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1 /* crypto/ec/ecp_smpl.c */
2 /*
3 * Includes code written by Lenka Fibikova <fibikova@exp-math.uni-essen.de>
4 * for the OpenSSL project. Includes code written by Bodo Moeller for the
5 * OpenSSL project.
6 */
7 /* ====================================================================
8 * Copyright (c) 1998-2002 The OpenSSL Project. All rights reserved.
9 *
10 * Redistribution and use in source and binary forms, with or without
11 * modification, are permitted provided that the following conditions
12 * are met:
13 *
14 * 1. Redistributions of source code must retain the above copyright
15 * notice, this list of conditions and the following disclaimer.
16 *
17 * 2. Redistributions in binary form must reproduce the above copyright
18 * notice, this list of conditions and the following disclaimer in
19 * the documentation and/or other materials provided with the
20 * distribution.
21 *
22 * 3. All advertising materials mentioning features or use of this
23 * software must display the following acknowledgment:
24 * "This product includes software developed by the OpenSSL Project
25 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
26 *
27 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
28 * endorse or promote products derived from this software without
29 * prior written permission. For written permission, please contact
30 * openssl-core@openssl.org.
31 *
32 * 5. Products derived from this software may not be called "OpenSSL"
33 * nor may "OpenSSL" appear in their names without prior written
34 * permission of the OpenSSL Project.
35 *
36 * 6. Redistributions of any form whatsoever must retain the following
37 * acknowledgment:
38 * "This product includes software developed by the OpenSSL Project
39 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
40 *
41 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
42 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
43 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
44 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
45 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
46 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
47 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
48 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
49 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
50 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
51 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
52 * OF THE POSSIBILITY OF SUCH DAMAGE.
53 * ====================================================================
54 *
55 * This product includes cryptographic software written by Eric Young
56 * (eay@cryptsoft.com). This product includes software written by Tim
57 * Hudson (tjh@cryptsoft.com).
58 *
59 */
60 /* ====================================================================
61 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
62 * Portions of this software developed by SUN MICROSYSTEMS, INC.,
63 * and contributed to the OpenSSL project.
64 */
65
66 #include <openssl/err.h>
67 #include <openssl/symhacks.h>
68
69 #include "ec_lcl.h"
70
71 const EC_METHOD *EC_GFp_simple_method(void)
72 {
73 static const EC_METHOD ret = {
74 NID_X9_62_prime_field,
75 ec_GFp_simple_group_init,
76 ec_GFp_simple_group_finish,
77 ec_GFp_simple_group_clear_finish,
78 ec_GFp_simple_group_copy,
79 ec_GFp_simple_group_set_curve,
80 ec_GFp_simple_group_get_curve,
81 ec_GFp_simple_group_get_degree,
82 ec_GFp_simple_group_check_discriminant,
83 ec_GFp_simple_point_init,
84 ec_GFp_simple_point_finish,
85 ec_GFp_simple_point_clear_finish,
86 ec_GFp_simple_point_copy,
87 ec_GFp_simple_point_set_to_infinity,
88 ec_GFp_simple_set_Jprojective_coordinates_GFp,
89 ec_GFp_simple_get_Jprojective_coordinates_GFp,
90 ec_GFp_simple_point_set_affine_coordinates,
91 ec_GFp_simple_point_get_affine_coordinates,
92 ec_GFp_simple_set_compressed_coordinates,
93 ec_GFp_simple_point2oct,
94 ec_GFp_simple_oct2point,
95 ec_GFp_simple_add,
96 ec_GFp_simple_dbl,
97 ec_GFp_simple_invert,
98 ec_GFp_simple_is_at_infinity,
99 ec_GFp_simple_is_on_curve,
100 ec_GFp_simple_cmp,
101 ec_GFp_simple_make_affine,
102 ec_GFp_simple_points_make_affine,
103 0 /* mul */ ,
104 0 /* precompute_mult */ ,
105 0 /* have_precompute_mult */ ,
106 ec_GFp_simple_field_mul,
107 ec_GFp_simple_field_sqr,
108 0 /* field_div */ ,
109 0 /* field_encode */ ,
110 0 /* field_decode */ ,
111 0 /* field_set_to_one */
112 };
113
114 return &ret;
115 }
116
117 /*
118 * Most method functions in this file are designed to work with
119 * non-trivial representations of field elements if necessary
120 * (see ecp_mont.c): while standard modular addition and subtraction
121 * are used, the field_mul and field_sqr methods will be used for
122 * multiplication, and field_encode and field_decode (if defined)
123 * will be used for converting between representations.
124 *
125 * Functions ec_GFp_simple_points_make_affine() and
126 * ec_GFp_simple_point_get_affine_coordinates() specifically assume
127 * that if a non-trivial representation is used, it is a Montgomery
128 * representation (i.e. 'encoding' means multiplying by some factor R).
129 */
130
131 int ec_GFp_simple_group_init(EC_GROUP *group)
132 {
133 BN_init(&group->field);
134 BN_init(&group->a);
135 BN_init(&group->b);
136 group->a_is_minus3 = 0;
137 return 1;
138 }
139
140 void ec_GFp_simple_group_finish(EC_GROUP *group)
141 {
142 BN_free(&group->field);
143 BN_free(&group->a);
144 BN_free(&group->b);
145 }
146
147 void ec_GFp_simple_group_clear_finish(EC_GROUP *group)
148 {
149 BN_clear_free(&group->field);
150 BN_clear_free(&group->a);
151 BN_clear_free(&group->b);
152 }
153
154 int ec_GFp_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src)
155 {
156 if (!BN_copy(&dest->field, &src->field))
157 return 0;
158 if (!BN_copy(&dest->a, &src->a))
159 return 0;
160 if (!BN_copy(&dest->b, &src->b))
161 return 0;
162
163 dest->a_is_minus3 = src->a_is_minus3;
164
165 return 1;
166 }
167
168 int ec_GFp_simple_group_set_curve(EC_GROUP *group,
169 const BIGNUM *p, const BIGNUM *a,
170 const BIGNUM *b, BN_CTX *ctx)
171 {
172 int ret = 0;
173 BN_CTX *new_ctx = NULL;
174 BIGNUM *tmp_a;
175
176 /* p must be a prime > 3 */
177 if (BN_num_bits(p) <= 2 || !BN_is_odd(p)) {
178 ECerr(EC_F_EC_GFP_SIMPLE_GROUP_SET_CURVE, EC_R_INVALID_FIELD);
179 return 0;
180 }
181
182 if (ctx == NULL) {
183 ctx = new_ctx = BN_CTX_new();
184 if (ctx == NULL)
185 return 0;
186 }
187
188 BN_CTX_start(ctx);
189 tmp_a = BN_CTX_get(ctx);
190 if (tmp_a == NULL)
191 goto err;
192
193 /* group->field */
194 if (!BN_copy(&group->field, p))
195 goto err;
196 BN_set_negative(&group->field, 0);
197
198 /* group->a */
199 if (!BN_nnmod(tmp_a, a, p, ctx))
200 goto err;
201 if (group->meth->field_encode) {
202 if (!group->meth->field_encode(group, &group->a, tmp_a, ctx))
203 goto err;
204 } else if (!BN_copy(&group->a, tmp_a))
205 goto err;
206
207 /* group->b */
208 if (!BN_nnmod(&group->b, b, p, ctx))
209 goto err;
210 if (group->meth->field_encode)
211 if (!group->meth->field_encode(group, &group->b, &group->b, ctx))
212 goto err;
213
214 /* group->a_is_minus3 */
215 if (!BN_add_word(tmp_a, 3))
216 goto err;
217 group->a_is_minus3 = (0 == BN_cmp(tmp_a, &group->field));
218
219 ret = 1;
220
221 err:
222 BN_CTX_end(ctx);
223 if (new_ctx != NULL)
224 BN_CTX_free(new_ctx);
225 return ret;
226 }
227
228 int ec_GFp_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a,
229 BIGNUM *b, BN_CTX *ctx)
230 {
231 int ret = 0;
232 BN_CTX *new_ctx = NULL;
233
234 if (p != NULL) {
235 if (!BN_copy(p, &group->field))
236 return 0;
237 }
238
239 if (a != NULL || b != NULL) {
240 if (group->meth->field_decode) {
241 if (ctx == NULL) {
242 ctx = new_ctx = BN_CTX_new();
243 if (ctx == NULL)
244 return 0;
245 }
246 if (a != NULL) {
247 if (!group->meth->field_decode(group, a, &group->a, ctx))
248 goto err;
249 }
250 if (b != NULL) {
251 if (!group->meth->field_decode(group, b, &group->b, ctx))
252 goto err;
253 }
254 } else {
255 if (a != NULL) {
256 if (!BN_copy(a, &group->a))
257 goto err;
258 }
259 if (b != NULL) {
260 if (!BN_copy(b, &group->b))
261 goto err;
262 }
263 }
264 }
265
266 ret = 1;
267
268 err:
269 if (new_ctx)
270 BN_CTX_free(new_ctx);
271 return ret;
272 }
273
274 int ec_GFp_simple_group_get_degree(const EC_GROUP *group)
275 {
276 return BN_num_bits(&group->field);
277 }
278
279 int ec_GFp_simple_group_check_discriminant(const EC_GROUP *group, BN_CTX *ctx)
280 {
281 int ret = 0;
282 BIGNUM *a, *b, *order, *tmp_1, *tmp_2;
283 const BIGNUM *p = &group->field;
284 BN_CTX *new_ctx = NULL;
285
286 if (ctx == NULL) {
287 ctx = new_ctx = BN_CTX_new();
288 if (ctx == NULL) {
289 ECerr(EC_F_EC_GFP_SIMPLE_GROUP_CHECK_DISCRIMINANT,
290 ERR_R_MALLOC_FAILURE);
291 goto err;
292 }
293 }
294 BN_CTX_start(ctx);
295 a = BN_CTX_get(ctx);
296 b = BN_CTX_get(ctx);
297 tmp_1 = BN_CTX_get(ctx);
298 tmp_2 = BN_CTX_get(ctx);
299 order = BN_CTX_get(ctx);
300 if (order == NULL)
301 goto err;
302
303 if (group->meth->field_decode) {
304 if (!group->meth->field_decode(group, a, &group->a, ctx))
305 goto err;
306 if (!group->meth->field_decode(group, b, &group->b, ctx))
307 goto err;
308 } else {
309 if (!BN_copy(a, &group->a))
310 goto err;
311 if (!BN_copy(b, &group->b))
312 goto err;
313 }
314
315 /*-
316 * check the discriminant:
317 * y^2 = x^3 + a*x + b is an elliptic curve <=> 4*a^3 + 27*b^2 != 0 (mod p)
318 * 0 =< a, b < p
319 */
320 if (BN_is_zero(a)) {
321 if (BN_is_zero(b))
322 goto err;
323 } else if (!BN_is_zero(b)) {
324 if (!BN_mod_sqr(tmp_1, a, p, ctx))
325 goto err;
326 if (!BN_mod_mul(tmp_2, tmp_1, a, p, ctx))
327 goto err;
328 if (!BN_lshift(tmp_1, tmp_2, 2))
329 goto err;
330 /* tmp_1 = 4*a^3 */
331
332 if (!BN_mod_sqr(tmp_2, b, p, ctx))
333 goto err;
334 if (!BN_mul_word(tmp_2, 27))
335 goto err;
336 /* tmp_2 = 27*b^2 */
337
338 if (!BN_mod_add(a, tmp_1, tmp_2, p, ctx))
339 goto err;
340 if (BN_is_zero(a))
341 goto err;
342 }
343 ret = 1;
344
345 err:
346 if (ctx != NULL)
347 BN_CTX_end(ctx);
348 if (new_ctx != NULL)
349 BN_CTX_free(new_ctx);
350 return ret;
351 }
352
353 int ec_GFp_simple_point_init(EC_POINT *point)
354 {
355 BN_init(&point->X);
356 BN_init(&point->Y);
357 BN_init(&point->Z);
358 point->Z_is_one = 0;
359
360 return 1;
361 }
362
363 void ec_GFp_simple_point_finish(EC_POINT *point)
364 {
365 BN_free(&point->X);
366 BN_free(&point->Y);
367 BN_free(&point->Z);
368 }
369
370 void ec_GFp_simple_point_clear_finish(EC_POINT *point)
371 {
372 BN_clear_free(&point->X);
373 BN_clear_free(&point->Y);
374 BN_clear_free(&point->Z);
375 point->Z_is_one = 0;
376 }
377
378 int ec_GFp_simple_point_copy(EC_POINT *dest, const EC_POINT *src)
379 {
380 if (!BN_copy(&dest->X, &src->X))
381 return 0;
382 if (!BN_copy(&dest->Y, &src->Y))
383 return 0;
384 if (!BN_copy(&dest->Z, &src->Z))
385 return 0;
386 dest->Z_is_one = src->Z_is_one;
387
388 return 1;
389 }
390
391 int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *group,
392 EC_POINT *point)
393 {
394 point->Z_is_one = 0;
395 BN_zero(&point->Z);
396 return 1;
397 }
398
399 int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *group,
400 EC_POINT *point,
401 const BIGNUM *x,
402 const BIGNUM *y,
403 const BIGNUM *z,
404 BN_CTX *ctx)
405 {
406 BN_CTX *new_ctx = NULL;
407 int ret = 0;
408
409 if (ctx == NULL) {
410 ctx = new_ctx = BN_CTX_new();
411 if (ctx == NULL)
412 return 0;
413 }
414
415 if (x != NULL) {
416 if (!BN_nnmod(&point->X, x, &group->field, ctx))
417 goto err;
418 if (group->meth->field_encode) {
419 if (!group->meth->field_encode(group, &point->X, &point->X, ctx))
420 goto err;
421 }
422 }
423
424 if (y != NULL) {
425 if (!BN_nnmod(&point->Y, y, &group->field, ctx))
426 goto err;
427 if (group->meth->field_encode) {
428 if (!group->meth->field_encode(group, &point->Y, &point->Y, ctx))
429 goto err;
430 }
431 }
432
433 if (z != NULL) {
434 int Z_is_one;
435
436 if (!BN_nnmod(&point->Z, z, &group->field, ctx))
437 goto err;
438 Z_is_one = BN_is_one(&point->Z);
439 if (group->meth->field_encode) {
440 if (Z_is_one && (group->meth->field_set_to_one != 0)) {
441 if (!group->meth->field_set_to_one(group, &point->Z, ctx))
442 goto err;
443 } else {
444 if (!group->
445 meth->field_encode(group, &point->Z, &point->Z, ctx))
446 goto err;
447 }
448 }
449 point->Z_is_one = Z_is_one;
450 }
451
452 ret = 1;
453
454 err:
455 if (new_ctx != NULL)
456 BN_CTX_free(new_ctx);
457 return ret;
458 }
459
460 int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *group,
461 const EC_POINT *point,
462 BIGNUM *x, BIGNUM *y,
463 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 if (ctx == NULL) {
470 ctx = new_ctx = BN_CTX_new();
471 if (ctx == NULL)
472 return 0;
473 }
474
475 if (x != NULL) {
476 if (!group->meth->field_decode(group, x, &point->X, ctx))
477 goto err;
478 }
479 if (y != NULL) {
480 if (!group->meth->field_decode(group, y, &point->Y, ctx))
481 goto err;
482 }
483 if (z != NULL) {
484 if (!group->meth->field_decode(group, z, &point->Z, ctx))
485 goto err;
486 }
487 } else {
488 if (x != NULL) {
489 if (!BN_copy(x, &point->X))
490 goto err;
491 }
492 if (y != NULL) {
493 if (!BN_copy(y, &point->Y))
494 goto err;
495 }
496 if (z != NULL) {
497 if (!BN_copy(z, &point->Z))
498 goto err;
499 }
500 }
501
502 ret = 1;
503
504 err:
505 if (new_ctx != NULL)
506 BN_CTX_free(new_ctx);
507 return ret;
508 }
509
510 int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *group,
511 EC_POINT *point,
512 const BIGNUM *x,
513 const BIGNUM *y, BN_CTX *ctx)
514 {
515 if (x == NULL || y == NULL) {
516 /*
517 * unlike for projective coordinates, we do not tolerate this
518 */
519 ECerr(EC_F_EC_GFP_SIMPLE_POINT_SET_AFFINE_COORDINATES,
520 ERR_R_PASSED_NULL_PARAMETER);
521 return 0;
522 }
523
524 return EC_POINT_set_Jprojective_coordinates_GFp(group, point, x, y,
525 BN_value_one(), ctx);
526 }
527
528 int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *group,
529 const EC_POINT *point,
530 BIGNUM *x, BIGNUM *y,
531 BN_CTX *ctx)
532 {
533 BN_CTX *new_ctx = NULL;
534 BIGNUM *Z, *Z_1, *Z_2, *Z_3;
535 const BIGNUM *Z_;
536 int ret = 0;
537
538 if (EC_POINT_is_at_infinity(group, point)) {
539 ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES,
540 EC_R_POINT_AT_INFINITY);
541 return 0;
542 }
543
544 if (ctx == NULL) {
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)
556 goto err;
557
558 /* transform (X, Y, Z) into (x, y) := (X/Z^2, Y/Z^3) */
559
560 if (group->meth->field_decode) {
561 if (!group->meth->field_decode(group, Z, &point->Z, ctx))
562 goto err;
563 Z_ = Z;
564 } else {
565 Z_ = &point->Z;
566 }
567
568 if (BN_is_one(Z_)) {
569 if (group->meth->field_decode) {
570 if (x != NULL) {
571 if (!group->meth->field_decode(group, x, &point->X, ctx))
572 goto err;
573 }
574 if (y != NULL) {
575 if (!group->meth->field_decode(group, y, &point->Y, ctx))
576 goto err;
577 }
578 } else {
579 if (x != NULL) {
580 if (!BN_copy(x, &point->X))
581 goto err;
582 }
583 if (y != NULL) {
584 if (!BN_copy(y, &point->Y))
585 goto err;
586 }
587 }
588 } else {
589 if (!BN_mod_inverse(Z_1, Z_, &group->field, ctx)) {
590 ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES,
591 ERR_R_BN_LIB);
592 goto err;
593 }
594
595 if (group->meth->field_encode == 0) {
596 /* field_sqr works on standard representation */
597 if (!group->meth->field_sqr(group, Z_2, Z_1, ctx))
598 goto err;
599 } else {
600 if (!BN_mod_sqr(Z_2, Z_1, &group->field, ctx))
601 goto err;
602 }
603
604 if (x != NULL) {
605 /*
606 * in the Montgomery case, field_mul will cancel out Montgomery
607 * factor in X:
608 */
609 if (!group->meth->field_mul(group, x, &point->X, Z_2, ctx))
610 goto err;
611 }
612
613 if (y != NULL) {
614 if (group->meth->field_encode == 0) {
615 /*
616 * field_mul works on standard representation
617 */
618 if (!group->meth->field_mul(group, Z_3, Z_2, Z_1, ctx))
619 goto err;
620 } else {
621 if (!BN_mod_mul(Z_3, Z_2, Z_1, &group->field, ctx))
622 goto err;
623 }
624
625 /*
626 * in the Montgomery case, field_mul will cancel out Montgomery
627 * factor in Y:
628 */
629 if (!group->meth->field_mul(group, y, &point->Y, Z_3, ctx))
630 goto err;
631 }
632 }
633
634 ret = 1;
635
636 err:
637 BN_CTX_end(ctx);
638 if (new_ctx != NULL)
639 BN_CTX_free(new_ctx);
640 return ret;
641 }
642
643 int ec_GFp_simple_set_compressed_coordinates(const EC_GROUP *group,
644 EC_POINT *point,
645 const BIGNUM *x_, int y_bit,
646 BN_CTX *ctx)
647 {
648 BN_CTX *new_ctx = NULL;
649 BIGNUM *tmp1, *tmp2, *x, *y;
650 int ret = 0;
651
652 /* clear error queue */
653 ERR_clear_error();
654
655 if (ctx == NULL) {
656 ctx = new_ctx = BN_CTX_new();
657 if (ctx == NULL)
658 return 0;
659 }
660
661 y_bit = (y_bit != 0);
662
663 BN_CTX_start(ctx);
664 tmp1 = BN_CTX_get(ctx);
665 tmp2 = BN_CTX_get(ctx);
666 x = BN_CTX_get(ctx);
667 y = BN_CTX_get(ctx);
668 if (y == NULL)
669 goto err;
670
671 /*-
672 * Recover y. We have a Weierstrass equation
673 * y^2 = x^3 + a*x + b,
674 * so y is one of the square roots of x^3 + a*x + b.
675 */
676
677 /* tmp1 := x^3 */
678 if (!BN_nnmod(x, x_, &group->field, ctx))
679 goto err;
680 if (group->meth->field_decode == 0) {
681 /* field_{sqr,mul} work on standard representation */
682 if (!group->meth->field_sqr(group, tmp2, x_, ctx))
683 goto err;
684 if (!group->meth->field_mul(group, tmp1, tmp2, x_, ctx))
685 goto err;
686 } else {
687 if (!BN_mod_sqr(tmp2, x_, &group->field, ctx))
688 goto err;
689 if (!BN_mod_mul(tmp1, tmp2, x_, &group->field, ctx))
690 goto err;
691 }
692
693 /* tmp1 := tmp1 + a*x */
694 if (group->a_is_minus3) {
695 if (!BN_mod_lshift1_quick(tmp2, x, &group->field))
696 goto err;
697 if (!BN_mod_add_quick(tmp2, tmp2, x, &group->field))
698 goto err;
699 if (!BN_mod_sub_quick(tmp1, tmp1, tmp2, &group->field))
700 goto err;
701 } else {
702 if (group->meth->field_decode) {
703 if (!group->meth->field_decode(group, tmp2, &group->a, ctx))
704 goto err;
705 if (!BN_mod_mul(tmp2, tmp2, x, &group->field, ctx))
706 goto err;
707 } else {
708 /* field_mul works on standard representation */
709 if (!group->meth->field_mul(group, tmp2, &group->a, x, ctx))
710 goto err;
711 }
712
713 if (!BN_mod_add_quick(tmp1, tmp1, tmp2, &group->field))
714 goto err;
715 }
716
717 /* tmp1 := tmp1 + b */
718 if (group->meth->field_decode) {
719 if (!group->meth->field_decode(group, tmp2, &group->b, ctx))
720 goto err;
721 if (!BN_mod_add_quick(tmp1, tmp1, tmp2, &group->field))
722 goto err;
723 } else {
724 if (!BN_mod_add_quick(tmp1, tmp1, &group->b, &group->field))
725 goto err;
726 }
727
728 if (!BN_mod_sqrt(y, tmp1, &group->field, ctx)) {
729 unsigned long err = ERR_peek_last_error();
730
731 if (ERR_GET_LIB(err) == ERR_LIB_BN
732 && ERR_GET_REASON(err) == BN_R_NOT_A_SQUARE) {
733 ERR_clear_error();
734 ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES,
735 EC_R_INVALID_COMPRESSED_POINT);
736 } else
737 ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES,
738 ERR_R_BN_LIB);
739 goto err;
740 }
741
742 if (y_bit != BN_is_odd(y)) {
743 if (BN_is_zero(y)) {
744 int kron;
745
746 kron = BN_kronecker(x, &group->field, ctx);
747 if (kron == -2)
748 goto err;
749
750 if (kron == 1)
751 ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES,
752 EC_R_INVALID_COMPRESSION_BIT);
753 else
754 /*
755 * BN_mod_sqrt() should have cought this error (not a square)
756 */
757 ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES,
758 EC_R_INVALID_COMPRESSED_POINT);
759 goto err;
760 }
761 if (!BN_usub(y, &group->field, y))
762 goto err;
763 }
764 if (y_bit != BN_is_odd(y)) {
765 ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES,
766 ERR_R_INTERNAL_ERROR);
767 goto err;
768 }
769
770 if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx))
771 goto err;
772
773 ret = 1;
774
775 err:
776 BN_CTX_end(ctx);
777 if (new_ctx != NULL)
778 BN_CTX_free(new_ctx);
779 return ret;
780 }
781
782 size_t ec_GFp_simple_point2oct(const EC_GROUP *group, const EC_POINT *point,
783 point_conversion_form_t form,
784 unsigned char *buf, size_t len, BN_CTX *ctx)
785 {
786 size_t ret;
787 BN_CTX *new_ctx = NULL;
788 int used_ctx = 0;
789 BIGNUM *x, *y;
790 size_t field_len, i, skip;
791
792 if ((form != POINT_CONVERSION_COMPRESSED)
793 && (form != POINT_CONVERSION_UNCOMPRESSED)
794 && (form != POINT_CONVERSION_HYBRID)) {
795 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_INVALID_FORM);
796 goto err;
797 }
798
799 if (EC_POINT_is_at_infinity(group, point)) {
800 /* encodes to a single 0 octet */
801 if (buf != NULL) {
802 if (len < 1) {
803 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);
804 return 0;
805 }
806 buf[0] = 0;
807 }
808 return 1;
809 }
810
811 /* ret := required output buffer length */
812 field_len = BN_num_bytes(&group->field);
813 ret =
814 (form ==
815 POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2 * field_len;
816
817 /* if 'buf' is NULL, just return required length */
818 if (buf != NULL) {
819 if (len < ret) {
820 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);
821 goto err;
822 }
823
824 if (ctx == NULL) {
825 ctx = new_ctx = BN_CTX_new();
826 if (ctx == NULL)
827 return 0;
828 }
829
830 BN_CTX_start(ctx);
831 used_ctx = 1;
832 x = BN_CTX_get(ctx);
833 y = BN_CTX_get(ctx);
834 if (y == NULL)
835 goto err;
836
837 if (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx))
838 goto err;
839
840 if ((form == POINT_CONVERSION_COMPRESSED
841 || form == POINT_CONVERSION_HYBRID) && BN_is_odd(y))
842 buf[0] = form + 1;
843 else
844 buf[0] = form;
845
846 i = 1;
847
848 skip = field_len - BN_num_bytes(x);
849 if (skip > field_len) {
850 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
851 goto err;
852 }
853 while (skip > 0) {
854 buf[i++] = 0;
855 skip--;
856 }
857 skip = BN_bn2bin(x, buf + i);
858 i += skip;
859 if (i != 1 + field_len) {
860 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
861 goto err;
862 }
863
864 if (form == POINT_CONVERSION_UNCOMPRESSED
865 || form == POINT_CONVERSION_HYBRID) {
866 skip = field_len - BN_num_bytes(y);
867 if (skip > field_len) {
868 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
869 goto err;
870 }
871 while (skip > 0) {
872 buf[i++] = 0;
873 skip--;
874 }
875 skip = BN_bn2bin(y, buf + i);
876 i += skip;
877 }
878
879 if (i != ret) {
880 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
881 goto err;
882 }
883 }
884
885 if (used_ctx)
886 BN_CTX_end(ctx);
887 if (new_ctx != NULL)
888 BN_CTX_free(new_ctx);
889 return ret;
890
891 err:
892 if (used_ctx)
893 BN_CTX_end(ctx);
894 if (new_ctx != NULL)
895 BN_CTX_free(new_ctx);
896 return 0;
897 }
898
899 int ec_GFp_simple_oct2point(const EC_GROUP *group, EC_POINT *point,
900 const unsigned char *buf, size_t len, BN_CTX *ctx)
901 {
902 point_conversion_form_t form;
903 int y_bit;
904 BN_CTX *new_ctx = NULL;
905 BIGNUM *x, *y;
906 size_t field_len, enc_len;
907 int ret = 0;
908
909 if (len == 0) {
910 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_BUFFER_TOO_SMALL);
911 return 0;
912 }
913 form = buf[0];
914 y_bit = form & 1;
915 form = form & ~1U;
916 if ((form != 0) && (form != POINT_CONVERSION_COMPRESSED)
917 && (form != POINT_CONVERSION_UNCOMPRESSED)
918 && (form != POINT_CONVERSION_HYBRID)) {
919 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
920 return 0;
921 }
922 if ((form == 0 || form == POINT_CONVERSION_UNCOMPRESSED) && y_bit) {
923 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
924 return 0;
925 }
926
927 if (form == 0) {
928 if (len != 1) {
929 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
930 return 0;
931 }
932
933 return EC_POINT_set_to_infinity(group, point);
934 }
935
936 field_len = BN_num_bytes(&group->field);
937 enc_len =
938 (form ==
939 POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2 * field_len;
940
941 if (len != enc_len) {
942 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
943 return 0;
944 }
945
946 if (ctx == NULL) {
947 ctx = new_ctx = BN_CTX_new();
948 if (ctx == NULL)
949 return 0;
950 }
951
952 BN_CTX_start(ctx);
953 x = BN_CTX_get(ctx);
954 y = BN_CTX_get(ctx);
955 if (y == NULL)
956 goto err;
957
958 if (!BN_bin2bn(buf + 1, field_len, x))
959 goto err;
960 if (BN_ucmp(x, &group->field) >= 0) {
961 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
962 goto err;
963 }
964
965 if (form == POINT_CONVERSION_COMPRESSED) {
966 if (!EC_POINT_set_compressed_coordinates_GFp
967 (group, point, x, y_bit, ctx))
968 goto err;
969 } else {
970 if (!BN_bin2bn(buf + 1 + field_len, field_len, y))
971 goto err;
972 if (BN_ucmp(y, &group->field) >= 0) {
973 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
974 goto err;
975 }
976 if (form == POINT_CONVERSION_HYBRID) {
977 if (y_bit != BN_is_odd(y)) {
978 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
979 goto err;
980 }
981 }
982
983 if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx))
984 goto err;
985 }
986
987 /* test required by X9.62 */
988 if (!EC_POINT_is_on_curve(group, point, ctx)) {
989 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_POINT_IS_NOT_ON_CURVE);
990 goto err;
991 }
992
993 ret = 1;
994
995 err:
996 BN_CTX_end(ctx);
997 if (new_ctx != NULL)
998 BN_CTX_free(new_ctx);
999 return ret;
1000 }
1001
1002 int ec_GFp_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a,
1003 const EC_POINT *b, BN_CTX *ctx)
1004 {
1005 int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *,
1006 const BIGNUM *, BN_CTX *);
1007 int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
1008 const BIGNUM *p;
1009 BN_CTX *new_ctx = NULL;
1010 BIGNUM *n0, *n1, *n2, *n3, *n4, *n5, *n6;
1011 int ret = 0;
1012
1013 if (a == b)
1014 return EC_POINT_dbl(group, r, a, ctx);
1015 if (EC_POINT_is_at_infinity(group, a))
1016 return EC_POINT_copy(r, b);
1017 if (EC_POINT_is_at_infinity(group, b))
1018 return EC_POINT_copy(r, a);
1019
1020 field_mul = group->meth->field_mul;
1021 field_sqr = group->meth->field_sqr;
1022 p = &group->field;
1023
1024 if (ctx == NULL) {
1025 ctx = new_ctx = BN_CTX_new();
1026 if (ctx == NULL)
1027 return 0;
1028 }
1029
1030 BN_CTX_start(ctx);
1031 n0 = BN_CTX_get(ctx);
1032 n1 = BN_CTX_get(ctx);
1033 n2 = BN_CTX_get(ctx);
1034 n3 = BN_CTX_get(ctx);
1035 n4 = BN_CTX_get(ctx);
1036 n5 = BN_CTX_get(ctx);
1037 n6 = BN_CTX_get(ctx);
1038 if (n6 == NULL)
1039 goto end;
1040
1041 /*
1042 * Note that in this function we must not read components of 'a' or 'b'
1043 * once we have written the corresponding components of 'r'. ('r' might
1044 * be one of 'a' or 'b'.)
1045 */
1046
1047 /* n1, n2 */
1048 if (b->Z_is_one) {
1049 if (!BN_copy(n1, &a->X))
1050 goto end;
1051 if (!BN_copy(n2, &a->Y))
1052 goto end;
1053 /* n1 = X_a */
1054 /* n2 = Y_a */
1055 } else {
1056 if (!field_sqr(group, n0, &b->Z, ctx))
1057 goto end;
1058 if (!field_mul(group, n1, &a->X, n0, ctx))
1059 goto end;
1060 /* n1 = X_a * Z_b^2 */
1061
1062 if (!field_mul(group, n0, n0, &b->Z, ctx))
1063 goto end;
1064 if (!field_mul(group, n2, &a->Y, n0, ctx))
1065 goto end;
1066 /* n2 = Y_a * Z_b^3 */
1067 }
1068
1069 /* n3, n4 */
1070 if (a->Z_is_one) {
1071 if (!BN_copy(n3, &b->X))
1072 goto end;
1073 if (!BN_copy(n4, &b->Y))
1074 goto end;
1075 /* n3 = X_b */
1076 /* n4 = Y_b */
1077 } else {
1078 if (!field_sqr(group, n0, &a->Z, ctx))
1079 goto end;
1080 if (!field_mul(group, n3, &b->X, n0, ctx))
1081 goto end;
1082 /* n3 = X_b * Z_a^2 */
1083
1084 if (!field_mul(group, n0, n0, &a->Z, ctx))
1085 goto end;
1086 if (!field_mul(group, n4, &b->Y, n0, ctx))
1087 goto end;
1088 /* n4 = Y_b * Z_a^3 */
1089 }
1090
1091 /* n5, n6 */
1092 if (!BN_mod_sub_quick(n5, n1, n3, p))
1093 goto end;
1094 if (!BN_mod_sub_quick(n6, n2, n4, p))
1095 goto end;
1096 /* n5 = n1 - n3 */
1097 /* n6 = n2 - n4 */
1098
1099 if (BN_is_zero(n5)) {
1100 if (BN_is_zero(n6)) {
1101 /* a is the same point as b */
1102 BN_CTX_end(ctx);
1103 ret = EC_POINT_dbl(group, r, a, ctx);
1104 ctx = NULL;
1105 goto end;
1106 } else {
1107 /* a is the inverse of b */
1108 BN_zero(&r->Z);
1109 r->Z_is_one = 0;
1110 ret = 1;
1111 goto end;
1112 }
1113 }
1114
1115 /* 'n7', 'n8' */
1116 if (!BN_mod_add_quick(n1, n1, n3, p))
1117 goto end;
1118 if (!BN_mod_add_quick(n2, n2, n4, p))
1119 goto end;
1120 /* 'n7' = n1 + n3 */
1121 /* 'n8' = n2 + n4 */
1122
1123 /* Z_r */
1124 if (a->Z_is_one && b->Z_is_one) {
1125 if (!BN_copy(&r->Z, n5))
1126 goto end;
1127 } else {
1128 if (a->Z_is_one) {
1129 if (!BN_copy(n0, &b->Z))
1130 goto end;
1131 } else if (b->Z_is_one) {
1132 if (!BN_copy(n0, &a->Z))
1133 goto end;
1134 } else {
1135 if (!field_mul(group, n0, &a->Z, &b->Z, ctx))
1136 goto end;
1137 }
1138 if (!field_mul(group, &r->Z, n0, n5, ctx))
1139 goto end;
1140 }
1141 r->Z_is_one = 0;
1142 /* Z_r = Z_a * Z_b * n5 */
1143
1144 /* X_r */
1145 if (!field_sqr(group, n0, n6, ctx))
1146 goto end;
1147 if (!field_sqr(group, n4, n5, ctx))
1148 goto end;
1149 if (!field_mul(group, n3, n1, n4, ctx))
1150 goto end;
1151 if (!BN_mod_sub_quick(&r->X, n0, n3, p))
1152 goto end;
1153 /* X_r = n6^2 - n5^2 * 'n7' */
1154
1155 /* 'n9' */
1156 if (!BN_mod_lshift1_quick(n0, &r->X, p))
1157 goto end;
1158 if (!BN_mod_sub_quick(n0, n3, n0, p))
1159 goto end;
1160 /* n9 = n5^2 * 'n7' - 2 * X_r */
1161
1162 /* Y_r */
1163 if (!field_mul(group, n0, n0, n6, ctx))
1164 goto end;
1165 if (!field_mul(group, n5, n4, n5, ctx))
1166 goto end; /* now n5 is n5^3 */
1167 if (!field_mul(group, n1, n2, n5, ctx))
1168 goto end;
1169 if (!BN_mod_sub_quick(n0, n0, n1, p))
1170 goto end;
1171 if (BN_is_odd(n0))
1172 if (!BN_add(n0, n0, p))
1173 goto end;
1174 /* now 0 <= n0 < 2*p, and n0 is even */
1175 if (!BN_rshift1(&r->Y, n0))
1176 goto end;
1177 /* Y_r = (n6 * 'n9' - 'n8' * 'n5^3') / 2 */
1178
1179 ret = 1;
1180
1181 end:
1182 if (ctx) /* otherwise we already called BN_CTX_end */
1183 BN_CTX_end(ctx);
1184 if (new_ctx != NULL)
1185 BN_CTX_free(new_ctx);
1186 return ret;
1187 }
1188
1189 int ec_GFp_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a,
1190 BN_CTX *ctx)
1191 {
1192 int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *,
1193 const BIGNUM *, BN_CTX *);
1194 int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
1195 const BIGNUM *p;
1196 BN_CTX *new_ctx = NULL;
1197 BIGNUM *n0, *n1, *n2, *n3;
1198 int ret = 0;
1199
1200 if (EC_POINT_is_at_infinity(group, a)) {
1201 BN_zero(&r->Z);
1202 r->Z_is_one = 0;
1203 return 1;
1204 }
1205
1206 field_mul = group->meth->field_mul;
1207 field_sqr = group->meth->field_sqr;
1208 p = &group->field;
1209
1210 if (ctx == NULL) {
1211 ctx = new_ctx = BN_CTX_new();
1212 if (ctx == NULL)
1213 return 0;
1214 }
1215
1216 BN_CTX_start(ctx);
1217 n0 = BN_CTX_get(ctx);
1218 n1 = BN_CTX_get(ctx);
1219 n2 = BN_CTX_get(ctx);
1220 n3 = BN_CTX_get(ctx);
1221 if (n3 == NULL)
1222 goto err;
1223
1224 /*
1225 * Note that in this function we must not read components of 'a' once we
1226 * have written the corresponding components of 'r'. ('r' might the same
1227 * as 'a'.)
1228 */
1229
1230 /* n1 */
1231 if (a->Z_is_one) {
1232 if (!field_sqr(group, n0, &a->X, ctx))
1233 goto err;
1234 if (!BN_mod_lshift1_quick(n1, n0, p))
1235 goto err;
1236 if (!BN_mod_add_quick(n0, n0, n1, p))
1237 goto err;
1238 if (!BN_mod_add_quick(n1, n0, &group->a, p))
1239 goto err;
1240 /* n1 = 3 * X_a^2 + a_curve */
1241 } else if (group->a_is_minus3) {
1242 if (!field_sqr(group, n1, &a->Z, ctx))
1243 goto err;
1244 if (!BN_mod_add_quick(n0, &a->X, n1, p))
1245 goto err;
1246 if (!BN_mod_sub_quick(n2, &a->X, n1, p))
1247 goto err;
1248 if (!field_mul(group, n1, n0, n2, ctx))
1249 goto err;
1250 if (!BN_mod_lshift1_quick(n0, n1, p))
1251 goto err;
1252 if (!BN_mod_add_quick(n1, n0, n1, p))
1253 goto err;
1254 /*-
1255 * n1 = 3 * (X_a + Z_a^2) * (X_a - Z_a^2)
1256 * = 3 * X_a^2 - 3 * Z_a^4
1257 */
1258 } else {
1259 if (!field_sqr(group, n0, &a->X, ctx))
1260 goto err;
1261 if (!BN_mod_lshift1_quick(n1, n0, p))
1262 goto err;
1263 if (!BN_mod_add_quick(n0, n0, n1, p))
1264 goto err;
1265 if (!field_sqr(group, n1, &a->Z, ctx))
1266 goto err;
1267 if (!field_sqr(group, n1, n1, ctx))
1268 goto err;
1269 if (!field_mul(group, n1, n1, &group->a, ctx))
1270 goto err;
1271 if (!BN_mod_add_quick(n1, n1, n0, p))
1272 goto err;
1273 /* n1 = 3 * X_a^2 + a_curve * Z_a^4 */
1274 }
1275
1276 /* Z_r */
1277 if (a->Z_is_one) {
1278 if (!BN_copy(n0, &a->Y))
1279 goto err;
1280 } else {
1281 if (!field_mul(group, n0, &a->Y, &a->Z, ctx))
1282 goto err;
1283 }
1284 if (!BN_mod_lshift1_quick(&r->Z, n0, p))
1285 goto err;
1286 r->Z_is_one = 0;
1287 /* Z_r = 2 * Y_a * Z_a */
1288
1289 /* n2 */
1290 if (!field_sqr(group, n3, &a->Y, ctx))
1291 goto err;
1292 if (!field_mul(group, n2, &a->X, n3, ctx))
1293 goto err;
1294 if (!BN_mod_lshift_quick(n2, n2, 2, p))
1295 goto err;
1296 /* n2 = 4 * X_a * Y_a^2 */
1297
1298 /* X_r */
1299 if (!BN_mod_lshift1_quick(n0, n2, p))
1300 goto err;
1301 if (!field_sqr(group, &r->X, n1, ctx))
1302 goto err;
1303 if (!BN_mod_sub_quick(&r->X, &r->X, n0, p))
1304 goto err;
1305 /* X_r = n1^2 - 2 * n2 */
1306
1307 /* n3 */
1308 if (!field_sqr(group, n0, n3, ctx))
1309 goto err;
1310 if (!BN_mod_lshift_quick(n3, n0, 3, p))
1311 goto err;
1312 /* n3 = 8 * Y_a^4 */
1313
1314 /* Y_r */
1315 if (!BN_mod_sub_quick(n0, n2, &r->X, p))
1316 goto err;
1317 if (!field_mul(group, n0, n1, n0, ctx))
1318 goto err;
1319 if (!BN_mod_sub_quick(&r->Y, n0, n3, p))
1320 goto err;
1321 /* Y_r = n1 * (n2 - X_r) - n3 */
1322
1323 ret = 1;
1324
1325 err:
1326 BN_CTX_end(ctx);
1327 if (new_ctx != NULL)
1328 BN_CTX_free(new_ctx);
1329 return ret;
1330 }
1331
1332 int ec_GFp_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
1333 {
1334 if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(&point->Y))
1335 /* point is its own inverse */
1336 return 1;
1337
1338 return BN_usub(&point->Y, &group->field, &point->Y);
1339 }
1340
1341 int ec_GFp_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point)
1342 {
1343 return BN_is_zero(&point->Z);
1344 }
1345
1346 int ec_GFp_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point,
1347 BN_CTX *ctx)
1348 {
1349 int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *,
1350 const BIGNUM *, BN_CTX *);
1351 int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
1352 const BIGNUM *p;
1353 BN_CTX *new_ctx = NULL;
1354 BIGNUM *rh, *tmp, *Z4, *Z6;
1355 int ret = -1;
1356
1357 if (EC_POINT_is_at_infinity(group, point))
1358 return 1;
1359
1360 field_mul = group->meth->field_mul;
1361 field_sqr = group->meth->field_sqr;
1362 p = &group->field;
1363
1364 if (ctx == NULL) {
1365 ctx = new_ctx = BN_CTX_new();
1366 if (ctx == NULL)
1367 return -1;
1368 }
1369
1370 BN_CTX_start(ctx);
1371 rh = BN_CTX_get(ctx);
1372 tmp = BN_CTX_get(ctx);
1373 Z4 = BN_CTX_get(ctx);
1374 Z6 = BN_CTX_get(ctx);
1375 if (Z6 == NULL)
1376 goto err;
1377
1378 /*-
1379 * We have a curve defined by a Weierstrass equation
1380 * y^2 = x^3 + a*x + b.
1381 * The point to consider is given in Jacobian projective coordinates
1382 * where (X, Y, Z) represents (x, y) = (X/Z^2, Y/Z^3).
1383 * Substituting this and multiplying by Z^6 transforms the above equation into
1384 * Y^2 = X^3 + a*X*Z^4 + b*Z^6.
1385 * To test this, we add up the right-hand side in 'rh'.
1386 */
1387
1388 /* rh := X^2 */
1389 if (!field_sqr(group, rh, &point->X, ctx))
1390 goto err;
1391
1392 if (!point->Z_is_one) {
1393 if (!field_sqr(group, tmp, &point->Z, ctx))
1394 goto err;
1395 if (!field_sqr(group, Z4, tmp, ctx))
1396 goto err;
1397 if (!field_mul(group, Z6, Z4, tmp, ctx))
1398 goto err;
1399
1400 /* rh := (rh + a*Z^4)*X */
1401 if (group->a_is_minus3) {
1402 if (!BN_mod_lshift1_quick(tmp, Z4, p))
1403 goto err;
1404 if (!BN_mod_add_quick(tmp, tmp, Z4, p))
1405 goto err;
1406 if (!BN_mod_sub_quick(rh, rh, tmp, p))
1407 goto err;
1408 if (!field_mul(group, rh, rh, &point->X, ctx))
1409 goto err;
1410 } else {
1411 if (!field_mul(group, tmp, Z4, &group->a, ctx))
1412 goto err;
1413 if (!BN_mod_add_quick(rh, rh, tmp, p))
1414 goto err;
1415 if (!field_mul(group, rh, rh, &point->X, ctx))
1416 goto err;
1417 }
1418
1419 /* rh := rh + b*Z^6 */
1420 if (!field_mul(group, tmp, &group->b, Z6, ctx))
1421 goto err;
1422 if (!BN_mod_add_quick(rh, rh, tmp, p))
1423 goto err;
1424 } else {
1425 /* point->Z_is_one */
1426
1427 /* rh := (rh + a)*X */
1428 if (!BN_mod_add_quick(rh, rh, &group->a, p))
1429 goto err;
1430 if (!field_mul(group, rh, rh, &point->X, ctx))
1431 goto err;
1432 /* rh := rh + b */
1433 if (!BN_mod_add_quick(rh, rh, &group->b, p))
1434 goto err;
1435 }
1436
1437 /* 'lh' := Y^2 */
1438 if (!field_sqr(group, tmp, &point->Y, ctx))
1439 goto err;
1440
1441 ret = (0 == BN_ucmp(tmp, rh));
1442
1443 err:
1444 BN_CTX_end(ctx);
1445 if (new_ctx != NULL)
1446 BN_CTX_free(new_ctx);
1447 return ret;
1448 }
1449
1450 int ec_GFp_simple_cmp(const EC_GROUP *group, const EC_POINT *a,
1451 const EC_POINT *b, BN_CTX *ctx)
1452 {
1453 /*-
1454 * return values:
1455 * -1 error
1456 * 0 equal (in affine coordinates)
1457 * 1 not equal
1458 */
1459
1460 int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *,
1461 const BIGNUM *, BN_CTX *);
1462 int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
1463 BN_CTX *new_ctx = NULL;
1464 BIGNUM *tmp1, *tmp2, *Za23, *Zb23;
1465 const BIGNUM *tmp1_, *tmp2_;
1466 int ret = -1;
1467
1468 if (EC_POINT_is_at_infinity(group, a)) {
1469 return EC_POINT_is_at_infinity(group, b) ? 0 : 1;
1470 }
1471
1472 if (EC_POINT_is_at_infinity(group, b))
1473 return 1;
1474
1475 if (a->Z_is_one && b->Z_is_one) {
1476 return ((BN_cmp(&a->X, &b->X) == 0)
1477 && BN_cmp(&a->Y, &b->Y) == 0) ? 0 : 1;
1478 }
1479
1480 field_mul = group->meth->field_mul;
1481 field_sqr = group->meth->field_sqr;
1482
1483 if (ctx == NULL) {
1484 ctx = new_ctx = BN_CTX_new();
1485 if (ctx == NULL)
1486 return -1;
1487 }
1488
1489 BN_CTX_start(ctx);
1490 tmp1 = BN_CTX_get(ctx);
1491 tmp2 = BN_CTX_get(ctx);
1492 Za23 = BN_CTX_get(ctx);
1493 Zb23 = BN_CTX_get(ctx);
1494 if (Zb23 == NULL)
1495 goto end;
1496
1497 /*-
1498 * We have to decide whether
1499 * (X_a/Z_a^2, Y_a/Z_a^3) = (X_b/Z_b^2, Y_b/Z_b^3),
1500 * or equivalently, whether
1501 * (X_a*Z_b^2, Y_a*Z_b^3) = (X_b*Z_a^2, Y_b*Z_a^3).
1502 */
1503
1504 if (!b->Z_is_one) {
1505 if (!field_sqr(group, Zb23, &b->Z, ctx))
1506 goto end;
1507 if (!field_mul(group, tmp1, &a->X, Zb23, ctx))
1508 goto end;
1509 tmp1_ = tmp1;
1510 } else
1511 tmp1_ = &a->X;
1512 if (!a->Z_is_one) {
1513 if (!field_sqr(group, Za23, &a->Z, ctx))
1514 goto end;
1515 if (!field_mul(group, tmp2, &b->X, Za23, ctx))
1516 goto end;
1517 tmp2_ = tmp2;
1518 } else
1519 tmp2_ = &b->X;
1520
1521 /* compare X_a*Z_b^2 with X_b*Z_a^2 */
1522 if (BN_cmp(tmp1_, tmp2_) != 0) {
1523 ret = 1; /* points differ */
1524 goto end;
1525 }
1526
1527 if (!b->Z_is_one) {
1528 if (!field_mul(group, Zb23, Zb23, &b->Z, ctx))
1529 goto end;
1530 if (!field_mul(group, tmp1, &a->Y, Zb23, ctx))
1531 goto end;
1532 /* tmp1_ = tmp1 */
1533 } else
1534 tmp1_ = &a->Y;
1535 if (!a->Z_is_one) {
1536 if (!field_mul(group, Za23, Za23, &a->Z, ctx))
1537 goto end;
1538 if (!field_mul(group, tmp2, &b->Y, Za23, ctx))
1539 goto end;
1540 /* tmp2_ = tmp2 */
1541 } else
1542 tmp2_ = &b->Y;
1543
1544 /* compare Y_a*Z_b^3 with Y_b*Z_a^3 */
1545 if (BN_cmp(tmp1_, tmp2_) != 0) {
1546 ret = 1; /* points differ */
1547 goto end;
1548 }
1549
1550 /* points are equal */
1551 ret = 0;
1552
1553 end:
1554 BN_CTX_end(ctx);
1555 if (new_ctx != NULL)
1556 BN_CTX_free(new_ctx);
1557 return ret;
1558 }
1559
1560 int ec_GFp_simple_make_affine(const EC_GROUP *group, EC_POINT *point,
1561 BN_CTX *ctx)
1562 {
1563 BN_CTX *new_ctx = NULL;
1564 BIGNUM *x, *y;
1565 int ret = 0;
1566
1567 if (point->Z_is_one || EC_POINT_is_at_infinity(group, point))
1568 return 1;
1569
1570 if (ctx == NULL) {
1571 ctx = new_ctx = BN_CTX_new();
1572 if (ctx == NULL)
1573 return 0;
1574 }
1575
1576 BN_CTX_start(ctx);
1577 x = BN_CTX_get(ctx);
1578 y = BN_CTX_get(ctx);
1579 if (y == NULL)
1580 goto err;
1581
1582 if (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx))
1583 goto err;
1584 if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx))
1585 goto err;
1586 if (!point->Z_is_one) {
1587 ECerr(EC_F_EC_GFP_SIMPLE_MAKE_AFFINE, ERR_R_INTERNAL_ERROR);
1588 goto err;
1589 }
1590
1591 ret = 1;
1592
1593 err:
1594 BN_CTX_end(ctx);
1595 if (new_ctx != NULL)
1596 BN_CTX_free(new_ctx);
1597 return ret;
1598 }
1599
1600 int ec_GFp_simple_points_make_affine(const EC_GROUP *group, size_t num,
1601 EC_POINT *points[], BN_CTX *ctx)
1602 {
1603 BN_CTX *new_ctx = NULL;
1604 BIGNUM *tmp, *tmp_Z;
1605 BIGNUM **prod_Z = NULL;
1606 size_t i;
1607 int ret = 0;
1608
1609 if (num == 0)
1610 return 1;
1611
1612 if (ctx == NULL) {
1613 ctx = new_ctx = BN_CTX_new();
1614 if (ctx == NULL)
1615 return 0;
1616 }
1617
1618 BN_CTX_start(ctx);
1619 tmp = BN_CTX_get(ctx);
1620 tmp_Z = BN_CTX_get(ctx);
1621 if (tmp == NULL || tmp_Z == NULL)
1622 goto err;
1623
1624 prod_Z = OPENSSL_malloc(num * sizeof prod_Z[0]);
1625 if (prod_Z == NULL)
1626 goto err;
1627 for (i = 0; i < num; i++) {
1628 prod_Z[i] = BN_new();
1629 if (prod_Z[i] == NULL)
1630 goto err;
1631 }
1632
1633 /*
1634 * Set each prod_Z[i] to the product of points[0]->Z .. points[i]->Z,
1635 * skipping any zero-valued inputs (pretend that they're 1).
1636 */
1637
1638 if (!BN_is_zero(&points[0]->Z)) {
1639 if (!BN_copy(prod_Z[0], &points[0]->Z))
1640 goto err;
1641 } else {
1642 if (group->meth->field_set_to_one != 0) {
1643 if (!group->meth->field_set_to_one(group, prod_Z[0], ctx))
1644 goto err;
1645 } else {
1646 if (!BN_one(prod_Z[0]))
1647 goto err;
1648 }
1649 }
1650
1651 for (i = 1; i < num; i++) {
1652 if (!BN_is_zero(&points[i]->Z)) {
1653 if (!group->meth->field_mul(group, prod_Z[i], prod_Z[i - 1],
1654 &points[i]->Z, ctx))
1655 goto err;
1656 } else {
1657 if (!BN_copy(prod_Z[i], prod_Z[i - 1]))
1658 goto err;
1659 }
1660 }
1661
1662 /*
1663 * Now use a single explicit inversion to replace every non-zero
1664 * points[i]->Z by its inverse.
1665 */
1666
1667 if (!BN_mod_inverse(tmp, prod_Z[num - 1], &group->field, ctx)) {
1668 ECerr(EC_F_EC_GFP_SIMPLE_POINTS_MAKE_AFFINE, ERR_R_BN_LIB);
1669 goto err;
1670 }
1671 if (group->meth->field_encode != 0) {
1672 /*
1673 * In the Montgomery case, we just turned R*H (representing H) into
1674 * 1/(R*H), but we need R*(1/H) (representing 1/H); i.e. we need to
1675 * multiply by the Montgomery factor twice.
1676 */
1677 if (!group->meth->field_encode(group, tmp, tmp, ctx))
1678 goto err;
1679 if (!group->meth->field_encode(group, tmp, tmp, ctx))
1680 goto err;
1681 }
1682
1683 for (i = num - 1; i > 0; --i) {
1684 /*
1685 * Loop invariant: tmp is the product of the inverses of points[0]->Z
1686 * .. points[i]->Z (zero-valued inputs skipped).
1687 */
1688 if (!BN_is_zero(&points[i]->Z)) {
1689 /*
1690 * Set tmp_Z to the inverse of points[i]->Z (as product of Z
1691 * inverses 0 .. i, Z values 0 .. i - 1).
1692 */
1693 if (!group->
1694 meth->field_mul(group, tmp_Z, prod_Z[i - 1], tmp, ctx))
1695 goto err;
1696 /*
1697 * Update tmp to satisfy the loop invariant for i - 1.
1698 */
1699 if (!group->meth->field_mul(group, tmp, tmp, &points[i]->Z, ctx))
1700 goto err;
1701 /* Replace points[i]->Z by its inverse. */
1702 if (!BN_copy(&points[i]->Z, tmp_Z))
1703 goto err;
1704 }
1705 }
1706
1707 if (!BN_is_zero(&points[0]->Z)) {
1708 /* Replace points[0]->Z by its inverse. */
1709 if (!BN_copy(&points[0]->Z, tmp))
1710 goto err;
1711 }
1712
1713 /* Finally, fix up the X and Y coordinates for all points. */
1714
1715 for (i = 0; i < num; i++) {
1716 EC_POINT *p = points[i];
1717
1718 if (!BN_is_zero(&p->Z)) {
1719 /* turn (X, Y, 1/Z) into (X/Z^2, Y/Z^3, 1) */
1720
1721 if (!group->meth->field_sqr(group, tmp, &p->Z, ctx))
1722 goto err;
1723 if (!group->meth->field_mul(group, &p->X, &p->X, tmp, ctx))
1724 goto err;
1725
1726 if (!group->meth->field_mul(group, tmp, tmp, &p->Z, ctx))
1727 goto err;
1728 if (!group->meth->field_mul(group, &p->Y, &p->Y, tmp, ctx))
1729 goto err;
1730
1731 if (group->meth->field_set_to_one != 0) {
1732 if (!group->meth->field_set_to_one(group, &p->Z, ctx))
1733 goto err;
1734 } else {
1735 if (!BN_one(&p->Z))
1736 goto err;
1737 }
1738 p->Z_is_one = 1;
1739 }
1740 }
1741
1742 ret = 1;
1743
1744 err:
1745 BN_CTX_end(ctx);
1746 if (new_ctx != NULL)
1747 BN_CTX_free(new_ctx);
1748 if (prod_Z != NULL) {
1749 for (i = 0; i < num; i++) {
1750 if (prod_Z[i] == NULL)
1751 break;
1752 BN_clear_free(prod_Z[i]);
1753 }
1754 OPENSSL_free(prod_Z);
1755 }
1756 return ret;
1757 }
1758
1759 int ec_GFp_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a,
1760 const BIGNUM *b, BN_CTX *ctx)
1761 {
1762 return BN_mod_mul(r, a, b, &group->field, ctx);
1763 }
1764
1765 int ec_GFp_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a,
1766 BN_CTX *ctx)
1767 {
1768 return BN_mod_sqr(r, a, &group->field, ctx);
1769 }
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