| File: | src/lib/libcrypto/ec/ecp_smpl.c |
| Warning: | line 310, column 7 Although the value stored to 'order' is used in the enclosing expression, the value is never actually read from 'order' |
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| 1 | /* $OpenBSD: ecp_smpl.c,v 1.33 2021/09/08 17:29:21 tb Exp $ */ |
| 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 | |
| 67 | #include "bn_lcl.h" |
| 68 | #include "ec_lcl.h" |
| 69 | |
| 70 | const EC_METHOD * |
| 71 | EC_GFp_simple_method(void) |
| 72 | { |
| 73 | static const EC_METHOD ret = { |
| 74 | .flags = EC_FLAGS_DEFAULT_OCT0x1, |
| 75 | .field_type = NID_X9_62_prime_field406, |
| 76 | .group_init = ec_GFp_simple_group_init, |
| 77 | .group_finish = ec_GFp_simple_group_finish, |
| 78 | .group_clear_finish = ec_GFp_simple_group_clear_finish, |
| 79 | .group_copy = ec_GFp_simple_group_copy, |
| 80 | .group_set_curve = ec_GFp_simple_group_set_curve, |
| 81 | .group_get_curve = ec_GFp_simple_group_get_curve, |
| 82 | .group_get_degree = ec_GFp_simple_group_get_degree, |
| 83 | .group_order_bits = ec_group_simple_order_bits, |
| 84 | .group_check_discriminant = |
| 85 | ec_GFp_simple_group_check_discriminant, |
| 86 | .point_init = ec_GFp_simple_point_init, |
| 87 | .point_finish = ec_GFp_simple_point_finish, |
| 88 | .point_clear_finish = ec_GFp_simple_point_clear_finish, |
| 89 | .point_copy = ec_GFp_simple_point_copy, |
| 90 | .point_set_to_infinity = ec_GFp_simple_point_set_to_infinity, |
| 91 | .point_set_Jprojective_coordinates = |
| 92 | ec_GFp_simple_set_Jprojective_coordinates, |
| 93 | .point_get_Jprojective_coordinates = |
| 94 | ec_GFp_simple_get_Jprojective_coordinates, |
| 95 | .point_set_affine_coordinates = |
| 96 | ec_GFp_simple_point_set_affine_coordinates, |
| 97 | .point_get_affine_coordinates = |
| 98 | ec_GFp_simple_point_get_affine_coordinates, |
| 99 | .add = ec_GFp_simple_add, |
| 100 | .dbl = ec_GFp_simple_dbl, |
| 101 | .invert = ec_GFp_simple_invert, |
| 102 | .is_at_infinity = ec_GFp_simple_is_at_infinity, |
| 103 | .is_on_curve = ec_GFp_simple_is_on_curve, |
| 104 | .point_cmp = ec_GFp_simple_cmp, |
| 105 | .make_affine = ec_GFp_simple_make_affine, |
| 106 | .points_make_affine = ec_GFp_simple_points_make_affine, |
| 107 | .mul_generator_ct = ec_GFp_simple_mul_generator_ct, |
| 108 | .mul_single_ct = ec_GFp_simple_mul_single_ct, |
| 109 | .mul_double_nonct = ec_GFp_simple_mul_double_nonct, |
| 110 | .field_mul = ec_GFp_simple_field_mul, |
| 111 | .field_sqr = ec_GFp_simple_field_sqr, |
| 112 | .blind_coordinates = ec_GFp_simple_blind_coordinates, |
| 113 | }; |
| 114 | |
| 115 | return &ret; |
| 116 | } |
| 117 | |
| 118 | |
| 119 | /* Most method functions in this file are designed to work with |
| 120 | * non-trivial representations of field elements if necessary |
| 121 | * (see ecp_mont.c): while standard modular addition and subtraction |
| 122 | * are used, the field_mul and field_sqr methods will be used for |
| 123 | * multiplication, and field_encode and field_decode (if defined) |
| 124 | * will be used for converting between representations. |
| 125 | |
| 126 | * Functions ec_GFp_simple_points_make_affine() and |
| 127 | * ec_GFp_simple_point_get_affine_coordinates() specifically assume |
| 128 | * that if a non-trivial representation is used, it is a Montgomery |
| 129 | * representation (i.e. 'encoding' means multiplying by some factor R). |
| 130 | */ |
| 131 | |
| 132 | |
| 133 | int |
| 134 | ec_GFp_simple_group_init(EC_GROUP * group) |
| 135 | { |
| 136 | BN_init(&group->field); |
| 137 | BN_init(&group->a); |
| 138 | BN_init(&group->b); |
| 139 | group->a_is_minus3 = 0; |
| 140 | return 1; |
| 141 | } |
| 142 | |
| 143 | |
| 144 | void |
| 145 | ec_GFp_simple_group_finish(EC_GROUP * group) |
| 146 | { |
| 147 | BN_free(&group->field); |
| 148 | BN_free(&group->a); |
| 149 | BN_free(&group->b); |
| 150 | } |
| 151 | |
| 152 | |
| 153 | void |
| 154 | ec_GFp_simple_group_clear_finish(EC_GROUP * group) |
| 155 | { |
| 156 | BN_clear_free(&group->field); |
| 157 | BN_clear_free(&group->a); |
| 158 | BN_clear_free(&group->b); |
| 159 | } |
| 160 | |
| 161 | |
| 162 | int |
| 163 | ec_GFp_simple_group_copy(EC_GROUP * dest, const EC_GROUP * src) |
| 164 | { |
| 165 | if (!BN_copy(&dest->field, &src->field)) |
| 166 | return 0; |
| 167 | if (!BN_copy(&dest->a, &src->a)) |
| 168 | return 0; |
| 169 | if (!BN_copy(&dest->b, &src->b)) |
| 170 | return 0; |
| 171 | |
| 172 | dest->a_is_minus3 = src->a_is_minus3; |
| 173 | |
| 174 | return 1; |
| 175 | } |
| 176 | |
| 177 | |
| 178 | int |
| 179 | ec_GFp_simple_group_set_curve(EC_GROUP * group, |
| 180 | const BIGNUM * p, const BIGNUM * a, const BIGNUM * b, BN_CTX * ctx) |
| 181 | { |
| 182 | int ret = 0; |
| 183 | BN_CTX *new_ctx = NULL((void *)0); |
| 184 | BIGNUM *tmp_a; |
| 185 | |
| 186 | /* p must be a prime > 3 */ |
| 187 | if (BN_num_bits(p) <= 2 || !BN_is_odd(p)) { |
| 188 | ECerror(EC_R_INVALID_FIELD)ERR_put_error(16,(0xfff),(103),"/usr/src/lib/libcrypto/ec/ecp_smpl.c" ,188); |
| 189 | return 0; |
| 190 | } |
| 191 | if (ctx == NULL((void *)0)) { |
| 192 | ctx = new_ctx = BN_CTX_new(); |
| 193 | if (ctx == NULL((void *)0)) |
| 194 | return 0; |
| 195 | } |
| 196 | BN_CTX_start(ctx); |
| 197 | if ((tmp_a = BN_CTX_get(ctx)) == NULL((void *)0)) |
| 198 | goto err; |
| 199 | |
| 200 | /* group->field */ |
| 201 | if (!BN_copy(&group->field, p)) |
| 202 | goto err; |
| 203 | BN_set_negative(&group->field, 0); |
| 204 | |
| 205 | /* group->a */ |
| 206 | if (!BN_nnmod(tmp_a, a, p, ctx)) |
| 207 | goto err; |
| 208 | if (group->meth->field_encode) { |
| 209 | if (!group->meth->field_encode(group, &group->a, tmp_a, ctx)) |
| 210 | goto err; |
| 211 | } else if (!BN_copy(&group->a, tmp_a)) |
| 212 | goto err; |
| 213 | |
| 214 | /* group->b */ |
| 215 | if (!BN_nnmod(&group->b, b, p, ctx)) |
| 216 | goto err; |
| 217 | if (group->meth->field_encode) |
| 218 | if (!group->meth->field_encode(group, &group->b, &group->b, ctx)) |
| 219 | goto err; |
| 220 | |
| 221 | /* group->a_is_minus3 */ |
| 222 | if (!BN_add_word(tmp_a, 3)) |
| 223 | goto err; |
| 224 | group->a_is_minus3 = (0 == BN_cmp(tmp_a, &group->field)); |
| 225 | |
| 226 | ret = 1; |
| 227 | |
| 228 | err: |
| 229 | BN_CTX_end(ctx); |
| 230 | BN_CTX_free(new_ctx); |
| 231 | return ret; |
| 232 | } |
| 233 | |
| 234 | |
| 235 | int |
| 236 | ec_GFp_simple_group_get_curve(const EC_GROUP * group, BIGNUM * p, BIGNUM * a, BIGNUM * b, BN_CTX * ctx) |
| 237 | { |
| 238 | int ret = 0; |
| 239 | BN_CTX *new_ctx = NULL((void *)0); |
| 240 | |
| 241 | if (p != NULL((void *)0)) { |
| 242 | if (!BN_copy(p, &group->field)) |
| 243 | return 0; |
| 244 | } |
| 245 | if (a != NULL((void *)0) || b != NULL((void *)0)) { |
| 246 | if (group->meth->field_decode) { |
| 247 | if (ctx == NULL((void *)0)) { |
| 248 | ctx = new_ctx = BN_CTX_new(); |
| 249 | if (ctx == NULL((void *)0)) |
| 250 | return 0; |
| 251 | } |
| 252 | if (a != NULL((void *)0)) { |
| 253 | if (!group->meth->field_decode(group, a, &group->a, ctx)) |
| 254 | goto err; |
| 255 | } |
| 256 | if (b != NULL((void *)0)) { |
| 257 | if (!group->meth->field_decode(group, b, &group->b, ctx)) |
| 258 | goto err; |
| 259 | } |
| 260 | } else { |
| 261 | if (a != NULL((void *)0)) { |
| 262 | if (!BN_copy(a, &group->a)) |
| 263 | goto err; |
| 264 | } |
| 265 | if (b != NULL((void *)0)) { |
| 266 | if (!BN_copy(b, &group->b)) |
| 267 | goto err; |
| 268 | } |
| 269 | } |
| 270 | } |
| 271 | ret = 1; |
| 272 | |
| 273 | err: |
| 274 | BN_CTX_free(new_ctx); |
| 275 | return ret; |
| 276 | } |
| 277 | |
| 278 | |
| 279 | int |
| 280 | ec_GFp_simple_group_get_degree(const EC_GROUP * group) |
| 281 | { |
| 282 | return BN_num_bits(&group->field); |
| 283 | } |
| 284 | |
| 285 | |
| 286 | int |
| 287 | 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((void *)0); |
| 293 | |
| 294 | if (ctx == NULL((void *)0)) { |
| 295 | ctx = new_ctx = BN_CTX_new(); |
| 296 | if (ctx == NULL((void *)0)) { |
| 297 | ECerror(ERR_R_MALLOC_FAILURE)ERR_put_error(16,(0xfff),((1|64)),"/usr/src/lib/libcrypto/ec/ecp_smpl.c" ,297); |
| 298 | goto err; |
| 299 | } |
| 300 | } |
| 301 | BN_CTX_start(ctx); |
| 302 | if ((a = BN_CTX_get(ctx)) == NULL((void *)0)) |
| 303 | goto err; |
| 304 | if ((b = BN_CTX_get(ctx)) == NULL((void *)0)) |
| 305 | goto err; |
| 306 | if ((tmp_1 = BN_CTX_get(ctx)) == NULL((void *)0)) |
| 307 | goto err; |
| 308 | if ((tmp_2 = BN_CTX_get(ctx)) == NULL((void *)0)) |
| 309 | goto err; |
| 310 | if ((order = BN_CTX_get(ctx)) == NULL((void *)0)) |
Although the value stored to 'order' is used in the enclosing expression, the value is never actually read from 'order' | |
| 311 | goto err; |
| 312 | |
| 313 | if (group->meth->field_decode) { |
| 314 | if (!group->meth->field_decode(group, a, &group->a, ctx)) |
| 315 | goto err; |
| 316 | if (!group->meth->field_decode(group, b, &group->b, ctx)) |
| 317 | goto err; |
| 318 | } else { |
| 319 | if (!BN_copy(a, &group->a)) |
| 320 | goto err; |
| 321 | if (!BN_copy(b, &group->b)) |
| 322 | goto err; |
| 323 | } |
| 324 | |
| 325 | /* |
| 326 | * check the discriminant: y^2 = x^3 + a*x + b is an elliptic curve |
| 327 | * <=> 4*a^3 + 27*b^2 != 0 (mod p) 0 =< a, b < p |
| 328 | */ |
| 329 | if (BN_is_zero(a)) { |
| 330 | if (BN_is_zero(b)) |
| 331 | goto err; |
| 332 | } else if (!BN_is_zero(b)) { |
| 333 | if (!BN_mod_sqr(tmp_1, a, p, ctx)) |
| 334 | goto err; |
| 335 | if (!BN_mod_mul(tmp_2, tmp_1, a, p, ctx)) |
| 336 | goto err; |
| 337 | if (!BN_lshift(tmp_1, tmp_2, 2)) |
| 338 | goto err; |
| 339 | /* tmp_1 = 4*a^3 */ |
| 340 | |
| 341 | if (!BN_mod_sqr(tmp_2, b, p, ctx)) |
| 342 | goto err; |
| 343 | if (!BN_mul_word(tmp_2, 27)) |
| 344 | goto err; |
| 345 | /* tmp_2 = 27*b^2 */ |
| 346 | |
| 347 | if (!BN_mod_add(a, tmp_1, tmp_2, p, ctx)) |
| 348 | goto err; |
| 349 | if (BN_is_zero(a)) |
| 350 | goto err; |
| 351 | } |
| 352 | ret = 1; |
| 353 | |
| 354 | err: |
| 355 | if (ctx != NULL((void *)0)) |
| 356 | BN_CTX_end(ctx); |
| 357 | BN_CTX_free(new_ctx); |
| 358 | return ret; |
| 359 | } |
| 360 | |
| 361 | |
| 362 | int |
| 363 | ec_GFp_simple_point_init(EC_POINT * point) |
| 364 | { |
| 365 | BN_init(&point->X); |
| 366 | BN_init(&point->Y); |
| 367 | BN_init(&point->Z); |
| 368 | point->Z_is_one = 0; |
| 369 | |
| 370 | return 1; |
| 371 | } |
| 372 | |
| 373 | |
| 374 | void |
| 375 | ec_GFp_simple_point_finish(EC_POINT * point) |
| 376 | { |
| 377 | BN_free(&point->X); |
| 378 | BN_free(&point->Y); |
| 379 | BN_free(&point->Z); |
| 380 | } |
| 381 | |
| 382 | |
| 383 | void |
| 384 | ec_GFp_simple_point_clear_finish(EC_POINT * point) |
| 385 | { |
| 386 | BN_clear_free(&point->X); |
| 387 | BN_clear_free(&point->Y); |
| 388 | BN_clear_free(&point->Z); |
| 389 | point->Z_is_one = 0; |
| 390 | } |
| 391 | |
| 392 | |
| 393 | int |
| 394 | ec_GFp_simple_point_copy(EC_POINT * dest, const EC_POINT * src) |
| 395 | { |
| 396 | if (!BN_copy(&dest->X, &src->X)) |
| 397 | return 0; |
| 398 | if (!BN_copy(&dest->Y, &src->Y)) |
| 399 | return 0; |
| 400 | if (!BN_copy(&dest->Z, &src->Z)) |
| 401 | return 0; |
| 402 | dest->Z_is_one = src->Z_is_one; |
| 403 | |
| 404 | return 1; |
| 405 | } |
| 406 | |
| 407 | |
| 408 | int |
| 409 | ec_GFp_simple_point_set_to_infinity(const EC_GROUP * group, EC_POINT * point) |
| 410 | { |
| 411 | point->Z_is_one = 0; |
| 412 | BN_zero(&point->Z)(BN_set_word((&point->Z),0)); |
| 413 | return 1; |
| 414 | } |
| 415 | |
| 416 | |
| 417 | int |
| 418 | ec_GFp_simple_set_Jprojective_coordinates(const EC_GROUP *group, |
| 419 | EC_POINT *point, const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, |
| 420 | BN_CTX *ctx) |
| 421 | { |
| 422 | BN_CTX *new_ctx = NULL((void *)0); |
| 423 | int ret = 0; |
| 424 | |
| 425 | if (ctx == NULL((void *)0)) { |
| 426 | ctx = new_ctx = BN_CTX_new(); |
| 427 | if (ctx == NULL((void *)0)) |
| 428 | return 0; |
| 429 | } |
| 430 | if (x != NULL((void *)0)) { |
| 431 | if (!BN_nnmod(&point->X, x, &group->field, ctx)) |
| 432 | goto err; |
| 433 | if (group->meth->field_encode) { |
| 434 | if (!group->meth->field_encode(group, &point->X, &point->X, ctx)) |
| 435 | goto err; |
| 436 | } |
| 437 | } |
| 438 | if (y != NULL((void *)0)) { |
| 439 | if (!BN_nnmod(&point->Y, y, &group->field, ctx)) |
| 440 | goto err; |
| 441 | if (group->meth->field_encode) { |
| 442 | if (!group->meth->field_encode(group, &point->Y, &point->Y, ctx)) |
| 443 | goto err; |
| 444 | } |
| 445 | } |
| 446 | if (z != NULL((void *)0)) { |
| 447 | int Z_is_one; |
| 448 | |
| 449 | if (!BN_nnmod(&point->Z, z, &group->field, ctx)) |
| 450 | goto err; |
| 451 | Z_is_one = BN_is_one(&point->Z); |
| 452 | if (group->meth->field_encode) { |
| 453 | if (Z_is_one && (group->meth->field_set_to_one != 0)) { |
| 454 | if (!group->meth->field_set_to_one(group, &point->Z, ctx)) |
| 455 | goto err; |
| 456 | } else { |
| 457 | if (!group->meth->field_encode(group, &point->Z, &point->Z, ctx)) |
| 458 | goto err; |
| 459 | } |
| 460 | } |
| 461 | point->Z_is_one = Z_is_one; |
| 462 | } |
| 463 | ret = 1; |
| 464 | |
| 465 | err: |
| 466 | BN_CTX_free(new_ctx); |
| 467 | return ret; |
| 468 | } |
| 469 | |
| 470 | int |
| 471 | ec_GFp_simple_get_Jprojective_coordinates(const EC_GROUP *group, |
| 472 | const EC_POINT *point, BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *ctx) |
| 473 | { |
| 474 | BN_CTX *new_ctx = NULL((void *)0); |
| 475 | int ret = 0; |
| 476 | |
| 477 | if (group->meth->field_decode != 0) { |
| 478 | if (ctx == NULL((void *)0)) { |
| 479 | ctx = new_ctx = BN_CTX_new(); |
| 480 | if (ctx == NULL((void *)0)) |
| 481 | return 0; |
| 482 | } |
| 483 | if (x != NULL((void *)0)) { |
| 484 | if (!group->meth->field_decode(group, x, &point->X, ctx)) |
| 485 | goto err; |
| 486 | } |
| 487 | if (y != NULL((void *)0)) { |
| 488 | if (!group->meth->field_decode(group, y, &point->Y, ctx)) |
| 489 | goto err; |
| 490 | } |
| 491 | if (z != NULL((void *)0)) { |
| 492 | if (!group->meth->field_decode(group, z, &point->Z, ctx)) |
| 493 | goto err; |
| 494 | } |
| 495 | } else { |
| 496 | if (x != NULL((void *)0)) { |
| 497 | if (!BN_copy(x, &point->X)) |
| 498 | goto err; |
| 499 | } |
| 500 | if (y != NULL((void *)0)) { |
| 501 | if (!BN_copy(y, &point->Y)) |
| 502 | goto err; |
| 503 | } |
| 504 | if (z != NULL((void *)0)) { |
| 505 | if (!BN_copy(z, &point->Z)) |
| 506 | goto err; |
| 507 | } |
| 508 | } |
| 509 | |
| 510 | ret = 1; |
| 511 | |
| 512 | err: |
| 513 | BN_CTX_free(new_ctx); |
| 514 | return ret; |
| 515 | } |
| 516 | |
| 517 | int |
| 518 | ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP * group, EC_POINT * point, |
| 519 | const BIGNUM * x, const BIGNUM * y, BN_CTX * ctx) |
| 520 | { |
| 521 | if (x == NULL((void *)0) || y == NULL((void *)0)) { |
| 522 | /* unlike for projective coordinates, we do not tolerate this */ |
| 523 | ECerror(ERR_R_PASSED_NULL_PARAMETER)ERR_put_error(16,(0xfff),((3|64)),"/usr/src/lib/libcrypto/ec/ecp_smpl.c" ,523); |
| 524 | return 0; |
| 525 | } |
| 526 | return EC_POINT_set_Jprojective_coordinates(group, point, x, y, |
| 527 | BN_value_one(), ctx); |
| 528 | } |
| 529 | |
| 530 | int |
| 531 | ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP * group, const EC_POINT * point, |
| 532 | BIGNUM * x, BIGNUM * y, BN_CTX * ctx) |
| 533 | { |
| 534 | BN_CTX *new_ctx = NULL((void *)0); |
| 535 | BIGNUM *Z, *Z_1, *Z_2, *Z_3; |
| 536 | const BIGNUM *Z_; |
| 537 | int ret = 0; |
| 538 | |
| 539 | if (EC_POINT_is_at_infinity(group, point) > 0) { |
| 540 | ECerror(EC_R_POINT_AT_INFINITY)ERR_put_error(16,(0xfff),(106),"/usr/src/lib/libcrypto/ec/ecp_smpl.c" ,540); |
| 541 | return 0; |
| 542 | } |
| 543 | if (ctx == NULL((void *)0)) { |
| 544 | ctx = new_ctx = BN_CTX_new(); |
| 545 | if (ctx == NULL((void *)0)) |
| 546 | return 0; |
| 547 | } |
| 548 | BN_CTX_start(ctx); |
| 549 | if ((Z = BN_CTX_get(ctx)) == NULL((void *)0)) |
| 550 | goto err; |
| 551 | if ((Z_1 = BN_CTX_get(ctx)) == NULL((void *)0)) |
| 552 | goto err; |
| 553 | if ((Z_2 = BN_CTX_get(ctx)) == NULL((void *)0)) |
| 554 | goto err; |
| 555 | if ((Z_3 = BN_CTX_get(ctx)) == NULL((void *)0)) |
| 556 | goto err; |
| 557 | |
| 558 | /* transform (X, Y, Z) into (x, y) := (X/Z^2, Y/Z^3) */ |
| 559 | |
| 560 | if (group->meth->field_decode) { |
| 561 | if (!group->meth->field_decode(group, Z, &point->Z, ctx)) |
| 562 | goto err; |
| 563 | Z_ = Z; |
| 564 | } else { |
| 565 | Z_ = &point->Z; |
| 566 | } |
| 567 | |
| 568 | if (BN_is_one(Z_)) { |
| 569 | if (group->meth->field_decode) { |
| 570 | if (x != NULL((void *)0)) { |
| 571 | if (!group->meth->field_decode(group, x, &point->X, ctx)) |
| 572 | goto err; |
| 573 | } |
| 574 | if (y != NULL((void *)0)) { |
| 575 | if (!group->meth->field_decode(group, y, &point->Y, ctx)) |
| 576 | goto err; |
| 577 | } |
| 578 | } else { |
| 579 | if (x != NULL((void *)0)) { |
| 580 | if (!BN_copy(x, &point->X)) |
| 581 | goto err; |
| 582 | } |
| 583 | if (y != NULL((void *)0)) { |
| 584 | if (!BN_copy(y, &point->Y)) |
| 585 | goto err; |
| 586 | } |
| 587 | } |
| 588 | } else { |
| 589 | if (!BN_mod_inverse_ct(Z_1, Z_, &group->field, ctx)) { |
| 590 | ECerror(ERR_R_BN_LIB)ERR_put_error(16,(0xfff),(3),"/usr/src/lib/libcrypto/ec/ecp_smpl.c" ,590); |
| 591 | goto err; |
| 592 | } |
| 593 | if (group->meth->field_encode == 0) { |
| 594 | /* field_sqr works on standard representation */ |
| 595 | if (!group->meth->field_sqr(group, Z_2, Z_1, ctx)) |
| 596 | goto err; |
| 597 | } else { |
| 598 | if (!BN_mod_sqr(Z_2, Z_1, &group->field, ctx)) |
| 599 | goto err; |
| 600 | } |
| 601 | |
| 602 | if (x != NULL((void *)0)) { |
| 603 | /* |
| 604 | * in the Montgomery case, field_mul will cancel out |
| 605 | * Montgomery factor in X: |
| 606 | */ |
| 607 | if (!group->meth->field_mul(group, x, &point->X, Z_2, ctx)) |
| 608 | goto err; |
| 609 | } |
| 610 | if (y != NULL((void *)0)) { |
| 611 | if (group->meth->field_encode == 0) { |
| 612 | /* field_mul works on standard representation */ |
| 613 | if (!group->meth->field_mul(group, Z_3, Z_2, Z_1, ctx)) |
| 614 | goto err; |
| 615 | } else { |
| 616 | if (!BN_mod_mul(Z_3, Z_2, Z_1, &group->field, ctx)) |
| 617 | goto err; |
| 618 | } |
| 619 | |
| 620 | /* |
| 621 | * in the Montgomery case, field_mul will cancel out |
| 622 | * Montgomery factor in Y: |
| 623 | */ |
| 624 | if (!group->meth->field_mul(group, y, &point->Y, Z_3, ctx)) |
| 625 | goto err; |
| 626 | } |
| 627 | } |
| 628 | |
| 629 | ret = 1; |
| 630 | |
| 631 | err: |
| 632 | BN_CTX_end(ctx); |
| 633 | BN_CTX_free(new_ctx); |
| 634 | return ret; |
| 635 | } |
| 636 | |
| 637 | int |
| 638 | ec_GFp_simple_add(const EC_GROUP * group, EC_POINT * r, const EC_POINT * a, const EC_POINT * b, BN_CTX * ctx) |
| 639 | { |
| 640 | int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *); |
| 641 | int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); |
| 642 | const BIGNUM *p; |
| 643 | BN_CTX *new_ctx = NULL((void *)0); |
| 644 | BIGNUM *n0, *n1, *n2, *n3, *n4, *n5, *n6; |
| 645 | int ret = 0; |
| 646 | |
| 647 | if (a == b) |
| 648 | return EC_POINT_dbl(group, r, a, ctx); |
| 649 | if (EC_POINT_is_at_infinity(group, a) > 0) |
| 650 | return EC_POINT_copy(r, b); |
| 651 | if (EC_POINT_is_at_infinity(group, b) > 0) |
| 652 | return EC_POINT_copy(r, a); |
| 653 | |
| 654 | field_mul = group->meth->field_mul; |
| 655 | field_sqr = group->meth->field_sqr; |
| 656 | p = &group->field; |
| 657 | |
| 658 | if (ctx == NULL((void *)0)) { |
| 659 | ctx = new_ctx = BN_CTX_new(); |
| 660 | if (ctx == NULL((void *)0)) |
| 661 | return 0; |
| 662 | } |
| 663 | BN_CTX_start(ctx); |
| 664 | if ((n0 = BN_CTX_get(ctx)) == NULL((void *)0)) |
| 665 | goto end; |
| 666 | if ((n1 = BN_CTX_get(ctx)) == NULL((void *)0)) |
| 667 | goto end; |
| 668 | if ((n2 = BN_CTX_get(ctx)) == NULL((void *)0)) |
| 669 | goto end; |
| 670 | if ((n3 = BN_CTX_get(ctx)) == NULL((void *)0)) |
| 671 | goto end; |
| 672 | if ((n4 = BN_CTX_get(ctx)) == NULL((void *)0)) |
| 673 | goto end; |
| 674 | if ((n5 = BN_CTX_get(ctx)) == NULL((void *)0)) |
| 675 | goto end; |
| 676 | if ((n6 = BN_CTX_get(ctx)) == NULL((void *)0)) |
| 677 | goto end; |
| 678 | |
| 679 | /* |
| 680 | * Note that in this function we must not read components of 'a' or |
| 681 | * 'b' once we have written the corresponding components of 'r'. ('r' |
| 682 | * might be one of 'a' or 'b'.) |
| 683 | */ |
| 684 | |
| 685 | /* n1, n2 */ |
| 686 | if (b->Z_is_one) { |
| 687 | if (!BN_copy(n1, &a->X)) |
| 688 | goto end; |
| 689 | if (!BN_copy(n2, &a->Y)) |
| 690 | goto end; |
| 691 | /* n1 = X_a */ |
| 692 | /* n2 = Y_a */ |
| 693 | } else { |
| 694 | if (!field_sqr(group, n0, &b->Z, ctx)) |
| 695 | goto end; |
| 696 | if (!field_mul(group, n1, &a->X, n0, ctx)) |
| 697 | goto end; |
| 698 | /* n1 = X_a * Z_b^2 */ |
| 699 | |
| 700 | if (!field_mul(group, n0, n0, &b->Z, ctx)) |
| 701 | goto end; |
| 702 | if (!field_mul(group, n2, &a->Y, n0, ctx)) |
| 703 | goto end; |
| 704 | /* n2 = Y_a * Z_b^3 */ |
| 705 | } |
| 706 | |
| 707 | /* n3, n4 */ |
| 708 | if (a->Z_is_one) { |
| 709 | if (!BN_copy(n3, &b->X)) |
| 710 | goto end; |
| 711 | if (!BN_copy(n4, &b->Y)) |
| 712 | goto end; |
| 713 | /* n3 = X_b */ |
| 714 | /* n4 = Y_b */ |
| 715 | } else { |
| 716 | if (!field_sqr(group, n0, &a->Z, ctx)) |
| 717 | goto end; |
| 718 | if (!field_mul(group, n3, &b->X, n0, ctx)) |
| 719 | goto end; |
| 720 | /* n3 = X_b * Z_a^2 */ |
| 721 | |
| 722 | if (!field_mul(group, n0, n0, &a->Z, ctx)) |
| 723 | goto end; |
| 724 | if (!field_mul(group, n4, &b->Y, n0, ctx)) |
| 725 | goto end; |
| 726 | /* n4 = Y_b * Z_a^3 */ |
| 727 | } |
| 728 | |
| 729 | /* n5, n6 */ |
| 730 | if (!BN_mod_sub_quick(n5, n1, n3, p)) |
| 731 | goto end; |
| 732 | if (!BN_mod_sub_quick(n6, n2, n4, p)) |
| 733 | goto end; |
| 734 | /* n5 = n1 - n3 */ |
| 735 | /* n6 = n2 - n4 */ |
| 736 | |
| 737 | if (BN_is_zero(n5)) { |
| 738 | if (BN_is_zero(n6)) { |
| 739 | /* a is the same point as b */ |
| 740 | BN_CTX_end(ctx); |
| 741 | ret = EC_POINT_dbl(group, r, a, ctx); |
| 742 | ctx = NULL((void *)0); |
| 743 | goto end; |
| 744 | } else { |
| 745 | /* a is the inverse of b */ |
| 746 | BN_zero(&r->Z)(BN_set_word((&r->Z),0)); |
| 747 | r->Z_is_one = 0; |
| 748 | ret = 1; |
| 749 | goto end; |
| 750 | } |
| 751 | } |
| 752 | /* 'n7', 'n8' */ |
| 753 | if (!BN_mod_add_quick(n1, n1, n3, p)) |
| 754 | goto end; |
| 755 | if (!BN_mod_add_quick(n2, n2, n4, p)) |
| 756 | goto end; |
| 757 | /* 'n7' = n1 + n3 */ |
| 758 | /* 'n8' = n2 + n4 */ |
| 759 | |
| 760 | /* Z_r */ |
| 761 | if (a->Z_is_one && b->Z_is_one) { |
| 762 | if (!BN_copy(&r->Z, n5)) |
| 763 | goto end; |
| 764 | } else { |
| 765 | if (a->Z_is_one) { |
| 766 | if (!BN_copy(n0, &b->Z)) |
| 767 | goto end; |
| 768 | } else if (b->Z_is_one) { |
| 769 | if (!BN_copy(n0, &a->Z)) |
| 770 | goto end; |
| 771 | } else { |
| 772 | if (!field_mul(group, n0, &a->Z, &b->Z, ctx)) |
| 773 | goto end; |
| 774 | } |
| 775 | if (!field_mul(group, &r->Z, n0, n5, ctx)) |
| 776 | goto end; |
| 777 | } |
| 778 | r->Z_is_one = 0; |
| 779 | /* Z_r = Z_a * Z_b * n5 */ |
| 780 | |
| 781 | /* X_r */ |
| 782 | if (!field_sqr(group, n0, n6, ctx)) |
| 783 | goto end; |
| 784 | if (!field_sqr(group, n4, n5, ctx)) |
| 785 | goto end; |
| 786 | if (!field_mul(group, n3, n1, n4, ctx)) |
| 787 | goto end; |
| 788 | if (!BN_mod_sub_quick(&r->X, n0, n3, p)) |
| 789 | goto end; |
| 790 | /* X_r = n6^2 - n5^2 * 'n7' */ |
| 791 | |
| 792 | /* 'n9' */ |
| 793 | if (!BN_mod_lshift1_quick(n0, &r->X, p)) |
| 794 | goto end; |
| 795 | if (!BN_mod_sub_quick(n0, n3, n0, p)) |
| 796 | goto end; |
| 797 | /* n9 = n5^2 * 'n7' - 2 * X_r */ |
| 798 | |
| 799 | /* Y_r */ |
| 800 | if (!field_mul(group, n0, n0, n6, ctx)) |
| 801 | goto end; |
| 802 | if (!field_mul(group, n5, n4, n5, ctx)) |
| 803 | goto end; /* now n5 is n5^3 */ |
| 804 | if (!field_mul(group, n1, n2, n5, ctx)) |
| 805 | goto end; |
| 806 | if (!BN_mod_sub_quick(n0, n0, n1, p)) |
| 807 | goto end; |
| 808 | if (BN_is_odd(n0)) |
| 809 | if (!BN_add(n0, n0, p)) |
| 810 | goto end; |
| 811 | /* now 0 <= n0 < 2*p, and n0 is even */ |
| 812 | if (!BN_rshift1(&r->Y, n0)) |
| 813 | goto end; |
| 814 | /* Y_r = (n6 * 'n9' - 'n8' * 'n5^3') / 2 */ |
| 815 | |
| 816 | ret = 1; |
| 817 | |
| 818 | end: |
| 819 | if (ctx) /* otherwise we already called BN_CTX_end */ |
| 820 | BN_CTX_end(ctx); |
| 821 | BN_CTX_free(new_ctx); |
| 822 | return ret; |
| 823 | } |
| 824 | |
| 825 | |
| 826 | int |
| 827 | ec_GFp_simple_dbl(const EC_GROUP * group, EC_POINT * r, const EC_POINT * a, BN_CTX * ctx) |
| 828 | { |
| 829 | int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *); |
| 830 | int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); |
| 831 | const BIGNUM *p; |
| 832 | BN_CTX *new_ctx = NULL((void *)0); |
| 833 | BIGNUM *n0, *n1, *n2, *n3; |
| 834 | int ret = 0; |
| 835 | |
| 836 | if (EC_POINT_is_at_infinity(group, a) > 0) { |
| 837 | BN_zero(&r->Z)(BN_set_word((&r->Z),0)); |
| 838 | r->Z_is_one = 0; |
| 839 | return 1; |
| 840 | } |
| 841 | field_mul = group->meth->field_mul; |
| 842 | field_sqr = group->meth->field_sqr; |
| 843 | p = &group->field; |
| 844 | |
| 845 | if (ctx == NULL((void *)0)) { |
| 846 | ctx = new_ctx = BN_CTX_new(); |
| 847 | if (ctx == NULL((void *)0)) |
| 848 | return 0; |
| 849 | } |
| 850 | BN_CTX_start(ctx); |
| 851 | if ((n0 = BN_CTX_get(ctx)) == NULL((void *)0)) |
| 852 | goto err; |
| 853 | if ((n1 = BN_CTX_get(ctx)) == NULL((void *)0)) |
| 854 | goto err; |
| 855 | if ((n2 = BN_CTX_get(ctx)) == NULL((void *)0)) |
| 856 | goto err; |
| 857 | if ((n3 = BN_CTX_get(ctx)) == NULL((void *)0)) |
| 858 | goto err; |
| 859 | |
| 860 | /* |
| 861 | * Note that in this function we must not read components of 'a' once |
| 862 | * we have written the corresponding components of 'r'. ('r' might |
| 863 | * the same as 'a'.) |
| 864 | */ |
| 865 | |
| 866 | /* n1 */ |
| 867 | if (a->Z_is_one) { |
| 868 | if (!field_sqr(group, n0, &a->X, ctx)) |
| 869 | goto err; |
| 870 | if (!BN_mod_lshift1_quick(n1, n0, p)) |
| 871 | goto err; |
| 872 | if (!BN_mod_add_quick(n0, n0, n1, p)) |
| 873 | goto err; |
| 874 | if (!BN_mod_add_quick(n1, n0, &group->a, p)) |
| 875 | goto err; |
| 876 | /* n1 = 3 * X_a^2 + a_curve */ |
| 877 | } else if (group->a_is_minus3) { |
| 878 | if (!field_sqr(group, n1, &a->Z, ctx)) |
| 879 | goto err; |
| 880 | if (!BN_mod_add_quick(n0, &a->X, n1, p)) |
| 881 | goto err; |
| 882 | if (!BN_mod_sub_quick(n2, &a->X, n1, p)) |
| 883 | goto err; |
| 884 | if (!field_mul(group, n1, n0, n2, ctx)) |
| 885 | goto err; |
| 886 | if (!BN_mod_lshift1_quick(n0, n1, p)) |
| 887 | goto err; |
| 888 | if (!BN_mod_add_quick(n1, n0, n1, p)) |
| 889 | goto err; |
| 890 | /* |
| 891 | * n1 = 3 * (X_a + Z_a^2) * (X_a - Z_a^2) = 3 * X_a^2 - 3 * |
| 892 | * Z_a^4 |
| 893 | */ |
| 894 | } else { |
| 895 | if (!field_sqr(group, n0, &a->X, ctx)) |
| 896 | goto err; |
| 897 | if (!BN_mod_lshift1_quick(n1, n0, p)) |
| 898 | goto err; |
| 899 | if (!BN_mod_add_quick(n0, n0, n1, p)) |
| 900 | goto err; |
| 901 | if (!field_sqr(group, n1, &a->Z, ctx)) |
| 902 | goto err; |
| 903 | if (!field_sqr(group, n1, n1, ctx)) |
| 904 | goto err; |
| 905 | if (!field_mul(group, n1, n1, &group->a, ctx)) |
| 906 | goto err; |
| 907 | if (!BN_mod_add_quick(n1, n1, n0, p)) |
| 908 | goto err; |
| 909 | /* n1 = 3 * X_a^2 + a_curve * Z_a^4 */ |
| 910 | } |
| 911 | |
| 912 | /* Z_r */ |
| 913 | if (a->Z_is_one) { |
| 914 | if (!BN_copy(n0, &a->Y)) |
| 915 | goto err; |
| 916 | } else { |
| 917 | if (!field_mul(group, n0, &a->Y, &a->Z, ctx)) |
| 918 | goto err; |
| 919 | } |
| 920 | if (!BN_mod_lshift1_quick(&r->Z, n0, p)) |
| 921 | goto err; |
| 922 | r->Z_is_one = 0; |
| 923 | /* Z_r = 2 * Y_a * Z_a */ |
| 924 | |
| 925 | /* n2 */ |
| 926 | if (!field_sqr(group, n3, &a->Y, ctx)) |
| 927 | goto err; |
| 928 | if (!field_mul(group, n2, &a->X, n3, ctx)) |
| 929 | goto err; |
| 930 | if (!BN_mod_lshift_quick(n2, n2, 2, p)) |
| 931 | goto err; |
| 932 | /* n2 = 4 * X_a * Y_a^2 */ |
| 933 | |
| 934 | /* X_r */ |
| 935 | if (!BN_mod_lshift1_quick(n0, n2, p)) |
| 936 | goto err; |
| 937 | if (!field_sqr(group, &r->X, n1, ctx)) |
| 938 | goto err; |
| 939 | if (!BN_mod_sub_quick(&r->X, &r->X, n0, p)) |
| 940 | goto err; |
| 941 | /* X_r = n1^2 - 2 * n2 */ |
| 942 | |
| 943 | /* n3 */ |
| 944 | if (!field_sqr(group, n0, n3, ctx)) |
| 945 | goto err; |
| 946 | if (!BN_mod_lshift_quick(n3, n0, 3, p)) |
| 947 | goto err; |
| 948 | /* n3 = 8 * Y_a^4 */ |
| 949 | |
| 950 | /* Y_r */ |
| 951 | if (!BN_mod_sub_quick(n0, n2, &r->X, p)) |
| 952 | goto err; |
| 953 | if (!field_mul(group, n0, n1, n0, ctx)) |
| 954 | goto err; |
| 955 | if (!BN_mod_sub_quick(&r->Y, n0, n3, p)) |
| 956 | goto err; |
| 957 | /* Y_r = n1 * (n2 - X_r) - n3 */ |
| 958 | |
| 959 | ret = 1; |
| 960 | |
| 961 | err: |
| 962 | BN_CTX_end(ctx); |
| 963 | BN_CTX_free(new_ctx); |
| 964 | return ret; |
| 965 | } |
| 966 | |
| 967 | |
| 968 | int |
| 969 | ec_GFp_simple_invert(const EC_GROUP * group, EC_POINT * point, BN_CTX * ctx) |
| 970 | { |
| 971 | if (EC_POINT_is_at_infinity(group, point) > 0 || BN_is_zero(&point->Y)) |
| 972 | /* point is its own inverse */ |
| 973 | return 1; |
| 974 | |
| 975 | return BN_usub(&point->Y, &group->field, &point->Y); |
| 976 | } |
| 977 | |
| 978 | |
| 979 | int |
| 980 | ec_GFp_simple_is_at_infinity(const EC_GROUP * group, const EC_POINT * point) |
| 981 | { |
| 982 | return BN_is_zero(&point->Z); |
| 983 | } |
| 984 | |
| 985 | |
| 986 | int |
| 987 | ec_GFp_simple_is_on_curve(const EC_GROUP * group, const EC_POINT * point, BN_CTX * ctx) |
| 988 | { |
| 989 | int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *); |
| 990 | int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); |
| 991 | const BIGNUM *p; |
| 992 | BN_CTX *new_ctx = NULL((void *)0); |
| 993 | BIGNUM *rh, *tmp, *Z4, *Z6; |
| 994 | int ret = -1; |
| 995 | |
| 996 | if (EC_POINT_is_at_infinity(group, point) > 0) |
| 997 | return 1; |
| 998 | |
| 999 | field_mul = group->meth->field_mul; |
| 1000 | field_sqr = group->meth->field_sqr; |
| 1001 | p = &group->field; |
| 1002 | |
| 1003 | if (ctx == NULL((void *)0)) { |
| 1004 | ctx = new_ctx = BN_CTX_new(); |
| 1005 | if (ctx == NULL((void *)0)) |
| 1006 | return -1; |
| 1007 | } |
| 1008 | BN_CTX_start(ctx); |
| 1009 | if ((rh = BN_CTX_get(ctx)) == NULL((void *)0)) |
| 1010 | goto err; |
| 1011 | if ((tmp = BN_CTX_get(ctx)) == NULL((void *)0)) |
| 1012 | goto err; |
| 1013 | if ((Z4 = BN_CTX_get(ctx)) == NULL((void *)0)) |
| 1014 | goto err; |
| 1015 | if ((Z6 = BN_CTX_get(ctx)) == NULL((void *)0)) |
| 1016 | goto err; |
| 1017 | |
| 1018 | /* |
| 1019 | * We have a curve defined by a Weierstrass equation y^2 = x^3 + a*x |
| 1020 | * + b. The point to consider is given in Jacobian projective |
| 1021 | * coordinates where (X, Y, Z) represents (x, y) = (X/Z^2, Y/Z^3). |
| 1022 | * Substituting this and multiplying by Z^6 transforms the above |
| 1023 | * equation into Y^2 = X^3 + a*X*Z^4 + b*Z^6. To test this, we add up |
| 1024 | * the right-hand side in 'rh'. |
| 1025 | */ |
| 1026 | |
| 1027 | /* rh := X^2 */ |
| 1028 | if (!field_sqr(group, rh, &point->X, ctx)) |
| 1029 | goto err; |
| 1030 | |
| 1031 | if (!point->Z_is_one) { |
| 1032 | if (!field_sqr(group, tmp, &point->Z, ctx)) |
| 1033 | goto err; |
| 1034 | if (!field_sqr(group, Z4, tmp, ctx)) |
| 1035 | goto err; |
| 1036 | if (!field_mul(group, Z6, Z4, tmp, ctx)) |
| 1037 | goto err; |
| 1038 | |
| 1039 | /* rh := (rh + a*Z^4)*X */ |
| 1040 | if (group->a_is_minus3) { |
| 1041 | if (!BN_mod_lshift1_quick(tmp, Z4, p)) |
| 1042 | goto err; |
| 1043 | if (!BN_mod_add_quick(tmp, tmp, Z4, p)) |
| 1044 | goto err; |
| 1045 | if (!BN_mod_sub_quick(rh, rh, tmp, p)) |
| 1046 | goto err; |
| 1047 | if (!field_mul(group, rh, rh, &point->X, ctx)) |
| 1048 | goto err; |
| 1049 | } else { |
| 1050 | if (!field_mul(group, tmp, Z4, &group->a, ctx)) |
| 1051 | goto err; |
| 1052 | if (!BN_mod_add_quick(rh, rh, tmp, p)) |
| 1053 | goto err; |
| 1054 | if (!field_mul(group, rh, rh, &point->X, ctx)) |
| 1055 | goto err; |
| 1056 | } |
| 1057 | |
| 1058 | /* rh := rh + b*Z^6 */ |
| 1059 | if (!field_mul(group, tmp, &group->b, Z6, ctx)) |
| 1060 | goto err; |
| 1061 | if (!BN_mod_add_quick(rh, rh, tmp, p)) |
| 1062 | goto err; |
| 1063 | } else { |
| 1064 | /* point->Z_is_one */ |
| 1065 | |
| 1066 | /* rh := (rh + a)*X */ |
| 1067 | if (!BN_mod_add_quick(rh, rh, &group->a, p)) |
| 1068 | goto err; |
| 1069 | if (!field_mul(group, rh, rh, &point->X, ctx)) |
| 1070 | goto err; |
| 1071 | /* rh := rh + b */ |
| 1072 | if (!BN_mod_add_quick(rh, rh, &group->b, p)) |
| 1073 | goto err; |
| 1074 | } |
| 1075 | |
| 1076 | /* 'lh' := Y^2 */ |
| 1077 | if (!field_sqr(group, tmp, &point->Y, ctx)) |
| 1078 | goto err; |
| 1079 | |
| 1080 | ret = (0 == BN_ucmp(tmp, rh)); |
| 1081 | |
| 1082 | err: |
| 1083 | BN_CTX_end(ctx); |
| 1084 | BN_CTX_free(new_ctx); |
| 1085 | return ret; |
| 1086 | } |
| 1087 | |
| 1088 | |
| 1089 | int |
| 1090 | ec_GFp_simple_cmp(const EC_GROUP * group, const EC_POINT * a, const EC_POINT * b, BN_CTX * ctx) |
| 1091 | { |
| 1092 | /* |
| 1093 | * return values: -1 error 0 equal (in affine coordinates) 1 |
| 1094 | * not equal |
| 1095 | */ |
| 1096 | |
| 1097 | int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *); |
| 1098 | int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); |
| 1099 | BN_CTX *new_ctx = NULL((void *)0); |
| 1100 | BIGNUM *tmp1, *tmp2, *Za23, *Zb23; |
| 1101 | const BIGNUM *tmp1_, *tmp2_; |
| 1102 | int ret = -1; |
| 1103 | |
| 1104 | if (EC_POINT_is_at_infinity(group, a) > 0) { |
| 1105 | return EC_POINT_is_at_infinity(group, b) > 0 ? 0 : 1; |
| 1106 | } |
| 1107 | if (EC_POINT_is_at_infinity(group, b) > 0) |
| 1108 | return 1; |
| 1109 | |
| 1110 | if (a->Z_is_one && b->Z_is_one) { |
| 1111 | return ((BN_cmp(&a->X, &b->X) == 0) && BN_cmp(&a->Y, &b->Y) == 0) ? 0 : 1; |
| 1112 | } |
| 1113 | field_mul = group->meth->field_mul; |
| 1114 | field_sqr = group->meth->field_sqr; |
| 1115 | |
| 1116 | if (ctx == NULL((void *)0)) { |
| 1117 | ctx = new_ctx = BN_CTX_new(); |
| 1118 | if (ctx == NULL((void *)0)) |
| 1119 | return -1; |
| 1120 | } |
| 1121 | BN_CTX_start(ctx); |
| 1122 | if ((tmp1 = BN_CTX_get(ctx)) == NULL((void *)0)) |
| 1123 | goto end; |
| 1124 | if ((tmp2 = BN_CTX_get(ctx)) == NULL((void *)0)) |
| 1125 | goto end; |
| 1126 | if ((Za23 = BN_CTX_get(ctx)) == NULL((void *)0)) |
| 1127 | goto end; |
| 1128 | if ((Zb23 = BN_CTX_get(ctx)) == NULL((void *)0)) |
| 1129 | goto end; |
| 1130 | |
| 1131 | /* |
| 1132 | * We have to decide whether (X_a/Z_a^2, Y_a/Z_a^3) = (X_b/Z_b^2, |
| 1133 | * Y_b/Z_b^3), or equivalently, whether (X_a*Z_b^2, Y_a*Z_b^3) = |
| 1134 | * (X_b*Z_a^2, Y_b*Z_a^3). |
| 1135 | */ |
| 1136 | |
| 1137 | if (!b->Z_is_one) { |
| 1138 | if (!field_sqr(group, Zb23, &b->Z, ctx)) |
| 1139 | goto end; |
| 1140 | if (!field_mul(group, tmp1, &a->X, Zb23, ctx)) |
| 1141 | goto end; |
| 1142 | tmp1_ = tmp1; |
| 1143 | } else |
| 1144 | tmp1_ = &a->X; |
| 1145 | if (!a->Z_is_one) { |
| 1146 | if (!field_sqr(group, Za23, &a->Z, ctx)) |
| 1147 | goto end; |
| 1148 | if (!field_mul(group, tmp2, &b->X, Za23, ctx)) |
| 1149 | goto end; |
| 1150 | tmp2_ = tmp2; |
| 1151 | } else |
| 1152 | tmp2_ = &b->X; |
| 1153 | |
| 1154 | /* compare X_a*Z_b^2 with X_b*Z_a^2 */ |
| 1155 | if (BN_cmp(tmp1_, tmp2_) != 0) { |
| 1156 | ret = 1; /* points differ */ |
| 1157 | goto end; |
| 1158 | } |
| 1159 | if (!b->Z_is_one) { |
| 1160 | if (!field_mul(group, Zb23, Zb23, &b->Z, ctx)) |
| 1161 | goto end; |
| 1162 | if (!field_mul(group, tmp1, &a->Y, Zb23, ctx)) |
| 1163 | goto end; |
| 1164 | /* tmp1_ = tmp1 */ |
| 1165 | } else |
| 1166 | tmp1_ = &a->Y; |
| 1167 | if (!a->Z_is_one) { |
| 1168 | if (!field_mul(group, Za23, Za23, &a->Z, ctx)) |
| 1169 | goto end; |
| 1170 | if (!field_mul(group, tmp2, &b->Y, Za23, ctx)) |
| 1171 | goto end; |
| 1172 | /* tmp2_ = tmp2 */ |
| 1173 | } else |
| 1174 | tmp2_ = &b->Y; |
| 1175 | |
| 1176 | /* compare Y_a*Z_b^3 with Y_b*Z_a^3 */ |
| 1177 | if (BN_cmp(tmp1_, tmp2_) != 0) { |
| 1178 | ret = 1; /* points differ */ |
| 1179 | goto end; |
| 1180 | } |
| 1181 | /* points are equal */ |
| 1182 | ret = 0; |
| 1183 | |
| 1184 | end: |
| 1185 | BN_CTX_end(ctx); |
| 1186 | BN_CTX_free(new_ctx); |
| 1187 | return ret; |
| 1188 | } |
| 1189 | |
| 1190 | |
| 1191 | int |
| 1192 | ec_GFp_simple_make_affine(const EC_GROUP * group, EC_POINT * point, BN_CTX * ctx) |
| 1193 | { |
| 1194 | BN_CTX *new_ctx = NULL((void *)0); |
| 1195 | BIGNUM *x, *y; |
| 1196 | int ret = 0; |
| 1197 | |
| 1198 | if (point->Z_is_one || EC_POINT_is_at_infinity(group, point) > 0) |
| 1199 | return 1; |
| 1200 | |
| 1201 | if (ctx == NULL((void *)0)) { |
| 1202 | ctx = new_ctx = BN_CTX_new(); |
| 1203 | if (ctx == NULL((void *)0)) |
| 1204 | return 0; |
| 1205 | } |
| 1206 | BN_CTX_start(ctx); |
| 1207 | if ((x = BN_CTX_get(ctx)) == NULL((void *)0)) |
| 1208 | goto err; |
| 1209 | if ((y = BN_CTX_get(ctx)) == NULL((void *)0)) |
| 1210 | goto err; |
| 1211 | |
| 1212 | if (!EC_POINT_get_affine_coordinates(group, point, x, y, ctx)) |
| 1213 | goto err; |
| 1214 | if (!EC_POINT_set_affine_coordinates(group, point, x, y, ctx)) |
| 1215 | goto err; |
| 1216 | if (!point->Z_is_one) { |
| 1217 | ECerror(ERR_R_INTERNAL_ERROR)ERR_put_error(16,(0xfff),((4|64)),"/usr/src/lib/libcrypto/ec/ecp_smpl.c" ,1217); |
| 1218 | goto err; |
| 1219 | } |
| 1220 | ret = 1; |
| 1221 | |
| 1222 | err: |
| 1223 | BN_CTX_end(ctx); |
| 1224 | BN_CTX_free(new_ctx); |
| 1225 | return ret; |
| 1226 | } |
| 1227 | |
| 1228 | |
| 1229 | int |
| 1230 | ec_GFp_simple_points_make_affine(const EC_GROUP * group, size_t num, EC_POINT * points[], BN_CTX * ctx) |
| 1231 | { |
| 1232 | BN_CTX *new_ctx = NULL((void *)0); |
| 1233 | BIGNUM *tmp0, *tmp1; |
| 1234 | size_t pow2 = 0; |
| 1235 | BIGNUM **heap = NULL((void *)0); |
| 1236 | size_t i; |
| 1237 | int ret = 0; |
| 1238 | |
| 1239 | if (num == 0) |
| 1240 | return 1; |
| 1241 | |
| 1242 | if (ctx == NULL((void *)0)) { |
| 1243 | ctx = new_ctx = BN_CTX_new(); |
| 1244 | if (ctx == NULL((void *)0)) |
| 1245 | return 0; |
| 1246 | } |
| 1247 | BN_CTX_start(ctx); |
| 1248 | if ((tmp0 = BN_CTX_get(ctx)) == NULL((void *)0)) |
| 1249 | goto err; |
| 1250 | if ((tmp1 = BN_CTX_get(ctx)) == NULL((void *)0)) |
| 1251 | goto err; |
| 1252 | |
| 1253 | /* |
| 1254 | * Before converting the individual points, compute inverses of all Z |
| 1255 | * values. Modular inversion is rather slow, but luckily we can do |
| 1256 | * with a single explicit inversion, plus about 3 multiplications per |
| 1257 | * input value. |
| 1258 | */ |
| 1259 | |
| 1260 | pow2 = 1; |
| 1261 | while (num > pow2) |
| 1262 | pow2 <<= 1; |
| 1263 | /* |
| 1264 | * Now pow2 is the smallest power of 2 satifsying pow2 >= num. We |
| 1265 | * need twice that. |
| 1266 | */ |
| 1267 | pow2 <<= 1; |
| 1268 | |
| 1269 | heap = reallocarray(NULL((void *)0), pow2, sizeof heap[0]); |
| 1270 | if (heap == NULL((void *)0)) |
| 1271 | goto err; |
| 1272 | |
| 1273 | /* |
| 1274 | * The array is used as a binary tree, exactly as in heapsort: |
| 1275 | * |
| 1276 | * heap[1] heap[2] heap[3] heap[4] heap[5] |
| 1277 | * heap[6] heap[7] heap[8]heap[9] heap[10]heap[11] |
| 1278 | * heap[12]heap[13] heap[14] heap[15] |
| 1279 | * |
| 1280 | * We put the Z's in the last line; then we set each other node to the |
| 1281 | * product of its two child-nodes (where empty or 0 entries are |
| 1282 | * treated as ones); then we invert heap[1]; then we invert each |
| 1283 | * other node by replacing it by the product of its parent (after |
| 1284 | * inversion) and its sibling (before inversion). |
| 1285 | */ |
| 1286 | heap[0] = NULL((void *)0); |
| 1287 | for (i = pow2 / 2 - 1; i > 0; i--) |
| 1288 | heap[i] = NULL((void *)0); |
| 1289 | for (i = 0; i < num; i++) |
| 1290 | heap[pow2 / 2 + i] = &points[i]->Z; |
| 1291 | for (i = pow2 / 2 + num; i < pow2; i++) |
| 1292 | heap[i] = NULL((void *)0); |
| 1293 | |
| 1294 | /* set each node to the product of its children */ |
| 1295 | for (i = pow2 / 2 - 1; i > 0; i--) { |
| 1296 | heap[i] = BN_new(); |
| 1297 | if (heap[i] == NULL((void *)0)) |
| 1298 | goto err; |
| 1299 | |
| 1300 | if (heap[2 * i] != NULL((void *)0)) { |
| 1301 | if ((heap[2 * i + 1] == NULL((void *)0)) || BN_is_zero(heap[2 * i + 1])) { |
| 1302 | if (!BN_copy(heap[i], heap[2 * i])) |
| 1303 | goto err; |
| 1304 | } else { |
| 1305 | if (BN_is_zero(heap[2 * i])) { |
| 1306 | if (!BN_copy(heap[i], heap[2 * i + 1])) |
| 1307 | goto err; |
| 1308 | } else { |
| 1309 | if (!group->meth->field_mul(group, heap[i], |
| 1310 | heap[2 * i], heap[2 * i + 1], ctx)) |
| 1311 | goto err; |
| 1312 | } |
| 1313 | } |
| 1314 | } |
| 1315 | } |
| 1316 | |
| 1317 | /* invert heap[1] */ |
| 1318 | if (!BN_is_zero(heap[1])) { |
| 1319 | if (!BN_mod_inverse_ct(heap[1], heap[1], &group->field, ctx)) { |
| 1320 | ECerror(ERR_R_BN_LIB)ERR_put_error(16,(0xfff),(3),"/usr/src/lib/libcrypto/ec/ecp_smpl.c" ,1320); |
| 1321 | goto err; |
| 1322 | } |
| 1323 | } |
| 1324 | if (group->meth->field_encode != 0) { |
| 1325 | /* |
| 1326 | * in the Montgomery case, we just turned R*H (representing |
| 1327 | * H) into 1/(R*H), but we need R*(1/H) (representing |
| 1328 | * 1/H); i.e. we have need to multiply by the Montgomery |
| 1329 | * factor twice |
| 1330 | */ |
| 1331 | if (!group->meth->field_encode(group, heap[1], heap[1], ctx)) |
| 1332 | goto err; |
| 1333 | if (!group->meth->field_encode(group, heap[1], heap[1], ctx)) |
| 1334 | goto err; |
| 1335 | } |
| 1336 | /* set other heap[i]'s to their inverses */ |
| 1337 | for (i = 2; i < pow2 / 2 + num; i += 2) { |
| 1338 | /* i is even */ |
| 1339 | if ((heap[i + 1] != NULL((void *)0)) && !BN_is_zero(heap[i + 1])) { |
| 1340 | if (!group->meth->field_mul(group, tmp0, heap[i / 2], heap[i + 1], ctx)) |
| 1341 | goto err; |
| 1342 | if (!group->meth->field_mul(group, tmp1, heap[i / 2], heap[i], ctx)) |
| 1343 | goto err; |
| 1344 | if (!BN_copy(heap[i], tmp0)) |
| 1345 | goto err; |
| 1346 | if (!BN_copy(heap[i + 1], tmp1)) |
| 1347 | goto err; |
| 1348 | } else { |
| 1349 | if (!BN_copy(heap[i], heap[i / 2])) |
| 1350 | goto err; |
| 1351 | } |
| 1352 | } |
| 1353 | |
| 1354 | /* |
| 1355 | * we have replaced all non-zero Z's by their inverses, now fix up |
| 1356 | * all the points |
| 1357 | */ |
| 1358 | for (i = 0; i < num; i++) { |
| 1359 | EC_POINT *p = points[i]; |
| 1360 | |
| 1361 | if (!BN_is_zero(&p->Z)) { |
| 1362 | /* turn (X, Y, 1/Z) into (X/Z^2, Y/Z^3, 1) */ |
| 1363 | |
| 1364 | if (!group->meth->field_sqr(group, tmp1, &p->Z, ctx)) |
| 1365 | goto err; |
| 1366 | if (!group->meth->field_mul(group, &p->X, &p->X, tmp1, ctx)) |
| 1367 | goto err; |
| 1368 | |
| 1369 | if (!group->meth->field_mul(group, tmp1, tmp1, &p->Z, ctx)) |
| 1370 | goto err; |
| 1371 | if (!group->meth->field_mul(group, &p->Y, &p->Y, tmp1, ctx)) |
| 1372 | goto err; |
| 1373 | |
| 1374 | if (group->meth->field_set_to_one != 0) { |
| 1375 | if (!group->meth->field_set_to_one(group, &p->Z, ctx)) |
| 1376 | goto err; |
| 1377 | } else { |
| 1378 | if (!BN_one(&p->Z)BN_set_word((&p->Z), 1)) |
| 1379 | goto err; |
| 1380 | } |
| 1381 | p->Z_is_one = 1; |
| 1382 | } |
| 1383 | } |
| 1384 | |
| 1385 | ret = 1; |
| 1386 | |
| 1387 | err: |
| 1388 | BN_CTX_end(ctx); |
| 1389 | BN_CTX_free(new_ctx); |
| 1390 | if (heap != NULL((void *)0)) { |
| 1391 | /* |
| 1392 | * heap[pow2/2] .. heap[pow2-1] have not been allocated |
| 1393 | * locally! |
| 1394 | */ |
| 1395 | for (i = pow2 / 2 - 1; i > 0; i--) { |
| 1396 | BN_clear_free(heap[i]); |
| 1397 | } |
| 1398 | free(heap); |
| 1399 | } |
| 1400 | return ret; |
| 1401 | } |
| 1402 | |
| 1403 | |
| 1404 | int |
| 1405 | ec_GFp_simple_field_mul(const EC_GROUP * group, BIGNUM * r, const BIGNUM * a, const BIGNUM * b, BN_CTX * ctx) |
| 1406 | { |
| 1407 | return BN_mod_mul(r, a, b, &group->field, ctx); |
| 1408 | } |
| 1409 | |
| 1410 | int |
| 1411 | ec_GFp_simple_field_sqr(const EC_GROUP * group, BIGNUM * r, const BIGNUM * a, BN_CTX * ctx) |
| 1412 | { |
| 1413 | return BN_mod_sqr(r, a, &group->field, ctx); |
| 1414 | } |
| 1415 | |
| 1416 | /* |
| 1417 | * Apply randomization of EC point projective coordinates: |
| 1418 | * |
| 1419 | * (X, Y, Z) = (lambda^2 * X, lambda^3 * Y, lambda * Z) |
| 1420 | * |
| 1421 | * where lambda is in the interval [1, group->field). |
| 1422 | */ |
| 1423 | int |
| 1424 | ec_GFp_simple_blind_coordinates(const EC_GROUP *group, EC_POINT *p, BN_CTX *ctx) |
| 1425 | { |
| 1426 | BIGNUM *lambda = NULL((void *)0); |
| 1427 | BIGNUM *tmp = NULL((void *)0); |
| 1428 | int ret = 0; |
| 1429 | |
| 1430 | BN_CTX_start(ctx); |
| 1431 | if ((lambda = BN_CTX_get(ctx)) == NULL((void *)0)) |
| 1432 | goto err; |
| 1433 | if ((tmp = BN_CTX_get(ctx)) == NULL((void *)0)) |
| 1434 | goto err; |
| 1435 | |
| 1436 | /* Generate lambda in [1, group->field - 1] */ |
| 1437 | if (!bn_rand_interval(lambda, BN_value_one(), &group->field)) |
| 1438 | goto err; |
| 1439 | |
| 1440 | if (group->meth->field_encode != NULL((void *)0) && |
| 1441 | !group->meth->field_encode(group, lambda, lambda, ctx)) |
| 1442 | goto err; |
| 1443 | |
| 1444 | /* Z = lambda * Z */ |
| 1445 | if (!group->meth->field_mul(group, &p->Z, lambda, &p->Z, ctx)) |
| 1446 | goto err; |
| 1447 | |
| 1448 | /* tmp = lambda^2 */ |
| 1449 | if (!group->meth->field_sqr(group, tmp, lambda, ctx)) |
| 1450 | goto err; |
| 1451 | |
| 1452 | /* X = lambda^2 * X */ |
| 1453 | if (!group->meth->field_mul(group, &p->X, tmp, &p->X, ctx)) |
| 1454 | goto err; |
| 1455 | |
| 1456 | /* tmp = lambda^3 */ |
| 1457 | if (!group->meth->field_mul(group, tmp, tmp, lambda, ctx)) |
| 1458 | goto err; |
| 1459 | |
| 1460 | /* Y = lambda^3 * Y */ |
| 1461 | if (!group->meth->field_mul(group, &p->Y, tmp, &p->Y, ctx)) |
| 1462 | goto err; |
| 1463 | |
| 1464 | /* Disable optimized arithmetics after replacing Z by lambda * Z. */ |
| 1465 | p->Z_is_one = 0; |
| 1466 | |
| 1467 | ret = 1; |
| 1468 | |
| 1469 | err: |
| 1470 | BN_CTX_end(ctx); |
| 1471 | return ret; |
| 1472 | } |
| 1473 | |
| 1474 | |
| 1475 | #define EC_POINT_BN_set_flags(P, flags) do { \ |
| 1476 | BN_set_flags(&(P)->X, (flags)); \ |
| 1477 | BN_set_flags(&(P)->Y, (flags)); \ |
| 1478 | BN_set_flags(&(P)->Z, (flags)); \ |
| 1479 | } while(0) |
| 1480 | |
| 1481 | #define EC_POINT_CSWAP(c, a, b, w, t) do { \ |
| 1482 | if (!BN_swap_ct(c, &(a)->X, &(b)->X, w) || \ |
| 1483 | !BN_swap_ct(c, &(a)->Y, &(b)->Y, w) || \ |
| 1484 | !BN_swap_ct(c, &(a)->Z, &(b)->Z, w)) \ |
| 1485 | goto err; \ |
| 1486 | t = ((a)->Z_is_one ^ (b)->Z_is_one) & (c); \ |
| 1487 | (a)->Z_is_one ^= (t); \ |
| 1488 | (b)->Z_is_one ^= (t); \ |
| 1489 | } while(0) |
| 1490 | |
| 1491 | /* |
| 1492 | * This function computes (in constant time) a point multiplication over the |
| 1493 | * EC group. |
| 1494 | * |
| 1495 | * At a high level, it is Montgomery ladder with conditional swaps. |
| 1496 | * |
| 1497 | * It performs either a fixed point multiplication |
| 1498 | * (scalar * generator) |
| 1499 | * when point is NULL, or a variable point multiplication |
| 1500 | * (scalar * point) |
| 1501 | * when point is not NULL. |
| 1502 | * |
| 1503 | * scalar should be in the range [0,n) otherwise all constant time bets are off. |
| 1504 | * |
| 1505 | * NB: This says nothing about EC_POINT_add and EC_POINT_dbl, |
| 1506 | * which of course are not constant time themselves. |
| 1507 | * |
| 1508 | * The product is stored in r. |
| 1509 | * |
| 1510 | * Returns 1 on success, 0 otherwise. |
| 1511 | */ |
| 1512 | static int |
| 1513 | ec_GFp_simple_mul_ct(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, |
| 1514 | const EC_POINT *point, BN_CTX *ctx) |
| 1515 | { |
| 1516 | int i, cardinality_bits, group_top, kbit, pbit, Z_is_one; |
| 1517 | EC_POINT *s = NULL((void *)0); |
| 1518 | BIGNUM *k = NULL((void *)0); |
| 1519 | BIGNUM *lambda = NULL((void *)0); |
| 1520 | BIGNUM *cardinality = NULL((void *)0); |
| 1521 | BN_CTX *new_ctx = NULL((void *)0); |
| 1522 | int ret = 0; |
| 1523 | |
| 1524 | if (ctx == NULL((void *)0) && (ctx = new_ctx = BN_CTX_new()) == NULL((void *)0)) |
| 1525 | return 0; |
| 1526 | |
| 1527 | BN_CTX_start(ctx); |
| 1528 | |
| 1529 | if ((s = EC_POINT_new(group)) == NULL((void *)0)) |
| 1530 | goto err; |
| 1531 | |
| 1532 | if (point == NULL((void *)0)) { |
| 1533 | if (!EC_POINT_copy(s, group->generator)) |
| 1534 | goto err; |
| 1535 | } else { |
| 1536 | if (!EC_POINT_copy(s, point)) |
| 1537 | goto err; |
| 1538 | } |
| 1539 | |
| 1540 | EC_POINT_BN_set_flags(s, BN_FLG_CONSTTIME0x04); |
| 1541 | |
| 1542 | if ((cardinality = BN_CTX_get(ctx)) == NULL((void *)0)) |
| 1543 | goto err; |
| 1544 | if ((lambda = BN_CTX_get(ctx)) == NULL((void *)0)) |
| 1545 | goto err; |
| 1546 | if ((k = BN_CTX_get(ctx)) == NULL((void *)0)) |
| 1547 | goto err; |
| 1548 | if (!BN_mul(cardinality, &group->order, &group->cofactor, ctx)) |
| 1549 | goto err; |
| 1550 | |
| 1551 | /* |
| 1552 | * Group cardinalities are often on a word boundary. |
| 1553 | * So when we pad the scalar, some timing diff might |
| 1554 | * pop if it needs to be expanded due to carries. |
| 1555 | * So expand ahead of time. |
| 1556 | */ |
| 1557 | cardinality_bits = BN_num_bits(cardinality); |
| 1558 | group_top = cardinality->top; |
| 1559 | if ((bn_wexpand(k, group_top + 2)(((group_top + 2) <= (k)->dmax)?(k):bn_expand2((k),(group_top + 2))) == NULL((void *)0)) || |
| 1560 | (bn_wexpand(lambda, group_top + 2)(((group_top + 2) <= (lambda)->dmax)?(lambda):bn_expand2 ((lambda),(group_top + 2))) == NULL((void *)0))) |
| 1561 | goto err; |
| 1562 | |
| 1563 | if (!BN_copy(k, scalar)) |
| 1564 | goto err; |
| 1565 | |
| 1566 | BN_set_flags(k, BN_FLG_CONSTTIME0x04); |
| 1567 | |
| 1568 | if (BN_num_bits(k) > cardinality_bits || BN_is_negative(k)) { |
| 1569 | /* |
| 1570 | * This is an unusual input, and we don't guarantee |
| 1571 | * constant-timeness |
| 1572 | */ |
| 1573 | if (!BN_nnmod(k, k, cardinality, ctx)) |
| 1574 | goto err; |
| 1575 | } |
| 1576 | |
| 1577 | if (!BN_add(lambda, k, cardinality)) |
| 1578 | goto err; |
| 1579 | BN_set_flags(lambda, BN_FLG_CONSTTIME0x04); |
| 1580 | if (!BN_add(k, lambda, cardinality)) |
| 1581 | goto err; |
| 1582 | /* |
| 1583 | * lambda := scalar + cardinality |
| 1584 | * k := scalar + 2*cardinality |
| 1585 | */ |
| 1586 | kbit = BN_is_bit_set(lambda, cardinality_bits); |
| 1587 | if (!BN_swap_ct(kbit, k, lambda, group_top + 2)) |
| 1588 | goto err; |
| 1589 | |
| 1590 | group_top = group->field.top; |
| 1591 | if ((bn_wexpand(&s->X, group_top)(((group_top) <= (&s->X)->dmax)?(&s->X):bn_expand2 ((&s->X),(group_top))) == NULL((void *)0)) || |
| 1592 | (bn_wexpand(&s->Y, group_top)(((group_top) <= (&s->Y)->dmax)?(&s->Y):bn_expand2 ((&s->Y),(group_top))) == NULL((void *)0)) || |
| 1593 | (bn_wexpand(&s->Z, group_top)(((group_top) <= (&s->Z)->dmax)?(&s->Z):bn_expand2 ((&s->Z),(group_top))) == NULL((void *)0)) || |
| 1594 | (bn_wexpand(&r->X, group_top)(((group_top) <= (&r->X)->dmax)?(&r->X):bn_expand2 ((&r->X),(group_top))) == NULL((void *)0)) || |
| 1595 | (bn_wexpand(&r->Y, group_top)(((group_top) <= (&r->Y)->dmax)?(&r->Y):bn_expand2 ((&r->Y),(group_top))) == NULL((void *)0)) || |
| 1596 | (bn_wexpand(&r->Z, group_top)(((group_top) <= (&r->Z)->dmax)?(&r->Z):bn_expand2 ((&r->Z),(group_top))) == NULL((void *)0))) |
| 1597 | goto err; |
| 1598 | |
| 1599 | /* |
| 1600 | * Apply coordinate blinding for EC_POINT if the underlying EC_METHOD |
| 1601 | * implements it. |
| 1602 | */ |
| 1603 | if (!ec_point_blind_coordinates(group, s, ctx)) |
| 1604 | goto err; |
| 1605 | |
| 1606 | /* top bit is a 1, in a fixed pos */ |
| 1607 | if (!EC_POINT_copy(r, s)) |
| 1608 | goto err; |
| 1609 | |
| 1610 | EC_POINT_BN_set_flags(r, BN_FLG_CONSTTIME0x04); |
| 1611 | |
| 1612 | if (!EC_POINT_dbl(group, s, s, ctx)) |
| 1613 | goto err; |
| 1614 | |
| 1615 | pbit = 0; |
| 1616 | |
| 1617 | /* |
| 1618 | * The ladder step, with branches, is |
| 1619 | * |
| 1620 | * k[i] == 0: S = add(R, S), R = dbl(R) |
| 1621 | * k[i] == 1: R = add(S, R), S = dbl(S) |
| 1622 | * |
| 1623 | * Swapping R, S conditionally on k[i] leaves you with state |
| 1624 | * |
| 1625 | * k[i] == 0: T, U = R, S |
| 1626 | * k[i] == 1: T, U = S, R |
| 1627 | * |
| 1628 | * Then perform the ECC ops. |
| 1629 | * |
| 1630 | * U = add(T, U) |
| 1631 | * T = dbl(T) |
| 1632 | * |
| 1633 | * Which leaves you with state |
| 1634 | * |
| 1635 | * k[i] == 0: U = add(R, S), T = dbl(R) |
| 1636 | * k[i] == 1: U = add(S, R), T = dbl(S) |
| 1637 | * |
| 1638 | * Swapping T, U conditionally on k[i] leaves you with state |
| 1639 | * |
| 1640 | * k[i] == 0: R, S = T, U |
| 1641 | * k[i] == 1: R, S = U, T |
| 1642 | * |
| 1643 | * Which leaves you with state |
| 1644 | * |
| 1645 | * k[i] == 0: S = add(R, S), R = dbl(R) |
| 1646 | * k[i] == 1: R = add(S, R), S = dbl(S) |
| 1647 | * |
| 1648 | * So we get the same logic, but instead of a branch it's a |
| 1649 | * conditional swap, followed by ECC ops, then another conditional swap. |
| 1650 | * |
| 1651 | * Optimization: The end of iteration i and start of i-1 looks like |
| 1652 | * |
| 1653 | * ... |
| 1654 | * CSWAP(k[i], R, S) |
| 1655 | * ECC |
| 1656 | * CSWAP(k[i], R, S) |
| 1657 | * (next iteration) |
| 1658 | * CSWAP(k[i-1], R, S) |
| 1659 | * ECC |
| 1660 | * CSWAP(k[i-1], R, S) |
| 1661 | * ... |
| 1662 | * |
| 1663 | * So instead of two contiguous swaps, you can merge the condition |
| 1664 | * bits and do a single swap. |
| 1665 | * |
| 1666 | * k[i] k[i-1] Outcome |
| 1667 | * 0 0 No Swap |
| 1668 | * 0 1 Swap |
| 1669 | * 1 0 Swap |
| 1670 | * 1 1 No Swap |
| 1671 | * |
| 1672 | * This is XOR. pbit tracks the previous bit of k. |
| 1673 | */ |
| 1674 | |
| 1675 | for (i = cardinality_bits - 1; i >= 0; i--) { |
| 1676 | kbit = BN_is_bit_set(k, i) ^ pbit; |
| 1677 | EC_POINT_CSWAP(kbit, r, s, group_top, Z_is_one); |
| 1678 | if (!EC_POINT_add(group, s, r, s, ctx)) |
| 1679 | goto err; |
| 1680 | if (!EC_POINT_dbl(group, r, r, ctx)) |
| 1681 | goto err; |
| 1682 | /* |
| 1683 | * pbit logic merges this cswap with that of the |
| 1684 | * next iteration |
| 1685 | */ |
| 1686 | pbit ^= kbit; |
| 1687 | } |
| 1688 | /* one final cswap to move the right value into r */ |
| 1689 | EC_POINT_CSWAP(pbit, r, s, group_top, Z_is_one); |
| 1690 | |
| 1691 | ret = 1; |
| 1692 | |
| 1693 | err: |
| 1694 | EC_POINT_free(s); |
| 1695 | if (ctx != NULL((void *)0)) |
| 1696 | BN_CTX_end(ctx); |
| 1697 | BN_CTX_free(new_ctx); |
| 1698 | |
| 1699 | return ret; |
| 1700 | } |
| 1701 | |
| 1702 | #undef EC_POINT_BN_set_flags |
| 1703 | #undef EC_POINT_CSWAP |
| 1704 | |
| 1705 | int |
| 1706 | ec_GFp_simple_mul_generator_ct(const EC_GROUP *group, EC_POINT *r, |
| 1707 | const BIGNUM *scalar, BN_CTX *ctx) |
| 1708 | { |
| 1709 | return ec_GFp_simple_mul_ct(group, r, scalar, NULL((void *)0), ctx); |
| 1710 | } |
| 1711 | |
| 1712 | int |
| 1713 | ec_GFp_simple_mul_single_ct(const EC_GROUP *group, EC_POINT *r, |
| 1714 | const BIGNUM *scalar, const EC_POINT *point, BN_CTX *ctx) |
| 1715 | { |
| 1716 | return ec_GFp_simple_mul_ct(group, r, scalar, point, ctx); |
| 1717 | } |
| 1718 | |
| 1719 | int |
| 1720 | ec_GFp_simple_mul_double_nonct(const EC_GROUP *group, EC_POINT *r, |
| 1721 | const BIGNUM *g_scalar, const BIGNUM *p_scalar, const EC_POINT *point, |
| 1722 | BN_CTX *ctx) |
| 1723 | { |
| 1724 | return ec_wNAF_mul(group, r, g_scalar, 1, &point, &p_scalar, ctx); |
| 1725 | } |