], tmp1)) goto err; | |
| 1297 } | |
| 1298 else | |
| 1299 { | |
| 1300 if (!BN_copy(heap[i], heap[i/2])) goto err; | |
| 1301 } | |
| 1302 } | |
| 1303 | |
| 1304 /* we have replaced all non-zero Z's by their inverses, now fix up all t
he points */ | |
| 1305 for (i = 0; i < num; i++) | |
| 1306 { | |
| 1307 EC_POINT *p = points[i]; | |
| 1308 | |
| 1309 if (!BN_is_zero(&p->Z)) | |
| 1310 { | |
| 1311 /* turn (X, Y, 1/Z) into (X/Z^2, Y/Z^3, 1) */ | |
| 1312 | |
| 1313 if (!group->meth->field_sqr(group, tmp1, &p->Z, ctx)) go
to err; | |
| 1314 if (!group->meth->field_mul(group, &p->X, &p->X, tmp1, c
tx)) goto err; | |
| 1315 | |
| 1316 if (!group->meth->field_mul(group, tmp1, tmp1, &p->Z, ct
x)) goto err; | |
| 1317 if (!group->meth->field_mul(group, &p->Y, &p->Y, tmp1, c
tx)) goto err; | |
| 1318 | |
| 1319 if (group->meth->field_set_to_one != 0) | |
| 1320 { | |
| 1321 if (!group->meth->field_set_to_one(group, &p->Z,
ctx)) goto err; | |
| 1322 } | |
| 1323 else | |
| 1324 { | |
| 1325 if (!BN_one(&p->Z)) goto err; | |
| 1326 } | |
| 1327 p->Z_is_one = 1; | |
| 1328 } | |
| 1329 } | |
| 1330 | |
| 1331 ret = 1; | |
| 1332 | |
| 1333 err: | |
| 1334 BN_CTX_end(ctx); | |
| 1335 if (new_ctx != NULL) | |
| 1336 BN_CTX_free(new_ctx); | |
| 1337 if (heap != NULL) | |
| 1338 { | |
| 1339 /* heap[pow2/2] .. heap[pow2-1] have not been allocated locally!
*/ | |
| 1340 for (i = pow2/2 - 1; i > 0; i--) | |
| 1341 { | |
| 1342 if (heap[i] != NULL) | |
| 1343 BN_clear_free(heap[i]); | |
| 1344 } | |
| 1345 OPENSSL_free(heap); | |
| 1346 } | |
| 1347 return ret; | |
| 1348 } | |
| 1349 | |
| 1350 | |
| 1351 int ec_GFp_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, c
onst BIGNUM *b, BN_CTX *ctx) | |
| 1352 { | |
| 1353 return BN_mod_mul(r, a, b, &group->field, ctx); | |
| 1354 } | |
| 1355 | |
| 1356 | |
| 1357 int ec_GFp_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, B
N_CTX *ctx) | |
| 1358 { | |
| 1359 return BN_mod_sqr(r, a, &group->field, ctx); | |
| 1360 } | |
| OLD | NEW |
|---|
Chromium Code Reviews
Issue 2072073002:
Delete bundled copy of OpenSSL and replace with README. (Closed)
Base URL: https://chromium.googlesource.com/chromium/deps/openssl@master