crypto/ec/ec2_smpl.c

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