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Change BN_mod_sqrt() so that it verifies that the input value is
[thirdparty/openssl.git] / crypto / ec / ecp_smpl.c
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 #include "ec_lcl.h"
69
70 const EC_METHOD *EC_GFp_simple_method(void)
71 {
72 static const EC_METHOD ret = {
73 NID_X9_62_prime_field,
74 ec_GFp_simple_group_init,
75 ec_GFp_simple_group_finish,
76 ec_GFp_simple_group_clear_finish,
77 ec_GFp_simple_group_copy,
78 ec_GFp_simple_group_set_curve,
79 ec_GFp_simple_group_get_curve,
80 ec_GFp_simple_group_get_degree,
81 ec_GFp_simple_group_check_discriminant,
82 ec_GFp_simple_point_init,
83 ec_GFp_simple_point_finish,
84 ec_GFp_simple_point_clear_finish,
85 ec_GFp_simple_point_copy,
86 ec_GFp_simple_point_set_to_infinity,
87 ec_GFp_simple_set_Jprojective_coordinates_GFp,
88 ec_GFp_simple_get_Jprojective_coordinates_GFp,
89 ec_GFp_simple_point_set_affine_coordinates,
90 ec_GFp_simple_point_get_affine_coordinates,
91 ec_GFp_simple_set_compressed_coordinates,
92 ec_GFp_simple_point2oct,
93 ec_GFp_simple_oct2point,
94 ec_GFp_simple_add,
95 ec_GFp_simple_dbl,
96 ec_GFp_simple_invert,
97 0 /* mul */,
98 0 /* precompute_mult */,
99 ec_GFp_simple_is_at_infinity,
100 ec_GFp_simple_is_on_curve,
101 ec_GFp_simple_cmp,
102 ec_GFp_simple_make_affine,
103 ec_GFp_simple_points_make_affine,
104 ec_GFp_simple_field_mul,
105 ec_GFp_simple_field_sqr,
106 0 /* field_div */,
107 0 /* field_encode */,
108 0 /* field_decode */,
109 0 /* field_set_to_one */ };
110
111 return &ret;
112 }
113
114
115 int ec_GFp_simple_group_init(EC_GROUP *group)
116 {
117 BN_init(&group->field);
118 BN_init(&group->a);
119 BN_init(&group->b);
120 group->a_is_minus3 = 0;
121 return 1;
122 }
123
124
125 void ec_GFp_simple_group_finish(EC_GROUP *group)
126 {
127 BN_free(&group->field);
128 BN_free(&group->a);
129 BN_free(&group->b);
130 }
131
132
133 void ec_GFp_simple_group_clear_finish(EC_GROUP *group)
134 {
135 BN_clear_free(&group->field);
136 BN_clear_free(&group->a);
137 BN_clear_free(&group->b);
138 }
139
140
141 int ec_GFp_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src)
142 {
143 if (!BN_copy(&dest->field, &src->field)) return 0;
144 if (!BN_copy(&dest->a, &src->a)) return 0;
145 if (!BN_copy(&dest->b, &src->b)) return 0;
146
147 dest->a_is_minus3 = src->a_is_minus3;
148
149 return 1;
150 }
151
152
153 int ec_GFp_simple_group_set_curve(EC_GROUP *group,
154 const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
155 {
156 int ret = 0;
157 BN_CTX *new_ctx = NULL;
158 BIGNUM *tmp_a;
159
160 /* p must be a prime > 3 */
161 if (BN_num_bits(p) <= 2 || !BN_is_odd(p))
162 {
163 ECerr(EC_F_EC_GFP_SIMPLE_GROUP_SET_CURVE, EC_R_INVALID_FIELD);
164 return 0;
165 }
166
167 if (ctx == NULL)
168 {
169 ctx = new_ctx = BN_CTX_new();
170 if (ctx == NULL)
171 return 0;
172 }
173
174 BN_CTX_start(ctx);
175 tmp_a = BN_CTX_get(ctx);
176 if (tmp_a == NULL) goto err;
177
178 /* group->field */
179 if (!BN_copy(&group->field, p)) goto err;
180 group->field.neg = 0;
181
182 /* group->a */
183 if (!BN_nnmod(tmp_a, a, p, ctx)) goto err;
184 if (group->meth->field_encode)
185 { if (!group->meth->field_encode(group, &group->a, tmp_a, ctx)) goto err; }
186 else
187 if (!BN_copy(&group->a, tmp_a)) goto err;
188
189 /* group->b */
190 if (!BN_nnmod(&group->b, b, p, ctx)) goto err;
191 if (group->meth->field_encode)
192 if (!group->meth->field_encode(group, &group->b, &group->b, ctx)) goto err;
193
194 /* group->a_is_minus3 */
195 if (!BN_add_word(tmp_a, 3)) goto err;
196 group->a_is_minus3 = (0 == BN_cmp(tmp_a, &group->field));
197
198 ret = 1;
199
200 err:
201 BN_CTX_end(ctx);
202 if (new_ctx != NULL)
203 BN_CTX_free(new_ctx);
204 return ret;
205 }
206
207
208 int ec_GFp_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx)
209 {
210 int ret = 0;
211 BN_CTX *new_ctx = NULL;
212
213 if (p != NULL)
214 {
215 if (!BN_copy(p, &group->field)) return 0;
216 }
217
218 if (a != NULL || b != NULL)
219 {
220 if (group->meth->field_decode)
221 {
222 if (ctx == NULL)
223 {
224 ctx = new_ctx = BN_CTX_new();
225 if (ctx == NULL)
226 return 0;
227 }
228 if (a != NULL)
229 {
230 if (!group->meth->field_decode(group, a, &group->a, ctx)) goto err;
231 }
232 if (b != NULL)
233 {
234 if (!group->meth->field_decode(group, b, &group->b, ctx)) goto err;
235 }
236 }
237 else
238 {
239 if (a != NULL)
240 {
241 if (!BN_copy(a, &group->a)) goto err;
242 }
243 if (b != NULL)
244 {
245 if (!BN_copy(b, &group->b)) goto err;
246 }
247 }
248 }
249
250 ret = 1;
251
252 err:
253 if (new_ctx)
254 BN_CTX_free(new_ctx);
255 return ret;
256 }
257
258
259 int ec_GFp_simple_group_get_degree(const EC_GROUP *group)
260 {
261 return BN_num_bits(&group->field);
262 }
263
264
265 int ec_GFp_simple_group_check_discriminant(const EC_GROUP *group, BN_CTX *ctx)
266 {
267 int ret = 0;
268 BIGNUM *a,*b,*order,*tmp_1,*tmp_2;
269 const BIGNUM *p = &group->field;
270 BN_CTX *new_ctx = NULL;
271
272 if (ctx == NULL)
273 {
274 ctx = new_ctx = BN_CTX_new();
275 if (ctx == NULL)
276 {
277 ECerr(EC_F_EC_GFP_SIMPLE_GROUP_CHECK_DISCRIMINANT, ERR_R_MALLOC_FAILURE);
278 goto err;
279 }
280 }
281 BN_CTX_start(ctx);
282 a = BN_CTX_get(ctx);
283 b = BN_CTX_get(ctx);
284 tmp_1 = BN_CTX_get(ctx);
285 tmp_2 = BN_CTX_get(ctx);
286 order = BN_CTX_get(ctx);
287 if (order == NULL) goto err;
288
289 if (group->meth->field_decode)
290 {
291 if (!group->meth->field_decode(group, a, &group->a, ctx)) goto err;
292 if (!group->meth->field_decode(group, b, &group->b, ctx)) goto err;
293 }
294 else
295 {
296 if (!BN_copy(a, &group->a)) goto err;
297 if (!BN_copy(b, &group->b)) goto err;
298 }
299
300 /* check the discriminant:
301 * y^2 = x^3 + a*x + b is an elliptic curve <=> 4*a^3 + 27*b^2 != 0 (mod p)
302 * 0 =< a, b < p */
303 if (BN_is_zero(a))
304 {
305 if (BN_is_zero(b)) goto err;
306 }
307 else if (!BN_is_zero(b))
308 {
309 if (!BN_mod_sqr(tmp_1, a, p, ctx)) goto err;
310 if (!BN_mod_mul(tmp_2, tmp_1, a, p, ctx)) goto err;
311 if (!BN_lshift(tmp_1, tmp_2, 2)) goto err;
312 /* tmp_1 = 4*a^3 */
313
314 if (!BN_mod_sqr(tmp_2, b, p, ctx)) goto err;
315 if (!BN_mul_word(tmp_2, 27)) goto err;
316 /* tmp_2 = 27*b^2 */
317
318 if (!BN_mod_add(a, tmp_1, tmp_2, p, ctx)) goto err;
319 if (BN_is_zero(a)) goto err;
320 }
321 ret = 1;
322
323 err:
324 BN_CTX_end(ctx);
325 if (new_ctx != NULL)
326 BN_CTX_free(new_ctx);
327 return ret;
328 }
329
330
331 int ec_GFp_simple_point_init(EC_POINT *point)
332 {
333 BN_init(&point->X);
334 BN_init(&point->Y);
335 BN_init(&point->Z);
336 point->Z_is_one = 0;
337
338 return 1;
339 }
340
341
342 void ec_GFp_simple_point_finish(EC_POINT *point)
343 {
344 BN_free(&point->X);
345 BN_free(&point->Y);
346 BN_free(&point->Z);
347 }
348
349
350 void ec_GFp_simple_point_clear_finish(EC_POINT *point)
351 {
352 BN_clear_free(&point->X);
353 BN_clear_free(&point->Y);
354 BN_clear_free(&point->Z);
355 point->Z_is_one = 0;
356 }
357
358
359 int ec_GFp_simple_point_copy(EC_POINT *dest, const EC_POINT *src)
360 {
361 if (!BN_copy(&dest->X, &src->X)) return 0;
362 if (!BN_copy(&dest->Y, &src->Y)) return 0;
363 if (!BN_copy(&dest->Z, &src->Z)) return 0;
364 dest->Z_is_one = src->Z_is_one;
365
366 return 1;
367 }
368
369
370 int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *group, EC_POINT *point)
371 {
372 point->Z_is_one = 0;
373 return (BN_zero(&point->Z));
374 }
375
376
377 int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *group, EC_POINT *point,
378 const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *ctx)
379 {
380 BN_CTX *new_ctx = NULL;
381 int ret = 0;
382
383 if (ctx == NULL)
384 {
385 ctx = new_ctx = BN_CTX_new();
386 if (ctx == NULL)
387 return 0;
388 }
389
390 if (x != NULL)
391 {
392 if (!BN_nnmod(&point->X, x, &group->field, ctx)) goto err;
393 if (group->meth->field_encode)
394 {
395 if (!group->meth->field_encode(group, &point->X, &point->X, ctx)) goto err;
396 }
397 }
398
399 if (y != NULL)
400 {
401 if (!BN_nnmod(&point->Y, y, &group->field, ctx)) goto err;
402 if (group->meth->field_encode)
403 {
404 if (!group->meth->field_encode(group, &point->Y, &point->Y, ctx)) goto err;
405 }
406 }
407
408 if (z != NULL)
409 {
410 int Z_is_one;
411
412 if (!BN_nnmod(&point->Z, z, &group->field, ctx)) goto err;
413 Z_is_one = BN_is_one(&point->Z);
414 if (group->meth->field_encode)
415 {
416 if (Z_is_one && (group->meth->field_set_to_one != 0))
417 {
418 if (!group->meth->field_set_to_one(group, &point->Z, ctx)) goto err;
419 }
420 else
421 {
422 if (!group->meth->field_encode(group, &point->Z, &point->Z, ctx)) goto err;
423 }
424 }
425 point->Z_is_one = Z_is_one;
426 }
427
428 ret = 1;
429
430 err:
431 if (new_ctx != NULL)
432 BN_CTX_free(new_ctx);
433 return ret;
434 }
435
436
437 int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *group, const EC_POINT *point,
438 BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *ctx)
439 {
440 BN_CTX *new_ctx = NULL;
441 int ret = 0;
442
443 if (group->meth->field_decode != 0)
444 {
445 if (ctx == NULL)
446 {
447 ctx = new_ctx = BN_CTX_new();
448 if (ctx == NULL)
449 return 0;
450 }
451
452 if (x != NULL)
453 {
454 if (!group->meth->field_decode(group, x, &point->X, ctx)) goto err;
455 }
456 if (y != NULL)
457 {
458 if (!group->meth->field_decode(group, y, &point->Y, ctx)) goto err;
459 }
460 if (z != NULL)
461 {
462 if (!group->meth->field_decode(group, z, &point->Z, ctx)) goto err;
463 }
464 }
465 else
466 {
467 if (x != NULL)
468 {
469 if (!BN_copy(x, &point->X)) goto err;
470 }
471 if (y != NULL)
472 {
473 if (!BN_copy(y, &point->Y)) goto err;
474 }
475 if (z != NULL)
476 {
477 if (!BN_copy(z, &point->Z)) goto err;
478 }
479 }
480
481 ret = 1;
482
483 err:
484 if (new_ctx != NULL)
485 BN_CTX_free(new_ctx);
486 return ret;
487 }
488
489
490 int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *group, EC_POINT *point,
491 const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx)
492 {
493 if (x == NULL || y == NULL)
494 {
495 /* unlike for projective coordinates, we do not tolerate this */
496 ECerr(EC_F_EC_GFP_SIMPLE_POINT_SET_AFFINE_COORDINATES, ERR_R_PASSED_NULL_PARAMETER);
497 return 0;
498 }
499
500 return EC_POINT_set_Jprojective_coordinates_GFp(group, point, x, y, BN_value_one(), ctx);
501 }
502
503
504 int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point,
505 BIGNUM *x, BIGNUM *y, BN_CTX *ctx)
506 {
507 BN_CTX *new_ctx = NULL;
508 BIGNUM *X, *Y, *Z, *Z_1, *Z_2, *Z_3;
509 const BIGNUM *X_, *Y_, *Z_;
510 int ret = 0;
511
512 if (EC_POINT_is_at_infinity(group, point))
513 {
514 ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES, EC_R_POINT_AT_INFINITY);
515 return 0;
516 }
517
518 if (ctx == NULL)
519 {
520 ctx = new_ctx = BN_CTX_new();
521 if (ctx == NULL)
522 return 0;
523 }
524
525 BN_CTX_start(ctx);
526 X = BN_CTX_get(ctx);
527 Y = BN_CTX_get(ctx);
528 Z = BN_CTX_get(ctx);
529 Z_1 = BN_CTX_get(ctx);
530 Z_2 = BN_CTX_get(ctx);
531 Z_3 = BN_CTX_get(ctx);
532 if (Z_3 == NULL) goto err;
533
534 /* transform (X, Y, Z) into (x, y) := (X/Z^2, Y/Z^3) */
535
536 if (group->meth->field_decode)
537 {
538 if (!group->meth->field_decode(group, X, &point->X, ctx)) goto err;
539 if (!group->meth->field_decode(group, Y, &point->Y, ctx)) goto err;
540 if (!group->meth->field_decode(group, Z, &point->Z, ctx)) goto err;
541 X_ = X; Y_ = Y; Z_ = Z;
542 }
543 else
544 {
545 X_ = &point->X;
546 Y_ = &point->Y;
547 Z_ = &point->Z;
548 }
549
550 if (BN_is_one(Z_))
551 {
552 if (x != NULL)
553 {
554 if (!BN_copy(x, X_)) goto err;
555 }
556 if (y != NULL)
557 {
558 if (!BN_copy(y, Y_)) goto err;
559 }
560 }
561 else
562 {
563 if (!BN_mod_inverse(Z_1, Z_, &group->field, ctx))
564 {
565 ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES, ERR_R_BN_LIB);
566 goto err;
567 }
568
569 if (group->meth->field_encode == 0)
570 {
571 /* field_sqr works on standard representation */
572 if (!group->meth->field_sqr(group, Z_2, Z_1, ctx)) goto err;
573 }
574 else
575 {
576 if (!BN_mod_sqr(Z_2, Z_1, &group->field, ctx)) goto err;
577 }
578
579 if (x != NULL)
580 {
581 if (group->meth->field_encode == 0)
582 {
583 /* field_mul works on standard representation */
584 if (!group->meth->field_mul(group, x, X_, Z_2, ctx)) goto err;
585 }
586 else
587 {
588 if (!BN_mod_mul(x, X_, Z_2, &group->field, ctx)) goto err;
589 }
590 }
591
592 if (y != NULL)
593 {
594 if (group->meth->field_encode == 0)
595 {
596 /* field_mul works on standard representation */
597 if (!group->meth->field_mul(group, Z_3, Z_2, Z_1, ctx)) goto err;
598 if (!group->meth->field_mul(group, y, Y_, Z_3, ctx)) goto err;
599
600 }
601 else
602 {
603 if (!BN_mod_mul(Z_3, Z_2, Z_1, &group->field, ctx)) goto err;
604 if (!BN_mod_mul(y, Y_, Z_3, &group->field, ctx)) goto err;
605 }
606 }
607 }
608
609 ret = 1;
610
611 err:
612 BN_CTX_end(ctx);
613 if (new_ctx != NULL)
614 BN_CTX_free(new_ctx);
615 return ret;
616 }
617
618
619 int ec_GFp_simple_set_compressed_coordinates(const EC_GROUP *group, EC_POINT *point,
620 const BIGNUM *x_, int y_bit, BN_CTX *ctx)
621 {
622 BN_CTX *new_ctx = NULL;
623 BIGNUM *tmp1, *tmp2, *x, *y;
624 int ret = 0;
625
626 if (ctx == NULL)
627 {
628 ctx = new_ctx = BN_CTX_new();
629 if (ctx == NULL)
630 return 0;
631 }
632
633 y_bit = (y_bit != 0);
634
635 BN_CTX_start(ctx);
636 tmp1 = BN_CTX_get(ctx);
637 tmp2 = BN_CTX_get(ctx);
638 x = BN_CTX_get(ctx);
639 y = BN_CTX_get(ctx);
640 if (y == NULL) goto err;
641
642 /* Recover y. We have a Weierstrass equation
643 * y^2 = x^3 + a*x + b,
644 * so y is one of the square roots of x^3 + a*x + b.
645 */
646
647 /* tmp1 := x^3 */
648 if (!BN_nnmod(x, x_, &group->field,ctx)) goto err;
649 if (group->meth->field_decode == 0)
650 {
651 /* field_{sqr,mul} work on standard representation */
652 if (!group->meth->field_sqr(group, tmp2, x_, ctx)) goto err;
653 if (!group->meth->field_mul(group, tmp1, tmp2, x_, ctx)) goto err;
654 }
655 else
656 {
657 if (!BN_mod_sqr(tmp2, x_, &group->field, ctx)) goto err;
658 if (!BN_mod_mul(tmp1, tmp2, x_, &group->field, ctx)) goto err;
659 }
660
661 /* tmp1 := tmp1 + a*x */
662 if (group->a_is_minus3)
663 {
664 if (!BN_mod_lshift1_quick(tmp2, x, &group->field)) goto err;
665 if (!BN_mod_add_quick(tmp2, tmp2, x, &group->field)) goto err;
666 if (!BN_mod_sub_quick(tmp1, tmp1, tmp2, &group->field)) goto err;
667 }
668 else
669 {
670 if (group->meth->field_decode)
671 {
672 if (!group->meth->field_decode(group, tmp2, &group->a, ctx)) goto err;
673 if (!BN_mod_mul(tmp2, tmp2, x, &group->field, ctx)) goto err;
674 }
675 else
676 {
677 /* field_mul works on standard representation */
678 if (!group->meth->field_mul(group, tmp2, &group->a, x, ctx)) goto err;
679 }
680
681 if (!BN_mod_add_quick(tmp1, tmp1, tmp2, &group->field)) goto err;
682 }
683
684 /* tmp1 := tmp1 + b */
685 if (group->meth->field_decode)
686 {
687 if (!group->meth->field_decode(group, tmp2, &group->b, ctx)) goto err;
688 if (!BN_mod_add_quick(tmp1, tmp1, tmp2, &group->field)) goto err;
689 }
690 else
691 {
692 if (!BN_mod_add_quick(tmp1, tmp1, &group->b, &group->field)) goto err;
693 }
694
695 if (!BN_mod_sqrt(y, tmp1, &group->field, ctx))
696 {
697 unsigned long err = ERR_peek_error();
698
699 if (ERR_GET_LIB(err) == ERR_LIB_BN && ERR_GET_REASON(err) == BN_R_NOT_A_SQUARE)
700 {
701 (void)ERR_get_error();
702 ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, EC_R_INVALID_COMPRESSED_POINT);
703 }
704 else
705 ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, ERR_R_BN_LIB);
706 goto err;
707 }
708
709 if (y_bit != BN_is_odd(y))
710 {
711 if (BN_is_zero(y))
712 {
713 int kron;
714
715 kron = BN_kronecker(x, &group->field, ctx);
716 if (kron == -2) goto err;
717
718 if (kron == 1)
719 ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, EC_R_INVALID_COMPRESSION_BIT);
720 else
721 /* BN_mod_sqrt() should have cought this error (not a square) */
722 ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, EC_R_INVALID_COMPRESSED_POINT);
723 goto err;
724 }
725 if (!BN_usub(y, &group->field, y)) goto err;
726 }
727 if (y_bit != BN_is_odd(y))
728 {
729 ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, ERR_R_INTERNAL_ERROR);
730 goto err;
731 }
732
733 if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
734
735 ret = 1;
736
737 err:
738 BN_CTX_end(ctx);
739 if (new_ctx != NULL)
740 BN_CTX_free(new_ctx);
741 return ret;
742 }
743
744
745 size_t ec_GFp_simple_point2oct(const EC_GROUP *group, const EC_POINT *point, point_conversion_form_t form,
746 unsigned char *buf, size_t len, BN_CTX *ctx)
747 {
748 size_t ret;
749 BN_CTX *new_ctx = NULL;
750 int used_ctx = 0;
751 BIGNUM *x, *y;
752 size_t field_len, i, skip;
753
754 if ((form != POINT_CONVERSION_COMPRESSED)
755 && (form != POINT_CONVERSION_UNCOMPRESSED)
756 && (form != POINT_CONVERSION_HYBRID))
757 {
758 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_INVALID_FORM);
759 goto err;
760 }
761
762 if (EC_POINT_is_at_infinity(group, point))
763 {
764 /* encodes to a single 0 octet */
765 if (buf != NULL)
766 {
767 if (len < 1)
768 {
769 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);
770 return 0;
771 }
772 buf[0] = 0;
773 }
774 return 1;
775 }
776
777
778 /* ret := required output buffer length */
779 field_len = BN_num_bytes(&group->field);
780 ret = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len;
781
782 /* if 'buf' is NULL, just return required length */
783 if (buf != NULL)
784 {
785 if (len < ret)
786 {
787 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);
788 goto err;
789 }
790
791 if (ctx == NULL)
792 {
793 ctx = new_ctx = BN_CTX_new();
794 if (ctx == NULL)
795 return 0;
796 }
797
798 BN_CTX_start(ctx);
799 used_ctx = 1;
800 x = BN_CTX_get(ctx);
801 y = BN_CTX_get(ctx);
802 if (y == NULL) goto err;
803
804 if (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
805
806 if ((form == POINT_CONVERSION_COMPRESSED || form == POINT_CONVERSION_HYBRID) && BN_is_odd(y))
807 buf[0] = form + 1;
808 else
809 buf[0] = form;
810
811 i = 1;
812
813 skip = field_len - BN_num_bytes(x);
814 if (skip > field_len)
815 {
816 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
817 goto err;
818 }
819 while (skip > 0)
820 {
821 buf[i++] = 0;
822 skip--;
823 }
824 skip = BN_bn2bin(x, buf + i);
825 i += skip;
826 if (i != 1 + field_len)
827 {
828 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
829 goto err;
830 }
831
832 if (form == POINT_CONVERSION_UNCOMPRESSED || form == POINT_CONVERSION_HYBRID)
833 {
834 skip = field_len - BN_num_bytes(y);
835 if (skip > field_len)
836 {
837 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
838 goto err;
839 }
840 while (skip > 0)
841 {
842 buf[i++] = 0;
843 skip--;
844 }
845 skip = BN_bn2bin(y, buf + i);
846 i += skip;
847 }
848
849 if (i != ret)
850 {
851 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
852 goto err;
853 }
854 }
855
856 if (used_ctx)
857 BN_CTX_end(ctx);
858 if (new_ctx != NULL)
859 BN_CTX_free(new_ctx);
860 return ret;
861
862 err:
863 if (used_ctx)
864 BN_CTX_end(ctx);
865 if (new_ctx != NULL)
866 BN_CTX_free(new_ctx);
867 return 0;
868 }
869
870
871 int ec_GFp_simple_oct2point(const EC_GROUP *group, EC_POINT *point,
872 const unsigned char *buf, size_t len, BN_CTX *ctx)
873 {
874 point_conversion_form_t form;
875 int y_bit;
876 BN_CTX *new_ctx = NULL;
877 BIGNUM *x, *y;
878 size_t field_len, enc_len;
879 int ret = 0;
880
881 if (len == 0)
882 {
883 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_BUFFER_TOO_SMALL);
884 return 0;
885 }
886 form = buf[0];
887 y_bit = form & 1;
888 form = form & ~1;
889 if ((form != 0) && (form != POINT_CONVERSION_COMPRESSED)
890 && (form != POINT_CONVERSION_UNCOMPRESSED)
891 && (form != POINT_CONVERSION_HYBRID))
892 {
893 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
894 return 0;
895 }
896 if ((form == 0 || form == POINT_CONVERSION_UNCOMPRESSED) && y_bit)
897 {
898 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
899 return 0;
900 }
901
902 if (form == 0)
903 {
904 if (len != 1)
905 {
906 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
907 return 0;
908 }
909
910 return EC_POINT_set_to_infinity(group, point);
911 }
912
913 field_len = BN_num_bytes(&group->field);
914 enc_len = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len;
915
916 if (len != enc_len)
917 {
918 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
919 return 0;
920 }
921
922 if (ctx == NULL)
923 {
924 ctx = new_ctx = BN_CTX_new();
925 if (ctx == NULL)
926 return 0;
927 }
928
929 BN_CTX_start(ctx);
930 x = BN_CTX_get(ctx);
931 y = BN_CTX_get(ctx);
932 if (y == NULL) goto err;
933
934 if (!BN_bin2bn(buf + 1, field_len, x)) goto err;
935 if (BN_ucmp(x, &group->field) >= 0)
936 {
937 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
938 goto err;
939 }
940
941 if (form == POINT_CONVERSION_COMPRESSED)
942 {
943 if (!EC_POINT_set_compressed_coordinates_GFp(group, point, x, y_bit, ctx)) goto err;
944 }
945 else
946 {
947 if (!BN_bin2bn(buf + 1 + field_len, field_len, y)) goto err;
948 if (BN_ucmp(y, &group->field) >= 0)
949 {
950 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
951 goto err;
952 }
953 if (form == POINT_CONVERSION_HYBRID)
954 {
955 if (y_bit != BN_is_odd(y))
956 {
957 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
958 goto err;
959 }
960 }
961
962 if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
963 }
964
965 if (!EC_POINT_is_on_curve(group, point, ctx)) /* test required by X9.62 */
966 {
967 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_POINT_IS_NOT_ON_CURVE);
968 goto err;
969 }
970
971 ret = 1;
972
973 err:
974 BN_CTX_end(ctx);
975 if (new_ctx != NULL)
976 BN_CTX_free(new_ctx);
977 return ret;
978 }
979
980
981 int ec_GFp_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
982 {
983 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
984 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
985 const BIGNUM *p;
986 BN_CTX *new_ctx = NULL;
987 BIGNUM *n0, *n1, *n2, *n3, *n4, *n5, *n6;
988 int ret = 0;
989
990 if (a == b)
991 return EC_POINT_dbl(group, r, a, ctx);
992 if (EC_POINT_is_at_infinity(group, a))
993 return EC_POINT_copy(r, b);
994 if (EC_POINT_is_at_infinity(group, b))
995 return EC_POINT_copy(r, a);
996
997 field_mul = group->meth->field_mul;
998 field_sqr = group->meth->field_sqr;
999 p = &group->field;
1000
1001 if (ctx == NULL)
1002 {
1003 ctx = new_ctx = BN_CTX_new();
1004 if (ctx == NULL)
1005 return 0;
1006 }
1007
1008 BN_CTX_start(ctx);
1009 n0 = BN_CTX_get(ctx);
1010 n1 = BN_CTX_get(ctx);
1011 n2 = BN_CTX_get(ctx);
1012 n3 = BN_CTX_get(ctx);
1013 n4 = BN_CTX_get(ctx);
1014 n5 = BN_CTX_get(ctx);
1015 n6 = BN_CTX_get(ctx);
1016 if (n6 == NULL) goto end;
1017
1018 /* Note that in this function we must not read components of 'a' or 'b'
1019 * once we have written the corresponding components of 'r'.
1020 * ('r' might be one of 'a' or 'b'.)
1021 */
1022
1023 /* n1, n2 */
1024 if (b->Z_is_one)
1025 {
1026 if (!BN_copy(n1, &a->X)) goto end;
1027 if (!BN_copy(n2, &a->Y)) goto end;
1028 /* n1 = X_a */
1029 /* n2 = Y_a */
1030 }
1031 else
1032 {
1033 if (!field_sqr(group, n0, &b->Z, ctx)) goto end;
1034 if (!field_mul(group, n1, &a->X, n0, ctx)) goto end;
1035 /* n1 = X_a * Z_b^2 */
1036
1037 if (!field_mul(group, n0, n0, &b->Z, ctx)) goto end;
1038 if (!field_mul(group, n2, &a->Y, n0, ctx)) goto end;
1039 /* n2 = Y_a * Z_b^3 */
1040 }
1041
1042 /* n3, n4 */
1043 if (a->Z_is_one)
1044 {
1045 if (!BN_copy(n3, &b->X)) goto end;
1046 if (!BN_copy(n4, &b->Y)) goto end;
1047 /* n3 = X_b */
1048 /* n4 = Y_b */
1049 }
1050 else
1051 {
1052 if (!field_sqr(group, n0, &a->Z, ctx)) goto end;
1053 if (!field_mul(group, n3, &b->X, n0, ctx)) goto end;
1054 /* n3 = X_b * Z_a^2 */
1055
1056 if (!field_mul(group, n0, n0, &a->Z, ctx)) goto end;
1057 if (!field_mul(group, n4, &b->Y, n0, ctx)) goto end;
1058 /* n4 = Y_b * Z_a^3 */
1059 }
1060
1061 /* n5, n6 */
1062 if (!BN_mod_sub_quick(n5, n1, n3, p)) goto end;
1063 if (!BN_mod_sub_quick(n6, n2, n4, p)) goto end;
1064 /* n5 = n1 - n3 */
1065 /* n6 = n2 - n4 */
1066
1067 if (BN_is_zero(n5))
1068 {
1069 if (BN_is_zero(n6))
1070 {
1071 /* a is the same point as b */
1072 BN_CTX_end(ctx);
1073 ret = EC_POINT_dbl(group, r, a, ctx);
1074 ctx = NULL;
1075 goto end;
1076 }
1077 else
1078 {
1079 /* a is the inverse of b */
1080 if (!BN_zero(&r->Z)) goto end;
1081 r->Z_is_one = 0;
1082 ret = 1;
1083 goto end;
1084 }
1085 }
1086
1087 /* 'n7', 'n8' */
1088 if (!BN_mod_add_quick(n1, n1, n3, p)) goto end;
1089 if (!BN_mod_add_quick(n2, n2, n4, p)) goto end;
1090 /* 'n7' = n1 + n3 */
1091 /* 'n8' = n2 + n4 */
1092
1093 /* Z_r */
1094 if (a->Z_is_one && b->Z_is_one)
1095 {
1096 if (!BN_copy(&r->Z, n5)) goto end;
1097 }
1098 else
1099 {
1100 if (a->Z_is_one)
1101 { if (!BN_copy(n0, &b->Z)) goto end; }
1102 else if (b->Z_is_one)
1103 { if (!BN_copy(n0, &a->Z)) goto end; }
1104 else
1105 { if (!field_mul(group, n0, &a->Z, &b->Z, ctx)) goto end; }
1106 if (!field_mul(group, &r->Z, n0, n5, ctx)) goto end;
1107 }
1108 r->Z_is_one = 0;
1109 /* Z_r = Z_a * Z_b * n5 */
1110
1111 /* X_r */
1112 if (!field_sqr(group, n0, n6, ctx)) goto end;
1113 if (!field_sqr(group, n4, n5, ctx)) goto end;
1114 if (!field_mul(group, n3, n1, n4, ctx)) goto end;
1115 if (!BN_mod_sub_quick(&r->X, n0, n3, p)) goto end;
1116 /* X_r = n6^2 - n5^2 * 'n7' */
1117
1118 /* 'n9' */
1119 if (!BN_mod_lshift1_quick(n0, &r->X, p)) goto end;
1120 if (!BN_mod_sub_quick(n0, n3, n0, p)) goto end;
1121 /* n9 = n5^2 * 'n7' - 2 * X_r */
1122
1123 /* Y_r */
1124 if (!field_mul(group, n0, n0, n6, ctx)) goto end;
1125 if (!field_mul(group, n5, n4, n5, ctx)) goto end; /* now n5 is n5^3 */
1126 if (!field_mul(group, n1, n2, n5, ctx)) goto end;
1127 if (!BN_mod_sub_quick(n0, n0, n1, p)) goto end;
1128 if (BN_is_odd(n0))
1129 if (!BN_add(n0, n0, p)) goto end;
1130 /* now 0 <= n0 < 2*p, and n0 is even */
1131 if (!BN_rshift1(&r->Y, n0)) goto end;
1132 /* Y_r = (n6 * 'n9' - 'n8' * 'n5^3') / 2 */
1133
1134 ret = 1;
1135
1136 end:
1137 if (ctx) /* otherwise we already called BN_CTX_end */
1138 BN_CTX_end(ctx);
1139 if (new_ctx != NULL)
1140 BN_CTX_free(new_ctx);
1141 return ret;
1142 }
1143
1144
1145 int ec_GFp_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_CTX *ctx)
1146 {
1147 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
1148 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
1149 const BIGNUM *p;
1150 BN_CTX *new_ctx = NULL;
1151 BIGNUM *n0, *n1, *n2, *n3;
1152 int ret = 0;
1153
1154 if (EC_POINT_is_at_infinity(group, a))
1155 {
1156 if (!BN_zero(&r->Z)) return 0;
1157 r->Z_is_one = 0;
1158 return 1;
1159 }
1160
1161 field_mul = group->meth->field_mul;
1162 field_sqr = group->meth->field_sqr;
1163 p = &group->field;
1164
1165 if (ctx == NULL)
1166 {
1167 ctx = new_ctx = BN_CTX_new();
1168 if (ctx == NULL)
1169 return 0;
1170 }
1171
1172 BN_CTX_start(ctx);
1173 n0 = BN_CTX_get(ctx);
1174 n1 = BN_CTX_get(ctx);
1175 n2 = BN_CTX_get(ctx);
1176 n3 = BN_CTX_get(ctx);
1177 if (n3 == NULL) goto err;
1178
1179 /* Note that in this function we must not read components of 'a'
1180 * once we have written the corresponding components of 'r'.
1181 * ('r' might the same as 'a'.)
1182 */
1183
1184 /* n1 */
1185 if (a->Z_is_one)
1186 {
1187 if (!field_sqr(group, n0, &a->X, ctx)) goto err;
1188 if (!BN_mod_lshift1_quick(n1, n0, p)) goto err;
1189 if (!BN_mod_add_quick(n0, n0, n1, p)) goto err;
1190 if (!BN_mod_add_quick(n1, n0, &group->a, p)) goto err;
1191 /* n1 = 3 * X_a^2 + a_curve */
1192 }
1193 else if (group->a_is_minus3)
1194 {
1195 if (!field_sqr(group, n1, &a->Z, ctx)) goto err;
1196 if (!BN_mod_add_quick(n0, &a->X, n1, p)) goto err;
1197 if (!BN_mod_sub_quick(n2, &a->X, n1, p)) goto err;
1198 if (!field_mul(group, n1, n0, n2, ctx)) goto err;
1199 if (!BN_mod_lshift1_quick(n0, n1, p)) goto err;
1200 if (!BN_mod_add_quick(n1, n0, n1, p)) goto err;
1201 /* n1 = 3 * (X_a + Z_a^2) * (X_a - Z_a^2)
1202 * = 3 * X_a^2 - 3 * Z_a^4 */
1203 }
1204 else
1205 {
1206 if (!field_sqr(group, n0, &a->X, ctx)) goto err;
1207 if (!BN_mod_lshift1_quick(n1, n0, p)) goto err;
1208 if (!BN_mod_add_quick(n0, n0, n1, p)) goto err;
1209 if (!field_sqr(group, n1, &a->Z, ctx)) goto err;
1210 if (!field_sqr(group, n1, n1, ctx)) goto err;
1211 if (!field_mul(group, n1, n1, &group->a, ctx)) goto err;
1212 if (!BN_mod_add_quick(n1, n1, n0, p)) goto err;
1213 /* n1 = 3 * X_a^2 + a_curve * Z_a^4 */
1214 }
1215
1216 /* Z_r */
1217 if (a->Z_is_one)
1218 {
1219 if (!BN_copy(n0, &a->Y)) goto err;
1220 }
1221 else
1222 {
1223 if (!field_mul(group, n0, &a->Y, &a->Z, ctx)) goto err;
1224 }
1225 if (!BN_mod_lshift1_quick(&r->Z, n0, p)) goto err;
1226 r->Z_is_one = 0;
1227 /* Z_r = 2 * Y_a * Z_a */
1228
1229 /* n2 */
1230 if (!field_sqr(group, n3, &a->Y, ctx)) goto err;
1231 if (!field_mul(group, n2, &a->X, n3, ctx)) goto err;
1232 if (!BN_mod_lshift_quick(n2, n2, 2, p)) goto err;
1233 /* n2 = 4 * X_a * Y_a^2 */
1234
1235 /* X_r */
1236 if (!BN_mod_lshift1_quick(n0, n2, p)) goto err;
1237 if (!field_sqr(group, &r->X, n1, ctx)) goto err;
1238 if (!BN_mod_sub_quick(&r->X, &r->X, n0, p)) goto err;
1239 /* X_r = n1^2 - 2 * n2 */
1240
1241 /* n3 */
1242 if (!field_sqr(group, n0, n3, ctx)) goto err;
1243 if (!BN_mod_lshift_quick(n3, n0, 3, p)) goto err;
1244 /* n3 = 8 * Y_a^4 */
1245
1246 /* Y_r */
1247 if (!BN_mod_sub_quick(n0, n2, &r->X, p)) goto err;
1248 if (!field_mul(group, n0, n1, n0, ctx)) goto err;
1249 if (!BN_mod_sub_quick(&r->Y, n0, n3, p)) goto err;
1250 /* Y_r = n1 * (n2 - X_r) - n3 */
1251
1252 ret = 1;
1253
1254 err:
1255 BN_CTX_end(ctx);
1256 if (new_ctx != NULL)
1257 BN_CTX_free(new_ctx);
1258 return ret;
1259 }
1260
1261
1262 int ec_GFp_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
1263 {
1264 if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(&point->Y))
1265 /* point is its own inverse */
1266 return 1;
1267
1268 return BN_usub(&point->Y, &group->field, &point->Y);
1269 }
1270
1271
1272 int ec_GFp_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point)
1273 {
1274 return BN_is_zero(&point->Z);
1275 }
1276
1277
1278 int ec_GFp_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx)
1279 {
1280 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
1281 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
1282 const BIGNUM *p;
1283 BN_CTX *new_ctx = NULL;
1284 BIGNUM *rh, *tmp1, *tmp2, *Z4, *Z6;
1285 int ret = -1;
1286
1287 if (EC_POINT_is_at_infinity(group, point))
1288 return 1;
1289
1290 field_mul = group->meth->field_mul;
1291 field_sqr = group->meth->field_sqr;
1292 p = &group->field;
1293
1294 if (ctx == NULL)
1295 {
1296 ctx = new_ctx = BN_CTX_new();
1297 if (ctx == NULL)
1298 return -1;
1299 }
1300
1301 BN_CTX_start(ctx);
1302 rh = BN_CTX_get(ctx);
1303 tmp1 = BN_CTX_get(ctx);
1304 tmp2 = BN_CTX_get(ctx);
1305 Z4 = BN_CTX_get(ctx);
1306 Z6 = BN_CTX_get(ctx);
1307 if (Z6 == NULL) goto err;
1308
1309 /* We have a curve defined by a Weierstrass equation
1310 * y^2 = x^3 + a*x + b.
1311 * The point to consider is given in Jacobian projective coordinates
1312 * where (X, Y, Z) represents (x, y) = (X/Z^2, Y/Z^3).
1313 * Substituting this and multiplying by Z^6 transforms the above equation into
1314 * Y^2 = X^3 + a*X*Z^4 + b*Z^6.
1315 * To test this, we add up the right-hand side in 'rh'.
1316 */
1317
1318 /* rh := X^3 */
1319 if (!field_sqr(group, rh, &point->X, ctx)) goto err;
1320 if (!field_mul(group, rh, rh, &point->X, ctx)) goto err;
1321
1322 if (!point->Z_is_one)
1323 {
1324 if (!field_sqr(group, tmp1, &point->Z, ctx)) goto err;
1325 if (!field_sqr(group, Z4, tmp1, ctx)) goto err;
1326 if (!field_mul(group, Z6, Z4, tmp1, ctx)) goto err;
1327
1328 /* rh := rh + a*X*Z^4 */
1329 if (!field_mul(group, tmp1, &point->X, Z4, ctx)) goto err;
1330 if (group->a_is_minus3)
1331 {
1332 if (!BN_mod_lshift1_quick(tmp2, tmp1, p)) goto err;
1333 if (!BN_mod_add_quick(tmp2, tmp2, tmp1, p)) goto err;
1334 if (!BN_mod_sub_quick(rh, rh, tmp2, p)) goto err;
1335 }
1336 else
1337 {
1338 if (!field_mul(group, tmp2, tmp1, &group->a, ctx)) goto err;
1339 if (!BN_mod_add_quick(rh, rh, tmp2, p)) goto err;
1340 }
1341
1342 /* rh := rh + b*Z^6 */
1343 if (!field_mul(group, tmp1, &group->b, Z6, ctx)) goto err;
1344 if (!BN_mod_add_quick(rh, rh, tmp1, p)) goto err;
1345 }
1346 else
1347 {
1348 /* point->Z_is_one */
1349
1350 /* rh := rh + a*X */
1351 if (group->a_is_minus3)
1352 {
1353 if (!BN_mod_lshift1_quick(tmp2, &point->X, p)) goto err;
1354 if (!BN_mod_add_quick(tmp2, tmp2, &point->X, p)) goto err;
1355 if (!BN_mod_sub_quick(rh, rh, tmp2, p)) goto err;
1356 }
1357 else
1358 {
1359 if (!field_mul(group, tmp2, &point->X, &group->a, ctx)) goto err;
1360 if (!BN_mod_add_quick(rh, rh, tmp2, p)) goto err;
1361 }
1362
1363 /* rh := rh + b */
1364 if (!BN_mod_add_quick(rh, rh, &group->b, p)) goto err;
1365 }
1366
1367 /* 'lh' := Y^2 */
1368 if (!field_sqr(group, tmp1, &point->Y, ctx)) goto err;
1369
1370 ret = (0 == BN_cmp(tmp1, rh));
1371
1372 err:
1373 BN_CTX_end(ctx);
1374 if (new_ctx != NULL)
1375 BN_CTX_free(new_ctx);
1376 return ret;
1377 }
1378
1379
1380 int ec_GFp_simple_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
1381 {
1382 /* return values:
1383 * -1 error
1384 * 0 equal (in affine coordinates)
1385 * 1 not equal
1386 */
1387
1388 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
1389 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
1390 BN_CTX *new_ctx = NULL;
1391 BIGNUM *tmp1, *tmp2, *Za23, *Zb23;
1392 const BIGNUM *tmp1_, *tmp2_;
1393 int ret = -1;
1394
1395 if (EC_POINT_is_at_infinity(group, a))
1396 {
1397 return EC_POINT_is_at_infinity(group, b) ? 0 : 1;
1398 }
1399
1400 if (a->Z_is_one && b->Z_is_one)
1401 {
1402 return ((BN_cmp(&a->X, &b->X) == 0) && BN_cmp(&a->Y, &b->Y) == 0) ? 0 : 1;
1403 }
1404
1405 field_mul = group->meth->field_mul;
1406 field_sqr = group->meth->field_sqr;
1407
1408 if (ctx == NULL)
1409 {
1410 ctx = new_ctx = BN_CTX_new();
1411 if (ctx == NULL)
1412 return -1;
1413 }
1414
1415 BN_CTX_start(ctx);
1416 tmp1 = BN_CTX_get(ctx);
1417 tmp2 = BN_CTX_get(ctx);
1418 Za23 = BN_CTX_get(ctx);
1419 Zb23 = BN_CTX_get(ctx);
1420 if (Zb23 == NULL) goto end;
1421
1422 /* We have to decide whether
1423 * (X_a/Z_a^2, Y_a/Z_a^3) = (X_b/Z_b^2, Y_b/Z_b^3),
1424 * or equivalently, whether
1425 * (X_a*Z_b^2, Y_a*Z_b^3) = (X_b*Z_a^2, Y_b*Z_a^3).
1426 */
1427
1428 if (!b->Z_is_one)
1429 {
1430 if (!field_sqr(group, Zb23, &b->Z, ctx)) goto end;
1431 if (!field_mul(group, tmp1, &a->X, Zb23, ctx)) goto end;
1432 tmp1_ = tmp1;
1433 }
1434 else
1435 tmp1_ = &a->X;
1436 if (!a->Z_is_one)
1437 {
1438 if (!field_sqr(group, Za23, &a->Z, ctx)) goto end;
1439 if (!field_mul(group, tmp2, &b->X, Za23, ctx)) goto end;
1440 tmp2_ = tmp2;
1441 }
1442 else
1443 tmp2_ = &b->X;
1444
1445 /* compare X_a*Z_b^2 with X_b*Z_a^2 */
1446 if (BN_cmp(tmp1_, tmp2_) != 0)
1447 {
1448 ret = 1; /* points differ */
1449 goto end;
1450 }
1451
1452
1453 if (!b->Z_is_one)
1454 {
1455 if (!field_mul(group, Zb23, Zb23, &b->Z, ctx)) goto end;
1456 if (!field_mul(group, tmp1, &a->Y, Zb23, ctx)) goto end;
1457 /* tmp1_ = tmp1 */
1458 }
1459 else
1460 tmp1_ = &a->Y;
1461 if (!a->Z_is_one)
1462 {
1463 if (!field_mul(group, Za23, Za23, &a->Z, ctx)) goto end;
1464 if (!field_mul(group, tmp2, &b->Y, Za23, ctx)) goto end;
1465 /* tmp2_ = tmp2 */
1466 }
1467 else
1468 tmp2_ = &b->Y;
1469
1470 /* compare Y_a*Z_b^3 with Y_b*Z_a^3 */
1471 if (BN_cmp(tmp1_, tmp2_) != 0)
1472 {
1473 ret = 1; /* points differ */
1474 goto end;
1475 }
1476
1477 /* points are equal */
1478 ret = 0;
1479
1480 end:
1481 BN_CTX_end(ctx);
1482 if (new_ctx != NULL)
1483 BN_CTX_free(new_ctx);
1484 return ret;
1485 }
1486
1487
1488 int ec_GFp_simple_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
1489 {
1490 BN_CTX *new_ctx = NULL;
1491 BIGNUM *x, *y;
1492 int ret = 0;
1493
1494 if (point->Z_is_one || EC_POINT_is_at_infinity(group, point))
1495 return 1;
1496
1497 if (ctx == NULL)
1498 {
1499 ctx = new_ctx = BN_CTX_new();
1500 if (ctx == NULL)
1501 return 0;
1502 }
1503
1504 BN_CTX_start(ctx);
1505 x = BN_CTX_get(ctx);
1506 y = BN_CTX_get(ctx);
1507 if (y == NULL) goto err;
1508
1509 if (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
1510 if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
1511 if (!point->Z_is_one)
1512 {
1513 ECerr(EC_F_EC_GFP_SIMPLE_MAKE_AFFINE, ERR_R_INTERNAL_ERROR);
1514 goto err;
1515 }
1516
1517 ret = 1;
1518
1519 err:
1520 BN_CTX_end(ctx);
1521 if (new_ctx != NULL)
1522 BN_CTX_free(new_ctx);
1523 return ret;
1524 }
1525
1526
1527 int ec_GFp_simple_points_make_affine(const EC_GROUP *group, size_t num, EC_POINT *points[], BN_CTX *ctx)
1528 {
1529 BN_CTX *new_ctx = NULL;
1530 BIGNUM *tmp0, *tmp1;
1531 size_t pow2 = 0;
1532 BIGNUM **heap = NULL;
1533 size_t i;
1534 int ret = 0;
1535
1536 if (num == 0)
1537 return 1;
1538
1539 if (ctx == NULL)
1540 {
1541 ctx = new_ctx = BN_CTX_new();
1542 if (ctx == NULL)
1543 return 0;
1544 }
1545
1546 BN_CTX_start(ctx);
1547 tmp0 = BN_CTX_get(ctx);
1548 tmp1 = BN_CTX_get(ctx);
1549 if (tmp0 == NULL || tmp1 == NULL) goto err;
1550
1551 /* Before converting the individual points, compute inverses of all Z values.
1552 * Modular inversion is rather slow, but luckily we can do with a single
1553 * explicit inversion, plus about 3 multiplications per input value.
1554 */
1555
1556 pow2 = 1;
1557 while (num > pow2)
1558 pow2 <<= 1;
1559 /* Now pow2 is the smallest power of 2 satifsying pow2 >= num.
1560 * We need twice that. */
1561 pow2 <<= 1;
1562
1563 heap = OPENSSL_malloc(pow2 * sizeof heap[0]);
1564 if (heap == NULL) goto err;
1565
1566 /* The array is used as a binary tree, exactly as in heapsort:
1567 *
1568 * heap[1]
1569 * heap[2] heap[3]
1570 * heap[4] heap[5] heap[6] heap[7]
1571 * heap[8]heap[9] heap[10]heap[11] heap[12]heap[13] heap[14] heap[15]
1572 *
1573 * We put the Z's in the last line;
1574 * then we set each other node to the product of its two child-nodes (where
1575 * empty or 0 entries are treated as ones);
1576 * then we invert heap[1];
1577 * then we invert each other node by replacing it by the product of its
1578 * parent (after inversion) and its sibling (before inversion).
1579 */
1580 heap[0] = NULL;
1581 for (i = pow2/2 - 1; i > 0; i--)
1582 heap[i] = NULL;
1583 for (i = 0; i < num; i++)
1584 heap[pow2/2 + i] = &points[i]->Z;
1585 for (i = pow2/2 + num; i < pow2; i++)
1586 heap[i] = NULL;
1587
1588 /* set each node to the product of its children */
1589 for (i = pow2/2 - 1; i > 0; i--)
1590 {
1591 heap[i] = BN_new();
1592 if (heap[i] == NULL) goto err;
1593
1594 if (heap[2*i] != NULL)
1595 {
1596 if ((heap[2*i + 1] == NULL) || BN_is_zero(heap[2*i + 1]))
1597 {
1598 if (!BN_copy(heap[i], heap[2*i])) goto err;
1599 }
1600 else
1601 {
1602 if (BN_is_zero(heap[2*i]))
1603 {
1604 if (!BN_copy(heap[i], heap[2*i + 1])) goto err;
1605 }
1606 else
1607 {
1608 if (!group->meth->field_mul(group, heap[i],
1609 heap[2*i], heap[2*i + 1], ctx)) goto err;
1610 }
1611 }
1612 }
1613 }
1614
1615 /* invert heap[1] */
1616 if (!BN_is_zero(heap[1]))
1617 {
1618 if (!BN_mod_inverse(heap[1], heap[1], &group->field, ctx))
1619 {
1620 ECerr(EC_F_EC_GFP_SIMPLE_POINTS_MAKE_AFFINE, ERR_R_BN_LIB);
1621 goto err;
1622 }
1623 }
1624 if (group->meth->field_encode != 0)
1625 {
1626 /* in the Montgomery case, we just turned R*H (representing H)
1627 * into 1/(R*H), but we need R*(1/H) (representing 1/H);
1628 * i.e. we have need to multiply by the Montgomery factor twice */
1629 if (!group->meth->field_encode(group, heap[1], heap[1], ctx)) goto err;
1630 if (!group->meth->field_encode(group, heap[1], heap[1], ctx)) goto err;
1631 }
1632
1633 /* set other heap[i]'s to their inverses */
1634 for (i = 2; i < pow2/2 + num; i += 2)
1635 {
1636 /* i is even */
1637 if ((heap[i + 1] != NULL) && !BN_is_zero(heap[i + 1]))
1638 {
1639 if (!group->meth->field_mul(group, tmp0, heap[i/2], heap[i + 1], ctx)) goto err;
1640 if (!group->meth->field_mul(group, tmp1, heap[i/2], heap[i], ctx)) goto err;
1641 if (!BN_copy(heap[i], tmp0)) goto err;
1642 if (!BN_copy(heap[i + 1], tmp1)) goto err;
1643 }
1644 else
1645 {
1646 if (!BN_copy(heap[i], heap[i/2])) goto err;
1647 }
1648 }
1649
1650 /* we have replaced all non-zero Z's by their inverses, now fix up all the points */
1651 for (i = 0; i < num; i++)
1652 {
1653 EC_POINT *p = points[i];
1654
1655 if (!BN_is_zero(&p->Z))
1656 {
1657 /* turn (X, Y, 1/Z) into (X/Z^2, Y/Z^3, 1) */
1658
1659 if (!group->meth->field_sqr(group, tmp1, &p->Z, ctx)) goto err;
1660 if (!group->meth->field_mul(group, &p->X, &p->X, tmp1, ctx)) goto err;
1661
1662 if (!group->meth->field_mul(group, tmp1, tmp1, &p->Z, ctx)) goto err;
1663 if (!group->meth->field_mul(group, &p->Y, &p->Y, tmp1, ctx)) goto err;
1664
1665 if (group->meth->field_set_to_one != 0)
1666 {
1667 if (!group->meth->field_set_to_one(group, &p->Z, ctx)) goto err;
1668 }
1669 else
1670 {
1671 if (!BN_one(&p->Z)) goto err;
1672 }
1673 p->Z_is_one = 1;
1674 }
1675 }
1676
1677 ret = 1;
1678
1679 err:
1680 BN_CTX_end(ctx);
1681 if (new_ctx != NULL)
1682 BN_CTX_free(new_ctx);
1683 if (heap != NULL)
1684 {
1685 /* heap[pow2/2] .. heap[pow2-1] have not been allocated locally! */
1686 for (i = pow2/2 - 1; i > 0; i--)
1687 {
1688 if (heap[i] != NULL)
1689 BN_clear_free(heap[i]);
1690 }
1691 OPENSSL_free(heap);
1692 }
1693 return ret;
1694 }
1695
1696
1697 int ec_GFp_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
1698 {
1699 return BN_mod_mul(r, a, b, &group->field, ctx);
1700 }
1701
1702
1703 int ec_GFp_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx)
1704 {
1705 return BN_mod_sqr(r, a, &group->field, ctx);
1706 }
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