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