lib/libcrypto/ec/ec2_smpl.c

   1 /* $OpenBSD: ec2_smpl.c,v 1.15 2017/01/29 17:49:23 beck 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                 ECerror(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                         ECerror(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                 ECerror(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                 ECerror(EC_R_POINT_AT_INFINITY);
 417                 return 0;
 418         }
 419         if (BN_cmp(&point->Z, BN_value_one())) {
 420                 ECerror(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