1/* crypto/ec/ec2_smpl.c */ 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/err.h> 71 72#include "ec_lcl.h" 73 74#ifndef OPENSSL_NO_EC2M 75 76#ifdef OPENSSL_FIPS 77#include <openssl/fips.h> 78#endif 79 80 81const EC_METHOD *EC_GF2m_simple_method(void) 82 { 83 static const EC_METHOD ret = { 84 EC_FLAGS_DEFAULT_OCT, 85 NID_X9_62_characteristic_two_field, 86 ec_GF2m_simple_group_init, 87 ec_GF2m_simple_group_finish, 88 ec_GF2m_simple_group_clear_finish, 89 ec_GF2m_simple_group_copy, 90 ec_GF2m_simple_group_set_curve, 91 ec_GF2m_simple_group_get_curve, 92 ec_GF2m_simple_group_get_degree, 93 ec_GF2m_simple_group_check_discriminant, 94 ec_GF2m_simple_point_init, 95 ec_GF2m_simple_point_finish, 96 ec_GF2m_simple_point_clear_finish, 97 ec_GF2m_simple_point_copy, 98 ec_GF2m_simple_point_set_to_infinity, 99 0 /* set_Jprojective_coordinates_GFp */, 100 0 /* get_Jprojective_coordinates_GFp */, 101 ec_GF2m_simple_point_set_affine_coordinates, 102 ec_GF2m_simple_point_get_affine_coordinates, 103 0,0,0, 104 ec_GF2m_simple_add, 105 ec_GF2m_simple_dbl, 106 ec_GF2m_simple_invert, 107 ec_GF2m_simple_is_at_infinity, 108 ec_GF2m_simple_is_on_curve, 109 ec_GF2m_simple_cmp, 110 ec_GF2m_simple_make_affine, 111 ec_GF2m_simple_points_make_affine, 112 113 /* the following three method functions are defined in ec2_mult.c */ 114 ec_GF2m_simple_mul, 115 ec_GF2m_precompute_mult, 116 ec_GF2m_have_precompute_mult, 117 118 ec_GF2m_simple_field_mul, 119 ec_GF2m_simple_field_sqr, 120 ec_GF2m_simple_field_div, 121 0 /* field_encode */, 122 0 /* field_decode */, 123 0 /* field_set_to_one */ }; 124 125#ifdef OPENSSL_FIPS 126 if (FIPS_mode()) 127 return fips_ec_gf2m_simple_method(); 128#endif 129 130 return &ret; 131 } 132 133 134/* Initialize a GF(2^m)-based EC_GROUP structure. 135 * Note that all other members are handled by EC_GROUP_new. 136 */ 137int ec_GF2m_simple_group_init(EC_GROUP *group) 138 { 139 BN_init(&group->field); 140 BN_init(&group->a); 141 BN_init(&group->b); 142 return 1; 143 } 144 145 146/* Free a GF(2^m)-based EC_GROUP structure. 147 * Note that all other members are handled by EC_GROUP_free. 148 */ 149void ec_GF2m_simple_group_finish(EC_GROUP *group) 150 { 151 BN_free(&group->field); 152 BN_free(&group->a); 153 BN_free(&group->b); 154 } 155 156 157/* Clear and free a GF(2^m)-based EC_GROUP structure. 158 * Note that all other members are handled by EC_GROUP_clear_free. 159 */ 160void ec_GF2m_simple_group_clear_finish(EC_GROUP *group) 161 { 162 BN_clear_free(&group->field); 163 BN_clear_free(&group->a); 164 BN_clear_free(&group->b); 165 group->poly[0] = 0; 166 group->poly[1] = 0; 167 group->poly[2] = 0; 168 group->poly[3] = 0; 169 group->poly[4] = 0; 170 group->poly[5] = -1; 171 } 172 173 174/* Copy a GF(2^m)-based EC_GROUP structure. 175 * Note that all other members are handled by EC_GROUP_copy. 176 */ 177int ec_GF2m_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src) 178 { 179 int i; 180 if (!BN_copy(&dest->field, &src->field)) return 0; 181 if (!BN_copy(&dest->a, &src->a)) return 0; 182 if (!BN_copy(&dest->b, &src->b)) return 0; 183 dest->poly[0] = src->poly[0]; 184 dest->poly[1] = src->poly[1]; 185 dest->poly[2] = src->poly[2]; 186 dest->poly[3] = src->poly[3]; 187 dest->poly[4] = src->poly[4]; 188 dest->poly[5] = src->poly[5]; 189 if (bn_wexpand(&dest->a, (int)(dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) return 0; 190 if (bn_wexpand(&dest->b, (int)(dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) return 0; 191 for (i = dest->a.top; i < dest->a.dmax; i++) dest->a.d[i] = 0; 192 for (i = dest->b.top; i < dest->b.dmax; i++) dest->b.d[i] = 0; 193 return 1; 194 } 195 196 197/* Set the curve parameters of an EC_GROUP structure. */ 198int ec_GF2m_simple_group_set_curve(EC_GROUP *group, 199 const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) 200 { 201 int ret = 0, i; 202 203 /* group->field */ 204 if (!BN_copy(&group->field, p)) goto err; 205 i = BN_GF2m_poly2arr(&group->field, group->poly, 6) - 1; 206 if ((i != 5) && (i != 3)) 207 { 208 ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_SET_CURVE, EC_R_UNSUPPORTED_FIELD); 209 goto err; 210 } 211 212 /* group->a */ 213 if (!BN_GF2m_mod_arr(&group->a, a, group->poly)) goto err; 214 if(bn_wexpand(&group->a, (int)(group->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) goto err; 215 for (i = group->a.top; i < group->a.dmax; i++) group->a.d[i] = 0; 216 217 /* group->b */ 218 if (!BN_GF2m_mod_arr(&group->b, b, group->poly)) goto err; 219 if(bn_wexpand(&group->b, (int)(group->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) goto err; 220 for (i = group->b.top; i < group->b.dmax; i++) group->b.d[i] = 0; 221 222 ret = 1; 223 err: 224 return ret; 225 } 226 227 228/* Get the curve parameters of an EC_GROUP structure. 229 * If p, a, or b are NULL then there values will not be set but the method will return with success. 230 */ 231int ec_GF2m_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx) 232 { 233 int ret = 0; 234 235 if (p != NULL) 236 { 237 if (!BN_copy(p, &group->field)) return 0; 238 } 239 240 if (a != NULL) 241 { 242 if (!BN_copy(a, &group->a)) goto err; 243 } 244 245 if (b != NULL) 246 { 247 if (!BN_copy(b, &group->b)) goto err; 248 } 249 250 ret = 1; 251 252 err: 253 return ret; 254 } 255 256 257/* Gets the degree of the field. For a curve over GF(2^m) this is the value m. */ 258int ec_GF2m_simple_group_get_degree(const EC_GROUP *group) 259 { 260 return BN_num_bits(&group->field)-1; 261 } 262 263 264/* Checks the discriminant of the curve. 265 * y^2 + x*y = x^3 + a*x^2 + b is an elliptic curve <=> b != 0 (mod p) 266 */ 267int ec_GF2m_simple_group_check_discriminant(const EC_GROUP *group, BN_CTX *ctx) 268 { 269 int ret = 0; 270 BIGNUM *b; 271 BN_CTX *new_ctx = NULL; 272 273 if (ctx == NULL) 274 { 275 ctx = new_ctx = BN_CTX_new(); 276 if (ctx == NULL) 277 { 278 ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_CHECK_DISCRIMINANT, ERR_R_MALLOC_FAILURE); 279 goto err; 280 } 281 } 282 BN_CTX_start(ctx); 283 b = BN_CTX_get(ctx); 284 if (b == NULL) goto err; 285 286 if (!BN_GF2m_mod_arr(b, &group->b, group->poly)) goto err; 287 288 /* check the discriminant: 289 * y^2 + x*y = x^3 + a*x^2 + b is an elliptic curve <=> b != 0 (mod p) 290 */ 291 if (BN_is_zero(b)) goto err; 292 293 ret = 1; 294 295err: 296 if (ctx != NULL) 297 BN_CTX_end(ctx); 298 if (new_ctx != NULL) 299 BN_CTX_free(new_ctx); 300 return ret; 301 } 302 303 304/* Initializes an EC_POINT. */ 305int ec_GF2m_simple_point_init(EC_POINT *point) 306 { 307 BN_init(&point->X); 308 BN_init(&point->Y); 309 BN_init(&point->Z); 310 return 1; 311 } 312 313 314/* Frees an EC_POINT. */ 315void ec_GF2m_simple_point_finish(EC_POINT *point) 316 { 317 BN_free(&point->X); 318 BN_free(&point->Y); 319 BN_free(&point->Z); 320 } 321 322 323/* Clears and frees an EC_POINT. */ 324void ec_GF2m_simple_point_clear_finish(EC_POINT *point) 325 { 326 BN_clear_free(&point->X); 327 BN_clear_free(&point->Y); 328 BN_clear_free(&point->Z); 329 point->Z_is_one = 0; 330 } 331 332 333/* Copy the contents of one EC_POINT into another. Assumes dest is initialized. */ 334int ec_GF2m_simple_point_copy(EC_POINT *dest, const EC_POINT *src) 335 { 336 if (!BN_copy(&dest->X, &src->X)) return 0; 337 if (!BN_copy(&dest->Y, &src->Y)) return 0; 338 if (!BN_copy(&dest->Z, &src->Z)) return 0; 339 dest->Z_is_one = src->Z_is_one; 340 341 return 1; 342 } 343 344 345/* Set an EC_POINT to the point at infinity. 346 * A point at infinity is represented by having Z=0. 347 */ 348int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *group, EC_POINT *point) 349 { 350 point->Z_is_one = 0; 351 BN_zero(&point->Z); 352 return 1; 353 } 354 355 356/* Set the coordinates of an EC_POINT using affine coordinates. 357 * Note that the simple implementation only uses affine coordinates. 358 */ 359int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *group, EC_POINT *point, 360 const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx) 361 { 362 int ret = 0; 363 if (x == NULL || y == NULL) 364 { 365 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_SET_AFFINE_COORDINATES, ERR_R_PASSED_NULL_PARAMETER); 366 return 0; 367 } 368 369 if (!BN_copy(&point->X, x)) goto err; 370 BN_set_negative(&point->X, 0); 371 if (!BN_copy(&point->Y, y)) goto err; 372 BN_set_negative(&point->Y, 0); 373 if (!BN_copy(&point->Z, BN_value_one())) goto err; 374 BN_set_negative(&point->Z, 0); 375 point->Z_is_one = 1; 376 ret = 1; 377 378 err: 379 return ret; 380 } 381 382 383/* Gets the affine coordinates of an EC_POINT. 384 * Note that the simple implementation only uses affine coordinates. 385 */ 386int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point, 387 BIGNUM *x, BIGNUM *y, BN_CTX *ctx) 388 { 389 int ret = 0; 390 391 if (EC_POINT_is_at_infinity(group, point)) 392 { 393 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES, EC_R_POINT_AT_INFINITY); 394 return 0; 395 } 396 397 if (BN_cmp(&point->Z, BN_value_one())) 398 { 399 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); 400 return 0; 401 } 402 if (x != NULL) 403 { 404 if (!BN_copy(x, &point->X)) goto err; 405 BN_set_negative(x, 0); 406 } 407 if (y != NULL) 408 { 409 if (!BN_copy(y, &point->Y)) goto err; 410 BN_set_negative(y, 0); 411 } 412 ret = 1; 413 414 err: 415 return ret; 416 } 417 418/* Computes a + b and stores the result in r. r could be a or b, a could be b. 419 * Uses algorithm A.10.2 of IEEE P1363. 420 */ 421int ec_GF2m_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx) 422 { 423 BN_CTX *new_ctx = NULL; 424 BIGNUM *x0, *y0, *x1, *y1, *x2, *y2, *s, *t; 425 int ret = 0; 426 427 if (EC_POINT_is_at_infinity(group, a)) 428 { 429 if (!EC_POINT_copy(r, b)) return 0; 430 return 1; 431 } 432 433 if (EC_POINT_is_at_infinity(group, b)) 434 { 435 if (!EC_POINT_copy(r, a)) return 0; 436 return 1; 437 } 438 439 if (ctx == NULL) 440 { 441 ctx = new_ctx = BN_CTX_new(); 442 if (ctx == NULL) 443 return 0; 444 } 445 446 BN_CTX_start(ctx); 447 x0 = BN_CTX_get(ctx); 448 y0 = BN_CTX_get(ctx); 449 x1 = BN_CTX_get(ctx); 450 y1 = BN_CTX_get(ctx); 451 x2 = BN_CTX_get(ctx); 452 y2 = BN_CTX_get(ctx); 453 s = BN_CTX_get(ctx); 454 t = BN_CTX_get(ctx); 455 if (t == NULL) goto err; 456 457 if (a->Z_is_one) 458 { 459 if (!BN_copy(x0, &a->X)) goto err; 460 if (!BN_copy(y0, &a->Y)) goto err; 461 } 462 else 463 { 464 if (!EC_POINT_get_affine_coordinates_GF2m(group, a, x0, y0, ctx)) goto err; 465 } 466 if (b->Z_is_one) 467 { 468 if (!BN_copy(x1, &b->X)) goto err; 469 if (!BN_copy(y1, &b->Y)) goto err; 470 } 471 else 472 { 473 if (!EC_POINT_get_affine_coordinates_GF2m(group, b, x1, y1, ctx)) goto err; 474 } 475 476 477 if (BN_GF2m_cmp(x0, x1)) 478 { 479 if (!BN_GF2m_add(t, x0, x1)) goto err; 480 if (!BN_GF2m_add(s, y0, y1)) goto err; 481 if (!group->meth->field_div(group, s, s, t, ctx)) goto err; 482 if (!group->meth->field_sqr(group, x2, s, ctx)) goto err; 483 if (!BN_GF2m_add(x2, x2, &group->a)) goto err; 484 if (!BN_GF2m_add(x2, x2, s)) goto err; 485 if (!BN_GF2m_add(x2, x2, t)) goto err; 486 } 487 else 488 { 489 if (BN_GF2m_cmp(y0, y1) || BN_is_zero(x1)) 490 { 491 if (!EC_POINT_set_to_infinity(group, r)) goto err; 492 ret = 1; 493 goto err; 494 } 495 if (!group->meth->field_div(group, s, y1, x1, ctx)) goto err; 496 if (!BN_GF2m_add(s, s, x1)) goto err; 497 498 if (!group->meth->field_sqr(group, x2, s, ctx)) goto err; 499 if (!BN_GF2m_add(x2, x2, s)) goto err; 500 if (!BN_GF2m_add(x2, x2, &group->a)) goto err; 501 } 502 503 if (!BN_GF2m_add(y2, x1, x2)) goto err; 504 if (!group->meth->field_mul(group, y2, y2, s, ctx)) goto err; 505 if (!BN_GF2m_add(y2, y2, x2)) goto err; 506 if (!BN_GF2m_add(y2, y2, y1)) goto err; 507 508 if (!EC_POINT_set_affine_coordinates_GF2m(group, r, x2, y2, ctx)) goto err; 509 510 ret = 1; 511 512 err: 513 BN_CTX_end(ctx); 514 if (new_ctx != NULL) 515 BN_CTX_free(new_ctx); 516 return ret; 517 } 518 519 520/* Computes 2 * a and stores the result in r. r could be a. 521 * Uses algorithm A.10.2 of IEEE P1363. 522 */ 523int ec_GF2m_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_CTX *ctx) 524 { 525 return ec_GF2m_simple_add(group, r, a, a, ctx); 526 } 527 528 529int ec_GF2m_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx) 530 { 531 if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(&point->Y)) 532 /* point is its own inverse */ 533 return 1; 534 535 if (!EC_POINT_make_affine(group, point, ctx)) return 0; 536 return BN_GF2m_add(&point->Y, &point->X, &point->Y); 537 } 538 539 540/* Indicates whether the given point is the point at infinity. */ 541int ec_GF2m_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point) 542 { 543 return BN_is_zero(&point->Z); 544 } 545 546 547/* Determines whether the given EC_POINT is an actual point on the curve defined 548 * in the EC_GROUP. A point is valid if it satisfies the Weierstrass equation: 549 * y^2 + x*y = x^3 + a*x^2 + b. 550 */ 551int ec_GF2m_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx) 552 { 553 int ret = -1; 554 BN_CTX *new_ctx = NULL; 555 BIGNUM *lh, *y2; 556 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *); 557 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); 558 559 if (EC_POINT_is_at_infinity(group, point)) 560 return 1; 561 562 field_mul = group->meth->field_mul; 563 field_sqr = group->meth->field_sqr; 564 565 /* only support affine coordinates */ 566 if (!point->Z_is_one) return -1; 567 568 if (ctx == NULL) 569 { 570 ctx = new_ctx = BN_CTX_new(); 571 if (ctx == NULL) 572 return -1; 573 } 574 575 BN_CTX_start(ctx); 576 y2 = BN_CTX_get(ctx); 577 lh = BN_CTX_get(ctx); 578 if (lh == NULL) goto err; 579 580 /* We have a curve defined by a Weierstrass equation 581 * y^2 + x*y = x^3 + a*x^2 + b. 582 * <=> x^3 + a*x^2 + x*y + b + y^2 = 0 583 * <=> ((x + a) * x + y ) * x + b + y^2 = 0 584 */ 585 if (!BN_GF2m_add(lh, &point->X, &group->a)) goto err; 586 if (!field_mul(group, lh, lh, &point->X, ctx)) goto err; 587 if (!BN_GF2m_add(lh, lh, &point->Y)) goto err; 588 if (!field_mul(group, lh, lh, &point->X, ctx)) goto err; 589 if (!BN_GF2m_add(lh, lh, &group->b)) goto err; 590 if (!field_sqr(group, y2, &point->Y, ctx)) goto err; 591 if (!BN_GF2m_add(lh, lh, y2)) goto err; 592 ret = BN_is_zero(lh); 593 err: 594 if (ctx) BN_CTX_end(ctx); 595 if (new_ctx) BN_CTX_free(new_ctx); 596 return ret; 597 } 598 599 600/* Indicates whether two points are equal. 601 * Return values: 602 * -1 error 603 * 0 equal (in affine coordinates) 604 * 1 not equal 605 */ 606int ec_GF2m_simple_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx) 607 { 608 BIGNUM *aX, *aY, *bX, *bY; 609 BN_CTX *new_ctx = NULL; 610 int ret = -1; 611 612 if (EC_POINT_is_at_infinity(group, a)) 613 { 614 return EC_POINT_is_at_infinity(group, b) ? 0 : 1; 615 } 616 617 if (EC_POINT_is_at_infinity(group, b)) 618 return 1; 619 620 if (a->Z_is_one && b->Z_is_one) 621 { 622 return ((BN_cmp(&a->X, &b->X) == 0) && BN_cmp(&a->Y, &b->Y) == 0) ? 0 : 1; 623 } 624 625 if (ctx == NULL) 626 { 627 ctx = new_ctx = BN_CTX_new(); 628 if (ctx == NULL) 629 return -1; 630 } 631 632 BN_CTX_start(ctx); 633 aX = BN_CTX_get(ctx); 634 aY = BN_CTX_get(ctx); 635 bX = BN_CTX_get(ctx); 636 bY = BN_CTX_get(ctx); 637 if (bY == NULL) goto err; 638 639 if (!EC_POINT_get_affine_coordinates_GF2m(group, a, aX, aY, ctx)) goto err; 640 if (!EC_POINT_get_affine_coordinates_GF2m(group, b, bX, bY, ctx)) goto err; 641 ret = ((BN_cmp(aX, bX) == 0) && BN_cmp(aY, bY) == 0) ? 0 : 1; 642 643 err: 644 if (ctx) BN_CTX_end(ctx); 645 if (new_ctx) BN_CTX_free(new_ctx); 646 return ret; 647 } 648 649 650/* Forces the given EC_POINT to internally use affine coordinates. */ 651int ec_GF2m_simple_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx) 652 { 653 BN_CTX *new_ctx = NULL; 654 BIGNUM *x, *y; 655 int ret = 0; 656 657 if (point->Z_is_one || EC_POINT_is_at_infinity(group, point)) 658 return 1; 659 660 if (ctx == NULL) 661 { 662 ctx = new_ctx = BN_CTX_new(); 663 if (ctx == NULL) 664 return 0; 665 } 666 667 BN_CTX_start(ctx); 668 x = BN_CTX_get(ctx); 669 y = BN_CTX_get(ctx); 670 if (y == NULL) goto err; 671 672 if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err; 673 if (!BN_copy(&point->X, x)) goto err; 674 if (!BN_copy(&point->Y, y)) goto err; 675 if (!BN_one(&point->Z)) goto err; 676 677 ret = 1; 678 679 err: 680 if (ctx) BN_CTX_end(ctx); 681 if (new_ctx) BN_CTX_free(new_ctx); 682 return ret; 683 } 684 685 686/* Forces each of the EC_POINTs in the given array to use affine coordinates. */ 687int ec_GF2m_simple_points_make_affine(const EC_GROUP *group, size_t num, EC_POINT *points[], BN_CTX *ctx) 688 { 689 size_t i; 690 691 for (i = 0; i < num; i++) 692 { 693 if (!group->meth->make_affine(group, points[i], ctx)) return 0; 694 } 695 696 return 1; 697 } 698 699 700/* Wrapper to simple binary polynomial field multiplication implementation. */ 701int ec_GF2m_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) 702 { 703 return BN_GF2m_mod_mul_arr(r, a, b, group->poly, ctx); 704 } 705 706 707/* Wrapper to simple binary polynomial field squaring implementation. */ 708int ec_GF2m_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx) 709 { 710 return BN_GF2m_mod_sqr_arr(r, a, group->poly, ctx); 711 } 712 713 714/* Wrapper to simple binary polynomial field division implementation. */ 715int ec_GF2m_simple_field_div(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) 716 { 717 return BN_GF2m_mod_div(r, a, b, &group->field, ctx); 718 } 719 720#endif 721