1 /* $OpenBSD: ec2_smpl.c,v 1.13 2015/02/08 22:25:03 miod Exp $ */ 2 /* ==================================================================== 3 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. 4 * 5 * The Elliptic Curve Public-Key Crypto Library (ECC Code) included 6 * herein is developed by SUN MICROSYSTEMS, INC., and is contributed 7 * to the OpenSSL project. 8 * 9 * The ECC Code is licensed pursuant to the OpenSSL open source 10 * license provided below. 11 * 12 * The software is originally written by Sheueling Chang Shantz and 13 * Douglas Stebila of Sun Microsystems Laboratories. 14 * 15 */ 16 /* ==================================================================== 17 * Copyright (c) 1998-2005 The OpenSSL Project. All rights reserved. 18 * 19 * Redistribution and use in source and binary forms, with or without 20 * modification, are permitted provided that the following conditions 21 * are met: 22 * 23 * 1. Redistributions of source code must retain the above copyright 24 * notice, this list of conditions and the following disclaimer. 25 * 26 * 2. Redistributions in binary form must reproduce the above copyright 27 * notice, this list of conditions and the following disclaimer in 28 * the documentation and/or other materials provided with the 29 * distribution. 30 * 31 * 3. All advertising materials mentioning features or use of this 32 * software must display the following acknowledgment: 33 * "This product includes software developed by the OpenSSL Project 34 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" 35 * 36 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to 37 * endorse or promote products derived from this software without 38 * prior written permission. For written permission, please contact 39 * openssl-core@openssl.org. 40 * 41 * 5. Products derived from this software may not be called "OpenSSL" 42 * nor may "OpenSSL" appear in their names without prior written 43 * permission of the OpenSSL Project. 44 * 45 * 6. Redistributions of any form whatsoever must retain the following 46 * acknowledgment: 47 * "This product includes software developed by the OpenSSL Project 48 * for use in the OpenSSL Toolkit (http://www.openssl.org/)" 49 * 50 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY 51 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 52 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR 53 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR 54 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, 55 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT 56 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; 57 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 58 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, 59 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) 60 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED 61 * OF THE POSSIBILITY OF SUCH DAMAGE. 62 * ==================================================================== 63 * 64 * This product includes cryptographic software written by Eric Young 65 * (eay@cryptsoft.com). This product includes software written by Tim 66 * Hudson (tjh@cryptsoft.com). 67 * 68 */ 69 70 #include <openssl/opensslconf.h> 71 72 #include <openssl/err.h> 73 74 #include "ec_lcl.h" 75 76 #ifndef OPENSSL_NO_EC2M 77 78 const EC_METHOD * 79 EC_GF2m_simple_method(void) 80 { 81 static const EC_METHOD ret = { 82 .flags = EC_FLAGS_DEFAULT_OCT, 83 .field_type = NID_X9_62_characteristic_two_field, 84 .group_init = ec_GF2m_simple_group_init, 85 .group_finish = ec_GF2m_simple_group_finish, 86 .group_clear_finish = ec_GF2m_simple_group_clear_finish, 87 .group_copy = ec_GF2m_simple_group_copy, 88 .group_set_curve = ec_GF2m_simple_group_set_curve, 89 .group_get_curve = ec_GF2m_simple_group_get_curve, 90 .group_get_degree = ec_GF2m_simple_group_get_degree, 91 .group_check_discriminant = 92 ec_GF2m_simple_group_check_discriminant, 93 .point_init = ec_GF2m_simple_point_init, 94 .point_finish = ec_GF2m_simple_point_finish, 95 .point_clear_finish = ec_GF2m_simple_point_clear_finish, 96 .point_copy = ec_GF2m_simple_point_copy, 97 .point_set_to_infinity = ec_GF2m_simple_point_set_to_infinity, 98 .point_set_affine_coordinates = 99 ec_GF2m_simple_point_set_affine_coordinates, 100 .point_get_affine_coordinates = 101 ec_GF2m_simple_point_get_affine_coordinates, 102 .add = ec_GF2m_simple_add, 103 .dbl = ec_GF2m_simple_dbl, 104 .invert = ec_GF2m_simple_invert, 105 .is_at_infinity = ec_GF2m_simple_is_at_infinity, 106 .is_on_curve = ec_GF2m_simple_is_on_curve, 107 .point_cmp = ec_GF2m_simple_cmp, 108 .make_affine = ec_GF2m_simple_make_affine, 109 .points_make_affine = ec_GF2m_simple_points_make_affine, 110 111 /* 112 * the following three method functions are defined in 113 * ec2_mult.c 114 */ 115 .mul = ec_GF2m_simple_mul, 116 .precompute_mult = ec_GF2m_precompute_mult, 117 .have_precompute_mult = ec_GF2m_have_precompute_mult, 118 119 .field_mul = ec_GF2m_simple_field_mul, 120 .field_sqr = ec_GF2m_simple_field_sqr, 121 .field_div = ec_GF2m_simple_field_div, 122 }; 123 124 return &ret; 125 } 126 127 128 /* Initialize a GF(2^m)-based EC_GROUP structure. 129 * Note that all other members are handled by EC_GROUP_new. 130 */ 131 int 132 ec_GF2m_simple_group_init(EC_GROUP * group) 133 { 134 BN_init(&group->field); 135 BN_init(&group->a); 136 BN_init(&group->b); 137 return 1; 138 } 139 140 141 /* Free a GF(2^m)-based EC_GROUP structure. 142 * Note that all other members are handled by EC_GROUP_free. 143 */ 144 void 145 ec_GF2m_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 /* Clear and free a GF(2^m)-based EC_GROUP structure. 154 * Note that all other members are handled by EC_GROUP_clear_free. 155 */ 156 void 157 ec_GF2m_simple_group_clear_finish(EC_GROUP * group) 158 { 159 BN_clear_free(&group->field); 160 BN_clear_free(&group->a); 161 BN_clear_free(&group->b); 162 group->poly[0] = 0; 163 group->poly[1] = 0; 164 group->poly[2] = 0; 165 group->poly[3] = 0; 166 group->poly[4] = 0; 167 group->poly[5] = -1; 168 } 169 170 171 /* Copy a GF(2^m)-based EC_GROUP structure. 172 * Note that all other members are handled by EC_GROUP_copy. 173 */ 174 int 175 ec_GF2m_simple_group_copy(EC_GROUP * dest, const EC_GROUP * src) 176 { 177 int i; 178 179 if (!BN_copy(&dest->field, &src->field)) 180 return 0; 181 if (!BN_copy(&dest->a, &src->a)) 182 return 0; 183 if (!BN_copy(&dest->b, &src->b)) 184 return 0; 185 dest->poly[0] = src->poly[0]; 186 dest->poly[1] = src->poly[1]; 187 dest->poly[2] = src->poly[2]; 188 dest->poly[3] = src->poly[3]; 189 dest->poly[4] = src->poly[4]; 190 dest->poly[5] = src->poly[5]; 191 if (bn_wexpand(&dest->a, (int) (dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) 192 return 0; 193 if (bn_wexpand(&dest->b, (int) (dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) 194 return 0; 195 for (i = dest->a.top; i < dest->a.dmax; i++) 196 dest->a.d[i] = 0; 197 for (i = dest->b.top; i < dest->b.dmax; i++) 198 dest->b.d[i] = 0; 199 return 1; 200 } 201 202 203 /* Set the curve parameters of an EC_GROUP structure. */ 204 int 205 ec_GF2m_simple_group_set_curve(EC_GROUP * group, 206 const BIGNUM * p, const BIGNUM * a, const BIGNUM * b, BN_CTX * ctx) 207 { 208 int ret = 0, i; 209 210 /* group->field */ 211 if (!BN_copy(&group->field, p)) 212 goto err; 213 i = BN_GF2m_poly2arr(&group->field, group->poly, 6) - 1; 214 if ((i != 5) && (i != 3)) { 215 ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_SET_CURVE, EC_R_UNSUPPORTED_FIELD); 216 goto err; 217 } 218 /* group->a */ 219 if (!BN_GF2m_mod_arr(&group->a, a, group->poly)) 220 goto err; 221 if (bn_wexpand(&group->a, (int) (group->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) 222 goto err; 223 for (i = group->a.top; i < group->a.dmax; i++) 224 group->a.d[i] = 0; 225 226 /* group->b */ 227 if (!BN_GF2m_mod_arr(&group->b, b, group->poly)) 228 goto err; 229 if (bn_wexpand(&group->b, (int) (group->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) 230 goto err; 231 for (i = group->b.top; i < group->b.dmax; i++) 232 group->b.d[i] = 0; 233 234 ret = 1; 235 err: 236 return ret; 237 } 238 239 240 /* Get the curve parameters of an EC_GROUP structure. 241 * If p, a, or b are NULL then there values will not be set but the method will return with success. 242 */ 243 int 244 ec_GF2m_simple_group_get_curve(const EC_GROUP *group, 245 BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx) 246 { 247 int ret = 0; 248 249 if (p != NULL) { 250 if (!BN_copy(p, &group->field)) 251 return 0; 252 } 253 if (a != NULL) { 254 if (!BN_copy(a, &group->a)) 255 goto err; 256 } 257 if (b != NULL) { 258 if (!BN_copy(b, &group->b)) 259 goto err; 260 } 261 ret = 1; 262 263 err: 264 return ret; 265 } 266 267 268 /* Gets the degree of the field. For a curve over GF(2^m) this is the value m. */ 269 int 270 ec_GF2m_simple_group_get_degree(const EC_GROUP * group) 271 { 272 return BN_num_bits(&group->field) - 1; 273 } 274 275 276 /* Checks the discriminant of the curve. 277 * y^2 + x*y = x^3 + a*x^2 + b is an elliptic curve <=> b != 0 (mod p) 278 */ 279 int 280 ec_GF2m_simple_group_check_discriminant(const EC_GROUP * group, BN_CTX * ctx) 281 { 282 int ret = 0; 283 BIGNUM *b; 284 BN_CTX *new_ctx = NULL; 285 286 if (ctx == NULL) { 287 ctx = new_ctx = BN_CTX_new(); 288 if (ctx == NULL) { 289 ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_CHECK_DISCRIMINANT, ERR_R_MALLOC_FAILURE); 290 goto err; 291 } 292 } 293 BN_CTX_start(ctx); 294 if ((b = BN_CTX_get(ctx)) == NULL) 295 goto err; 296 297 if (!BN_GF2m_mod_arr(b, &group->b, group->poly)) 298 goto err; 299 300 /* 301 * check the discriminant: y^2 + x*y = x^3 + a*x^2 + b is an elliptic 302 * curve <=> b != 0 (mod p) 303 */ 304 if (BN_is_zero(b)) 305 goto err; 306 307 ret = 1; 308 309 err: 310 if (ctx != NULL) 311 BN_CTX_end(ctx); 312 BN_CTX_free(new_ctx); 313 return ret; 314 } 315 316 317 /* Initializes an EC_POINT. */ 318 int 319 ec_GF2m_simple_point_init(EC_POINT * point) 320 { 321 BN_init(&point->X); 322 BN_init(&point->Y); 323 BN_init(&point->Z); 324 return 1; 325 } 326 327 328 /* Frees an EC_POINT. */ 329 void 330 ec_GF2m_simple_point_finish(EC_POINT * point) 331 { 332 BN_free(&point->X); 333 BN_free(&point->Y); 334 BN_free(&point->Z); 335 } 336 337 338 /* Clears and frees an EC_POINT. */ 339 void 340 ec_GF2m_simple_point_clear_finish(EC_POINT * point) 341 { 342 BN_clear_free(&point->X); 343 BN_clear_free(&point->Y); 344 BN_clear_free(&point->Z); 345 point->Z_is_one = 0; 346 } 347 348 349 /* Copy the contents of one EC_POINT into another. Assumes dest is initialized. */ 350 int 351 ec_GF2m_simple_point_copy(EC_POINT * dest, const EC_POINT * src) 352 { 353 if (!BN_copy(&dest->X, &src->X)) 354 return 0; 355 if (!BN_copy(&dest->Y, &src->Y)) 356 return 0; 357 if (!BN_copy(&dest->Z, &src->Z)) 358 return 0; 359 dest->Z_is_one = src->Z_is_one; 360 361 return 1; 362 } 363 364 365 /* Set an EC_POINT to the point at infinity. 366 * A point at infinity is represented by having Z=0. 367 */ 368 int 369 ec_GF2m_simple_point_set_to_infinity(const EC_GROUP * group, EC_POINT * point) 370 { 371 point->Z_is_one = 0; 372 BN_zero(&point->Z); 373 return 1; 374 } 375 376 377 /* Set the coordinates of an EC_POINT using affine coordinates. 378 * Note that the simple implementation only uses affine coordinates. 379 */ 380 int 381 ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP * group, EC_POINT * point, 382 const BIGNUM * x, const BIGNUM * y, BN_CTX * ctx) 383 { 384 int ret = 0; 385 if (x == NULL || y == NULL) { 386 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_SET_AFFINE_COORDINATES, ERR_R_PASSED_NULL_PARAMETER); 387 return 0; 388 } 389 if (!BN_copy(&point->X, x)) 390 goto err; 391 BN_set_negative(&point->X, 0); 392 if (!BN_copy(&point->Y, y)) 393 goto err; 394 BN_set_negative(&point->Y, 0); 395 if (!BN_copy(&point->Z, BN_value_one())) 396 goto err; 397 BN_set_negative(&point->Z, 0); 398 point->Z_is_one = 1; 399 ret = 1; 400 401 err: 402 return ret; 403 } 404 405 406 /* Gets the affine coordinates of an EC_POINT. 407 * Note that the simple implementation only uses affine coordinates. 408 */ 409 int 410 ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *group, 411 const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx) 412 { 413 int ret = 0; 414 415 if (EC_POINT_is_at_infinity(group, point) > 0) { 416 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES, EC_R_POINT_AT_INFINITY); 417 return 0; 418 } 419 if (BN_cmp(&point->Z, BN_value_one())) { 420 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); 421 return 0; 422 } 423 if (x != NULL) { 424 if (!BN_copy(x, &point->X)) 425 goto err; 426 BN_set_negative(x, 0); 427 } 428 if (y != NULL) { 429 if (!BN_copy(y, &point->Y)) 430 goto err; 431 BN_set_negative(y, 0); 432 } 433 ret = 1; 434 435 err: 436 return ret; 437 } 438 439 /* Computes a + b and stores the result in r. r could be a or b, a could be b. 440 * Uses algorithm A.10.2 of IEEE P1363. 441 */ 442 int 443 ec_GF2m_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, 444 const EC_POINT *b, BN_CTX *ctx) 445 { 446 BN_CTX *new_ctx = NULL; 447 BIGNUM *x0, *y0, *x1, *y1, *x2, *y2, *s, *t; 448 int ret = 0; 449 450 if (EC_POINT_is_at_infinity(group, a) > 0) { 451 if (!EC_POINT_copy(r, b)) 452 return 0; 453 return 1; 454 } 455 if (EC_POINT_is_at_infinity(group, b) > 0) { 456 if (!EC_POINT_copy(r, a)) 457 return 0; 458 return 1; 459 } 460 if (ctx == NULL) { 461 ctx = new_ctx = BN_CTX_new(); 462 if (ctx == NULL) 463 return 0; 464 } 465 BN_CTX_start(ctx); 466 if ((x0 = BN_CTX_get(ctx)) == NULL) 467 goto err; 468 if ((y0 = BN_CTX_get(ctx)) == NULL) 469 goto err; 470 if ((x1 = BN_CTX_get(ctx)) == NULL) 471 goto err; 472 if ((y1 = BN_CTX_get(ctx)) == NULL) 473 goto err; 474 if ((x2 = BN_CTX_get(ctx)) == NULL) 475 goto err; 476 if ((y2 = BN_CTX_get(ctx)) == NULL) 477 goto err; 478 if ((s = BN_CTX_get(ctx)) == NULL) 479 goto err; 480 if ((t = BN_CTX_get(ctx)) == NULL) 481 goto err; 482 483 if (a->Z_is_one) { 484 if (!BN_copy(x0, &a->X)) 485 goto err; 486 if (!BN_copy(y0, &a->Y)) 487 goto err; 488 } else { 489 if (!EC_POINT_get_affine_coordinates_GF2m(group, a, x0, y0, ctx)) 490 goto err; 491 } 492 if (b->Z_is_one) { 493 if (!BN_copy(x1, &b->X)) 494 goto err; 495 if (!BN_copy(y1, &b->Y)) 496 goto err; 497 } else { 498 if (!EC_POINT_get_affine_coordinates_GF2m(group, b, x1, y1, ctx)) 499 goto err; 500 } 501 502 503 if (BN_GF2m_cmp(x0, x1)) { 504 if (!BN_GF2m_add(t, x0, x1)) 505 goto err; 506 if (!BN_GF2m_add(s, y0, y1)) 507 goto err; 508 if (!group->meth->field_div(group, s, s, t, ctx)) 509 goto err; 510 if (!group->meth->field_sqr(group, x2, s, ctx)) 511 goto err; 512 if (!BN_GF2m_add(x2, x2, &group->a)) 513 goto err; 514 if (!BN_GF2m_add(x2, x2, s)) 515 goto err; 516 if (!BN_GF2m_add(x2, x2, t)) 517 goto err; 518 } else { 519 if (BN_GF2m_cmp(y0, y1) || BN_is_zero(x1)) { 520 if (!EC_POINT_set_to_infinity(group, r)) 521 goto err; 522 ret = 1; 523 goto err; 524 } 525 if (!group->meth->field_div(group, s, y1, x1, ctx)) 526 goto err; 527 if (!BN_GF2m_add(s, s, x1)) 528 goto err; 529 530 if (!group->meth->field_sqr(group, x2, s, ctx)) 531 goto err; 532 if (!BN_GF2m_add(x2, x2, s)) 533 goto err; 534 if (!BN_GF2m_add(x2, x2, &group->a)) 535 goto err; 536 } 537 538 if (!BN_GF2m_add(y2, x1, x2)) 539 goto err; 540 if (!group->meth->field_mul(group, y2, y2, s, ctx)) 541 goto err; 542 if (!BN_GF2m_add(y2, y2, x2)) 543 goto err; 544 if (!BN_GF2m_add(y2, y2, y1)) 545 goto err; 546 547 if (!EC_POINT_set_affine_coordinates_GF2m(group, r, x2, y2, ctx)) 548 goto err; 549 550 ret = 1; 551 552 err: 553 BN_CTX_end(ctx); 554 BN_CTX_free(new_ctx); 555 return ret; 556 } 557 558 559 /* Computes 2 * a and stores the result in r. r could be a. 560 * Uses algorithm A.10.2 of IEEE P1363. 561 */ 562 int 563 ec_GF2m_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, 564 BN_CTX *ctx) 565 { 566 return ec_GF2m_simple_add(group, r, a, a, ctx); 567 } 568 569 int 570 ec_GF2m_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx) 571 { 572 if (EC_POINT_is_at_infinity(group, point) > 0 || BN_is_zero(&point->Y)) 573 /* point is its own inverse */ 574 return 1; 575 576 if (!EC_POINT_make_affine(group, point, ctx)) 577 return 0; 578 return BN_GF2m_add(&point->Y, &point->X, &point->Y); 579 } 580 581 582 /* Indicates whether the given point is the point at infinity. */ 583 int 584 ec_GF2m_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point) 585 { 586 return BN_is_zero(&point->Z); 587 } 588 589 590 /* Determines whether the given EC_POINT is an actual point on the curve defined 591 * in the EC_GROUP. A point is valid if it satisfies the Weierstrass equation: 592 * y^2 + x*y = x^3 + a*x^2 + b. 593 */ 594 int 595 ec_GF2m_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx) 596 { 597 int ret = -1; 598 BN_CTX *new_ctx = NULL; 599 BIGNUM *lh, *y2; 600 int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *); 601 int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); 602 603 if (EC_POINT_is_at_infinity(group, point) > 0) 604 return 1; 605 606 field_mul = group->meth->field_mul; 607 field_sqr = group->meth->field_sqr; 608 609 /* only support affine coordinates */ 610 if (!point->Z_is_one) 611 return -1; 612 613 if (ctx == NULL) { 614 ctx = new_ctx = BN_CTX_new(); 615 if (ctx == NULL) 616 return -1; 617 } 618 BN_CTX_start(ctx); 619 if ((y2 = BN_CTX_get(ctx)) == NULL) 620 goto err; 621 if ((lh = BN_CTX_get(ctx)) == NULL) 622 goto err; 623 624 /* 625 * We have a curve defined by a Weierstrass equation y^2 + x*y = x^3 626 * + a*x^2 + b. <=> x^3 + a*x^2 + x*y + b + y^2 = 0 <=> ((x + a) * x 627 * + y ) * x + b + y^2 = 0 628 */ 629 if (!BN_GF2m_add(lh, &point->X, &group->a)) 630 goto err; 631 if (!field_mul(group, lh, lh, &point->X, ctx)) 632 goto err; 633 if (!BN_GF2m_add(lh, lh, &point->Y)) 634 goto err; 635 if (!field_mul(group, lh, lh, &point->X, ctx)) 636 goto err; 637 if (!BN_GF2m_add(lh, lh, &group->b)) 638 goto err; 639 if (!field_sqr(group, y2, &point->Y, ctx)) 640 goto err; 641 if (!BN_GF2m_add(lh, lh, y2)) 642 goto err; 643 ret = BN_is_zero(lh); 644 err: 645 if (ctx) 646 BN_CTX_end(ctx); 647 BN_CTX_free(new_ctx); 648 return ret; 649 } 650 651 652 /* Indicates whether two points are equal. 653 * Return values: 654 * -1 error 655 * 0 equal (in affine coordinates) 656 * 1 not equal 657 */ 658 int 659 ec_GF2m_simple_cmp(const EC_GROUP *group, const EC_POINT *a, 660 const EC_POINT *b, BN_CTX *ctx) 661 { 662 BIGNUM *aX, *aY, *bX, *bY; 663 BN_CTX *new_ctx = NULL; 664 int ret = -1; 665 666 if (EC_POINT_is_at_infinity(group, a) > 0) { 667 return EC_POINT_is_at_infinity(group, b) > 0 ? 0 : 1; 668 } 669 if (EC_POINT_is_at_infinity(group, b) > 0) 670 return 1; 671 672 if (a->Z_is_one && b->Z_is_one) { 673 return ((BN_cmp(&a->X, &b->X) == 0) && BN_cmp(&a->Y, &b->Y) == 0) ? 0 : 1; 674 } 675 if (ctx == NULL) { 676 ctx = new_ctx = BN_CTX_new(); 677 if (ctx == NULL) 678 return -1; 679 } 680 BN_CTX_start(ctx); 681 if ((aX = BN_CTX_get(ctx)) == NULL) 682 goto err; 683 if ((aY = BN_CTX_get(ctx)) == NULL) 684 goto err; 685 if ((bX = BN_CTX_get(ctx)) == NULL) 686 goto err; 687 if ((bY = BN_CTX_get(ctx)) == NULL) 688 goto err; 689 690 if (!EC_POINT_get_affine_coordinates_GF2m(group, a, aX, aY, ctx)) 691 goto err; 692 if (!EC_POINT_get_affine_coordinates_GF2m(group, b, bX, bY, ctx)) 693 goto err; 694 ret = ((BN_cmp(aX, bX) == 0) && BN_cmp(aY, bY) == 0) ? 0 : 1; 695 696 err: 697 if (ctx) 698 BN_CTX_end(ctx); 699 BN_CTX_free(new_ctx); 700 return ret; 701 } 702 703 704 /* Forces the given EC_POINT to internally use affine coordinates. */ 705 int 706 ec_GF2m_simple_make_affine(const EC_GROUP * group, EC_POINT * point, BN_CTX * ctx) 707 { 708 BN_CTX *new_ctx = NULL; 709 BIGNUM *x, *y; 710 int ret = 0; 711 712 if (point->Z_is_one || EC_POINT_is_at_infinity(group, point) > 0) 713 return 1; 714 715 if (ctx == NULL) { 716 ctx = new_ctx = BN_CTX_new(); 717 if (ctx == NULL) 718 return 0; 719 } 720 BN_CTX_start(ctx); 721 if ((x = BN_CTX_get(ctx)) == NULL) 722 goto err; 723 if ((y = BN_CTX_get(ctx)) == NULL) 724 goto err; 725 726 if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx)) 727 goto err; 728 if (!BN_copy(&point->X, x)) 729 goto err; 730 if (!BN_copy(&point->Y, y)) 731 goto err; 732 if (!BN_one(&point->Z)) 733 goto err; 734 735 ret = 1; 736 737 err: 738 if (ctx) 739 BN_CTX_end(ctx); 740 BN_CTX_free(new_ctx); 741 return ret; 742 } 743 744 745 /* Forces each of the EC_POINTs in the given array to use affine coordinates. */ 746 int 747 ec_GF2m_simple_points_make_affine(const EC_GROUP *group, size_t num, 748 EC_POINT *points[], BN_CTX *ctx) 749 { 750 size_t i; 751 752 for (i = 0; i < num; i++) { 753 if (!group->meth->make_affine(group, points[i], ctx)) 754 return 0; 755 } 756 757 return 1; 758 } 759 760 761 /* Wrapper to simple binary polynomial field multiplication implementation. */ 762 int 763 ec_GF2m_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, 764 const BIGNUM *b, BN_CTX *ctx) 765 { 766 return BN_GF2m_mod_mul_arr(r, a, b, group->poly, ctx); 767 } 768 769 770 /* Wrapper to simple binary polynomial field squaring implementation. */ 771 int 772 ec_GF2m_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, 773 BN_CTX *ctx) 774 { 775 return BN_GF2m_mod_sqr_arr(r, a, group->poly, ctx); 776 } 777 778 779 /* Wrapper to simple binary polynomial field division implementation. */ 780 int 781 ec_GF2m_simple_field_div(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, 782 const BIGNUM *b, BN_CTX *ctx) 783 { 784 return BN_GF2m_mod_div(r, a, b, &group->field, ctx); 785 } 786 787 #endif 788