Alexandre Savard | 1b09e31 | 2012-08-07 20:33:29 -0400 | [diff] [blame^] | 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, BIGNUM *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 err; |
| 314 | if (!group->meth->field_decode(group, b, &group->b, ctx)) goto err; |
| 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_POINT *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 EC_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_PASSED_NULL_PARAMETER); |
| 521 | return 0; |
| 522 | } |
| 523 | |
| 524 | return EC_POINT_set_Jprojective_coordinates_GFp(group, point, x, y, BN_value_one(), ctx); |
| 525 | } |
| 526 | |
| 527 | |
| 528 | int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *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_POINT_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 err; |
| 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, ERR_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 Montgomery factor in X: */ |
| 614 | if (!group->meth->field_mul(group, x, &point->X, Z_2, ctx)) 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, ctx)) goto err; |
| 627 | } |
| 628 | |
| 629 | /* in the Montgomery case, field_mul will cancel out Montgomery factor in Y: */ |
| 630 | if (!group->meth->field_mul(group, y, &point->Y, Z_3, ctx)) 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, const EC_POINT *b, BN_CTX *ctx) |
| 644 | { |
| 645 | int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, 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 BIGNUM *, 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_CTX *ctx) |
| 941 | { |
| 942 | int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, 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 equation 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 BIGNUM *, 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 *ctx) |
| 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 values. |
| 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 (where |
| 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])) goto 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_LIB); |
| 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)) goto err; |
| 1284 | if (!group->meth->field_encode(group, heap[1], heap[1], ctx)) goto 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 the 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)) goto err; |
| 1314 | if (!group->meth->field_mul(group, &p->X, &p->X, tmp1, ctx)) goto err; |
| 1315 | |
| 1316 | if (!group->meth->field_mul(group, tmp1, tmp1, &p->Z, ctx)) goto err; |
| 1317 | if (!group->meth->field_mul(group, &p->Y, &p->Y, tmp1, ctx)) 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, const 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, BN_CTX *ctx) |
| 1358 | { |
| 1359 | return BN_mod_sqr(r, a, &group->field, ctx); |
| 1360 | } |