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Change internals of the EC library so that the functions
[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 /* ====================================================================
5 * Copyright (c) 1998-2002 The OpenSSL Project. All rights reserved.
6 *
7 * Redistribution and use in source and binary forms, with or without
8 * modification, are permitted provided that the following conditions
9 * are met:
10 *
11 * 1. Redistributions of source code must retain the above copyright
12 * notice, this list of conditions and the following disclaimer.
13 *
14 * 2. Redistributions in binary form must reproduce the above copyright
15 * notice, this list of conditions and the following disclaimer in
16 * the documentation and/or other materials provided with the
17 * distribution.
18 *
19 * 3. All advertising materials mentioning features or use of this
20 * software must display the following acknowledgment:
21 * "This product includes software developed by the OpenSSL Project
22 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
23 *
24 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
25 * endorse or promote products derived from this software without
26 * prior written permission. For written permission, please contact
27 * openssl-core@openssl.org.
28 *
29 * 5. Products derived from this software may not be called "OpenSSL"
30 * nor may "OpenSSL" appear in their names without prior written
31 * permission of the OpenSSL Project.
32 *
33 * 6. Redistributions of any form whatsoever must retain the following
34 * acknowledgment:
35 * "This product includes software developed by the OpenSSL Project
36 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
37 *
38 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
39 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
40 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
41 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
42 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
43 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
44 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
45 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
46 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
47 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
48 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
49 * OF THE POSSIBILITY OF SUCH DAMAGE.
50 * ====================================================================
51 *
52 * This product includes cryptographic software written by Eric Young
53 * (eay@cryptsoft.com). This product includes software written by Tim
54 * Hudson (tjh@cryptsoft.com).
55 *
56 */
57
58 #include <openssl/err.h>
59
60 #include "ec_lcl.h"
61
62
63 const EC_METHOD *EC_GFp_simple_method(void)
64 {
65 static const EC_METHOD ret = {
66 ec_GFp_simple_group_init,
67 ec_GFp_simple_group_finish,
68 ec_GFp_simple_group_clear_finish,
69 ec_GFp_simple_group_copy,
70 ec_GFp_simple_group_set_curve_GFp,
71 ec_GFp_simple_group_get_curve_GFp,
72 ec_GFp_simple_group_check_discriminant,
73 ec_GFp_simple_point_init,
74 ec_GFp_simple_point_finish,
75 ec_GFp_simple_point_clear_finish,
76 ec_GFp_simple_point_copy,
77 ec_GFp_simple_point_set_to_infinity,
78 ec_GFp_simple_set_Jprojective_coordinates_GFp,
79 ec_GFp_simple_get_Jprojective_coordinates_GFp,
80 ec_GFp_simple_point_set_affine_coordinates_GFp,
81 ec_GFp_simple_point_get_affine_coordinates_GFp,
82 ec_GFp_simple_set_compressed_coordinates_GFp,
83 ec_GFp_simple_point2oct,
84 ec_GFp_simple_oct2point,
85 ec_GFp_simple_add,
86 ec_GFp_simple_dbl,
87 ec_GFp_simple_invert,
88 ec_GFp_simple_is_at_infinity,
89 ec_GFp_simple_is_on_curve,
90 ec_GFp_simple_cmp,
91 ec_GFp_simple_make_affine,
92 ec_GFp_simple_points_make_affine,
93 ec_GFp_simple_field_mul,
94 ec_GFp_simple_field_sqr,
95 0 /* field_encode */,
96 0 /* field_decode */,
97 0 /* field_set_to_one */ };
98
99 return &ret;
100 }
101
102
103 int ec_GFp_simple_group_init(EC_GROUP *group)
104 {
105 BN_init(&group->field);
106 BN_init(&group->a);
107 BN_init(&group->b);
108 group->a_is_minus3 = 0;
109 return 1;
110 }
111
112
113 void ec_GFp_simple_group_finish(EC_GROUP *group)
114 {
115 BN_free(&group->field);
116 BN_free(&group->a);
117 BN_free(&group->b);
118 }
119
120
121 void ec_GFp_simple_group_clear_finish(EC_GROUP *group)
122 {
123 BN_clear_free(&group->field);
124 BN_clear_free(&group->a);
125 BN_clear_free(&group->b);
126 }
127
128
129 int ec_GFp_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src)
130 {
131 if (!BN_copy(&dest->field, &src->field)) return 0;
132 if (!BN_copy(&dest->a, &src->a)) return 0;
133 if (!BN_copy(&dest->b, &src->b)) return 0;
134
135 dest->a_is_minus3 = src->a_is_minus3;
136
137 return 1;
138 }
139
140
141 int ec_GFp_simple_group_set_curve_GFp(EC_GROUP *group,
142 const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
143 {
144 int ret = 0;
145 BN_CTX *new_ctx = NULL;
146 BIGNUM *tmp_a;
147
148 /* p must be a prime > 3 */
149 if (BN_num_bits(p) <= 2 || !BN_is_odd(p))
150 {
151 ECerr(EC_F_EC_GFP_SIMPLE_GROUP_SET_CURVE_GFP, EC_R_INVALID_FIELD);
152 return 0;
153 }
154
155 if (ctx == NULL)
156 {
157 ctx = new_ctx = BN_CTX_new();
158 if (ctx == NULL)
159 return 0;
160 }
161
162 BN_CTX_start(ctx);
163 tmp_a = BN_CTX_get(ctx);
164 if (tmp_a == NULL) goto err;
165
166 /* group->field */
167 if (!BN_copy(&group->field, p)) goto err;
168 group->field.neg = 0;
169
170 /* group->a */
171 if (!BN_nnmod(tmp_a, a, p, ctx)) goto err;
172 if (group->meth->field_encode)
173 { if (!group->meth->field_encode(group, &group->a, tmp_a, ctx)) goto err; }
174 else
175 if (!BN_copy(&group->a, tmp_a)) goto err;
176
177 /* group->b */
178 if (!BN_nnmod(&group->b, b, p, ctx)) goto err;
179 if (group->meth->field_encode)
180 if (!group->meth->field_encode(group, &group->b, &group->b, ctx)) goto err;
181
182 /* group->a_is_minus3 */
183 if (!BN_add_word(tmp_a, 3)) goto err;
184 group->a_is_minus3 = (0 == BN_cmp(tmp_a, &group->field));
185
186 ret = 1;
187
188 err:
189 BN_CTX_end(ctx);
190 if (new_ctx != NULL)
191 BN_CTX_free(new_ctx);
192 return ret;
193 }
194
195
196 int ec_GFp_simple_group_get_curve_GFp(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx)
197 {
198 int ret = 0;
199 BN_CTX *new_ctx = NULL;
200
201 if (p != NULL)
202 {
203 if (!BN_copy(p, &group->field)) return 0;
204 }
205
206 if (a != NULL || b != NULL)
207 {
208 if (group->meth->field_decode)
209 {
210 if (ctx == NULL)
211 {
212 ctx = new_ctx = BN_CTX_new();
213 if (ctx == NULL)
214 return 0;
215 }
216 if (a != NULL)
217 {
218 if (!group->meth->field_decode(group, a, &group->a, ctx)) goto err;
219 }
220 if (b != NULL)
221 {
222 if (!group->meth->field_decode(group, b, &group->b, ctx)) goto err;
223 }
224 }
225 else
226 {
227 if (a != NULL)
228 {
229 if (!BN_copy(a, &group->a)) goto err;
230 }
231 if (b != NULL)
232 {
233 if (!BN_copy(b, &group->b)) goto err;
234 }
235 }
236 }
237
238 ret = 1;
239
240 err:
241 if (new_ctx)
242 BN_CTX_free(new_ctx);
243 return ret;
244 }
245
246
247 int ec_GFp_simple_group_check_discriminant(const EC_GROUP *group, BN_CTX *ctx)
248 {
249 int ret = 0;
250 BIGNUM *a,*b,*order,*tmp_1,*tmp_2;
251 const BIGNUM *p = &group->field;
252 BN_CTX *new_ctx = NULL;
253
254 if (ctx == NULL)
255 {
256 ctx = new_ctx = BN_CTX_new();
257 if (ctx == NULL)
258 {
259 ECerr(EC_F_EC_GFP_SIMPLE_GROUP_CHECK_DISCRIMINANT, ERR_R_MALLOC_FAILURE);
260 goto err;
261 }
262 }
263 BN_CTX_start(ctx);
264 a = BN_CTX_get(ctx);
265 b = BN_CTX_get(ctx);
266 tmp_1 = BN_CTX_get(ctx);
267 tmp_2 = BN_CTX_get(ctx);
268 order = BN_CTX_get(ctx);
269 if (order == NULL) goto err;
270
271 if (group->meth->field_decode)
272 {
273 if (!group->meth->field_decode(group, a, &group->a, ctx)) goto err;
274 if (!group->meth->field_decode(group, b, &group->b, ctx)) goto err;
275 }
276 else
277 {
278 if (!BN_copy(a, &group->a)) goto err;
279 if (!BN_copy(b, &group->b)) goto err;
280 }
281
282 /* check the discriminant:
283 * y^2 = x^3 + a*x + b is an elliptic curve <=> 4*a^3 + 27*b^2 != 0 (mod p)
284 * 0 =< a, b < p */
285 if (BN_is_zero(a))
286 {
287 if (BN_is_zero(b)) goto err;
288 }
289 else if (!BN_is_zero(b))
290 {
291 if (!BN_mod_sqr(tmp_1, a, p, ctx)) goto err;
292 if (!BN_mod_mul(tmp_2, tmp_1, a, p, ctx)) goto err;
293 if (!BN_lshift(tmp_1, tmp_2, 2)) goto err;
294 /* tmp_1 = 4*a^3 */
295
296 if (!BN_mod_sqr(tmp_2, b, p, ctx)) goto err;
297 if (!BN_mul_word(tmp_2, 27)) goto err;
298 /* tmp_2 = 27*b^2 */
299
300 if (!BN_mod_add(a, tmp_1, tmp_2, p, ctx)) goto err;
301 if (BN_is_zero(a)) goto err;
302 }
303 ret = 1;
304
305 err:
306 BN_CTX_end(ctx);
307 if (new_ctx != NULL)
308 BN_CTX_free(new_ctx);
309 return ret;
310 }
311
312
313 int ec_GFp_simple_point_init(EC_POINT *point)
314 {
315 BN_init(&point->X);
316 BN_init(&point->Y);
317 BN_init(&point->Z);
318 point->Z_is_one = 0;
319
320 return 1;
321 }
322
323
324 void ec_GFp_simple_point_finish(EC_POINT *point)
325 {
326 BN_free(&point->X);
327 BN_free(&point->Y);
328 BN_free(&point->Z);
329 }
330
331
332 void ec_GFp_simple_point_clear_finish(EC_POINT *point)
333 {
334 BN_clear_free(&point->X);
335 BN_clear_free(&point->Y);
336 BN_clear_free(&point->Z);
337 point->Z_is_one = 0;
338 }
339
340
341 int ec_GFp_simple_point_copy(EC_POINT *dest, const EC_POINT *src)
342 {
343 if (!BN_copy(&dest->X, &src->X)) return 0;
344 if (!BN_copy(&dest->Y, &src->Y)) return 0;
345 if (!BN_copy(&dest->Z, &src->Z)) return 0;
346 dest->Z_is_one = src->Z_is_one;
347
348 return 1;
349 }
350
351
352 int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *group, EC_POINT *point)
353 {
354 point->Z_is_one = 0;
355 return (BN_zero(&point->Z));
356 }
357
358
359 int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *group, EC_POINT *point,
360 const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *ctx)
361 {
362 BN_CTX *new_ctx = NULL;
363 int ret = 0;
364
365 if (ctx == NULL)
366 {
367 ctx = new_ctx = BN_CTX_new();
368 if (ctx == NULL)
369 return 0;
370 }
371
372 if (x != NULL)
373 {
374 if (!BN_nnmod(&point->X, x, &group->field, ctx)) goto err;
375 if (group->meth->field_encode)
376 {
377 if (!group->meth->field_encode(group, &point->X, &point->X, ctx)) goto err;
378 }
379 }
380
381 if (y != NULL)
382 {
383 if (!BN_nnmod(&point->Y, y, &group->field, ctx)) goto err;
384 if (group->meth->field_encode)
385 {
386 if (!group->meth->field_encode(group, &point->Y, &point->Y, ctx)) goto err;
387 }
388 }
389
390 if (z != NULL)
391 {
392 int Z_is_one;
393
394 if (!BN_nnmod(&point->Z, z, &group->field, ctx)) goto err;
395 Z_is_one = BN_is_one(&point->Z);
396 if (group->meth->field_encode)
397 {
398 if (Z_is_one && (group->meth->field_set_to_one != 0))
399 {
400 if (!group->meth->field_set_to_one(group, &point->Z, ctx)) goto err;
401 }
402 else
403 {
404 if (!group->meth->field_encode(group, &point->Z, &point->Z, ctx)) goto err;
405 }
406 }
407 point->Z_is_one = Z_is_one;
408 }
409
410 ret = 1;
411
412 err:
413 if (new_ctx != NULL)
414 BN_CTX_free(new_ctx);
415 return ret;
416 }
417
418
419 int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *group, const EC_POINT *point,
420 BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *ctx)
421 {
422 BN_CTX *new_ctx = NULL;
423 int ret = 0;
424
425 if (group->meth->field_decode != 0)
426 {
427 if (ctx == NULL)
428 {
429 ctx = new_ctx = BN_CTX_new();
430 if (ctx == NULL)
431 return 0;
432 }
433
434 if (x != NULL)
435 {
436 if (!group->meth->field_decode(group, x, &point->X, ctx)) goto err;
437 }
438 if (y != NULL)
439 {
440 if (!group->meth->field_decode(group, y, &point->Y, ctx)) goto err;
441 }
442 if (z != NULL)
443 {
444 if (!group->meth->field_decode(group, z, &point->Z, ctx)) goto err;
445 }
446 }
447 else
448 {
449 if (x != NULL)
450 {
451 if (!BN_copy(x, &point->X)) goto err;
452 }
453 if (y != NULL)
454 {
455 if (!BN_copy(y, &point->Y)) goto err;
456 }
457 if (z != NULL)
458 {
459 if (!BN_copy(z, &point->Z)) goto err;
460 }
461 }
462
463 ret = 1;
464
465 err:
466 if (new_ctx != NULL)
467 BN_CTX_free(new_ctx);
468 return ret;
469 }
470
471
472 int ec_GFp_simple_point_set_affine_coordinates_GFp(const EC_GROUP *group, EC_POINT *point,
473 const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx)
474 {
475 if (x == NULL || y == NULL)
476 {
477 /* unlike for projective coordinates, we do not tolerate this */
478 ECerr(EC_F_EC_GFP_SIMPLE_POINT_SET_AFFINE_COORDINATES_GFP, ERR_R_PASSED_NULL_PARAMETER);
479 return 0;
480 }
481
482 return EC_POINT_set_Jprojective_coordinates_GFp(group, point, x, y, BN_value_one(), ctx);
483 }
484
485
486 int ec_GFp_simple_point_get_affine_coordinates_GFp(const EC_GROUP *group, const EC_POINT *point,
487 BIGNUM *x, BIGNUM *y, BN_CTX *ctx)
488 {
489 BN_CTX *new_ctx = NULL;
490 BIGNUM *X, *Y, *Z, *Z_1, *Z_2, *Z_3;
491 const BIGNUM *X_, *Y_, *Z_;
492 int ret = 0;
493
494 if (EC_POINT_is_at_infinity(group, point))
495 {
496 ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES_GFP, EC_R_POINT_AT_INFINITY);
497 return 0;
498 }
499
500 if (ctx == NULL)
501 {
502 ctx = new_ctx = BN_CTX_new();
503 if (ctx == NULL)
504 return 0;
505 }
506
507 BN_CTX_start(ctx);
508 X = BN_CTX_get(ctx);
509 Y = BN_CTX_get(ctx);
510 Z = BN_CTX_get(ctx);
511 Z_1 = BN_CTX_get(ctx);
512 Z_2 = BN_CTX_get(ctx);
513 Z_3 = BN_CTX_get(ctx);
514 if (Z_3 == NULL) goto err;
515
516 /* transform (X, Y, Z) into (x, y) := (X/Z^2, Y/Z^3) */
517
518 if (group->meth->field_decode)
519 {
520 if (!group->meth->field_decode(group, X, &point->X, ctx)) goto err;
521 if (!group->meth->field_decode(group, Y, &point->Y, ctx)) goto err;
522 if (!group->meth->field_decode(group, Z, &point->Z, ctx)) goto err;
523 X_ = X; Y_ = Y; Z_ = Z;
524 }
525 else
526 {
527 X_ = &point->X;
528 Y_ = &point->Y;
529 Z_ = &point->Z;
530 }
531
532 if (BN_is_one(Z_))
533 {
534 if (x != NULL)
535 {
536 if (!BN_copy(x, X_)) goto err;
537 }
538 if (y != NULL)
539 {
540 if (!BN_copy(y, Y_)) goto err;
541 }
542 }
543 else
544 {
545 if (!BN_mod_inverse(Z_1, Z_, &group->field, ctx))
546 {
547 ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES_GFP, ERR_R_BN_LIB);
548 goto err;
549 }
550
551 if (group->meth->field_encode == 0)
552 {
553 /* field_sqr works on standard representation */
554 if (!group->meth->field_sqr(group, Z_2, Z_1, ctx)) goto err;
555 }
556 else
557 {
558 if (!BN_mod_sqr(Z_2, Z_1, &group->field, ctx)) goto err;
559 }
560
561 if (x != NULL)
562 {
563 if (group->meth->field_encode == 0)
564 {
565 /* field_mul works on standard representation */
566 if (!group->meth->field_mul(group, x, X_, Z_2, ctx)) goto err;
567 }
568 else
569 {
570 if (!BN_mod_mul(x, X_, Z_2, &group->field, ctx)) goto err;
571 }
572 }
573
574 if (y != NULL)
575 {
576 if (group->meth->field_encode == 0)
577 {
578 /* field_mul works on standard representation */
579 if (!group->meth->field_mul(group, Z_3, Z_2, Z_1, ctx)) goto err;
580 if (!group->meth->field_mul(group, y, Y_, Z_3, ctx)) goto err;
581
582 }
583 else
584 {
585 if (!BN_mod_mul(Z_3, Z_2, Z_1, &group->field, ctx)) goto err;
586 if (!BN_mod_mul(y, Y_, Z_3, &group->field, ctx)) goto err;
587 }
588 }
589 }
590
591 ret = 1;
592
593 err:
594 BN_CTX_end(ctx);
595 if (new_ctx != NULL)
596 BN_CTX_free(new_ctx);
597 return ret;
598 }
599
600
601 int ec_GFp_simple_set_compressed_coordinates_GFp(const EC_GROUP *group, EC_POINT *point,
602 const BIGNUM *x_, int y_bit, BN_CTX *ctx)
603 {
604 BN_CTX *new_ctx = NULL;
605 BIGNUM *tmp1, *tmp2, *x, *y;
606 int ret = 0;
607
608 if (ctx == NULL)
609 {
610 ctx = new_ctx = BN_CTX_new();
611 if (ctx == NULL)
612 return 0;
613 }
614
615 y_bit = (y_bit != 0);
616
617 BN_CTX_start(ctx);
618 tmp1 = BN_CTX_get(ctx);
619 tmp2 = BN_CTX_get(ctx);
620 x = BN_CTX_get(ctx);
621 y = BN_CTX_get(ctx);
622 if (y == NULL) goto err;
623
624 /* Recover y. We have a Weierstrass equation
625 * y^2 = x^3 + a*x + b,
626 * so y is one of the square roots of x^3 + a*x + b.
627 */
628
629 /* tmp1 := x^3 */
630 if (!BN_nnmod(x, x_, &group->field,ctx)) goto err;
631 if (group->meth->field_decode == 0)
632 {
633 /* field_{sqr,mul} work on standard representation */
634 if (!group->meth->field_sqr(group, tmp2, x_, ctx)) goto err;
635 if (!group->meth->field_mul(group, tmp1, tmp2, x_, ctx)) goto err;
636 }
637 else
638 {
639 if (!BN_mod_sqr(tmp2, x_, &group->field, ctx)) goto err;
640 if (!BN_mod_mul(tmp1, tmp2, x_, &group->field, ctx)) goto err;
641 }
642
643 /* tmp1 := tmp1 + a*x */
644 if (group->a_is_minus3)
645 {
646 if (!BN_mod_lshift1_quick(tmp2, x, &group->field)) goto err;
647 if (!BN_mod_add_quick(tmp2, tmp2, x, &group->field)) goto err;
648 if (!BN_mod_sub_quick(tmp1, tmp1, tmp2, &group->field)) goto err;
649 }
650 else
651 {
652 if (group->meth->field_decode)
653 {
654 if (!group->meth->field_decode(group, tmp2, &group->a, ctx)) goto err;
655 if (!BN_mod_mul(tmp2, tmp2, x, &group->field, ctx)) goto err;
656 }
657 else
658 {
659 /* field_mul works on standard representation */
660 if (!group->meth->field_mul(group, tmp2, &group->a, x, ctx)) goto err;
661 }
662
663 if (!BN_mod_add_quick(tmp1, tmp1, tmp2, &group->field)) goto err;
664 }
665
666 /* tmp1 := tmp1 + b */
667 if (group->meth->field_decode)
668 {
669 if (!group->meth->field_decode(group, tmp2, &group->b, ctx)) goto err;
670 if (!BN_mod_add_quick(tmp1, tmp1, tmp2, &group->field)) goto err;
671 }
672 else
673 {
674 if (!BN_mod_add_quick(tmp1, tmp1, &group->b, &group->field)) goto err;
675 }
676
677 if (!BN_mod_sqrt(y, tmp1, &group->field, ctx))
678 {
679 unsigned long err = ERR_peek_error();
680
681 if (ERR_GET_LIB(err) == ERR_LIB_BN && ERR_GET_REASON(err) == BN_R_NOT_A_SQUARE)
682 {
683 (void)ERR_get_error();
684 ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES_GFP, EC_R_INVALID_COMPRESSED_POINT);
685 }
686 else
687 ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES_GFP, ERR_R_BN_LIB);
688 goto err;
689 }
690 /* If tmp1 is not a square (i.e. there is no point on the curve with
691 * our x), then y now is a nonsense value too */
692
693 if (y_bit != BN_is_odd(y))
694 {
695 if (BN_is_zero(y))
696 {
697 int kron;
698
699 kron = BN_kronecker(x, &group->field, ctx);
700 if (kron == -2) goto err;
701
702 if (kron == 1)
703 ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES_GFP, EC_R_INVALID_COMPRESSION_BIT);
704 else
705 ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES_GFP, EC_R_INVALID_COMPRESSED_POINT);
706 goto err;
707 }
708 if (!BN_usub(y, &group->field, y)) goto err;
709 }
710 if (y_bit != BN_is_odd(y))
711 {
712 ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES_GFP, ERR_R_INTERNAL_ERROR);
713 goto err;
714 }
715
716 if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
717
718 ret = 1;
719
720 err:
721 BN_CTX_end(ctx);
722 if (new_ctx != NULL)
723 BN_CTX_free(new_ctx);
724 return ret;
725 }
726
727
728 size_t ec_GFp_simple_point2oct(const EC_GROUP *group, const EC_POINT *point, point_conversion_form_t form,
729 unsigned char *buf, size_t len, BN_CTX *ctx)
730 {
731 size_t ret;
732 BN_CTX *new_ctx = NULL;
733 int used_ctx = 0;
734 BIGNUM *x, *y;
735 size_t field_len, i, skip;
736
737 if ((form != POINT_CONVERSION_COMPRESSED)
738 && (form != POINT_CONVERSION_UNCOMPRESSED)
739 && (form != POINT_CONVERSION_HYBRID))
740 {
741 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_INVALID_FORM);
742 goto err;
743 }
744
745 if (EC_POINT_is_at_infinity(group, point))
746 {
747 /* encodes to a single 0 octet */
748 if (buf != NULL)
749 {
750 if (len < 1)
751 {
752 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);
753 return 0;
754 }
755 buf[0] = 0;
756 }
757 return 1;
758 }
759
760
761 /* ret := required output buffer length */
762 field_len = BN_num_bytes(&group->field);
763 ret = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len;
764
765 /* if 'buf' is NULL, just return required length */
766 if (buf != NULL)
767 {
768 if (len < ret)
769 {
770 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);
771 goto err;
772 }
773
774 if (ctx == NULL)
775 {
776 ctx = new_ctx = BN_CTX_new();
777 if (ctx == NULL)
778 return 0;
779 }
780
781 BN_CTX_start(ctx);
782 used_ctx = 1;
783 x = BN_CTX_get(ctx);
784 y = BN_CTX_get(ctx);
785 if (y == NULL) goto err;
786
787 if (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
788
789 if ((form == POINT_CONVERSION_COMPRESSED || form == POINT_CONVERSION_HYBRID) && BN_is_odd(y))
790 buf[0] = form + 1;
791 else
792 buf[0] = form;
793
794 i = 1;
795
796 skip = field_len - BN_num_bytes(x);
797 if (skip > field_len)
798 {
799 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
800 goto err;
801 }
802 while (skip > 0)
803 {
804 buf[i++] = 0;
805 skip--;
806 }
807 skip = BN_bn2bin(x, buf + i);
808 i += skip;
809 if (i != 1 + field_len)
810 {
811 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
812 goto err;
813 }
814
815 if (form == POINT_CONVERSION_UNCOMPRESSED || form == POINT_CONVERSION_HYBRID)
816 {
817 skip = field_len - BN_num_bytes(y);
818 if (skip > field_len)
819 {
820 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
821 goto err;
822 }
823 while (skip > 0)
824 {
825 buf[i++] = 0;
826 skip--;
827 }
828 skip = BN_bn2bin(y, buf + i);
829 i += skip;
830 }
831
832 if (i != ret)
833 {
834 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
835 goto err;
836 }
837 }
838
839 if (used_ctx)
840 BN_CTX_end(ctx);
841 if (new_ctx != NULL)
842 BN_CTX_free(new_ctx);
843 return ret;
844
845 err:
846 if (used_ctx)
847 BN_CTX_end(ctx);
848 if (new_ctx != NULL)
849 BN_CTX_free(new_ctx);
850 return 0;
851 }
852
853
854 int ec_GFp_simple_oct2point(const EC_GROUP *group, EC_POINT *point,
855 const unsigned char *buf, size_t len, BN_CTX *ctx)
856 {
857 point_conversion_form_t form;
858 int y_bit;
859 BN_CTX *new_ctx = NULL;
860 BIGNUM *x, *y;
861 size_t field_len, enc_len;
862 int ret = 0;
863
864 if (len == 0)
865 {
866 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_BUFFER_TOO_SMALL);
867 return 0;
868 }
869 form = buf[0];
870 y_bit = form & 1;
871 form = form & ~1;
872 if ((form != 0) && (form != POINT_CONVERSION_COMPRESSED)
873 && (form != POINT_CONVERSION_UNCOMPRESSED)
874 && (form != POINT_CONVERSION_HYBRID))
875 {
876 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
877 return 0;
878 }
879 if ((form == 0 || form == POINT_CONVERSION_UNCOMPRESSED) && y_bit)
880 {
881 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
882 return 0;
883 }
884
885 if (form == 0)
886 {
887 if (len != 1)
888 {
889 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
890 return 0;
891 }
892
893 return EC_POINT_set_to_infinity(group, point);
894 }
895
896 field_len = BN_num_bytes(&group->field);
897 enc_len = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len;
898
899 if (len != enc_len)
900 {
901 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
902 return 0;
903 }
904
905 if (ctx == NULL)
906 {
907 ctx = new_ctx = BN_CTX_new();
908 if (ctx == NULL)
909 return 0;
910 }
911
912 BN_CTX_start(ctx);
913 x = BN_CTX_get(ctx);
914 y = BN_CTX_get(ctx);
915 if (y == NULL) goto err;
916
917 if (!BN_bin2bn(buf + 1, field_len, x)) goto err;
918 if (BN_ucmp(x, &group->field) >= 0)
919 {
920 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
921 goto err;
922 }
923
924 if (form == POINT_CONVERSION_COMPRESSED)
925 {
926 if (!EC_POINT_set_compressed_coordinates_GFp(group, point, x, y_bit, ctx)) goto err;
927 }
928 else
929 {
930 if (!BN_bin2bn(buf + 1 + field_len, field_len, y)) goto err;
931 if (BN_ucmp(y, &group->field) >= 0)
932 {
933 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
934 goto err;
935 }
936 if (form == POINT_CONVERSION_HYBRID)
937 {
938 if (y_bit != BN_is_odd(y))
939 {
940 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
941 goto err;
942 }
943 }
944
945 if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
946 }
947
948 if (!EC_POINT_is_on_curve(group, point, ctx)) /* test required by X9.62 */
949 {
950 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_POINT_IS_NOT_ON_CURVE);
951 goto err;
952 }
953
954 ret = 1;
955
956 err:
957 BN_CTX_end(ctx);
958 if (new_ctx != NULL)
959 BN_CTX_free(new_ctx);
960 return ret;
961 }
962
963
964 int ec_GFp_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
965 {
966 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
967 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
968 const BIGNUM *p;
969 BN_CTX *new_ctx = NULL;
970 BIGNUM *n0, *n1, *n2, *n3, *n4, *n5, *n6;
971 int ret = 0;
972
973 if (a == b)
974 return EC_POINT_dbl(group, r, a, ctx);
975 if (EC_POINT_is_at_infinity(group, a))
976 return EC_POINT_copy(r, b);
977 if (EC_POINT_is_at_infinity(group, b))
978 return EC_POINT_copy(r, a);
979
980 field_mul = group->meth->field_mul;
981 field_sqr = group->meth->field_sqr;
982 p = &group->field;
983
984 if (ctx == NULL)
985 {
986 ctx = new_ctx = BN_CTX_new();
987 if (ctx == NULL)
988 return 0;
989 }
990
991 BN_CTX_start(ctx);
992 n0 = BN_CTX_get(ctx);
993 n1 = BN_CTX_get(ctx);
994 n2 = BN_CTX_get(ctx);
995 n3 = BN_CTX_get(ctx);
996 n4 = BN_CTX_get(ctx);
997 n5 = BN_CTX_get(ctx);
998 n6 = BN_CTX_get(ctx);
999 if (n6 == NULL) goto end;
1000
1001 /* Note that in this function we must not read components of 'a' or 'b'
1002 * once we have written the corresponding components of 'r'.
1003 * ('r' might be one of 'a' or 'b'.)
1004 */
1005
1006 /* n1, n2 */
1007 if (b->Z_is_one)
1008 {
1009 if (!BN_copy(n1, &a->X)) goto end;
1010 if (!BN_copy(n2, &a->Y)) goto end;
1011 /* n1 = X_a */
1012 /* n2 = Y_a */
1013 }
1014 else
1015 {
1016 if (!field_sqr(group, n0, &b->Z, ctx)) goto end;
1017 if (!field_mul(group, n1, &a->X, n0, ctx)) goto end;
1018 /* n1 = X_a * Z_b^2 */
1019
1020 if (!field_mul(group, n0, n0, &b->Z, ctx)) goto end;
1021 if (!field_mul(group, n2, &a->Y, n0, ctx)) goto end;
1022 /* n2 = Y_a * Z_b^3 */
1023 }
1024
1025 /* n3, n4 */
1026 if (a->Z_is_one)
1027 {
1028 if (!BN_copy(n3, &b->X)) goto end;
1029 if (!BN_copy(n4, &b->Y)) goto end;
1030 /* n3 = X_b */
1031 /* n4 = Y_b */
1032 }
1033 else
1034 {
1035 if (!field_sqr(group, n0, &a->Z, ctx)) goto end;
1036 if (!field_mul(group, n3, &b->X, n0, ctx)) goto end;
1037 /* n3 = X_b * Z_a^2 */
1038
1039 if (!field_mul(group, n0, n0, &a->Z, ctx)) goto end;
1040 if (!field_mul(group, n4, &b->Y, n0, ctx)) goto end;
1041 /* n4 = Y_b * Z_a^3 */
1042 }
1043
1044 /* n5, n6 */
1045 if (!BN_mod_sub_quick(n5, n1, n3, p)) goto end;
1046 if (!BN_mod_sub_quick(n6, n2, n4, p)) goto end;
1047 /* n5 = n1 - n3 */
1048 /* n6 = n2 - n4 */
1049
1050 if (BN_is_zero(n5))
1051 {
1052 if (BN_is_zero(n6))
1053 {
1054 /* a is the same point as b */
1055 BN_CTX_end(ctx);
1056 ret = EC_POINT_dbl(group, r, a, ctx);
1057 ctx = NULL;
1058 goto end;
1059 }
1060 else
1061 {
1062 /* a is the inverse of b */
1063 if (!BN_zero(&r->Z)) goto end;
1064 r->Z_is_one = 0;
1065 ret = 1;
1066 goto end;
1067 }
1068 }
1069
1070 /* 'n7', 'n8' */
1071 if (!BN_mod_add_quick(n1, n1, n3, p)) goto end;
1072 if (!BN_mod_add_quick(n2, n2, n4, p)) goto end;
1073 /* 'n7' = n1 + n3 */
1074 /* 'n8' = n2 + n4 */
1075
1076 /* Z_r */
1077 if (a->Z_is_one && b->Z_is_one)
1078 {
1079 if (!BN_copy(&r->Z, n5)) goto end;
1080 }
1081 else
1082 {
1083 if (a->Z_is_one)
1084 { if (!BN_copy(n0, &b->Z)) goto end; }
1085 else if (b->Z_is_one)
1086 { if (!BN_copy(n0, &a->Z)) goto end; }
1087 else
1088 { if (!field_mul(group, n0, &a->Z, &b->Z, ctx)) goto end; }
1089 if (!field_mul(group, &r->Z, n0, n5, ctx)) goto end;
1090 }
1091 r->Z_is_one = 0;
1092 /* Z_r = Z_a * Z_b * n5 */
1093
1094 /* X_r */
1095 if (!field_sqr(group, n0, n6, ctx)) goto end;
1096 if (!field_sqr(group, n4, n5, ctx)) goto end;
1097 if (!field_mul(group, n3, n1, n4, ctx)) goto end;
1098 if (!BN_mod_sub_quick(&r->X, n0, n3, p)) goto end;
1099 /* X_r = n6^2 - n5^2 * 'n7' */
1100
1101 /* 'n9' */
1102 if (!BN_mod_lshift1_quick(n0, &r->X, p)) goto end;
1103 if (!BN_mod_sub_quick(n0, n3, n0, p)) goto end;
1104 /* n9 = n5^2 * 'n7' - 2 * X_r */
1105
1106 /* Y_r */
1107 if (!field_mul(group, n0, n0, n6, ctx)) goto end;
1108 if (!field_mul(group, n5, n4, n5, ctx)) goto end; /* now n5 is n5^3 */
1109 if (!field_mul(group, n1, n2, n5, ctx)) goto end;
1110 if (!BN_mod_sub_quick(n0, n0, n1, p)) goto end;
1111 if (BN_is_odd(n0))
1112 if (!BN_add(n0, n0, p)) goto end;
1113 /* now 0 <= n0 < 2*p, and n0 is even */
1114 if (!BN_rshift1(&r->Y, n0)) goto end;
1115 /* Y_r = (n6 * 'n9' - 'n8' * 'n5^3') / 2 */
1116
1117 ret = 1;
1118
1119 end:
1120 if (ctx) /* otherwise we already called BN_CTX_end */
1121 BN_CTX_end(ctx);
1122 if (new_ctx != NULL)
1123 BN_CTX_free(new_ctx);
1124 return ret;
1125 }
1126
1127
1128 int ec_GFp_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_CTX *ctx)
1129 {
1130 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
1131 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
1132 const BIGNUM *p;
1133 BN_CTX *new_ctx = NULL;
1134 BIGNUM *n0, *n1, *n2, *n3;
1135 int ret = 0;
1136
1137 if (EC_POINT_is_at_infinity(group, a))
1138 {
1139 if (!BN_zero(&r->Z)) return 0;
1140 r->Z_is_one = 0;
1141 return 1;
1142 }
1143
1144 field_mul = group->meth->field_mul;
1145 field_sqr = group->meth->field_sqr;
1146 p = &group->field;
1147
1148 if (ctx == NULL)
1149 {
1150 ctx = new_ctx = BN_CTX_new();
1151 if (ctx == NULL)
1152 return 0;
1153 }
1154
1155 BN_CTX_start(ctx);
1156 n0 = BN_CTX_get(ctx);
1157 n1 = BN_CTX_get(ctx);
1158 n2 = BN_CTX_get(ctx);
1159 n3 = BN_CTX_get(ctx);
1160 if (n3 == NULL) goto err;
1161
1162 /* Note that in this function we must not read components of 'a'
1163 * once we have written the corresponding components of 'r'.
1164 * ('r' might the same as 'a'.)
1165 */
1166
1167 /* n1 */
1168 if (a->Z_is_one)
1169 {
1170 if (!field_sqr(group, n0, &a->X, ctx)) goto err;
1171 if (!BN_mod_lshift1_quick(n1, n0, p)) goto err;
1172 if (!BN_mod_add_quick(n0, n0, n1, p)) goto err;
1173 if (!BN_mod_add_quick(n1, n0, &group->a, p)) goto err;
1174 /* n1 = 3 * X_a^2 + a_curve */
1175 }
1176 else if (group->a_is_minus3)
1177 {
1178 if (!field_sqr(group, n1, &a->Z, ctx)) goto err;
1179 if (!BN_mod_add_quick(n0, &a->X, n1, p)) goto err;
1180 if (!BN_mod_sub_quick(n2, &a->X, n1, p)) goto err;
1181 if (!field_mul(group, n1, n0, n2, ctx)) goto err;
1182 if (!BN_mod_lshift1_quick(n0, n1, p)) goto err;
1183 if (!BN_mod_add_quick(n1, n0, n1, p)) goto err;
1184 /* n1 = 3 * (X_a + Z_a^2) * (X_a - Z_a^2)
1185 * = 3 * X_a^2 - 3 * Z_a^4 */
1186 }
1187 else
1188 {
1189 if (!field_sqr(group, n0, &a->X, ctx)) goto err;
1190 if (!BN_mod_lshift1_quick(n1, n0, p)) goto err;
1191 if (!BN_mod_add_quick(n0, n0, n1, p)) goto err;
1192 if (!field_sqr(group, n1, &a->Z, ctx)) goto err;
1193 if (!field_sqr(group, n1, n1, ctx)) goto err;
1194 if (!field_mul(group, n1, n1, &group->a, ctx)) goto err;
1195 if (!BN_mod_add_quick(n1, n1, n0, p)) goto err;
1196 /* n1 = 3 * X_a^2 + a_curve * Z_a^4 */
1197 }
1198
1199 /* Z_r */
1200 if (a->Z_is_one)
1201 {
1202 if (!BN_copy(n0, &a->Y)) goto err;
1203 }
1204 else
1205 {
1206 if (!field_mul(group, n0, &a->Y, &a->Z, ctx)) goto err;
1207 }
1208 if (!BN_mod_lshift1_quick(&r->Z, n0, p)) goto err;
1209 r->Z_is_one = 0;
1210 /* Z_r = 2 * Y_a * Z_a */
1211
1212 /* n2 */
1213 if (!field_sqr(group, n3, &a->Y, ctx)) goto err;
1214 if (!field_mul(group, n2, &a->X, n3, ctx)) goto err;
1215 if (!BN_mod_lshift_quick(n2, n2, 2, p)) goto err;
1216 /* n2 = 4 * X_a * Y_a^2 */
1217
1218 /* X_r */
1219 if (!BN_mod_lshift1_quick(n0, n2, p)) goto err;
1220 if (!field_sqr(group, &r->X, n1, ctx)) goto err;
1221 if (!BN_mod_sub_quick(&r->X, &r->X, n0, p)) goto err;
1222 /* X_r = n1^2 - 2 * n2 */
1223
1224 /* n3 */
1225 if (!field_sqr(group, n0, n3, ctx)) goto err;
1226 if (!BN_mod_lshift_quick(n3, n0, 3, p)) goto err;
1227 /* n3 = 8 * Y_a^4 */
1228
1229 /* Y_r */
1230 if (!BN_mod_sub_quick(n0, n2, &r->X, p)) goto err;
1231 if (!field_mul(group, n0, n1, n0, ctx)) goto err;
1232 if (!BN_mod_sub_quick(&r->Y, n0, n3, p)) goto err;
1233 /* Y_r = n1 * (n2 - X_r) - n3 */
1234
1235 ret = 1;
1236
1237 err:
1238 BN_CTX_end(ctx);
1239 if (new_ctx != NULL)
1240 BN_CTX_free(new_ctx);
1241 return ret;
1242 }
1243
1244
1245 int ec_GFp_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
1246 {
1247 if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(&point->Y))
1248 /* point is its own inverse */
1249 return 1;
1250
1251 return BN_usub(&point->Y, &group->field, &point->Y);
1252 }
1253
1254
1255 int ec_GFp_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point)
1256 {
1257 return BN_is_zero(&point->Z);
1258 }
1259
1260
1261 int ec_GFp_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx)
1262 {
1263 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
1264 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
1265 const BIGNUM *p;
1266 BN_CTX *new_ctx = NULL;
1267 BIGNUM *rh, *tmp1, *tmp2, *Z4, *Z6;
1268 int ret = -1;
1269
1270 if (EC_POINT_is_at_infinity(group, point))
1271 return 1;
1272
1273 field_mul = group->meth->field_mul;
1274 field_sqr = group->meth->field_sqr;
1275 p = &group->field;
1276
1277 if (ctx == NULL)
1278 {
1279 ctx = new_ctx = BN_CTX_new();
1280 if (ctx == NULL)
1281 return -1;
1282 }
1283
1284 BN_CTX_start(ctx);
1285 rh = BN_CTX_get(ctx);
1286 tmp1 = BN_CTX_get(ctx);
1287 tmp2 = BN_CTX_get(ctx);
1288 Z4 = BN_CTX_get(ctx);
1289 Z6 = BN_CTX_get(ctx);
1290 if (Z6 == NULL) goto err;
1291
1292 /* We have a curve defined by a Weierstrass equation
1293 * y^2 = x^3 + a*x + b.
1294 * The point to consider is given in Jacobian projective coordinates
1295 * where (X, Y, Z) represents (x, y) = (X/Z^2, Y/Z^3).
1296 * Substituting this and multiplying by Z^6 transforms the above equation into
1297 * Y^2 = X^3 + a*X*Z^4 + b*Z^6.
1298 * To test this, we add up the right-hand side in 'rh'.
1299 */
1300
1301 /* rh := X^3 */
1302 if (!field_sqr(group, rh, &point->X, ctx)) goto err;
1303 if (!field_mul(group, rh, rh, &point->X, ctx)) goto err;
1304
1305 if (!point->Z_is_one)
1306 {
1307 if (!field_sqr(group, tmp1, &point->Z, ctx)) goto err;
1308 if (!field_sqr(group, Z4, tmp1, ctx)) goto err;
1309 if (!field_mul(group, Z6, Z4, tmp1, ctx)) goto err;
1310
1311 /* rh := rh + a*X*Z^4 */
1312 if (!field_mul(group, tmp1, &point->X, Z4, ctx)) goto err;
1313 if (group->a_is_minus3)
1314 {
1315 if (!BN_mod_lshift1_quick(tmp2, tmp1, p)) goto err;
1316 if (!BN_mod_add_quick(tmp2, tmp2, tmp1, p)) goto err;
1317 if (!BN_mod_sub_quick(rh, rh, tmp2, p)) goto err;
1318 }
1319 else
1320 {
1321 if (!field_mul(group, tmp2, tmp1, &group->a, ctx)) goto err;
1322 if (!BN_mod_add_quick(rh, rh, tmp2, p)) goto err;
1323 }
1324
1325 /* rh := rh + b*Z^6 */
1326 if (!field_mul(group, tmp1, &group->b, Z6, ctx)) goto err;
1327 if (!BN_mod_add_quick(rh, rh, tmp1, p)) goto err;
1328 }
1329 else
1330 {
1331 /* point->Z_is_one */
1332
1333 /* rh := rh + a*X */
1334 if (group->a_is_minus3)
1335 {
1336 if (!BN_mod_lshift1_quick(tmp2, &point->X, p)) goto err;
1337 if (!BN_mod_add_quick(tmp2, tmp2, &point->X, p)) goto err;
1338 if (!BN_mod_sub_quick(rh, rh, tmp2, p)) goto err;
1339 }
1340 else
1341 {
1342 if (!field_mul(group, tmp2, &point->X, &group->a, ctx)) goto err;
1343 if (!BN_mod_add_quick(rh, rh, tmp2, p)) goto err;
1344 }
1345
1346 /* rh := rh + b */
1347 if (!BN_mod_add_quick(rh, rh, &group->b, p)) goto err;
1348 }
1349
1350 /* 'lh' := Y^2 */
1351 if (!field_sqr(group, tmp1, &point->Y, ctx)) goto err;
1352
1353 ret = (0 == BN_cmp(tmp1, rh));
1354
1355 err:
1356 BN_CTX_end(ctx);
1357 if (new_ctx != NULL)
1358 BN_CTX_free(new_ctx);
1359 return ret;
1360 }
1361
1362
1363 int ec_GFp_simple_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
1364 {
1365 /* return values:
1366 * -1 error
1367 * 0 equal (in affine coordinates)
1368 * 1 not equal
1369 */
1370
1371 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
1372 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
1373 BN_CTX *new_ctx = NULL;
1374 BIGNUM *tmp1, *tmp2, *Za23, *Zb23;
1375 const BIGNUM *tmp1_, *tmp2_;
1376 int ret = -1;
1377
1378 if (EC_POINT_is_at_infinity(group, a))
1379 {
1380 return EC_POINT_is_at_infinity(group, b) ? 0 : 1;
1381 }
1382
1383 if (a->Z_is_one && b->Z_is_one)
1384 {
1385 return ((BN_cmp(&a->X, &b->X) == 0) && BN_cmp(&a->Y, &b->Y) == 0) ? 0 : 1;
1386 }
1387
1388 field_mul = group->meth->field_mul;
1389 field_sqr = group->meth->field_sqr;
1390
1391 if (ctx == NULL)
1392 {
1393 ctx = new_ctx = BN_CTX_new();
1394 if (ctx == NULL)
1395 return -1;
1396 }
1397
1398 BN_CTX_start(ctx);
1399 tmp1 = BN_CTX_get(ctx);
1400 tmp2 = BN_CTX_get(ctx);
1401 Za23 = BN_CTX_get(ctx);
1402 Zb23 = BN_CTX_get(ctx);
1403 if (Zb23 == NULL) goto end;
1404
1405 /* We have to decide whether
1406 * (X_a/Z_a^2, Y_a/Z_a^3) = (X_b/Z_b^2, Y_b/Z_b^3),
1407 * or equivalently, whether
1408 * (X_a*Z_b^2, Y_a*Z_b^3) = (X_b*Z_a^2, Y_b*Z_a^3).
1409 */
1410
1411 if (!b->Z_is_one)
1412 {
1413 if (!field_sqr(group, Zb23, &b->Z, ctx)) goto end;
1414 if (!field_mul(group, tmp1, &a->X, Zb23, ctx)) goto end;
1415 tmp1_ = tmp1;
1416 }
1417 else
1418 tmp1_ = &a->X;
1419 if (!a->Z_is_one)
1420 {
1421 if (!field_sqr(group, Za23, &a->Z, ctx)) goto end;
1422 if (!field_mul(group, tmp2, &b->X, Za23, ctx)) goto end;
1423 tmp2_ = tmp2;
1424 }
1425 else
1426 tmp2_ = &b->X;
1427
1428 /* compare X_a*Z_b^2 with X_b*Z_a^2 */
1429 if (BN_cmp(tmp1_, tmp2_) != 0)
1430 {
1431 ret = 1; /* points differ */
1432 goto end;
1433 }
1434
1435
1436 if (!b->Z_is_one)
1437 {
1438 if (!field_mul(group, Zb23, Zb23, &b->Z, ctx)) goto end;
1439 if (!field_mul(group, tmp1, &a->Y, Zb23, ctx)) goto end;
1440 /* tmp1_ = tmp1 */
1441 }
1442 else
1443 tmp1_ = &a->Y;
1444 if (!a->Z_is_one)
1445 {
1446 if (!field_mul(group, Za23, Za23, &a->Z, ctx)) goto end;
1447 if (!field_mul(group, tmp2, &b->Y, Za23, ctx)) goto end;
1448 /* tmp2_ = tmp2 */
1449 }
1450 else
1451 tmp2_ = &b->Y;
1452
1453 /* compare Y_a*Z_b^3 with Y_b*Z_a^3 */
1454 if (BN_cmp(tmp1_, tmp2_) != 0)
1455 {
1456 ret = 1; /* points differ */
1457 goto end;
1458 }
1459
1460 /* points are equal */
1461 ret = 0;
1462
1463 end:
1464 BN_CTX_end(ctx);
1465 if (new_ctx != NULL)
1466 BN_CTX_free(new_ctx);
1467 return ret;
1468 }
1469
1470
1471 int ec_GFp_simple_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
1472 {
1473 BN_CTX *new_ctx = NULL;
1474 BIGNUM *x, *y;
1475 int ret = 0;
1476
1477 if (point->Z_is_one || EC_POINT_is_at_infinity(group, point))
1478 return 1;
1479
1480 if (ctx == NULL)
1481 {
1482 ctx = new_ctx = BN_CTX_new();
1483 if (ctx == NULL)
1484 return 0;
1485 }
1486
1487 BN_CTX_start(ctx);
1488 x = BN_CTX_get(ctx);
1489 y = BN_CTX_get(ctx);
1490 if (y == NULL) goto err;
1491
1492 if (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
1493 if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
1494 if (!point->Z_is_one)
1495 {
1496 ECerr(EC_F_EC_GFP_SIMPLE_MAKE_AFFINE, ERR_R_INTERNAL_ERROR);
1497 goto err;
1498 }
1499
1500 ret = 1;
1501
1502 err:
1503 BN_CTX_end(ctx);
1504 if (new_ctx != NULL)
1505 BN_CTX_free(new_ctx);
1506 return ret;
1507 }
1508
1509
1510 int ec_GFp_simple_points_make_affine(const EC_GROUP *group, size_t num, EC_POINT *points[], BN_CTX *ctx)
1511 {
1512 BN_CTX *new_ctx = NULL;
1513 BIGNUM *tmp0, *tmp1;
1514 size_t pow2 = 0;
1515 BIGNUM **heap = NULL;
1516 size_t i;
1517 int ret = 0;
1518
1519 if (num == 0)
1520 return 1;
1521
1522 if (ctx == NULL)
1523 {
1524 ctx = new_ctx = BN_CTX_new();
1525 if (ctx == NULL)
1526 return 0;
1527 }
1528
1529 BN_CTX_start(ctx);
1530 tmp0 = BN_CTX_get(ctx);
1531 tmp1 = BN_CTX_get(ctx);
1532 if (tmp0 == NULL || tmp1 == NULL) goto err;
1533
1534 /* Before converting the individual points, compute inverses of all Z values.
1535 * Modular inversion is rather slow, but luckily we can do with a single
1536 * explicit inversion, plus about 3 multiplications per input value.
1537 */
1538
1539 pow2 = 1;
1540 while (num > pow2)
1541 pow2 <<= 1;
1542 /* Now pow2 is the smallest power of 2 satifsying pow2 >= num.
1543 * We need twice that. */
1544 pow2 <<= 1;
1545
1546 heap = OPENSSL_malloc(pow2 * sizeof heap[0]);
1547 if (heap == NULL) goto err;
1548
1549 /* The array is used as a binary tree, exactly as in heapsort:
1550 *
1551 * heap[1]
1552 * heap[2] heap[3]
1553 * heap[4] heap[5] heap[6] heap[7]
1554 * heap[8]heap[9] heap[10]heap[11] heap[12]heap[13] heap[14] heap[15]
1555 *
1556 * We put the Z's in the last line;
1557 * then we set each other node to the product of its two child-nodes (where
1558 * empty or 0 entries are treated as ones);
1559 * then we invert heap[1];
1560 * then we invert each other node by replacing it by the product of its
1561 * parent (after inversion) and its sibling (before inversion).
1562 */
1563 heap[0] = NULL;
1564 for (i = pow2/2 - 1; i > 0; i--)
1565 heap[i] = NULL;
1566 for (i = 0; i < num; i++)
1567 heap[pow2/2 + i] = &points[i]->Z;
1568 for (i = pow2/2 + num; i < pow2; i++)
1569 heap[i] = NULL;
1570
1571 /* set each node to the product of its children */
1572 for (i = pow2/2 - 1; i > 0; i--)
1573 {
1574 heap[i] = BN_new();
1575 if (heap[i] == NULL) goto err;
1576
1577 if (heap[2*i] != NULL)
1578 {
1579 if ((heap[2*i + 1] == NULL) || BN_is_zero(heap[2*i + 1]))
1580 {
1581 if (!BN_copy(heap[i], heap[2*i])) goto err;
1582 }
1583 else
1584 {
1585 if (BN_is_zero(heap[2*i]))
1586 {
1587 if (!BN_copy(heap[i], heap[2*i + 1])) goto err;
1588 }
1589 else
1590 {
1591 if (!group->meth->field_mul(group, heap[i],
1592 heap[2*i], heap[2*i + 1], ctx)) goto err;
1593 }
1594 }
1595 }
1596 }
1597
1598 /* invert heap[1] */
1599 if (!BN_is_zero(heap[1]))
1600 {
1601 if (!BN_mod_inverse(heap[1], heap[1], &group->field, ctx))
1602 {
1603 ECerr(EC_F_EC_GFP_SIMPLE_POINTS_MAKE_AFFINE, ERR_R_BN_LIB);
1604 goto err;
1605 }
1606 }
1607 if (group->meth->field_encode != 0)
1608 {
1609 /* in the Montgomery case, we just turned R*H (representing H)
1610 * into 1/(R*H), but we need R*(1/H) (representing 1/H);
1611 * i.e. we have need to multiply by the Montgomery factor twice */
1612 if (!group->meth->field_encode(group, heap[1], heap[1], ctx)) goto err;
1613 if (!group->meth->field_encode(group, heap[1], heap[1], ctx)) goto err;
1614 }
1615
1616 /* set other heap[i]'s to their inverses */
1617 for (i = 2; i < pow2/2 + num; i += 2)
1618 {
1619 /* i is even */
1620 if ((heap[i + 1] != NULL) && !BN_is_zero(heap[i + 1]))
1621 {
1622 if (!group->meth->field_mul(group, tmp0, heap[i/2], heap[i + 1], ctx)) goto err;
1623 if (!group->meth->field_mul(group, tmp1, heap[i/2], heap[i], ctx)) goto err;
1624 if (!BN_copy(heap[i], tmp0)) goto err;
1625 if (!BN_copy(heap[i + 1], tmp1)) goto err;
1626 }
1627 else
1628 {
1629 if (!BN_copy(heap[i], heap[i/2])) goto err;
1630 }
1631 }
1632
1633 /* we have replaced all non-zero Z's by their inverses, now fix up all the points */
1634 for (i = 0; i < num; i++)
1635 {
1636 EC_POINT *p = points[i];
1637
1638 if (!BN_is_zero(&p->Z))
1639 {
1640 /* turn (X, Y, 1/Z) into (X/Z^2, Y/Z^3, 1) */
1641
1642 if (!group->meth->field_sqr(group, tmp1, &p->Z, ctx)) goto err;
1643 if (!group->meth->field_mul(group, &p->X, &p->X, tmp1, ctx)) goto err;
1644
1645 if (!group->meth->field_mul(group, tmp1, tmp1, &p->Z, ctx)) goto err;
1646 if (!group->meth->field_mul(group, &p->Y, &p->Y, tmp1, ctx)) goto err;
1647
1648 if (group->meth->field_set_to_one != 0)
1649 {
1650 if (!group->meth->field_set_to_one(group, &p->Z, ctx)) goto err;
1651 }
1652 else
1653 {
1654 if (!BN_one(&p->Z)) goto err;
1655 }
1656 p->Z_is_one = 1;
1657 }
1658 }
1659
1660 ret = 1;
1661
1662 err:
1663 BN_CTX_end(ctx);
1664 if (new_ctx != NULL)
1665 BN_CTX_free(new_ctx);
1666 if (heap != NULL)
1667 {
1668 /* heap[pow2/2] .. heap[pow2-1] have not been allocated locally! */
1669 for (i = pow2/2 - 1; i > 0; i--)
1670 {
1671 if (heap[i] != NULL)
1672 BN_clear_free(heap[i]);
1673 }
1674 OPENSSL_free(heap);
1675 }
1676 return ret;
1677 }
1678
1679
1680 int ec_GFp_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
1681 {
1682 return BN_mod_mul(r, a, b, &group->field, ctx);
1683 }
1684
1685
1686 int ec_GFp_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx)
1687 {
1688 return BN_mod_sqr(r, a, &group->field, ctx);
1689 }
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