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
  71
  72 #include <openssl/err.h>
  73
  74 #include "internal/bn_int.h"
  75 #include "ec_lcl.h"
  76
  77 #ifndef OPENSSL_NO_EC2M
  78
  79
  80 const EC_METHOD *EC_GF2m_simple_method(void)
  81         {
  82         static const EC_METHOD ret = {
  83                 EC_FLAGS_DEFAULT_OCT,
  84                 NID_X9_62_characteristic_two_field,
  85                 ec_GF2m_simple_group_init,
  86                 ec_GF2m_simple_group_finish,
  87                 ec_GF2m_simple_group_clear_finish,
  88                 ec_GF2m_simple_group_copy,
  89                 ec_GF2m_simple_group_set_curve,
  90                 ec_GF2m_simple_group_get_curve,
  91                 ec_GF2m_simple_group_get_degree,
  92                 ec_GF2m_simple_group_check_discriminant,
  93                 ec_GF2m_simple_point_init,
  94                 ec_GF2m_simple_point_finish,
  95                 ec_GF2m_simple_point_clear_finish,
  96                 ec_GF2m_simple_point_copy,
  97                 ec_GF2m_simple_point_set_to_infinity,
  98                 0 /* set_Jprojective_coordinates_GFp */,
  99                 0 /* get_Jprojective_coordinates_GFp */,
 100                 ec_GF2m_simple_point_set_affine_coordinates,
 101                 ec_GF2m_simple_point_get_affine_coordinates,
 102                 0,0,0,
 103                 ec_GF2m_simple_add,
 104                 ec_GF2m_simple_dbl,
 105                 ec_GF2m_simple_invert,
 106                 ec_GF2m_simple_is_at_infinity,
 107                 ec_GF2m_simple_is_on_curve,
 108                 ec_GF2m_simple_cmp,
 109                 ec_GF2m_simple_make_affine,
 110                 ec_GF2m_simple_points_make_affine,
 111
 112                 /* the following three method functions are defined in ec2_mult.c */
 113                 ec_GF2m_simple_mul,
 114                 ec_GF2m_precompute_mult,
 115                 ec_GF2m_have_precompute_mult,
 116
 117                 ec_GF2m_simple_field_mul,
 118                 ec_GF2m_simple_field_sqr,
 119                 ec_GF2m_simple_field_div,
 120                 0 /* field_encode */,
 121                 0 /* field_decode */,
 122                 0 /* field_set_to_one */ };
 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 ec_GF2m_simple_group_init(EC_GROUP *group)
 132         {
 133         group->field = BN_new();
 134         group->a = BN_new();
 135         group->b = BN_new();
 136
 137         if(!group->field || !group->a || !group->b)
 138                 {
 139                 if(group->field) BN_free(group->field);
 140                 if(group->a) BN_free(group->a);
 141                 if(group->b) BN_free(group->b);
 142                 return 0;
 143                 }
 144         return 1;
 145         }
 146
 147
 148 /* Free a GF(2^m)-based EC_GROUP structure.
 149  * Note that all other members are handled by EC_GROUP_free.
 150  */
 151 void ec_GF2m_simple_group_finish(EC_GROUP *group)
 152         {
 153         BN_free(group->field);
 154         BN_free(group->a);
 155         BN_free(group->b);
 156         }
 157
 158
 159 /* Clear and free a GF(2^m)-based EC_GROUP structure.
 160  * Note that all other members are handled by EC_GROUP_clear_free.
 161  */
 162 void ec_GF2m_simple_group_clear_finish(EC_GROUP *group)
 163         {
 164         BN_clear_free(group->field);
 165         BN_clear_free(group->a);
 166         BN_clear_free(group->b);
 167         group->poly[0] = 0;
 168         group->poly[1] = 0;
 169         group->poly[2] = 0;
 170         group->poly[3] = 0;
 171         group->poly[4] = 0;
 172         group->poly[5] = -1;
 173         }
 174
 175
 176 /* Copy a GF(2^m)-based EC_GROUP structure.
 177  * Note that all other members are handled by EC_GROUP_copy.
 178  */
 179 int ec_GF2m_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src)
 180         {
 181         if (!BN_copy(dest->field, src->field)) return 0;
 182         if (!BN_copy(dest->a, src->a)) return 0;
 183         if (!BN_copy(dest->b, src->b)) return 0;
 184         dest->poly[0] = src->poly[0];
 185         dest->poly[1] = src->poly[1];
 186         dest->poly[2] = src->poly[2];
 187         dest->poly[3] = src->poly[3];
 188         dest->poly[4] = src->poly[4];
 189         dest->poly[5] = src->poly[5];
 190         if (bn_wexpand(dest->a, (int)(dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) return 0;
 191         if (bn_wexpand(dest->b, (int)(dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) return 0;
 192         bn_set_all_zero(dest->a);
 193         bn_set_all_zero(dest->b);
 194         return 1;
 195         }
 196
 197
 198 /* Set the curve parameters of an EC_GROUP structure. */
 199 int ec_GF2m_simple_group_set_curve(EC_GROUP *group,
 200         const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
 201         {
 202         int ret = 0, i;
 203
 204         /* group->field */
 205         if (!BN_copy(group->field, p)) goto err;
 206         i = BN_GF2m_poly2arr(group->field, group->poly, 6) - 1;
 207         if ((i != 5) && (i != 3))
 208                 {
 209                 ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_SET_CURVE, EC_R_UNSUPPORTED_FIELD);
 210                 goto err;
 211                 }
 212
 213         /* group->a */
 214         if (!BN_GF2m_mod_arr(group->a, a, group->poly)) goto err;
 215         if(bn_wexpand(group->a, (int)(group->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) goto err;
 216         bn_set_all_zero(group->a);
 217
 218         /* group->b */
 219         if (!BN_GF2m_mod_arr(group->b, b, group->poly)) goto err;
 220         if(bn_wexpand(group->b, (int)(group->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) goto err;
 221         bn_set_all_zero(group->b);
 222
 223         ret = 1;
 224   err:
 225         return ret;
 226         }
 227
 228
 229 /* Get the curve parameters of an EC_GROUP structure.
 230  * If p, a, or b are NULL then there values will not be set but the method will return with success.
 231  */
 232 int ec_GF2m_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx)
 233         {
 234         int ret = 0;
 235
 236         if (p != NULL)
 237                 {
 238                 if (!BN_copy(p, group->field)) return 0;
 239                 }
 240
 241         if (a != NULL)
 242                 {
 243                 if (!BN_copy(a, group->a)) goto err;
 244                 }
 245
 246         if (b != NULL)
 247                 {
 248                 if (!BN_copy(b, group->b)) goto err;
 249                 }
 250
 251         ret = 1;
 252
 253   err:
 254         return ret;
 255         }
 256
 257
 258 /* Gets the degree of the field.  For a curve over GF(2^m) this is the value m. */
 259 int ec_GF2m_simple_group_get_degree(const EC_GROUP *group)
 260         {
 261         return BN_num_bits(group->field)-1;
 262         }
 263
 264
 265 /* Checks the discriminant of the curve.
 266  * y^2 + x*y = x^3 + a*x^2 + b is an elliptic curve <=> b != 0 (mod p)
 267  */
 268 int ec_GF2m_simple_group_check_discriminant(const EC_GROUP *group, BN_CTX *ctx)
 269         {
 270         int ret = 0;
 271         BIGNUM *b;
 272         BN_CTX *new_ctx = NULL;
 273
 274         if (ctx == NULL)
 275                 {
 276                 ctx = new_ctx = BN_CTX_new();
 277                 if (ctx == NULL)
 278                         {
 279                         ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_CHECK_DISCRIMINANT, ERR_R_MALLOC_FAILURE);
 280                         goto err;
 281                         }
 282                 }
 283         BN_CTX_start(ctx);
 284         b = BN_CTX_get(ctx);
 285         if (b == NULL) goto err;
 286
 287         if (!BN_GF2m_mod_arr(b, group->b, group->poly)) goto err;
 288
 289         /* check the discriminant:
 290          * y^2 + x*y = x^3 + a*x^2 + b is an elliptic curve <=> b != 0 (mod p)
 291          */
 292         if (BN_is_zero(b)) goto err;
 293
 294         ret = 1;
 295
 296 err:
 297         if (ctx != NULL)
 298                 BN_CTX_end(ctx);
 299         if (new_ctx != NULL)
 300                 BN_CTX_free(new_ctx);
 301         return ret;
 302         }
 303
 304
 305 /* Initializes an EC_POINT. */
 306 int ec_GF2m_simple_point_init(EC_POINT *point)
 307         {
 308         point->X = BN_new();
 309         point->Y = BN_new();
 310         point->Z = BN_new();
 311
 312         if(!point->X || !point->Y || !point->Z)
 313                 {
 314                 if(point->X) BN_free(point->X);
 315                 if(point->Y) BN_free(point->Y);
 316                 if(point->Z) BN_free(point->Z);
 317                 return 0;
 318                 }
 319         return 1;
 320         }
 321
 322
 323 /* Frees an EC_POINT. */
 324 void ec_GF2m_simple_point_finish(EC_POINT *point)
 325         {
 326         BN_free(point->X);
 327         BN_free(point->Y);
 328         BN_free(point->Z);
 329         }
 330
 331
 332 /* Clears and frees an EC_POINT. */
 333 void ec_GF2m_simple_point_clear_finish(EC_POINT *point)
 334         {
 335         BN_clear_free(point->X);
 336         BN_clear_free(point->Y);
 337         BN_clear_free(point->Z);
 338         point->Z_is_one = 0;
 339         }
 340
 341
 342 /* Copy the contents of one EC_POINT into another.  Assumes dest is initialized. */
 343 int ec_GF2m_simple_point_copy(EC_POINT *dest, const EC_POINT *src)
 344         {
 345         if (!BN_copy(dest->X, src->X)) return 0;
 346         if (!BN_copy(dest->Y, src->Y)) return 0;
 347         if (!BN_copy(dest->Z, src->Z)) return 0;
 348         dest->Z_is_one = src->Z_is_one;
 349
 350         return 1;
 351         }
 352
 353
 354 /* Set an EC_POINT to the point at infinity.
 355  * A point at infinity is represented by having Z=0.
 356  */
 357 int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *group, EC_POINT *point)
 358         {
 359         point->Z_is_one = 0;
 360         BN_zero(point->Z);
 361         return 1;
 362         }
 363
 364
 365 /* Set the coordinates of an EC_POINT using affine coordinates.
 366  * Note that the simple implementation only uses affine coordinates.
 367  */
 368 int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *group, EC_POINT *point,
 369         const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx)
 370         {
 371         int ret = 0;
 372         if (x == NULL || y == NULL)
 373                 {
 374                 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_SET_AFFINE_COORDINATES, ERR_R_PASSED_NULL_PARAMETER);
 375                 return 0;
 376                 }
 377
 378         if (!BN_copy(point->X, x)) goto err;
 379         BN_set_negative(point->X, 0);
 380         if (!BN_copy(point->Y, y)) goto err;
 381         BN_set_negative(point->Y, 0);
 382         if (!BN_copy(point->Z, BN_value_one())) goto err;
 383         BN_set_negative(point->Z, 0);
 384         point->Z_is_one = 1;
 385         ret = 1;
 386
 387   err:
 388         return ret;
 389         }
 390
 391
 392 /* Gets the affine coordinates of an EC_POINT.
 393  * Note that the simple implementation only uses affine coordinates.
 394  */
 395 int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point,
 396         BIGNUM *x, BIGNUM *y, BN_CTX *ctx)
 397         {
 398         int ret = 0;
 399
 400         if (EC_POINT_is_at_infinity(group, point))
 401                 {
 402                 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES, EC_R_POINT_AT_INFINITY);
 403                 return 0;
 404                 }
 405
 406         if (BN_cmp(point->Z, BN_value_one()))
 407                 {
 408                 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
 409                 return 0;
 410                 }
 411         if (x != NULL)
 412                 {
 413                 if (!BN_copy(x, point->X)) goto err;
 414                 BN_set_negative(x, 0);
 415                 }
 416         if (y != NULL)
 417                 {
 418                 if (!BN_copy(y, point->Y)) goto err;
 419                 BN_set_negative(y, 0);
 420                 }
 421         ret = 1;
 422
 423  err:
 424         return ret;
 425         }
 426
 427 /* Computes a + b and stores the result in r.  r could be a or b, a could be b.
 428  * Uses algorithm A.10.2 of IEEE P1363.
 429  */
 430 int ec_GF2m_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
 431         {
 432         BN_CTX *new_ctx = NULL;
 433         BIGNUM *x0, *y0, *x1, *y1, *x2, *y2, *s, *t;
 434         int ret = 0;
 435
 436         if (EC_POINT_is_at_infinity(group, a))
 437                 {
 438                 if (!EC_POINT_copy(r, b)) return 0;
 439                 return 1;
 440                 }
 441
 442         if (EC_POINT_is_at_infinity(group, b))
 443                 {
 444                 if (!EC_POINT_copy(r, a)) return 0;
 445                 return 1;
 446                 }
 447
 448         if (ctx == NULL)
 449                 {
 450                 ctx = new_ctx = BN_CTX_new();
 451                 if (ctx == NULL)
 452                         return 0;
 453                 }
 454
 455         BN_CTX_start(ctx);
 456         x0 = BN_CTX_get(ctx);
 457         y0 = BN_CTX_get(ctx);
 458         x1 = BN_CTX_get(ctx);
 459         y1 = BN_CTX_get(ctx);
 460         x2 = BN_CTX_get(ctx);
 461         y2 = BN_CTX_get(ctx);
 462         s = BN_CTX_get(ctx);
 463         t = BN_CTX_get(ctx);
 464         if (t == NULL) goto err;
 465
 466         if (a->Z_is_one)
 467                 {
 468                 if (!BN_copy(x0, a->X)) goto err;
 469                 if (!BN_copy(y0, a->Y)) goto err;
 470                 }
 471         else
 472                 {
 473                 if (!EC_POINT_get_affine_coordinates_GF2m(group, a, x0, y0, ctx)) goto err;
 474                 }
 475         if (b->Z_is_one)
 476                 {
 477                 if (!BN_copy(x1, b->X)) goto err;
 478                 if (!BN_copy(y1, b->Y)) goto err;
 479                 }
 480         else
 481                 {
 482                 if (!EC_POINT_get_affine_coordinates_GF2m(group, b, x1, y1, ctx)) goto err;
 483                 }
 484
 485
 486         if (BN_GF2m_cmp(x0, x1))
 487                 {
 488                 if (!BN_GF2m_add(t, x0, x1)) goto err;
 489                 if (!BN_GF2m_add(s, y0, y1)) goto err;
 490                 if (!group->meth->field_div(group, s, s, t, ctx)) goto err;
 491                 if (!group->meth->field_sqr(group, x2, s, ctx)) goto err;
 492                 if (!BN_GF2m_add(x2, x2, group->a)) goto err;
 493                 if (!BN_GF2m_add(x2, x2, s)) goto err;
 494                 if (!BN_GF2m_add(x2, x2, t)) goto err;
 495                 }
 496         else
 497                 {
 498                 if (BN_GF2m_cmp(y0, y1) || BN_is_zero(x1))
 499                         {
 500                         if (!EC_POINT_set_to_infinity(group, r)) goto err;
 501                         ret = 1;
 502                         goto err;
 503                         }
 504                 if (!group->meth->field_div(group, s, y1, x1, ctx)) goto err;
 505                 if (!BN_GF2m_add(s, s, x1)) goto err;
 506
 507                 if (!group->meth->field_sqr(group, x2, s, ctx)) goto err;
 508                 if (!BN_GF2m_add(x2, x2, s)) goto err;
 509                 if (!BN_GF2m_add(x2, x2, group->a)) goto err;
 510                 }
 511
 512         if (!BN_GF2m_add(y2, x1, x2)) goto err;
 513         if (!group->meth->field_mul(group, y2, y2, s, ctx)) goto err;
 514         if (!BN_GF2m_add(y2, y2, x2)) goto err;
 515         if (!BN_GF2m_add(y2, y2, y1)) goto err;
 516
 517         if (!EC_POINT_set_affine_coordinates_GF2m(group, r, x2, y2, ctx)) goto err;
 518
 519         ret = 1;
 520
 521  err:
 522         BN_CTX_end(ctx);
 523         if (new_ctx != NULL)
 524                 BN_CTX_free(new_ctx);
 525         return ret;
 526         }
 527
 528
 529 /* Computes 2 * a and stores the result in r.  r could be a.
 530  * Uses algorithm A.10.2 of IEEE P1363.
 531  */
 532 int ec_GF2m_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_CTX *ctx)
 533         {
 534         return ec_GF2m_simple_add(group, r, a, a, ctx);
 535         }
 536
 537
 538 int ec_GF2m_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
 539         {
 540         if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(point->Y))
 541                 /* point is its own inverse */
 542                 return 1;
 543
 544         if (!EC_POINT_make_affine(group, point, ctx)) return 0;
 545         return BN_GF2m_add(point->Y, point->X, point->Y);
 546         }
 547
 548
 549 /* Indicates whether the given point is the point at infinity. */
 550 int ec_GF2m_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point)
 551         {
 552         return BN_is_zero(point->Z);
 553         }
 554
 555
 556 /*-
 557  * Determines whether the given EC_POINT is an actual point on the curve defined
 558  * in the EC_GROUP.  A point is valid if it satisfies the Weierstrass equation:
 559  *      y^2 + x*y = x^3 + a*x^2 + b.
 560  */
 561 int ec_GF2m_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx)
 562         {
 563         int ret = -1;
 564         BN_CTX *new_ctx = NULL;
 565         BIGNUM *lh, *y2;
 566         int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
 567         int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
 568
 569         if (EC_POINT_is_at_infinity(group, point))
 570                 return 1;
 571
 572         field_mul = group->meth->field_mul;
 573         field_sqr = group->meth->field_sqr;
 574
 575         /* only support affine coordinates */
 576         if (!point->Z_is_one) return -1;
 577
 578         if (ctx == NULL)
 579                 {
 580                 ctx = new_ctx = BN_CTX_new();
 581                 if (ctx == NULL)
 582                         return -1;
 583                 }
 584
 585         BN_CTX_start(ctx);
 586         y2 = BN_CTX_get(ctx);
 587         lh = BN_CTX_get(ctx);
 588         if (lh == NULL) goto err;
 589
 590         /*-
 591          * We have a curve defined by a Weierstrass equation
 592          *      y^2 + x*y = x^3 + a*x^2 + b.
 593          *  <=> x^3 + a*x^2 + x*y + b + y^2 = 0
 594          *  <=> ((x + a) * x + y ) * x + b + y^2 = 0
 595          */
 596         if (!BN_GF2m_add(lh, point->X, group->a)) goto err;
 597         if (!field_mul(group, lh, lh, point->X, ctx)) goto err;
 598         if (!BN_GF2m_add(lh, lh, point->Y)) goto err;
 599         if (!field_mul(group, lh, lh, point->X, ctx)) goto err;
 600         if (!BN_GF2m_add(lh, lh, group->b)) goto err;
 601         if (!field_sqr(group, y2, point->Y, ctx)) goto err;
 602         if (!BN_GF2m_add(lh, lh, y2)) goto err;
 603         ret = BN_is_zero(lh);
 604  err:
 605         if (ctx) BN_CTX_end(ctx);
 606         if (new_ctx) BN_CTX_free(new_ctx);
 607         return ret;
 608         }
 609
 610
 611 /*-
 612  * Indicates whether two points are equal.
 613  * Return values:
 614  *  -1   error
 615  *   0   equal (in affine coordinates)
 616  *   1   not equal
 617  */
 618 int ec_GF2m_simple_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
 619         {
 620         BIGNUM *aX, *aY, *bX, *bY;
 621         BN_CTX *new_ctx = NULL;
 622         int ret = -1;
 623
 624         if (EC_POINT_is_at_infinity(group, a))
 625                 {
 626                 return EC_POINT_is_at_infinity(group, b) ? 0 : 1;
 627                 }
 628
 629         if (EC_POINT_is_at_infinity(group, b))
 630                 return 1;
 631
 632         if (a->Z_is_one && b->Z_is_one)
 633                 {
 634                 return ((BN_cmp(a->X, b->X) == 0) && BN_cmp(a->Y, b->Y) == 0) ? 0 : 1;
 635                 }
 636
 637         if (ctx == NULL)
 638                 {
 639                 ctx = new_ctx = BN_CTX_new();
 640                 if (ctx == NULL)
 641                         return -1;
 642                 }
 643
 644         BN_CTX_start(ctx);
 645         aX = BN_CTX_get(ctx);
 646         aY = BN_CTX_get(ctx);
 647         bX = BN_CTX_get(ctx);
 648         bY = BN_CTX_get(ctx);
 649         if (bY == NULL) goto err;
 650
 651         if (!EC_POINT_get_affine_coordinates_GF2m(group, a, aX, aY, ctx)) goto err;
 652         if (!EC_POINT_get_affine_coordinates_GF2m(group, b, bX, bY, ctx)) goto err;
 653         ret = ((BN_cmp(aX, bX) == 0) && BN_cmp(aY, bY) == 0) ? 0 : 1;
 654
 655   err:
 656         if (ctx) BN_CTX_end(ctx);
 657         if (new_ctx) BN_CTX_free(new_ctx);
 658         return ret;
 659         }
 660
 661
 662 /* Forces the given EC_POINT to internally use affine coordinates. */
 663 int ec_GF2m_simple_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
 664         {
 665         BN_CTX *new_ctx = NULL;
 666         BIGNUM *x, *y;
 667         int ret = 0;
 668
 669         if (point->Z_is_one || EC_POINT_is_at_infinity(group, point))
 670                 return 1;
 671
 672         if (ctx == NULL)
 673                 {
 674                 ctx = new_ctx = BN_CTX_new();
 675                 if (ctx == NULL)
 676                         return 0;
 677                 }
 678
 679         BN_CTX_start(ctx);
 680         x = BN_CTX_get(ctx);
 681         y = BN_CTX_get(ctx);
 682         if (y == NULL) goto err;
 683
 684         if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err;
 685         if (!BN_copy(point->X, x)) goto err;
 686         if (!BN_copy(point->Y, y)) goto err;
 687         if (!BN_one(point->Z)) goto err;
 688
 689         ret = 1;
 690
 691   err:
 692         if (ctx) BN_CTX_end(ctx);
 693         if (new_ctx) BN_CTX_free(new_ctx);
 694         return ret;
 695         }
 696
 697
 698 /* Forces each of the EC_POINTs in the given array to use affine coordinates. */
 699 int ec_GF2m_simple_points_make_affine(const EC_GROUP *group, size_t num, EC_POINT *points[], BN_CTX *ctx)
 700         {
 701         size_t i;
 702
 703         for (i = 0; i < num; i++)
 704                 {
 705                 if (!group->meth->make_affine(group, points[i], ctx)) return 0;
 706                 }
 707
 708         return 1;
 709         }
 710
 711
 712 /* Wrapper to simple binary polynomial field multiplication implementation. */
 713 int ec_GF2m_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
 714         {
 715         return BN_GF2m_mod_mul_arr(r, a, b, group->poly, ctx);
 716         }
 717
 718
 719 /* Wrapper to simple binary polynomial field squaring implementation. */
 720 int ec_GF2m_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx)
 721         {
 722         return BN_GF2m_mod_sqr_arr(r, a, group->poly, ctx);
 723         }
 724
 725
 726 /* Wrapper to simple binary polynomial field division implementation. */
 727 int ec_GF2m_simple_field_div(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
 728         {
 729         return BN_GF2m_mod_div(r, a, b, group->field, ctx);
 730         }
 731
 732 #endif