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More method functions for EC_GFp_simple_method.
[thirdparty/openssl.git] / crypto / ec / ecp_smpl.c
CommitLineData
f8fe20e0 1/* crypto/ec/ecp_smpl.c */
60428dbf
BM		 2/* Includes code written by Lenka Fibikova <fibikova@exp-math.uni-essen.de>
3 * for the OpenSSL project. */
f8fe20e0
BM		 4/* ====================================================================
5 * Copyright (c) 1998-2001 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
60428dbf
BM		 58#include <openssl/err.h>
59
f8fe20e0 60#include "ec_lcl.h"
0657bf9c
BM		 61
62
63const EC_METHOD *EC_GFp_simple_method(void)
64 {
58fc6229
BM		 65 static const EC_METHOD ret = {
66 ec_GFp_simple_group_init,
67 ec_GFp_simple_group_set_curve_GFp,
68 ec_GFp_simple_group_finish,
69 ec_GFp_simple_group_clear_finish,
70 ec_GFp_simple_group_copy,
71 ec_GFp_simple_group_set_generator,
72 /* TODO: 'set' and 'get' functions for EC_GROUPs */
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,
226cc7de
BM		 77 ec_GFp_simple_point_set_to_infinity,
78 ec_GFp_simple_point_set_affine_coordinates_GFp,
79 ec_GFp_simple_point_get_affine_coordinates_GFp,
80 /* TODO: other 'set' and 'get' functions for EC_POINTs */
58fc6229
BM		 81 ec_GFp_simple_point2oct,
82 ec_GFp_simple_oct2point,
83 ec_GFp_simple_add,
84 ec_GFp_simple_dbl,
85 ec_GFp_simple_is_at_infinity,
86 ec_GFp_simple_is_on_curve,
87 ec_GFp_simple_make_affine,
60428dbf 88 ec_GFp_simple_field_mul,
58fc6229
BM		 89 ec_GFp_simple_field_sqr,
90 0 /* field_encode */,
91 0 /* field_decode */ };
0657bf9c
BM		 92
93 return &ret;
94 }
60428dbf
BM		 95
96
97int ec_GFp_simple_group_init(EC_GROUP *group)
98 {
99 BN_init(&group->field);
100 BN_init(&group->a);
101 BN_init(&group->b);
102 group->a_is_minus3 = 0;
103 group->generator = NULL;
104 BN_init(&group->order);
105 BN_init(&group->cofactor);
106 return 1;
107 }
108
109
110int ec_GFp_simple_group_set_curve_GFp(EC_GROUP *group,
111 const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
112 {
113 int ret = 0;
114 BN_CTX *new_ctx = NULL;
115 BIGNUM *tmp_a;
116
117 if (ctx == NULL)
118 {
119 ctx = new_ctx = BN_CTX_new();
120 if (ctx == NULL)
121 return 0;
122 }
60428dbf 123
226cc7de 124 BN_CTX_start(ctx);
60428dbf
BM		 125 tmp_a = BN_CTX_get(ctx);
126 if (tmp_a == NULL) goto err;
127
128 /* group->field */
129 if (!BN_copy(&group->field, p)) goto err;
130 group->field.neg = 0;
131
132 /* group->a */
133 if (!BN_nnmod(tmp_a, a, p, ctx)) goto err;
134 if (group->meth->field_encode)
135 { if (!group->meth->field_encode(group, &group->a, tmp_a, ctx)) goto err; }
136 else
137 if (!BN_copy(&group->a, tmp_a)) goto err;
138
139 /* group->b */
140 if (!BN_nnmod(&group->b, b, p, ctx)) goto err;
141 if (group->meth->field_encode)
142 if (!group->meth->field_encode(group, &group->b, &group->b, ctx)) goto err;
143
144 /* group->a_is_minus3 */
145 if (!BN_add_word(tmp_a, 3)) goto err;
146 group->a_is_minus3 = (0 == BN_cmp(tmp_a, &group->field));
147
148 ret = 1;
149
150 err:
151 BN_CTX_end(ctx);
152 if (new_ctx != NULL)
153 BN_CTX_free(new_ctx);
154 return ret;
155 }
156
157
158void ec_GFp_simple_group_finish(EC_GROUP *group)
159 {
160 BN_free(&group->field);
161 BN_free(&group->a);
162 BN_free(&group->b);
163 if (group->generator != NULL)
164 EC_POINT_free(group->generator);
165 BN_free(&group->order);
166 BN_free(&group->cofactor);
167 }
168
169
170void ec_GFp_simple_group_clear_finish(EC_GROUP *group)
171 {
172 BN_clear_free(&group->field);
173 BN_clear_free(&group->a);
174 BN_clear_free(&group->b);
175 if (group->generator != NULL)
176 {
177 EC_POINT_clear_free(group->generator);
178 group->generator = NULL;
179 }
180 BN_clear_free(&group->order);
181 BN_clear_free(&group->cofactor);
182 }
183
184
185int ec_GFp_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src)
186 {
187 if (!BN_copy(&dest->field, &src->field)) return 0;
188 if (!BN_copy(&dest->a, &src->a)) return 0;
189 if (!BN_copy(&dest->b, &src->b)) return 0;
190
191 dest->a_is_minus3 = src->a_is_minus3;
192
193 if (src->generator != NULL)
194 {
195 if (dest->generator == NULL)
196 {
197 dest->generator = EC_POINT_new(dest);
198 if (dest->generator == NULL) return 0;
199 }
200 if (!EC_POINT_copy(dest->generator, src->generator)) return 0;
201 }
202 else
203 {
204 /* src->generator == NULL */
205 if (dest->generator != NULL)
206 {
207 EC_POINT_clear_free(dest->generator);
208 dest->generator = NULL;
209 }
210 }
211
212 if (!BN_copy(&dest->order, &src->order)) return 0;
213 if (!BN_copy(&dest->cofactor, &src->cofactor)) return 0;
214
215 return 1;
216 }
217
218
219int ec_GFp_simple_group_set_generator(EC_GROUP *group, const EC_POINT *generator,
220 const BIGNUM *order, const BIGNUM *cofactor)
221 {
222 if (generator)
223 {
224 ECerr(EC_F_EC_GFP_SIMPLE_GROUP_SET_GENERATOR, ERR_R_PASSED_NULL_PARAMETER);
225 return 0 ;
226 }
227
228 if (group->generator == NULL)
229 {
230 group->generator = EC_POINT_new(group);
231 if (group->generator == NULL) return 0;
232 }
233 if (!EC_POINT_copy(group->generator, generator)) return 0;
234
235 if (order != NULL)
236 { if (!BN_copy(&group->order, order)) return 0; }
237 else
238 { if (!BN_zero(&group->order)) return 0; }
239
240 if (cofactor != NULL)
241 { if (!BN_copy(&group->cofactor, cofactor)) return 0; }
242 else
243 { if (!BN_zero(&group->cofactor)) return 0; }
244
245 return 1;
246 }
247
248
249/* TODO: 'set' and 'get' functions for EC_GROUPs */
250
251
252int ec_GFp_simple_point_init(EC_POINT *point)
253 {
254 BN_init(&point->X);
255 BN_init(&point->Y);
256 BN_init(&point->Z);
257 point->Z_is_one = 0;
258
259 return 1;
260 }
261
262
263void ec_GFp_simple_point_finish(EC_POINT *point)
264 {
265 BN_free(&point->X);
266 BN_free(&point->Y);
267 BN_free(&point->Z);
268 }
269
270
271void ec_GFp_simple_point_clear_finish(EC_POINT *point)
272 {
273 BN_clear_free(&point->X);
274 BN_clear_free(&point->Y);
275 BN_clear_free(&point->Z);
276 point->Z_is_one = 0;
277 }
278
279
280int ec_GFp_simple_point_copy(EC_POINT *dest, const EC_POINT *src)
281 {
282 if (!BN_copy(&dest->X, &src->X)) return 0;
283 if (!BN_copy(&dest->Y, &src->Y)) return 0;
284 if (!BN_copy(&dest->Z, &src->Z)) return 0;
285 dest->Z_is_one = src->Z_is_one;
286
287 return 1;
288 }
289
290
226cc7de
BM		 291int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *group, EC_POINT *point)
292 {
293 point->Z_is_one = 0;
294 return (BN_zero(&point->Z));
295 }
296
297
298int ec_GFp_simple_point_set_affine_coordinates_GFp(const EC_GROUP *group, EC_POINT *point,
299 const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx)
300 {
301 BN_CTX *new_ctx = NULL;
302 int ret = 0;
303
304 if (!BN_copy(&point->X, x)) goto err;
305 if (!BN_copy(&point->Y, y)) goto err;
306 if (!BN_one(&point->Z)) goto err;
307
308 if (group->meth->field_encode)
309 {
310 if (ctx == NULL)
311 {
312 ctx = new_ctx = BN_CTX_new();
313 if (ctx == NULL)
314 return 0;
315 }
316
317 if (!group->meth->field_encode(group, &point->X, &point->X, ctx)) goto err;
318 if (!group->meth->field_encode(group, &point->Y, &point->Y, ctx)) goto err;
319 if (!group->meth->field_encode(group, &point->Z, &point->Z, ctx)) goto err;
320 }
321
322 point->Z_is_one = 1;
323
324 err:
325 if (new_ctx != NULL)
326 BN_CTX_free(new_ctx);
327 return ret;
328 }
329
330
331int ec_GFp_simple_point_get_affine_coordinates_GFp(const EC_GROUP *group, const EC_POINT *point,
332 BIGNUM *x, BIGNUM *y, BN_CTX *ctx)
333 {
334 BN_CTX *new_ctx = NULL;
335 BIGNUM *X, *Y, *Z, *Z_1, *Z_2, *Z_3;
336 const BIGNUM *X_, *Y_, *Z_;
337 int ret = 0;
338
339 if (EC_POINT_is_at_infinity(group, point))
340 {
341 ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES_GFP, EC_R_POINT_AT_INFINITY);
342 return 0;
343 }
344
345 if (ctx == NULL)
346 {
347 ctx = new_ctx = BN_CTX_new();
348 if (ctx == NULL)
349 return 0;
350 }
351
352 BN_CTX_start(ctx);
353 X = BN_CTX_get(ctx);
354 Y = BN_CTX_get(ctx);
355 Z = BN_CTX_get(ctx);
356 Z_1 = BN_CTX_get(ctx);
357 Z_2 = BN_CTX_get(ctx);
358 Z_3 = BN_CTX_get(ctx);
359 if (Z_3 == NULL) goto err;
360
361 /* transform (X, Y, Z) into (x, y) := (X/Z^2, Y/Z^3) */
362
363 if (group->meth->field_decode)
364 {
365 if (!group->meth->field_decode(group, X, &point->X, ctx)) goto err;
366 if (!group->meth->field_decode(group, Y, &point->Y, ctx)) goto err;
367 if (!group->meth->field_decode(group, Z, &point->Z, ctx)) goto err;
368 X_ = X; Y_ = Y; Z_ = Z;
369 }
370 else
371 {
372 X_ = &point->X;
373 Y_ = &point->Y;
374 Z_ = &point->Z;
375 }
376
377 if (BN_is_one(Z_))
378 {
379 if (!BN_copy(x, X_)) goto err;
380 if (!BN_copy(y, Y_)) goto err;
381 }
382 else
383 {
384 if (!BN_mod_inverse(Z_1, Z_, &group->field, ctx))
385 {
386 ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES_GFP, ERR_R_BN_LIB);
387 goto err;
388 }
389 if (!BN_mod_sqr(Z_2, Z_1, &group->field, ctx)) goto err;
390 if (!BN_mod_mul(Z_3, Z_2, Z_1, &group->field, ctx)) goto err;
391
392 if (!BN_mod_mul(x, X_, Z_2, &group->field, ctx)) goto err;
393 if (!BN_mod_mul(y, Y_, Z_3, &group->field, ctx)) goto err;
394 }
395
396 ret = 1;
397
398 err:
399 BN_CTX_end(ctx);
400 if (new_ctx != NULL)
401 BN_CTX_free(new_ctx);
402 return ret;
403 }
404
405
406/* TODO: other 'set' and 'get' functions for EC_POINTs */
60428dbf
BM		 407
408
409size_t ec_GFp_simple_point2oct(const EC_GROUP *group, const EC_POINT *point, point_conversion_form_t form,
226cc7de
BM		 410 unsigned char *buf, size_t len, BN_CTX *ctx)
411 {
412 size_t ret;
413 BN_CTX *new_ctx = NULL;
414 int used_ctx = 0;
415 BIGNUM *x, *y;
416 size_t field_len, i, skip;
417
418 if ((form != POINT_CONVERSION_COMPRESSED)
419 && (form != POINT_CONVERSION_UNCOMPRESSED)
420 && (form != POINT_CONVERSION_HYBRID))
421 {
422 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_INVALID_FORM);
423 goto err;
424 }
425
426 if (EC_POINT_is_at_infinity(group, point))
427 {
428 /* encodes to a single 0 octet */
429 if (buf != NULL)
430 {
431 if (len < 1)
432 {
433 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);
434 return 0;
435 }
436 buf[0] = 0;
437 }
438 return 1;
439 }
440
441
442 /* ret := required output buffer length */
443 field_len = BN_num_bytes(&group->field);
444 ret = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len;
445
446 /* if 'buf' is NULL, just return required length */
447 if (buf != NULL)
448 {
449 if (len < ret)
450 {
451 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);
452 goto err;
453 }
454
455 if (ctx == NULL)
456 {
457 ctx = new_ctx = BN_CTX_new();
458 if (ctx == NULL)
459 return 0;
460 }
461
462 BN_CTX_start(ctx);
463 used_ctx = 1;
464 x = BN_CTX_get(ctx);
465 y = BN_CTX_get(ctx);
466 if (y == NULL) goto err;
467
468 if (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
469
470 if ((form == POINT_CONVERSION_COMPRESSED || form == POINT_CONVERSION_HYBRID) && BN_is_bit_set(y, 0))
471 buf[0] = form + 1;
472 else
473 buf[0] = form;
474
475 i = 1;
476
477 skip = field_len - BN_num_bytes(x);
478 if (skip > field_len)
479 {
480 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
481 goto err;
482 }
483 while (skip > 0)
484 {
485 buf[i++] = 0;
486 skip--;
487 }
488 skip = BN_bn2bin(x, buf + i);
489 i += skip;
490 if (i != 1 + field_len)
491 {
492 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
493 goto err;
494 }
495
496 if (form == POINT_CONVERSION_UNCOMPRESSED || form == POINT_CONVERSION_HYBRID)
497 {
498 skip = field_len - BN_num_bytes(y);
499 if (skip > field_len)
500 {
501 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
502 goto err;
503 }
504 while (skip > 0)
505 {
506 buf[i++] = 0;
507 skip--;
508 }
509 skip = BN_bn2bin(y, buf + i);
510 i += skip;
511 }
512
513 if (i != ret)
514 {
515 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
516 goto err;
517 }
518 }
519
520 if (used_ctx)
521 BN_CTX_end(ctx);
522 if (new_ctx != NULL)
523 BN_CTX_free(new_ctx);
524 return ret;
525
526 err:
527 if (used_ctx)
528 BN_CTX_end(ctx);
529 if (new_ctx != NULL)
530 BN_CTX_free(new_ctx);
531 return 0;
532 }
60428dbf
BM		 533
534
535int ec_GFp_simple_oct2point(const EC_GROUP *group, EC_POINT *point,
226cc7de
BM		 536 const unsigned char *buf, size_t len, BN_CTX *ctx)
537 {
538 point_conversion_form_t form;
539 int y_bit;
540 BN_CTX *new_ctx = NULL;
541 BIGNUM *x, *y;
542 size_t field_len, enc_len;
543 int ret = 0;
544
545 if (len <= 0)
546 {
547 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_BUFFER_TOO_SMALL);
548 return 0;
549 }
550 form = buf[0];
551 y_bit = form & 1;
552 form = form & ~1;
553 if ((form != 0) && (form != POINT_CONVERSION_COMPRESSED)
554 && (form != POINT_CONVERSION_UNCOMPRESSED)
555 && (form != POINT_CONVERSION_HYBRID))
556 {
557 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
558 return 0;
559 }
560 if ((form == 0 || form == POINT_CONVERSION_UNCOMPRESSED) && y_bit)
561 {
562 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
563 return 0;
564 }
565
566 if (form == 0)
567 {
568 if (len != 1)
569 {
570 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
571 return 0;
572 }
573
574 return EC_POINT_set_to_infinity(group, point);
575 }
576
577 field_len = BN_num_bytes(&group->field);
578 enc_len = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len;
579
580 if (len != enc_len)
581 {
582 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
583 return 0;
584 }
585
586 if (ctx == NULL)
587 {
588 ctx = new_ctx = BN_CTX_new();
589 if (ctx == NULL)
590 return 0;
591 }
592
593 BN_CTX_start(ctx);
594 x = BN_CTX_get(ctx);
595 y = BN_CTX_get(ctx);
596 if (y == NULL) goto err;
597
598 if (!BN_bin2bn(buf + 1, field_len, x)) goto err;
599 if (BN_ucmp(x, &group->field) >= 0)
600 {
601 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
602 goto err;
603 }
604
605 if (form != POINT_CONVERSION_COMPRESSED)
606 {
607 if (!BN_bin2bn(buf + 1 + field_len, field_len, y)) goto err;
608 if (BN_ucmp(y, &group->field) >= 0)
609 {
610 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
611 goto err;
612 }
613 if (form == POINT_CONVERSION_HYBRID)
614 {
615 if (y_bit != BN_is_bit_set(y, 0))
616 {
617 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
618 goto err;
619 }
620 }
621 }
622
623 if (form == POINT_CONVERSION_COMPRESSED)
624 {
625 /* Recover y. We have a Weierstrass equation
626 * y^2 = x^3 + a*x + b,
627 * so y is one of the square roots of x^3 + a*x + b.
628 */
629
630 BIGNUM *tmp1, *tmp2;
631
632 tmp1 = BN_CTX_get(ctx);
633 tmp2 = BN_CTX_get(ctx);
634 if (tmp2 == NULL) goto err;
635
636 /* tmp1 := x^3 */
637 if (!BN_mod_sqr(tmp2, x, &group->field, ctx)) goto err;
638 if (!BN_mod_mul(tmp1, tmp2, x, &group->field, ctx)) goto err;
639
640 /* tmp1 := tmp1 + a*x */
641 if (group->a_is_minus3)
642 {
643 if (!BN_mod_lshift1_quick(tmp2, x, &group->field)) goto err;
644 if (!BN_mod_add_quick(tmp2, tmp2, x, &group->field)) goto err;
645 if (!BN_mod_sub_quick(tmp1, tmp1, tmp2, &group->field)) goto err;
646 }
647 else
648 {
649 if (!BN_mod_mul(tmp2, &group->a, x, &group->field, ctx)) goto err;
650 if (!BN_mod_add_quick(tmp1, tmp1, tmp2, &group->field)) goto err;
651 }
652
653 /* tmp1 := tmp1 + b */
654 if (!BN_mod_add_quick(tmp1, tmp1, &group->b, &group->field)) goto err;
655
656 if (!BN_mod_sqrt(y, tmp1, &group->field, ctx))
657 {
658 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, ERR_R_BN_LIB);
659 goto err;
660 }
661
662 if (y_bit != BN_is_bit_set(y, 0))
663 {
664 if (!BN_usub(y, &group->field, y)) goto err;
665 }
666 if (y_bit != BN_is_bit_set(y, 0))
667 {
668 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, ERR_R_INTERNAL_ERROR);
669 goto err;
670 }
671 }
672
673 if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
674
675 if (!EC_POINT_is_on_curve(group, point, ctx)) /* test required by X9.62 */
676 {
677 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_POINT_IS_NOT_ON_CURVE);
678 goto err;
679 }
680
681 ret = 1;
682
683 err:
684 BN_CTX_end(ctx);
685 if (new_ctx != NULL)
686 BN_CTX_free(new_ctx);
687 return ret;
688 }
60428dbf
BM		 689
690
691int ec_GFp_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
692 {
693 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
694 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
695 const BIGNUM *p;
696 BN_CTX *new_ctx = NULL;
697 BIGNUM *n0, *n1, *n2, *n3, *n4, *n5, *n6;
698 int ret = 0;
699
700 if (a == b)
701 return EC_POINT_dbl(group, r, a, ctx);
702 if (EC_POINT_is_at_infinity(group, a))
703 return EC_POINT_copy(r, b);
704 if (EC_POINT_is_at_infinity(group, b))
705 return EC_POINT_copy(r, a);
706
707 field_mul = group->meth->field_mul;
708 field_sqr = group->meth->field_sqr;
709 p = &group->field;
710
711 if (ctx == NULL)
712 {
713 ctx = new_ctx = BN_CTX_new();
714 if (ctx == NULL)
715 return 0;
716 }
60428dbf 717
226cc7de 718 BN_CTX_start(ctx);
60428dbf
BM		 719 n0 = BN_CTX_get(ctx);
720 n1 = BN_CTX_get(ctx);
721 n2 = BN_CTX_get(ctx);
722 n3 = BN_CTX_get(ctx);
723 n4 = BN_CTX_get(ctx);
724 n5 = BN_CTX_get(ctx);
725 n6 = BN_CTX_get(ctx);
726 if (n6 == NULL) goto end;
727
728 /* n1, n2 */
729 if (b->Z_is_one)
730 {
731 if (!BN_copy(n1, &a->X)) goto end;
732 if (!BN_copy(n2, &a->Y)) goto end;
733 /* n1 = X_a */
734 /* n2 = Y_a */
735 }
736 else
737 {
738 if (!field_sqr(group, n0, &b->Z, ctx)) goto end;
739 if (!field_mul(group, n1, &a->X, n0, ctx)) goto end;
740 /* n1 = X_a * Z_b^2 */
741
742 if (!field_mul(group, n0, n0, &b->Z, ctx)) goto end;
743 if (!field_mul(group, n2, &a->Y, n0, ctx)) goto end;
744 /* n2 = Y_a * Z_b^3 */
745 }
746
747 /* n3, n4 */
748 if (a->Z_is_one)
749 {
750 if (!BN_copy(n3, &b->X)) goto end;
751 if (!BN_copy(n4, &b->Y)) goto end;
752 /* n3 = X_b */
753 /* n4 = Y_b */
754 }
755 else
756 {
757 if (!field_sqr(group, n0, &a->Z, ctx)) goto end;
758 if (!field_mul(group, n3, &b->X, n0, ctx)) goto end;
759 /* n3 = X_b * Z_a^2 */
760
761 if (!field_mul(group, n0, n0, &a->Z, ctx)) goto end;
762 if (!field_mul(group, n4, &b->Y, n0, ctx)) goto end;
763 /* n4 = Y_b * Z_a^3 */
764 }
765
766 /* n5, n6 */
767 if (!BN_mod_sub_quick(n5, n1, n3, p)) goto end;
768 if (!BN_mod_sub_quick(n6, n2, n4, p)) goto end;
769 /* n5 = n1 - n3 */
770 /* n6 = n2 - n4 */
771
772 if (BN_is_zero(n5))
773 {
774 if (BN_is_zero(n6))
775 {
776 /* a is the same point as b */
777 BN_CTX_end(ctx);
60428dbf 778 ret = EC_POINT_dbl(group, r, a, ctx);
e869d4bd 779 ctx = NULL;
60428dbf
BM		 780 goto end;
781 }
782 else
783 {
784 /* a is the inverse of b */
785 if (!BN_zero(&r->Z)) goto end;
786 r->Z_is_one = 0;
787 ret = 1;
788 goto end;
789 }
790 }
791
792 /* 'n7', 'n8' */
793 if (!BN_mod_add_quick(n1, n1, n3, p)) goto end;
794 if (!BN_mod_add_quick(n2, n2, n4, p)) goto end;
795 /* 'n7' = n1 + n3 */
796 /* 'n8' = n2 + n4 */
797
798 /* Z_r */
799 if (a->Z_is_one && b->Z_is_one)
800 {
801 if (!BN_copy(&r->Z, n5)) goto end;
802 }
803 else
804 {
805 if (a->Z_is_one)
806 { if (!BN_copy(n0, &b->Z)) goto end; }
807 else if (b->Z_is_one)
808 { if (!BN_copy(n0, &a->Z)) goto end; }
809 else
810 { if (!field_mul(group, n0, &a->Z, &b->Z, ctx)) goto end; }
811 if (!field_mul(group, &r->Z, n0, n5, ctx)) goto end;
812 }
813 r->Z_is_one = 0;
814 /* Z_r = Z_a * Z_b * n5 */
815
816 /* X_r */
817 if (!field_sqr(group, n0, n6, ctx)) goto end;
818 if (!field_sqr(group, n4, n5, ctx)) goto end;
819 if (!field_mul(group, n3, n1, n4, ctx)) goto end;
820 if (!BN_mod_sub_quick(&r->X, n0, n3, p)) goto end;
821 /* X_r = n6^2 - n5^2 * 'n7' */
822
823 /* 'n9' */
824 if (!BN_mod_lshift1_quick(n0, &r->X, p)) goto end;
825 if (!BN_mod_sub_quick(n0, n3, n0, p)) goto end;
826 /* n9 = n5^2 * 'n7' - 2 * X_r */
827
828 /* Y_r */
829 if (!field_mul(group, n0, n0, n6, ctx)) goto end;
830 if (!field_mul(group, n5, n4, n5, ctx)) goto end; /* now n5 is n5^3 */
831 if (!field_mul(group, n1, n2, n5, ctx)) goto end;
832 if (!BN_mod_sub_quick(n0, n0, n1, p)) goto end;
833 if (BN_is_odd(n0))
834 if (!BN_add(n0, n0, p)) goto end;
835 /* now 0 <= n0 < 2*p, and n0 is even */
836 if (!BN_rshift1(&r->Y, n0)) goto end;
837 /* Y_r = (n6 * 'n9' - 'n8' * 'n5^3') / 2 */
838
839 ret = 1;
840
841 end:
842 if (ctx) /* otherwise we already called BN_CTX_end */
843 BN_CTX_end(ctx);
844 if (new_ctx != NULL)
845 BN_CTX_free(new_ctx);
846 return ret;
847 }
848
849
850int ec_GFp_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_CTX *ctx)
851 {
852 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
853 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
854 const BIGNUM *p;
855 BN_CTX *new_ctx = NULL;
856 BIGNUM *n0, *n1, *n2, *n3;
857 int ret = 0;
858
859 if (EC_POINT_is_at_infinity(group, a))
860 {
861 if (!BN_zero(&r->Z)) return 0;
862 r->Z_is_one = 0;
863 return 1;
864 }
865
866 field_mul = group->meth->field_mul;
867 field_sqr = group->meth->field_sqr;
868 p = &group->field;
869
870 if (ctx == NULL)
871 {
872 ctx = new_ctx = BN_CTX_new();
873 if (ctx == NULL)
874 return 0;
875 }
60428dbf 876
226cc7de 877 BN_CTX_start(ctx);
60428dbf
BM		 878 n0 = BN_CTX_get(ctx);
879 n1 = BN_CTX_get(ctx);
880 n2 = BN_CTX_get(ctx);
881 n3 = BN_CTX_get(ctx);
882 if (n3 == NULL) goto err;
883
60428dbf
BM		 884 /* n1 */
885 if (a->Z_is_one)
886 {
887 if (!field_sqr(group, n0, &a->X, ctx)) goto err;
888 if (!BN_mod_lshift1_quick(n1, n0, p)) goto err;
889 if (!BN_mod_add_quick(n0, n0, n1, p)) goto err;
890 if (!BN_mod_add_quick(n1, n0, &group->a, p)) goto err;
891 /* n1 = 3 * X_a^2 + a_curve */
892 }
893 else if (group->a_is_minus3)
894 {
895 if (!field_sqr(group, n1, &a->Z, ctx)) goto err;
896 if (!BN_mod_add_quick(n0, &a->X, n1, p)) goto err;
897 if (!BN_mod_sub_quick(n2, &a->X, n1, p)) goto err;
898 if (!field_mul(group, n1, n0, n2, ctx)) goto err;
899 if (!BN_mod_lshift1_quick(n0, n1, p)) goto err;
900 if (!BN_mod_add_quick(n1, n0, n1, p)) goto err;
901 /* n1 = 3 * (X_a + Z_a^2) * (X_a - Z_a^2)
902 * = 3 * X_a^2 - 3 * Z_a^4 */
903 }
904 else
905 {
906 if (!field_sqr(group, n0, &a->X, ctx)) goto err;
907 if (!BN_mod_lshift1_quick(n1, n0, p)) goto err;
908 if (!BN_mod_add_quick(n0, n0, n1, p)) goto err;
909 if (!field_sqr(group, n1, &a->Z, ctx)) goto err;
910 if (!field_sqr(group, n1, n1, ctx)) goto err;
911 if (!field_mul(group, n1, n1, &group->a, ctx)) goto err;
912 if (!BN_mod_add_quick(n1, n1, n0, p)) goto err;
913 /* n1 = 3 * X_a^2 + a_curve * Z_a^4 */
914 }
915
916 /* Z_r */
917 if (a->Z_is_one)
918 {
919 if (!BN_copy(n0, &a->Y)) goto err;
920 }
921 else
922 {
923 if (!field_mul(group, n0, &a->Y, &a->Z, ctx)) goto err;
924 }
925 if (!BN_mod_lshift1_quick(&r->Z, n0, p)) goto err;
926 r->Z_is_one = 0;
927 /* Z_r = 2 * Y_a * Z_a */
928
929 /* n2 */
930 if (!field_sqr(group, n3, &a->Y, ctx)) goto err;
931 if (!field_mul(group, n2, &a->X, n3, ctx)) goto err;
932 if (!BN_mod_lshift_quick(n2, n2, 2, p)) goto err;
933 /* n2 = 4 * X_a * Y_a^2 */
934
935 /* X_r */
936 if (!BN_mod_lshift1_quick(n0, n2, p)) goto err;
937 if (!field_sqr(group, &r->X, n1, ctx)) goto err;
938 if (!BN_mod_sub_quick(&r->X, &r->X, n0, p)) goto err;
939 /* X_r = n1^2 - 2 * n2 */
940
941 /* n3 */
942 if (!field_sqr(group, n0, n3, ctx)) goto err;
943 if (!BN_mod_lshift_quick(n3, n0, 3, p)) goto err;
944 /* n3 = 8 * Y_a^4 */
945
946 /* Y_r */
947 if (!BN_mod_sub_quick(n0, n2, &r->X, p)) goto err;
948 if (!field_mul(group, n0, n1, n0, ctx)) goto err;
949 if (!BN_mod_sub_quick(&r->Y, n0, n3, p)) goto err;
950 /* Y_r = n1 * (n2 - X_r) - n3 */
951
952 ret = 1;
953
954 err:
955 BN_CTX_end(ctx);
956 if (new_ctx != NULL)
957 BN_CTX_free(new_ctx);
958 return ret;
959 }
960
961
962int ec_GFp_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point)
963 {
964 return BN_is_zero(&point->Z);
965 }
966
967
e869d4bd
BM		 968int ec_GFp_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx)
969 {
970 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
971 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
972 const BIGNUM *p;
973 BN_CTX *new_ctx = NULL;
974 BIGNUM *rh, *tmp1, *tmp2, *Z4, *Z6;
975 int ret = -1;
60428dbf 976
e869d4bd
BM		 977 if (EC_POINT_is_at_infinity(group, point))
978 return 1;
979
980 field_mul = group->meth->field_mul;
981 field_sqr = group->meth->field_sqr;
982 p = &group->field;
60428dbf 983
e869d4bd
BM		 984 if (ctx == NULL)
985 {
986 ctx = new_ctx = BN_CTX_new();
987 if (ctx == NULL)
226cc7de 988 return -1;
e869d4bd 989 }
e869d4bd 990
226cc7de 991 BN_CTX_start(ctx);
e869d4bd
BM		 992 rh = BN_CTX_get(ctx);
993 tmp1 = BN_CTX_get(ctx);
994 tmp2 = BN_CTX_get(ctx);
995 Z4 = BN_CTX_get(ctx);
996 Z6 = BN_CTX_get(ctx);
997 if (Z6 == NULL) goto err;
998
999 /* We have a curve defined by a Weierstrass equation
1000 * y^2 = x^3 + a*x + b.
1001 * The point to consider is given in Jacobian projective coordinates
1002 * where (X, Y, Z) represents (x, y) = (X/Z^2, Y/Z^3).
1003 * Substituting this and multiplying by Z^6 transforms the above equation into
1004 * Y^2 = X^3 + a*X*Z^4 + b*Z^6.
1005 * To test this, we add up the right-hand side in 'rh'.
1006 */
1007
1008 /* rh := X^3 */
1009 if (!field_sqr(group, rh, &point->X, ctx)) goto err;
1010 if (!field_mul(group, rh, rh, &point->X, ctx)) goto err;
1011
1012 if (!point->Z_is_one)
1013 {
1014 if (!field_sqr(group, tmp1, &point->Z, ctx)) goto err;
1015 if (!field_sqr(group, Z4, tmp1, ctx)) goto err;
1016 if (!field_mul(group, Z6, Z4, tmp1, ctx)) goto err;
1017
1018 /* rh := rh + a*X*Z^4 */
1019 if (!field_mul(group, tmp1, &point->X, Z4, ctx)) goto err;
1020 if (&group->a_is_minus3)
1021 {
1022 if (!BN_mod_lshift1_quick(tmp2, tmp1, p)) goto err;
1023 if (!BN_mod_add_quick(tmp2, tmp2, tmp1, p)) goto err;
1024 if (!BN_mod_sub_quick(rh, rh, tmp2, p)) goto err;
1025 }
1026 else
1027 {
1028 if (!field_mul(group, tmp2, tmp1, &group->a, ctx)) goto err;
1029 if (!BN_mod_add_quick(rh, rh, tmp2, p)) goto err;
1030 }
1031
1032 /* rh := rh + b*Z^6 */
1033 if (!field_mul(group, tmp1, &group->b, Z6, ctx)) goto err;
1034 if (!BN_mod_add_quick(rh, rh, tmp1, p)) goto err;
1035 }
1036 else
1037 {
1038 /* point->Z_is_one */
1039
1040 /* rh := rh + a*X */
1041 if (&group->a_is_minus3)
1042 {
1043 if (!BN_mod_lshift1_quick(tmp2, &point->X, p)) goto err;
1044 if (!BN_mod_add_quick(tmp2, tmp2, &point->X, p)) goto err;
1045 if (!BN_mod_sub_quick(rh, rh, tmp2, p)) goto err;
1046 }
1047 else
1048 {
1049 if (!field_mul(group, tmp2, &point->X, &group->a, ctx)) goto err;
1050 if (!BN_mod_add_quick(rh, rh, tmp2, p)) goto err;
1051 }
1052
1053 /* rh := rh + b */
1054 if (!BN_mod_add_quick(rh, rh, &group->b, p)) goto err;
1055 }
1056
1057 /* 'lh' := Y^2 */
1058 if (!field_sqr(group, tmp1, &point->Y, ctx)) goto err;
1059
1060 ret = (0 == BN_cmp(tmp1, rh));
1061
1062 err:
1063 BN_CTX_end(ctx);
1064 if (new_ctx != NULL)
1065 BN_CTX_free(new_ctx);
1066 return ret;
1067 }
1068
1069
1070int ec_GFp_simple_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
1071 {
1072 BN_CTX *new_ctx = NULL;
226cc7de 1073 BIGNUM *x, *y;
e869d4bd
BM		 1074 int ret = 0;
1075
1076 if (point->Z_is_one || EC_POINT_is_at_infinity(group, point))
1077 return 1;
1078
1079 if (ctx == NULL)
1080 {
1081 ctx = new_ctx = BN_CTX_new();
1082 if (ctx == NULL)
1083 return 0;
1084 }
e869d4bd 1085
226cc7de
BM		 1086 BN_CTX_start(ctx);
1087 x = BN_CTX_get(ctx);
1088 y = BN_CTX_get(ctx);
1089 if (y == NULL) goto err;
e869d4bd 1090
226cc7de
BM		 1091 if (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
1092 if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
1093 if (!point->Z_is_one)
e869d4bd 1094 {
226cc7de
BM		 1095 ECerr(EC_F_EC_GFP_SIMPLE_MAKE_AFFINE, ERR_R_INTERNAL_ERROR);
1096 goto err;
e869d4bd 1097 }
e869d4bd 1098
e869d4bd
BM		 1099 ret = 1;
1100
226cc7de 1101 err:
e869d4bd
BM		 1102 BN_CTX_end(ctx);
1103 if (new_ctx != NULL)
1104 BN_CTX_free(new_ctx);
1105 return ret;
1106 }
60428dbf
BM		 1107
1108
1109int ec_GFp_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
1110 {
1111 return BN_mod_mul(r, a, b, &group->field, ctx);
1112 }
1113
1114
1115int ec_GFp_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx)
1116 {
1117 return BN_mod_sqr(r, a, &group->field, ctx);
1118 }
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