]> git.ipfire.org Git - thirdparty/openssl.git/blame - crypto/ec/ecp_smpl.c
projects / thirdparty / openssl.git / blame
? search:
summary | shortlog | log | commit | commitdiff | tree
blob | blame (incremental) | history | HEAD
mark all block comments that need format preserving so that
[thirdparty/openssl.git] / crypto / ec / ecp_smpl.c
CommitLineData
f8fe20e0 1/* crypto/ec/ecp_smpl.c */
60428dbf 2/* Includes code written by Lenka Fibikova <fibikova@exp-math.uni-essen.de>
35b73a1f
BM		 3 * for the OpenSSL project.
4 * Includes code written by Bodo Moeller for the OpenSSL project.
5*/
f8fe20e0 6/* ====================================================================
af28dd6c 7 * Copyright (c) 1998-2002 The OpenSSL Project. All rights reserved.
f8fe20e0
BM		 8 *
9 * Redistribution and use in source and binary forms, with or without
10 * modification, are permitted provided that the following conditions
11 * are met:
12 *
13 * 1. Redistributions of source code must retain the above copyright
14 * notice, this list of conditions and the following disclaimer.
15 *
16 * 2. Redistributions in binary form must reproduce the above copyright
17 * notice, this list of conditions and the following disclaimer in
18 * the documentation and/or other materials provided with the
19 * distribution.
20 *
21 * 3. All advertising materials mentioning features or use of this
22 * software must display the following acknowledgment:
23 * "This product includes software developed by the OpenSSL Project
24 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
25 *
26 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
27 * endorse or promote products derived from this software without
28 * prior written permission. For written permission, please contact
29 * openssl-core@openssl.org.
30 *
31 * 5. Products derived from this software may not be called "OpenSSL"
32 * nor may "OpenSSL" appear in their names without prior written
33 * permission of the OpenSSL Project.
34 *
35 * 6. Redistributions of any form whatsoever must retain the following
36 * acknowledgment:
37 * "This product includes software developed by the OpenSSL Project
38 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
39 *
40 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
41 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
42 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
43 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
44 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
45 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
46 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
47 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
48 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
49 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
50 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
51 * OF THE POSSIBILITY OF SUCH DAMAGE.
52 * ====================================================================
53 *
54 * This product includes cryptographic software written by Eric Young
55 * (eay@cryptsoft.com). This product includes software written by Tim
56 * Hudson (tjh@cryptsoft.com).
57 *
58 */
7793f30e
BM		 59/* ====================================================================
60 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
61 * Portions of this software developed by SUN MICROSYSTEMS, INC.,
62 * and contributed to the OpenSSL project.
63 */
f8fe20e0 64
73e45b2d 65
84b08eee 66
60428dbf 67#include <openssl/err.h>
02cbedc3 68#include <openssl/symhacks.h>
60428dbf 69
f8fe20e0 70#include "ec_lcl.h"
0657bf9c 71
0657bf9c
BM		 72const EC_METHOD *EC_GFp_simple_method(void)
73 {
58fc6229 74 static const EC_METHOD ret = {
84b08eee 75 EC_FLAGS_DEFAULT_OCT,
458c2917 76 NID_X9_62_prime_field,
58fc6229 77 ec_GFp_simple_group_init,
58fc6229
BM		 78 ec_GFp_simple_group_finish,
79 ec_GFp_simple_group_clear_finish,
80 ec_GFp_simple_group_copy,
35b73a1f
BM		 81 ec_GFp_simple_group_set_curve,
82 ec_GFp_simple_group_get_curve,
7793f30e 83 ec_GFp_simple_group_get_degree,
17d6bb81 84 ec_GFp_simple_group_check_discriminant,
58fc6229
BM		 85 ec_GFp_simple_point_init,
86 ec_GFp_simple_point_finish,
87 ec_GFp_simple_point_clear_finish,
88 ec_GFp_simple_point_copy,
226cc7de 89 ec_GFp_simple_point_set_to_infinity,
1d5bd6cf
BM		 90 ec_GFp_simple_set_Jprojective_coordinates_GFp,
91 ec_GFp_simple_get_Jprojective_coordinates_GFp,
35b73a1f
BM		 92 ec_GFp_simple_point_set_affine_coordinates,
93 ec_GFp_simple_point_get_affine_coordinates,
84b08eee 94 0,0,0,
58fc6229
BM		 95 ec_GFp_simple_add,
96 ec_GFp_simple_dbl,
1d5bd6cf 97 ec_GFp_simple_invert,
58fc6229
BM		 98 ec_GFp_simple_is_at_infinity,
99 ec_GFp_simple_is_on_curve,
1d5bd6cf 100 ec_GFp_simple_cmp,
58fc6229 101 ec_GFp_simple_make_affine,
48fe4d62 102 ec_GFp_simple_points_make_affine,
37c660ff
BM		 103 0 /* mul */,
104 0 /* precompute_mult */,
105 0 /* have_precompute_mult */,
60428dbf 106 ec_GFp_simple_field_mul,
58fc6229 107 ec_GFp_simple_field_sqr,
7793f30e 108 0 /* field_div */,
58fc6229 109 0 /* field_encode */,
48fe4d62
BM		 110 0 /* field_decode */,
111 0 /* field_set_to_one */ };
0657bf9c
BM		 112
113 return &ret;
114 }
60428dbf
BM		 115
116
922fa76e
BM		 117/* Most method functions in this file are designed to work with
118 * non-trivial representations of field elements if necessary
119 * (see ecp_mont.c): while standard modular addition and subtraction
120 * are used, the field_mul and field_sqr methods will be used for
121 * multiplication, and field_encode and field_decode (if defined)
122 * will be used for converting between representations.
123
124 * Functions ec_GFp_simple_points_make_affine() and
125 * ec_GFp_simple_point_get_affine_coordinates() specifically assume
126 * that if a non-trivial representation is used, it is a Montgomery
127 * representation (i.e. 'encoding' means multiplying by some factor R).
128 */
129
130
60428dbf
BM		 131int ec_GFp_simple_group_init(EC_GROUP *group)
132 {
5784a521
MC		 133 group->field = BN_new();
134 group->a = BN_new();
135 group->b = BN_new();
136 if(!group->field || !group->a || !group->b)
137 {
138 if(!group->field) BN_free(group->field);
139 if(!group->a) BN_free(group->a);
140 if(!group->b) BN_free(group->b);
141 return 0;
142 }
60428dbf 143 group->a_is_minus3 = 0;
60428dbf
BM		 144 return 1;
145 }
146
147
bb62a8b0
BM		 148void ec_GFp_simple_group_finish(EC_GROUP *group)
149 {
5784a521
MC		 150 BN_free(group->field);
151 BN_free(group->a);
152 BN_free(group->b);
bb62a8b0
BM		 153 }
154
155
156void ec_GFp_simple_group_clear_finish(EC_GROUP *group)
157 {
5784a521
MC		 158 BN_clear_free(group->field);
159 BN_clear_free(group->a);
160 BN_clear_free(group->b);
bb62a8b0
BM		 161 }
162
163
164int ec_GFp_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src)
165 {
5784a521
MC		 166 if (!BN_copy(dest->field, src->field)) return 0;
167 if (!BN_copy(dest->a, src->a)) return 0;
168 if (!BN_copy(dest->b, src->b)) return 0;
bb62a8b0
BM		 169
170 dest->a_is_minus3 = src->a_is_minus3;
171
bb62a8b0
BM		 172 return 1;
173 }
174
175
35b73a1f 176int ec_GFp_simple_group_set_curve(EC_GROUP *group,
60428dbf
BM		 177 const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
178 {
179 int ret = 0;
180 BN_CTX *new_ctx = NULL;
181 BIGNUM *tmp_a;
182
1d5bd6cf
BM		 183 /* p must be a prime > 3 */
184 if (BN_num_bits(p) <= 2 || !BN_is_odd(p))
185 {
35b73a1f 186 ECerr(EC_F_EC_GFP_SIMPLE_GROUP_SET_CURVE, EC_R_INVALID_FIELD);
1d5bd6cf
BM		 187 return 0;
188 }
189
60428dbf
BM		 190 if (ctx == NULL)
191 {
192 ctx = new_ctx = BN_CTX_new();
193 if (ctx == NULL)
194 return 0;
195 }
60428dbf 196
226cc7de 197 BN_CTX_start(ctx);
60428dbf
BM		 198 tmp_a = BN_CTX_get(ctx);
199 if (tmp_a == NULL) goto err;
200
201 /* group->field */
5784a521
MC		 202 if (!BN_copy(group->field, p)) goto err;
203 BN_set_negative(group->field, 0);
60428dbf
BM		 204
205 /* group->a */
206 if (!BN_nnmod(tmp_a, a, p, ctx)) goto err;
207 if (group->meth->field_encode)
5784a521 208 { if (!group->meth->field_encode(group, group->a, tmp_a, ctx)) goto err; }
60428dbf 209 else
5784a521 210 if (!BN_copy(group->a, tmp_a)) goto err;
60428dbf
BM		 211
212 /* group->b */
5784a521 213 if (!BN_nnmod(group->b, b, p, ctx)) goto err;
60428dbf 214 if (group->meth->field_encode)
5784a521 215 if (!group->meth->field_encode(group, group->b, group->b, ctx)) goto err;
60428dbf
BM		 216
217 /* group->a_is_minus3 */
218 if (!BN_add_word(tmp_a, 3)) goto err;
5784a521 219 group->a_is_minus3 = (0 == BN_cmp(tmp_a, group->field));
60428dbf
BM		 220
221 ret = 1;
222
223 err:
224 BN_CTX_end(ctx);
225 if (new_ctx != NULL)
226 BN_CTX_free(new_ctx);
227 return ret;
228 }
229
230
35b73a1f 231int ec_GFp_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx)
60428dbf 232 {
bb62a8b0
BM		 233 int ret = 0;
234 BN_CTX *new_ctx = NULL;
235
236 if (p != NULL)
60428dbf 237 {
5784a521 238 if (!BN_copy(p, group->field)) return 0;
60428dbf 239 }
60428dbf 240
bb62a8b0 241 if (a != NULL || b != NULL)
60428dbf 242 {
bb62a8b0 243 if (group->meth->field_decode)
60428dbf 244 {
bb62a8b0
BM		 245 if (ctx == NULL)
246 {
247 ctx = new_ctx = BN_CTX_new();
248 if (ctx == NULL)
249 return 0;
250 }
251 if (a != NULL)
252 {
5784a521 253 if (!group->meth->field_decode(group, a, group->a, ctx)) goto err;
bb62a8b0
BM		 254 }
255 if (b != NULL)
256 {
5784a521 257 if (!group->meth->field_decode(group, b, group->b, ctx)) goto err;
bb62a8b0 258 }
60428dbf 259 }
bb62a8b0 260 else
60428dbf 261 {
bb62a8b0
BM		 262 if (a != NULL)
263 {
5784a521 264 if (!BN_copy(a, group->a)) goto err;
bb62a8b0
BM		 265 }
266 if (b != NULL)
267 {
5784a521 268 if (!BN_copy(b, group->b)) goto err;
bb62a8b0 269 }
60428dbf
BM		 270 }
271 }
bb62a8b0
BM		 272
273 ret = 1;
274
275 err:
276 if (new_ctx)
277 BN_CTX_free(new_ctx);
278 return ret;
60428dbf
BM		 279 }
280
281
7793f30e
BM		 282int ec_GFp_simple_group_get_degree(const EC_GROUP *group)
283 {
5784a521 284 return BN_num_bits(group->field);
7793f30e
BM		 285 }
286
287
17d6bb81 288int ec_GFp_simple_group_check_discriminant(const EC_GROUP *group, BN_CTX *ctx)
af28dd6c
BM		 289 {
290 int ret = 0;
291 BIGNUM *a,*b,*order,*tmp_1,*tmp_2;
5784a521 292 const BIGNUM *p = group->field;
af28dd6c 293 BN_CTX *new_ctx = NULL;
af28dd6c
BM		 294
295 if (ctx == NULL)
296 {
297 ctx = new_ctx = BN_CTX_new();
298 if (ctx == NULL)
299 {
17d6bb81 300 ECerr(EC_F_EC_GFP_SIMPLE_GROUP_CHECK_DISCRIMINANT, ERR_R_MALLOC_FAILURE);
af28dd6c
BM		 301 goto err;
302 }
303 }
304 BN_CTX_start(ctx);
305 a = BN_CTX_get(ctx);
306 b = BN_CTX_get(ctx);
307 tmp_1 = BN_CTX_get(ctx);
308 tmp_2 = BN_CTX_get(ctx);
309 order = BN_CTX_get(ctx);
310 if (order == NULL) goto err;
311
312 if (group->meth->field_decode)
313 {
5784a521
MC		 314 if (!group->meth->field_decode(group, a, group->a, ctx)) goto err;
315 if (!group->meth->field_decode(group, b, group->b, ctx)) goto err;
af28dd6c
BM		 316 }
317 else
318 {
5784a521
MC		 319 if (!BN_copy(a, group->a)) goto err;
320 if (!BN_copy(b, group->b)) goto err;
af28dd6c
BM		 321 }
322
1d97c843
TH		 323 /*-
324 * check the discriminant:
af28dd6c 325 * y^2 = x^3 + a*x + b is an elliptic curve <=> 4*a^3 + 27*b^2 != 0 (mod p)
1d97c843
TH		 326 * 0 =< a, b < p
327 */
af28dd6c
BM		 328 if (BN_is_zero(a))
329 {
17d6bb81 330 if (BN_is_zero(b)) goto err;
af28dd6c
BM		 331 }
332 else if (!BN_is_zero(b))
333 {
334 if (!BN_mod_sqr(tmp_1, a, p, ctx)) goto err;
335 if (!BN_mod_mul(tmp_2, tmp_1, a, p, ctx)) goto err;
336 if (!BN_lshift(tmp_1, tmp_2, 2)) goto err;
337 /* tmp_1 = 4*a^3 */
338
339 if (!BN_mod_sqr(tmp_2, b, p, ctx)) goto err;
340 if (!BN_mul_word(tmp_2, 27)) goto err;
341 /* tmp_2 = 27*b^2 */
342
343 if (!BN_mod_add(a, tmp_1, tmp_2, p, ctx)) goto err;
17d6bb81 344 if (BN_is_zero(a)) goto err;
af28dd6c 345 }
af28dd6c
BM		 346 ret = 1;
347
348err:
47d55666
NL		 349 if (ctx != NULL)
350 BN_CTX_end(ctx);
af28dd6c
BM		 351 if (new_ctx != NULL)
352 BN_CTX_free(new_ctx);
af28dd6c
BM		 353 return ret;
354 }
355
356
60428dbf
BM		 357int ec_GFp_simple_point_init(EC_POINT *point)
358 {
5784a521
MC		 359 point->X = BN_new();
360 point->Y = BN_new();
361 point->Z = BN_new();
60428dbf
BM		 362 point->Z_is_one = 0;
363
5784a521
MC		 364 if(!point->X || !point->Y || !point->Z)
365 {
366 if(point->X) BN_free(point->X);
367 if(point->Y) BN_free(point->Y);
368 if(point->Z) BN_free(point->Z);
369 return 0;
370 }
60428dbf
BM		 371 return 1;
372 }
373
374
375void ec_GFp_simple_point_finish(EC_POINT *point)
376 {
5784a521
MC		 377 BN_free(point->X);
378 BN_free(point->Y);
379 BN_free(point->Z);
60428dbf
BM		 380 }
381
382
383void ec_GFp_simple_point_clear_finish(EC_POINT *point)
384 {
5784a521
MC		 385 BN_clear_free(point->X);
386 BN_clear_free(point->Y);
387 BN_clear_free(point->Z);
60428dbf
BM		 388 point->Z_is_one = 0;
389 }
390
391
392int ec_GFp_simple_point_copy(EC_POINT *dest, const EC_POINT *src)
393 {
5784a521
MC		 394 if (!BN_copy(dest->X, src->X)) return 0;
395 if (!BN_copy(dest->Y, src->Y)) return 0;
396 if (!BN_copy(dest->Z, src->Z)) return 0;
60428dbf
BM		 397 dest->Z_is_one = src->Z_is_one;
398
399 return 1;
400 }
401
402
226cc7de
BM		 403int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *group, EC_POINT *point)
404 {
405 point->Z_is_one = 0;
5784a521 406 BN_zero(point->Z);
b6358c89 407 return 1;
226cc7de
BM		 408 }
409
410
1d5bd6cf 411int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *group, EC_POINT *point,
bb62a8b0
BM		 412 const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *ctx)
413 {
414 BN_CTX *new_ctx = NULL;
415 int ret = 0;
416
417 if (ctx == NULL)
418 {
419 ctx = new_ctx = BN_CTX_new();
420 if (ctx == NULL)
421 return 0;
422 }
1d5bd6cf 423
bb62a8b0
BM		 424 if (x != NULL)
425 {
5784a521 426 if (!BN_nnmod(point->X, x, group->field, ctx)) goto err;
bb62a8b0
BM		 427 if (group->meth->field_encode)
428 {
5784a521 429 if (!group->meth->field_encode(group, point->X, point->X, ctx)) goto err;
bb62a8b0
BM		 430 }
431 }
432
433 if (y != NULL)
434 {
5784a521 435 if (!BN_nnmod(point->Y, y, group->field, ctx)) goto err;
bb62a8b0
BM		 436 if (group->meth->field_encode)
437 {
5784a521 438 if (!group->meth->field_encode(group, point->Y, point->Y, ctx)) goto err;
bb62a8b0
BM		 439 }
440 }
441
442 if (z != NULL)
443 {
444 int Z_is_one;
1d5bd6cf 445
5784a521
MC		 446 if (!BN_nnmod(point->Z, z, group->field, ctx)) goto err;
447 Z_is_one = BN_is_one(point->Z);
bb62a8b0
BM		 448 if (group->meth->field_encode)
449 {
48fe4d62
BM		 450 if (Z_is_one && (group->meth->field_set_to_one != 0))
451 {
5784a521 452 if (!group->meth->field_set_to_one(group, point->Z, ctx)) goto err;
48fe4d62
BM		 453 }
454 else
455 {
5784a521 456 if (!group->meth->field_encode(group, point->Z, point->Z, ctx)) goto err;
48fe4d62 457 }
bb62a8b0
BM		 458 }
459 point->Z_is_one = Z_is_one;
460 }
dd616752
DSH		 461
462 ret = 1;
bb62a8b0
BM		 463
464 err:
465 if (new_ctx != NULL)
466 BN_CTX_free(new_ctx);
467 return ret;
468 }
1d5bd6cf
BM		 469
470
bb62a8b0
BM		 471int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *group, const EC_POINT *point,
472 BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *ctx)
226cc7de
BM		 473 {
474 BN_CTX *new_ctx = NULL;
475 int ret = 0;
bb62a8b0
BM		 476
477 if (group->meth->field_decode != 0)
226cc7de
BM		 478 {
479 if (ctx == NULL)
480 {
481 ctx = new_ctx = BN_CTX_new();
482 if (ctx == NULL)
483 return 0;
484 }
226cc7de 485
bb62a8b0
BM		 486 if (x != NULL)
487 {
5784a521 488 if (!group->meth->field_decode(group, x, point->X, ctx)) goto err;
bb62a8b0
BM		 489 }
490 if (y != NULL)
491 {
5784a521 492 if (!group->meth->field_decode(group, y, point->Y, ctx)) goto err;
bb62a8b0
BM		 493 }
494 if (z != NULL)
495 {
5784a521 496 if (!group->meth->field_decode(group, z, point->Z, ctx)) goto err;
bb62a8b0
BM		 497 }
498 }
499 else
500 {
501 if (x != NULL)
502 {
5784a521 503 if (!BN_copy(x, point->X)) goto err;
bb62a8b0
BM		 504 }
505 if (y != NULL)
506 {
5784a521 507 if (!BN_copy(y, point->Y)) goto err;
bb62a8b0
BM		 508 }
509 if (z != NULL)
510 {
5784a521 511 if (!BN_copy(z, point->Z)) goto err;
bb62a8b0
BM		 512 }
513 }
226cc7de 514
bb62a8b0
BM		 515 ret = 1;
516
226cc7de
BM		 517 err:
518 if (new_ctx != NULL)
519 BN_CTX_free(new_ctx);
520 return ret;
521 }
522
523
35b73a1f 524int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *group, EC_POINT *point,
bb62a8b0
BM		 525 const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx)
526 {
527 if (x == NULL || y == NULL)
528 {
529 /* unlike for projective coordinates, we do not tolerate this */
35b73a1f 530 ECerr(EC_F_EC_GFP_SIMPLE_POINT_SET_AFFINE_COORDINATES, ERR_R_PASSED_NULL_PARAMETER);
bb62a8b0
BM		 531 return 0;
532 }
533
534 return EC_POINT_set_Jprojective_coordinates_GFp(group, point, x, y, BN_value_one(), ctx);
535 }
536
537
35b73a1f 538int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point,
226cc7de
BM		 539 BIGNUM *x, BIGNUM *y, BN_CTX *ctx)
540 {
541 BN_CTX *new_ctx = NULL;
13744514
BM		 542 BIGNUM *Z, *Z_1, *Z_2, *Z_3;
543 const BIGNUM *Z_;
226cc7de
BM		 544 int ret = 0;
545
546 if (EC_POINT_is_at_infinity(group, point))
547 {
35b73a1f 548 ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES, EC_R_POINT_AT_INFINITY);
226cc7de
BM		 549 return 0;
550 }
551
552 if (ctx == NULL)
553 {
554 ctx = new_ctx = BN_CTX_new();
555 if (ctx == NULL)
556 return 0;
557 }
558
559 BN_CTX_start(ctx);
226cc7de
BM		 560 Z = BN_CTX_get(ctx);
561 Z_1 = BN_CTX_get(ctx);
562 Z_2 = BN_CTX_get(ctx);
563 Z_3 = BN_CTX_get(ctx);
564 if (Z_3 == NULL) goto err;
565
566 /* transform (X, Y, Z) into (x, y) := (X/Z^2, Y/Z^3) */
567
568 if (group->meth->field_decode)
569 {
5784a521 570 if (!group->meth->field_decode(group, Z, point->Z, ctx)) goto err;
13744514 571 Z_ = Z;
226cc7de
BM		 572 }
573 else
574 {
5784a521 575 Z_ = point->Z;
226cc7de
BM		 576 }
577
578 if (BN_is_one(Z_))
579 {
13744514 580 if (group->meth->field_decode)
1d5bd6cf 581 {
13744514
BM		 582 if (x != NULL)
583 {
5784a521 584 if (!group->meth->field_decode(group, x, point->X, ctx)) goto err;
13744514
BM		 585 }
586 if (y != NULL)
587 {
5784a521 588 if (!group->meth->field_decode(group, y, point->Y, ctx)) goto err;
13744514 589 }
1d5bd6cf 590 }
13744514 591 else
1d5bd6cf 592 {
13744514
BM		 593 if (x != NULL)
594 {
5784a521 595 if (!BN_copy(x, point->X)) goto err;
13744514
BM		 596 }
597 if (y != NULL)
598 {
5784a521 599 if (!BN_copy(y, point->Y)) goto err;
13744514 600 }
1d5bd6cf 601 }
226cc7de
BM		 602 }
603 else
604 {
5784a521 605 if (!BN_mod_inverse(Z_1, Z_, group->field, ctx))
226cc7de 606 {
35b73a1f 607 ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES, ERR_R_BN_LIB);
226cc7de
BM		 608 goto err;
609 }
48fe4d62
BM		 610
611 if (group->meth->field_encode == 0)
612 {
613 /* field_sqr works on standard representation */
614 if (!group->meth->field_sqr(group, Z_2, Z_1, ctx)) goto err;
615 }
616 else
617 {
5784a521 618 if (!BN_mod_sqr(Z_2, Z_1, group->field, ctx)) goto err;
48fe4d62 619 }
226cc7de 620
1d5bd6cf
BM		 621 if (x != NULL)
622 {
13744514 623 /* in the Montgomery case, field_mul will cancel out Montgomery factor in X: */
5784a521 624 if (!group->meth->field_mul(group, x, point->X, Z_2, ctx)) goto err;
1d5bd6cf
BM		 625 }
626
627 if (y != NULL)
628 {
48fe4d62
BM		 629 if (group->meth->field_encode == 0)
630 {
631 /* field_mul works on standard representation */
632 if (!group->meth->field_mul(group, Z_3, Z_2, Z_1, ctx)) goto err;
48fe4d62
BM		 633 }
634 else
635 {
5784a521 636 if (!BN_mod_mul(Z_3, Z_2, Z_1, group->field, ctx)) goto err;
48fe4d62 637 }
13744514
BM		 638
639 /* in the Montgomery case, field_mul will cancel out Montgomery factor in Y: */
5784a521 640 if (!group->meth->field_mul(group, y, point->Y, Z_3, ctx)) goto err;
1d5bd6cf 641 }
226cc7de
BM		 642 }
643
644 ret = 1;
645
646 err:
647 BN_CTX_end(ctx);
648 if (new_ctx != NULL)
649 BN_CTX_free(new_ctx);
650 return ret;
651 }
652
60428dbf
BM		 653int ec_GFp_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
654 {
655 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
656 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
657 const BIGNUM *p;
658 BN_CTX *new_ctx = NULL;
659 BIGNUM *n0, *n1, *n2, *n3, *n4, *n5, *n6;
660 int ret = 0;
661
662 if (a == b)
663 return EC_POINT_dbl(group, r, a, ctx);
664 if (EC_POINT_is_at_infinity(group, a))
665 return EC_POINT_copy(r, b);
666 if (EC_POINT_is_at_infinity(group, b))
667 return EC_POINT_copy(r, a);
668
669 field_mul = group->meth->field_mul;
670 field_sqr = group->meth->field_sqr;
5784a521 671 p = group->field;
60428dbf
BM		 672
673 if (ctx == NULL)
674 {
675 ctx = new_ctx = BN_CTX_new();
676 if (ctx == NULL)
677 return 0;
678 }
60428dbf 679
226cc7de 680 BN_CTX_start(ctx);
60428dbf
BM		 681 n0 = BN_CTX_get(ctx);
682 n1 = BN_CTX_get(ctx);
683 n2 = BN_CTX_get(ctx);
684 n3 = BN_CTX_get(ctx);
685 n4 = BN_CTX_get(ctx);
686 n5 = BN_CTX_get(ctx);
687 n6 = BN_CTX_get(ctx);
688 if (n6 == NULL) goto end;
689
1d5bd6cf
BM		 690 /* Note that in this function we must not read components of 'a' or 'b'
691 * once we have written the corresponding components of 'r'.
692 * ('r' might be one of 'a' or 'b'.)
693 */
694
60428dbf
BM		 695 /* n1, n2 */
696 if (b->Z_is_one)
697 {
5784a521
MC		 698 if (!BN_copy(n1, a->X)) goto end;
699 if (!BN_copy(n2, a->Y)) goto end;
60428dbf
BM		 700 /* n1 = X_a */
701 /* n2 = Y_a */
702 }
703 else
704 {
5784a521
MC		 705 if (!field_sqr(group, n0, b->Z, ctx)) goto end;
706 if (!field_mul(group, n1, a->X, n0, ctx)) goto end;
60428dbf
BM		 707 /* n1 = X_a * Z_b^2 */
708
5784a521
MC		 709 if (!field_mul(group, n0, n0, b->Z, ctx)) goto end;
710 if (!field_mul(group, n2, a->Y, n0, ctx)) goto end;
60428dbf
BM		 711 /* n2 = Y_a * Z_b^3 */
712 }
713
714 /* n3, n4 */
715 if (a->Z_is_one)
716 {
5784a521
MC		 717 if (!BN_copy(n3, b->X)) goto end;
718 if (!BN_copy(n4, b->Y)) goto end;
60428dbf
BM		 719 /* n3 = X_b */
720 /* n4 = Y_b */
721 }
722 else
723 {
5784a521
MC		 724 if (!field_sqr(group, n0, a->Z, ctx)) goto end;
725 if (!field_mul(group, n3, b->X, n0, ctx)) goto end;
60428dbf
BM		 726 /* n3 = X_b * Z_a^2 */
727
5784a521
MC		 728 if (!field_mul(group, n0, n0, a->Z, ctx)) goto end;
729 if (!field_mul(group, n4, b->Y, n0, ctx)) goto end;
60428dbf
BM		 730 /* n4 = Y_b * Z_a^3 */
731 }
732
733 /* n5, n6 */
734 if (!BN_mod_sub_quick(n5, n1, n3, p)) goto end;
735 if (!BN_mod_sub_quick(n6, n2, n4, p)) goto end;
736 /* n5 = n1 - n3 */
737 /* n6 = n2 - n4 */
738
739 if (BN_is_zero(n5))
740 {
741 if (BN_is_zero(n6))
742 {
743 /* a is the same point as b */
744 BN_CTX_end(ctx);
60428dbf 745 ret = EC_POINT_dbl(group, r, a, ctx);
e869d4bd 746 ctx = NULL;
60428dbf
BM		 747 goto end;
748 }
749 else
750 {
751 /* a is the inverse of b */
5784a521 752 BN_zero(r->Z);
60428dbf
BM		 753 r->Z_is_one = 0;
754 ret = 1;
755 goto end;
756 }
757 }
758
759 /* 'n7', 'n8' */
760 if (!BN_mod_add_quick(n1, n1, n3, p)) goto end;
761 if (!BN_mod_add_quick(n2, n2, n4, p)) goto end;
762 /* 'n7' = n1 + n3 */
763 /* 'n8' = n2 + n4 */
764
765 /* Z_r */
766 if (a->Z_is_one && b->Z_is_one)
767 {
5784a521 768 if (!BN_copy(r->Z, n5)) goto end;
60428dbf
BM		 769 }
770 else
771 {
772 if (a->Z_is_one)
5784a521 773 { if (!BN_copy(n0, b->Z)) goto end; }
60428dbf 774 else if (b->Z_is_one)
5784a521 775 { if (!BN_copy(n0, a->Z)) goto end; }
60428dbf 776 else
5784a521
MC		 777 { if (!field_mul(group, n0, a->Z, b->Z, ctx)) goto end; }
778 if (!field_mul(group, r->Z, n0, n5, ctx)) goto end;
60428dbf
BM		 779 }
780 r->Z_is_one = 0;
781 /* Z_r = Z_a * Z_b * n5 */
782
783 /* X_r */
784 if (!field_sqr(group, n0, n6, ctx)) goto end;
785 if (!field_sqr(group, n4, n5, ctx)) goto end;
786 if (!field_mul(group, n3, n1, n4, ctx)) goto end;
5784a521 787 if (!BN_mod_sub_quick(r->X, n0, n3, p)) goto end;
60428dbf
BM		 788 /* X_r = n6^2 - n5^2 * 'n7' */
789
790 /* 'n9' */
5784a521 791 if (!BN_mod_lshift1_quick(n0, r->X, p)) goto end;
60428dbf
BM		 792 if (!BN_mod_sub_quick(n0, n3, n0, p)) goto end;
793 /* n9 = n5^2 * 'n7' - 2 * X_r */
794
795 /* Y_r */
796 if (!field_mul(group, n0, n0, n6, ctx)) goto end;
797 if (!field_mul(group, n5, n4, n5, ctx)) goto end; /* now n5 is n5^3 */
798 if (!field_mul(group, n1, n2, n5, ctx)) goto end;
799 if (!BN_mod_sub_quick(n0, n0, n1, p)) goto end;
800 if (BN_is_odd(n0))
801 if (!BN_add(n0, n0, p)) goto end;
802 /* now 0 <= n0 < 2*p, and n0 is even */
5784a521 803 if (!BN_rshift1(r->Y, n0)) goto end;
60428dbf
BM		 804 /* Y_r = (n6 * 'n9' - 'n8' * 'n5^3') / 2 */
805
806 ret = 1;
807
808 end:
809 if (ctx) /* otherwise we already called BN_CTX_end */
810 BN_CTX_end(ctx);
811 if (new_ctx != NULL)
812 BN_CTX_free(new_ctx);
813 return ret;
814 }
815
816
817int ec_GFp_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_CTX *ctx)
818 {
819 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
820 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
821 const BIGNUM *p;
822 BN_CTX *new_ctx = NULL;
823 BIGNUM *n0, *n1, *n2, *n3;
824 int ret = 0;
825
826 if (EC_POINT_is_at_infinity(group, a))
827 {
5784a521 828 BN_zero(r->Z);
60428dbf
BM		 829 r->Z_is_one = 0;
830 return 1;
831 }
832
833 field_mul = group->meth->field_mul;
834 field_sqr = group->meth->field_sqr;
5784a521 835 p = group->field;
60428dbf
BM		 836
837 if (ctx == NULL)
838 {
839 ctx = new_ctx = BN_CTX_new();
840 if (ctx == NULL)
841 return 0;
842 }
60428dbf 843
226cc7de 844 BN_CTX_start(ctx);
60428dbf
BM		 845 n0 = BN_CTX_get(ctx);
846 n1 = BN_CTX_get(ctx);
847 n2 = BN_CTX_get(ctx);
848 n3 = BN_CTX_get(ctx);
849 if (n3 == NULL) goto err;
850
1d5bd6cf
BM		 851 /* Note that in this function we must not read components of 'a'
852 * once we have written the corresponding components of 'r'.
853 * ('r' might the same as 'a'.)
854 */
855
60428dbf
BM		 856 /* n1 */
857 if (a->Z_is_one)
858 {
5784a521 859 if (!field_sqr(group, n0, a->X, ctx)) goto err;
60428dbf
BM		 860 if (!BN_mod_lshift1_quick(n1, n0, p)) goto err;
861 if (!BN_mod_add_quick(n0, n0, n1, p)) goto err;
5784a521 862 if (!BN_mod_add_quick(n1, n0, group->a, p)) goto err;
60428dbf
BM		 863 /* n1 = 3 * X_a^2 + a_curve */
864 }
865 else if (group->a_is_minus3)
866 {
5784a521
MC		 867 if (!field_sqr(group, n1, a->Z, ctx)) goto err;
868 if (!BN_mod_add_quick(n0, a->X, n1, p)) goto err;
869 if (!BN_mod_sub_quick(n2, a->X, n1, p)) goto err;
60428dbf
BM		 870 if (!field_mul(group, n1, n0, n2, ctx)) goto err;
871 if (!BN_mod_lshift1_quick(n0, n1, p)) goto err;
872 if (!BN_mod_add_quick(n1, n0, n1, p)) goto err;
873 /* n1 = 3 * (X_a + Z_a^2) * (X_a - Z_a^2)
874 * = 3 * X_a^2 - 3 * Z_a^4 */
875 }
876 else
877 {
5784a521 878 if (!field_sqr(group, n0, a->X, ctx)) goto err;
60428dbf
BM		 879 if (!BN_mod_lshift1_quick(n1, n0, p)) goto err;
880 if (!BN_mod_add_quick(n0, n0, n1, p)) goto err;
5784a521 881 if (!field_sqr(group, n1, a->Z, ctx)) goto err;
60428dbf 882 if (!field_sqr(group, n1, n1, ctx)) goto err;
5784a521 883 if (!field_mul(group, n1, n1, group->a, ctx)) goto err;
60428dbf
BM		 884 if (!BN_mod_add_quick(n1, n1, n0, p)) goto err;
885 /* n1 = 3 * X_a^2 + a_curve * Z_a^4 */
886 }
887
888 /* Z_r */
889 if (a->Z_is_one)
890 {
5784a521 891 if (!BN_copy(n0, a->Y)) goto err;
60428dbf
BM		 892 }
893 else
894 {
5784a521 895 if (!field_mul(group, n0, a->Y, a->Z, ctx)) goto err;
60428dbf 896 }
5784a521 897 if (!BN_mod_lshift1_quick(r->Z, n0, p)) goto err;
60428dbf
BM		 898 r->Z_is_one = 0;
899 /* Z_r = 2 * Y_a * Z_a */
900
901 /* n2 */
5784a521
MC		 902 if (!field_sqr(group, n3, a->Y, ctx)) goto err;
903 if (!field_mul(group, n2, a->X, n3, ctx)) goto err;
60428dbf
BM		 904 if (!BN_mod_lshift_quick(n2, n2, 2, p)) goto err;
905 /* n2 = 4 * X_a * Y_a^2 */
906
907 /* X_r */
908 if (!BN_mod_lshift1_quick(n0, n2, p)) goto err;
5784a521
MC		 909 if (!field_sqr(group, r->X, n1, ctx)) goto err;
910 if (!BN_mod_sub_quick(r->X, r->X, n0, p)) goto err;
60428dbf
BM		 911 /* X_r = n1^2 - 2 * n2 */
912
913 /* n3 */
914 if (!field_sqr(group, n0, n3, ctx)) goto err;
915 if (!BN_mod_lshift_quick(n3, n0, 3, p)) goto err;
916 /* n3 = 8 * Y_a^4 */
917
918 /* Y_r */
5784a521 919 if (!BN_mod_sub_quick(n0, n2, r->X, p)) goto err;
60428dbf 920 if (!field_mul(group, n0, n1, n0, ctx)) goto err;
5784a521 921 if (!BN_mod_sub_quick(r->Y, n0, n3, p)) goto err;
60428dbf
BM		 922 /* Y_r = n1 * (n2 - X_r) - n3 */
923
924 ret = 1;
925
926 err:
927 BN_CTX_end(ctx);
928 if (new_ctx != NULL)
929 BN_CTX_free(new_ctx);
930 return ret;
931 }
932
933
bb62a8b0
BM		 934int ec_GFp_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
935 {
5784a521 936 if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(point->Y))
bb62a8b0
BM		 937 /* point is its own inverse */
938 return 1;
939
5784a521 940 return BN_usub(point->Y, group->field, point->Y);
bb62a8b0 941 }
1d5bd6cf
BM		 942
943
60428dbf
BM		 944int ec_GFp_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point)
945 {
5784a521 946 return BN_is_zero(point->Z);
60428dbf
BM		 947 }
948
949
e869d4bd
BM		 950int ec_GFp_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx)
951 {
952 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
953 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
954 const BIGNUM *p;
955 BN_CTX *new_ctx = NULL;
7f5b4dd1 956 BIGNUM *rh, *tmp, *Z4, *Z6;
e869d4bd 957 int ret = -1;
60428dbf 958
e869d4bd
BM		 959 if (EC_POINT_is_at_infinity(group, point))
960 return 1;
961
962 field_mul = group->meth->field_mul;
963 field_sqr = group->meth->field_sqr;
5784a521 964 p = group->field;
60428dbf 965
e869d4bd
BM		 966 if (ctx == NULL)
967 {
968 ctx = new_ctx = BN_CTX_new();
969 if (ctx == NULL)
226cc7de 970 return -1;
e869d4bd 971 }
e869d4bd 972
226cc7de 973 BN_CTX_start(ctx);
e869d4bd 974 rh = BN_CTX_get(ctx);
7f5b4dd1 975 tmp = BN_CTX_get(ctx);
e869d4bd
BM		 976 Z4 = BN_CTX_get(ctx);
977 Z6 = BN_CTX_get(ctx);
978 if (Z6 == NULL) goto err;
979
1d97c843
TH		 980 /*-
981 * We have a curve defined by a Weierstrass equation
e869d4bd
BM		 982 * y^2 = x^3 + a*x + b.
983 * The point to consider is given in Jacobian projective coordinates
984 * where (X, Y, Z) represents (x, y) = (X/Z^2, Y/Z^3).
985 * Substituting this and multiplying by Z^6 transforms the above equation into
986 * Y^2 = X^3 + a*X*Z^4 + b*Z^6.
987 * To test this, we add up the right-hand side in 'rh'.
988 */
989
7f5b4dd1 990 /* rh := X^2 */
5784a521 991 if (!field_sqr(group, rh, point->X, ctx)) goto err;
e869d4bd
BM		 992
993 if (!point->Z_is_one)
994 {
5784a521 995 if (!field_sqr(group, tmp, point->Z, ctx)) goto err;
7f5b4dd1
GT		 996 if (!field_sqr(group, Z4, tmp, ctx)) goto err;
997 if (!field_mul(group, Z6, Z4, tmp, ctx)) goto err;
e869d4bd 998
7f5b4dd1 999 /* rh := (rh + a*Z^4)*X */
bb62a8b0 1000 if (group->a_is_minus3)
e869d4bd 1001 {
7f5b4dd1
GT		 1002 if (!BN_mod_lshift1_quick(tmp, Z4, p)) goto err;
1003 if (!BN_mod_add_quick(tmp, tmp, Z4, p)) goto err;
1004 if (!BN_mod_sub_quick(rh, rh, tmp, p)) goto err;
5784a521 1005 if (!field_mul(group, rh, rh, point->X, ctx)) goto err;
e869d4bd
BM		 1006 }
1007 else
1008 {
5784a521 1009 if (!field_mul(group, tmp, Z4, group->a, ctx)) goto err;
7f5b4dd1 1010 if (!BN_mod_add_quick(rh, rh, tmp, p)) goto err;
5784a521 1011 if (!field_mul(group, rh, rh, point->X, ctx)) goto err;
e869d4bd
BM		 1012 }
1013
1014 /* rh := rh + b*Z^6 */
5784a521 1015 if (!field_mul(group, tmp, group->b, Z6, ctx)) goto err;
7f5b4dd1 1016 if (!BN_mod_add_quick(rh, rh, tmp, p)) goto err;
e869d4bd
BM		 1017 }
1018 else
1019 {
1020 /* point->Z_is_one */
1021
7f5b4dd1 1022 /* rh := (rh + a)*X */
5784a521
MC		 1023 if (!BN_mod_add_quick(rh, rh, group->a, p)) goto err;
1024 if (!field_mul(group, rh, rh, point->X, ctx)) goto err;
e869d4bd 1025 /* rh := rh + b */
5784a521 1026 if (!BN_mod_add_quick(rh, rh, group->b, p)) goto err;
e869d4bd
BM		 1027 }
1028
1029 /* 'lh' := Y^2 */
5784a521 1030 if (!field_sqr(group, tmp, point->Y, ctx)) goto err;
e869d4bd 1031
7f5b4dd1 1032 ret = (0 == BN_ucmp(tmp, rh));
e869d4bd
BM		 1033
1034 err:
1035 BN_CTX_end(ctx);
1036 if (new_ctx != NULL)
1037 BN_CTX_free(new_ctx);
1038 return ret;
1039 }
1040
1041
bb62a8b0
BM		 1042int ec_GFp_simple_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
1043 {
1044 /* return values:
1045 * -1 error
1046 * 0 equal (in affine coordinates)
1047 * 1 not equal
1048 */
1049
1050 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
1051 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
1052 BN_CTX *new_ctx = NULL;
1053 BIGNUM *tmp1, *tmp2, *Za23, *Zb23;
1054 const BIGNUM *tmp1_, *tmp2_;
1055 int ret = -1;
1056
1057 if (EC_POINT_is_at_infinity(group, a))
1058 {
1059 return EC_POINT_is_at_infinity(group, b) ? 0 : 1;
1060 }
0aa1aedb
DSH		 1061
1062 if (EC_POINT_is_at_infinity(group, b))
1063 return 1;
bb62a8b0
BM		 1064
1065 if (a->Z_is_one && b->Z_is_one)
1066 {
5784a521 1067 return ((BN_cmp(a->X, b->X) == 0) && BN_cmp(a->Y, b->Y) == 0) ? 0 : 1;
bb62a8b0
BM		 1068 }
1069
1070 field_mul = group->meth->field_mul;
1071 field_sqr = group->meth->field_sqr;
1072
1073 if (ctx == NULL)
1074 {
1075 ctx = new_ctx = BN_CTX_new();
1076 if (ctx == NULL)
1077 return -1;
1078 }
1079
1080 BN_CTX_start(ctx);
1081 tmp1 = BN_CTX_get(ctx);
1082 tmp2 = BN_CTX_get(ctx);
1083 Za23 = BN_CTX_get(ctx);
1084 Zb23 = BN_CTX_get(ctx);
1085 if (Zb23 == NULL) goto end;
1086
1d97c843
TH		 1087 /*-
1088 * We have to decide whether
bb62a8b0
BM		 1089 * (X_a/Z_a^2, Y_a/Z_a^3) = (X_b/Z_b^2, Y_b/Z_b^3),
1090 * or equivalently, whether
1091 * (X_a*Z_b^2, Y_a*Z_b^3) = (X_b*Z_a^2, Y_b*Z_a^3).
1092 */
1093
1094 if (!b->Z_is_one)
1095 {
5784a521
MC		 1096 if (!field_sqr(group, Zb23, b->Z, ctx)) goto end;
1097 if (!field_mul(group, tmp1, a->X, Zb23, ctx)) goto end;
bb62a8b0
BM		 1098 tmp1_ = tmp1;
1099 }
1100 else
5784a521 1101 tmp1_ = a->X;
bb62a8b0
BM		 1102 if (!a->Z_is_one)
1103 {
5784a521
MC		 1104 if (!field_sqr(group, Za23, a->Z, ctx)) goto end;
1105 if (!field_mul(group, tmp2, b->X, Za23, ctx)) goto end;
bb62a8b0
BM		 1106 tmp2_ = tmp2;
1107 }
1108 else
5784a521 1109 tmp2_ = b->X;
bb62a8b0
BM		 1110
1111 /* compare X_a*Z_b^2 with X_b*Z_a^2 */
1112 if (BN_cmp(tmp1_, tmp2_) != 0)
1113 {
1114 ret = 1; /* points differ */
1115 goto end;
1116 }
1117
1118
1119 if (!b->Z_is_one)
1120 {
5784a521
MC		 1121 if (!field_mul(group, Zb23, Zb23, b->Z, ctx)) goto end;
1122 if (!field_mul(group, tmp1, a->Y, Zb23, ctx)) goto end;
42909e39 1123 /* tmp1_ = tmp1 */
bb62a8b0 1124 }
42909e39 1125 else
5784a521 1126 tmp1_ = a->Y;
bb62a8b0
BM		 1127 if (!a->Z_is_one)
1128 {
5784a521
MC		 1129 if (!field_mul(group, Za23, Za23, a->Z, ctx)) goto end;
1130 if (!field_mul(group, tmp2, b->Y, Za23, ctx)) goto end;
42909e39 1131 /* tmp2_ = tmp2 */
bb62a8b0 1132 }
42909e39 1133 else
5784a521 1134 tmp2_ = b->Y;
bb62a8b0
BM		 1135
1136 /* compare Y_a*Z_b^3 with Y_b*Z_a^3 */
1137 if (BN_cmp(tmp1_, tmp2_) != 0)
1138 {
1139 ret = 1; /* points differ */
1140 goto end;
1141 }
1142
1143 /* points are equal */
1144 ret = 0;
1145
1146 end:
1147 BN_CTX_end(ctx);
1148 if (new_ctx != NULL)
1149 BN_CTX_free(new_ctx);
1150 return ret;
1151 }
1d5bd6cf 1152
dd616752 1153
e869d4bd
BM		 1154int ec_GFp_simple_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
1155 {
1156 BN_CTX *new_ctx = NULL;
226cc7de 1157 BIGNUM *x, *y;
e869d4bd
BM		 1158 int ret = 0;
1159
1160 if (point->Z_is_one || EC_POINT_is_at_infinity(group, point))
1161 return 1;
1162
1163 if (ctx == NULL)
1164 {
1165 ctx = new_ctx = BN_CTX_new();
1166 if (ctx == NULL)
1167 return 0;
1168 }
e869d4bd 1169
226cc7de
BM		 1170 BN_CTX_start(ctx);
1171 x = BN_CTX_get(ctx);
1172 y = BN_CTX_get(ctx);
1173 if (y == NULL) goto err;
e869d4bd 1174
226cc7de
BM		 1175 if (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
1176 if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
1177 if (!point->Z_is_one)
e869d4bd 1178 {
226cc7de
BM		 1179 ECerr(EC_F_EC_GFP_SIMPLE_MAKE_AFFINE, ERR_R_INTERNAL_ERROR);
1180 goto err;
e869d4bd 1181 }
e869d4bd 1182
e869d4bd
BM		 1183 ret = 1;
1184
226cc7de 1185 err:
e869d4bd
BM		 1186 BN_CTX_end(ctx);
1187 if (new_ctx != NULL)
1188 BN_CTX_free(new_ctx);
1189 return ret;
1190 }
60428dbf
BM		 1191
1192
48fe4d62
BM		 1193int ec_GFp_simple_points_make_affine(const EC_GROUP *group, size_t num, EC_POINT *points[], BN_CTX *ctx)
1194 {
1195 BN_CTX *new_ctx = NULL;
0fe73d6c
BM		 1196 BIGNUM *tmp, *tmp_Z;
1197 BIGNUM **prod_Z = NULL;
48fe4d62
BM		 1198 size_t i;
1199 int ret = 0;
1200
1201 if (num == 0)
1202 return 1;
1203
1204 if (ctx == NULL)
1205 {
1206 ctx = new_ctx = BN_CTX_new();
1207 if (ctx == NULL)
1208 return 0;
1209 }
1210
1211 BN_CTX_start(ctx);
0fe73d6c
BM		 1212 tmp = BN_CTX_get(ctx);
1213 tmp_Z = BN_CTX_get(ctx);
1214 if (tmp == NULL || tmp_Z == NULL) goto err;
48fe4d62 1215
0fe73d6c
BM		 1216 prod_Z = OPENSSL_malloc(num * sizeof prod_Z[0]);
1217 if (prod_Z == NULL) goto err;
1218 for (i = 0; i < num; i++)
1219 {
1220 prod_Z[i] = BN_new();
1221 if (prod_Z[i] == NULL) goto err;
1222 }
48fe4d62 1223
0fe73d6c
BM		 1224 /* Set each prod_Z[i] to the product of points[0]->Z .. points[i]->Z,
1225 * skipping any zero-valued inputs (pretend that they're 1). */
48fe4d62 1226
5784a521 1227 if (!BN_is_zero(points[0]->Z))
48fe4d62 1228 {
5784a521 1229 if (!BN_copy(prod_Z[0], points[0]->Z)) goto err;
0fe73d6c
BM		 1230 }
1231 else
1232 {
1233 if (group->meth->field_set_to_one != 0)
48fe4d62 1234 {
0fe73d6c
BM		 1235 if (!group->meth->field_set_to_one(group, prod_Z[0], ctx)) goto err;
1236 }
1237 else
1238 {
1239 if (!BN_one(prod_Z[0])) goto err;
48fe4d62
BM		 1240 }
1241 }
1242
0fe73d6c 1243 for (i = 1; i < num; i++)
48fe4d62 1244 {
5784a521 1245 if (!BN_is_zero(points[i]->Z))
48fe4d62 1246 {
5784a521 1247 if (!group->meth->field_mul(group, prod_Z[i], prod_Z[i - 1], points[i]->Z, ctx)) goto err;
0fe73d6c
BM		 1248 }
1249 else
1250 {
1251 if (!BN_copy(prod_Z[i], prod_Z[i - 1])) goto err;
48fe4d62
BM		 1252 }
1253 }
0fe73d6c
BM		 1254
1255 /* Now use a single explicit inversion to replace every
1256 * non-zero points[i]->Z by its inverse. */
1257
5784a521 1258 if (!BN_mod_inverse(tmp, prod_Z[num - 1], group->field, ctx))
0fe73d6c
BM		 1259 {
1260 ECerr(EC_F_EC_GFP_SIMPLE_POINTS_MAKE_AFFINE, ERR_R_BN_LIB);
1261 goto err;
1262 }
48fe4d62
BM		 1263 if (group->meth->field_encode != 0)
1264 {
0fe73d6c 1265 /* In the Montgomery case, we just turned R*H (representing H)
48fe4d62 1266 * into 1/(R*H), but we need R*(1/H) (representing 1/H);
0fe73d6c
BM		 1267 * i.e. we need to multiply by the Montgomery factor twice. */
1268 if (!group->meth->field_encode(group, tmp, tmp, ctx)) goto err;
1269 if (!group->meth->field_encode(group, tmp, tmp, ctx)) goto err;
48fe4d62
BM		 1270 }
1271
0fe73d6c 1272 for (i = num - 1; i > 0; --i)
48fe4d62 1273 {
0fe73d6c
BM		 1274 /* Loop invariant: tmp is the product of the inverses of
1275 * points[0]->Z .. points[i]->Z (zero-valued inputs skipped). */
5784a521 1276 if (!BN_is_zero(points[i]->Z))
48fe4d62 1277 {
0fe73d6c
BM		 1278 /* Set tmp_Z to the inverse of points[i]->Z (as product
1279 * of Z inverses 0 .. i, Z values 0 .. i - 1). */
1280 if (!group->meth->field_mul(group, tmp_Z, prod_Z[i - 1], tmp, ctx)) goto err;
1281 /* Update tmp to satisfy the loop invariant for i - 1. */
5784a521 1282 if (!group->meth->field_mul(group, tmp, tmp, points[i]->Z, ctx)) goto err;
0fe73d6c 1283 /* Replace points[i]->Z by its inverse. */
5784a521 1284 if (!BN_copy(points[i]->Z, tmp_Z)) goto err;
48fe4d62
BM		 1285 }
1286 }
1287
5784a521 1288 if (!BN_is_zero(points[0]->Z))
0fe73d6c
BM		 1289 {
1290 /* Replace points[0]->Z by its inverse. */
5784a521 1291 if (!BN_copy(points[0]->Z, tmp)) goto err;
0fe73d6c
BM		 1292 }
1293
1294 /* Finally, fix up the X and Y coordinates for all points. */
1295
48fe4d62
BM		 1296 for (i = 0; i < num; i++)
1297 {
1298 EC_POINT *p = points[i];
0fe73d6c 1299
5784a521 1300 if (!BN_is_zero(p->Z))
48fe4d62
BM		 1301 {
1302 /* turn (X, Y, 1/Z) into (X/Z^2, Y/Z^3, 1) */
1303
5784a521
MC		 1304 if (!group->meth->field_sqr(group, tmp, p->Z, ctx)) goto err;
1305 if (!group->meth->field_mul(group, p->X, p->X, tmp, ctx)) goto err;
0fe73d6c 1306
5784a521
MC		 1307 if (!group->meth->field_mul(group, tmp, tmp, p->Z, ctx)) goto err;
1308 if (!group->meth->field_mul(group, p->Y, p->Y, tmp, ctx)) goto err;
48fe4d62 1309
48fe4d62
BM		 1310 if (group->meth->field_set_to_one != 0)
1311 {
5784a521 1312 if (!group->meth->field_set_to_one(group, p->Z, ctx)) goto err;
48fe4d62
BM		 1313 }
1314 else
1315 {
5784a521 1316 if (!BN_one(p->Z)) goto err;
48fe4d62
BM		 1317 }
1318 p->Z_is_one = 1;
1319 }
1320 }
1321
1322 ret = 1;
0fe73d6c 1323
48fe4d62
BM		 1324 err:
1325 BN_CTX_end(ctx);
1326 if (new_ctx != NULL)
1327 BN_CTX_free(new_ctx);
0fe73d6c 1328 if (prod_Z != NULL)
48fe4d62 1329 {
0fe73d6c 1330 for (i = 0; i < num; i++)
48fe4d62 1331 {
16602b5c
BM		 1332 if (prod_Z[i] == NULL) break;
1333 BN_clear_free(prod_Z[i]);
48fe4d62 1334 }
0fe73d6c 1335 OPENSSL_free(prod_Z);
48fe4d62
BM		 1336 }
1337 return ret;
1338 }
1339
1340
60428dbf
BM		 1341int ec_GFp_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
1342 {
5784a521 1343 return BN_mod_mul(r, a, b, group->field, ctx);
60428dbf
BM		 1344 }
1345
1346
1347int ec_GFp_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx)
1348 {
5784a521 1349 return BN_mod_sqr(r, a, group->field, ctx);
60428dbf 1350 }
A mirror of the official openssl repository