]>
Commit | Line | Data |
---|---|---|
f8fe20e0 | 1 | /* crypto/ec/ecp_smpl.c */ |
0f113f3e MC |
2 | /* |
3 | * Includes code written by Lenka Fibikova <fibikova@exp-math.uni-essen.de> | |
4 | * for the OpenSSL project. Includes code written by Bodo Moeller for the | |
5 | * OpenSSL project. | |
6 | */ | |
f8fe20e0 | 7 | /* ==================================================================== |
af28dd6c | 8 | * Copyright (c) 1998-2002 The OpenSSL Project. All rights reserved. |
f8fe20e0 BM |
9 | * |
10 | * Redistribution and use in source and binary forms, with or without | |
11 | * modification, are permitted provided that the following conditions | |
12 | * are met: | |
13 | * | |
14 | * 1. Redistributions of source code must retain the above copyright | |
0f113f3e | 15 | * notice, this list of conditions and the following disclaimer. |
f8fe20e0 BM |
16 | * |
17 | * 2. Redistributions in binary form must reproduce the above copyright | |
18 | * notice, this list of conditions and the following disclaimer in | |
19 | * the documentation and/or other materials provided with the | |
20 | * distribution. | |
21 | * | |
22 | * 3. All advertising materials mentioning features or use of this | |
23 | * software must display the following acknowledgment: | |
24 | * "This product includes software developed by the OpenSSL Project | |
25 | * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" | |
26 | * | |
27 | * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to | |
28 | * endorse or promote products derived from this software without | |
29 | * prior written permission. For written permission, please contact | |
30 | * openssl-core@openssl.org. | |
31 | * | |
32 | * 5. Products derived from this software may not be called "OpenSSL" | |
33 | * nor may "OpenSSL" appear in their names without prior written | |
34 | * permission of the OpenSSL Project. | |
35 | * | |
36 | * 6. Redistributions of any form whatsoever must retain the following | |
37 | * acknowledgment: | |
38 | * "This product includes software developed by the OpenSSL Project | |
39 | * for use in the OpenSSL Toolkit (http://www.openssl.org/)" | |
40 | * | |
41 | * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY | |
42 | * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE | |
43 | * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR | |
44 | * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR | |
45 | * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, | |
46 | * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT | |
47 | * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; | |
48 | * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) | |
49 | * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, | |
50 | * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) | |
51 | * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED | |
52 | * OF THE POSSIBILITY OF SUCH DAMAGE. | |
53 | * ==================================================================== | |
54 | * | |
55 | * This product includes cryptographic software written by Eric Young | |
56 | * (eay@cryptsoft.com). This product includes software written by Tim | |
57 | * Hudson (tjh@cryptsoft.com). | |
58 | * | |
59 | */ | |
7793f30e BM |
60 | /* ==================================================================== |
61 | * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. | |
62 | * Portions of this software developed by SUN MICROSYSTEMS, INC., | |
63 | * and contributed to the OpenSSL project. | |
64 | */ | |
f8fe20e0 | 65 | |
60428dbf | 66 | #include <openssl/err.h> |
02cbedc3 | 67 | #include <openssl/symhacks.h> |
60428dbf | 68 | |
f8fe20e0 | 69 | #include "ec_lcl.h" |
0657bf9c | 70 | |
0657bf9c | 71 | const EC_METHOD *EC_GFp_simple_method(void) |
0f113f3e MC |
72 | { |
73 | static const EC_METHOD ret = { | |
74 | EC_FLAGS_DEFAULT_OCT, | |
75 | NID_X9_62_prime_field, | |
76 | ec_GFp_simple_group_init, | |
77 | ec_GFp_simple_group_finish, | |
78 | ec_GFp_simple_group_clear_finish, | |
79 | ec_GFp_simple_group_copy, | |
80 | ec_GFp_simple_group_set_curve, | |
81 | ec_GFp_simple_group_get_curve, | |
82 | ec_GFp_simple_group_get_degree, | |
83 | ec_GFp_simple_group_check_discriminant, | |
84 | ec_GFp_simple_point_init, | |
85 | ec_GFp_simple_point_finish, | |
86 | ec_GFp_simple_point_clear_finish, | |
87 | ec_GFp_simple_point_copy, | |
88 | ec_GFp_simple_point_set_to_infinity, | |
89 | ec_GFp_simple_set_Jprojective_coordinates_GFp, | |
90 | ec_GFp_simple_get_Jprojective_coordinates_GFp, | |
91 | ec_GFp_simple_point_set_affine_coordinates, | |
92 | ec_GFp_simple_point_get_affine_coordinates, | |
93 | 0, 0, 0, | |
94 | ec_GFp_simple_add, | |
95 | ec_GFp_simple_dbl, | |
96 | ec_GFp_simple_invert, | |
97 | ec_GFp_simple_is_at_infinity, | |
98 | ec_GFp_simple_is_on_curve, | |
99 | ec_GFp_simple_cmp, | |
100 | ec_GFp_simple_make_affine, | |
101 | ec_GFp_simple_points_make_affine, | |
102 | 0 /* mul */ , | |
103 | 0 /* precompute_mult */ , | |
104 | 0 /* have_precompute_mult */ , | |
105 | ec_GFp_simple_field_mul, | |
106 | ec_GFp_simple_field_sqr, | |
107 | 0 /* field_div */ , | |
108 | 0 /* field_encode */ , | |
109 | 0 /* field_decode */ , | |
110 | 0 /* field_set_to_one */ | |
111 | }; | |
112 | ||
113 | return &ret; | |
114 | } | |
60428dbf | 115 | |
3a83462d MC |
116 | /* |
117 | * Most method functions in this file are designed to work with | |
922fa76e BM |
118 | * non-trivial representations of field elements if necessary |
119 | * (see ecp_mont.c): while standard modular addition and subtraction | |
120 | * are used, the field_mul and field_sqr methods will be used for | |
121 | * multiplication, and field_encode and field_decode (if defined) | |
122 | * will be used for converting between representations. | |
3a83462d | 123 | * |
922fa76e BM |
124 | * Functions ec_GFp_simple_points_make_affine() and |
125 | * ec_GFp_simple_point_get_affine_coordinates() specifically assume | |
126 | * that if a non-trivial representation is used, it is a Montgomery | |
127 | * representation (i.e. 'encoding' means multiplying by some factor R). | |
128 | */ | |
129 | ||
60428dbf | 130 | int ec_GFp_simple_group_init(EC_GROUP *group) |
0f113f3e MC |
131 | { |
132 | group->field = BN_new(); | |
133 | group->a = BN_new(); | |
134 | group->b = BN_new(); | |
135 | if (!group->field || !group->a || !group->b) { | |
136 | if (!group->field) | |
137 | BN_free(group->field); | |
138 | if (!group->a) | |
139 | BN_free(group->a); | |
140 | if (!group->b) | |
141 | BN_free(group->b); | |
142 | return 0; | |
143 | } | |
144 | group->a_is_minus3 = 0; | |
145 | return 1; | |
146 | } | |
60428dbf | 147 | |
bb62a8b0 | 148 | void ec_GFp_simple_group_finish(EC_GROUP *group) |
0f113f3e MC |
149 | { |
150 | BN_free(group->field); | |
151 | BN_free(group->a); | |
152 | BN_free(group->b); | |
153 | } | |
bb62a8b0 BM |
154 | |
155 | void ec_GFp_simple_group_clear_finish(EC_GROUP *group) | |
0f113f3e MC |
156 | { |
157 | BN_clear_free(group->field); | |
158 | BN_clear_free(group->a); | |
159 | BN_clear_free(group->b); | |
160 | } | |
bb62a8b0 BM |
161 | |
162 | int ec_GFp_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src) | |
0f113f3e MC |
163 | { |
164 | if (!BN_copy(dest->field, src->field)) | |
165 | return 0; | |
166 | if (!BN_copy(dest->a, src->a)) | |
167 | return 0; | |
168 | if (!BN_copy(dest->b, src->b)) | |
169 | return 0; | |
bb62a8b0 | 170 | |
0f113f3e | 171 | dest->a_is_minus3 = src->a_is_minus3; |
bb62a8b0 | 172 | |
0f113f3e MC |
173 | return 1; |
174 | } | |
bb62a8b0 | 175 | |
35b73a1f | 176 | int ec_GFp_simple_group_set_curve(EC_GROUP *group, |
0f113f3e MC |
177 | const BIGNUM *p, const BIGNUM *a, |
178 | const BIGNUM *b, BN_CTX *ctx) | |
179 | { | |
180 | int ret = 0; | |
181 | BN_CTX *new_ctx = NULL; | |
182 | BIGNUM *tmp_a; | |
183 | ||
184 | /* p must be a prime > 3 */ | |
185 | if (BN_num_bits(p) <= 2 || !BN_is_odd(p)) { | |
186 | ECerr(EC_F_EC_GFP_SIMPLE_GROUP_SET_CURVE, EC_R_INVALID_FIELD); | |
187 | return 0; | |
188 | } | |
189 | ||
190 | if (ctx == NULL) { | |
191 | ctx = new_ctx = BN_CTX_new(); | |
192 | if (ctx == NULL) | |
193 | return 0; | |
194 | } | |
195 | ||
196 | BN_CTX_start(ctx); | |
197 | tmp_a = BN_CTX_get(ctx); | |
198 | if (tmp_a == NULL) | |
199 | goto err; | |
200 | ||
201 | /* group->field */ | |
202 | if (!BN_copy(group->field, p)) | |
203 | goto err; | |
204 | BN_set_negative(group->field, 0); | |
205 | ||
206 | /* group->a */ | |
207 | if (!BN_nnmod(tmp_a, a, p, ctx)) | |
208 | goto err; | |
209 | if (group->meth->field_encode) { | |
210 | if (!group->meth->field_encode(group, group->a, tmp_a, ctx)) | |
211 | goto err; | |
212 | } else if (!BN_copy(group->a, tmp_a)) | |
213 | goto err; | |
214 | ||
215 | /* group->b */ | |
216 | if (!BN_nnmod(group->b, b, p, ctx)) | |
217 | goto err; | |
218 | if (group->meth->field_encode) | |
219 | if (!group->meth->field_encode(group, group->b, group->b, ctx)) | |
220 | goto err; | |
221 | ||
222 | /* group->a_is_minus3 */ | |
223 | if (!BN_add_word(tmp_a, 3)) | |
224 | goto err; | |
225 | group->a_is_minus3 = (0 == BN_cmp(tmp_a, group->field)); | |
226 | ||
227 | ret = 1; | |
60428dbf BM |
228 | |
229 | err: | |
0f113f3e MC |
230 | BN_CTX_end(ctx); |
231 | if (new_ctx != NULL) | |
232 | BN_CTX_free(new_ctx); | |
233 | return ret; | |
234 | } | |
235 | ||
236 | int ec_GFp_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, | |
237 | BIGNUM *b, BN_CTX *ctx) | |
238 | { | |
239 | int ret = 0; | |
240 | BN_CTX *new_ctx = NULL; | |
241 | ||
242 | if (p != NULL) { | |
243 | if (!BN_copy(p, group->field)) | |
244 | return 0; | |
245 | } | |
246 | ||
247 | if (a != NULL || b != NULL) { | |
248 | if (group->meth->field_decode) { | |
249 | if (ctx == NULL) { | |
250 | ctx = new_ctx = BN_CTX_new(); | |
251 | if (ctx == NULL) | |
252 | return 0; | |
253 | } | |
254 | if (a != NULL) { | |
255 | if (!group->meth->field_decode(group, a, group->a, ctx)) | |
256 | goto err; | |
257 | } | |
258 | if (b != NULL) { | |
259 | if (!group->meth->field_decode(group, b, group->b, ctx)) | |
260 | goto err; | |
261 | } | |
262 | } else { | |
263 | if (a != NULL) { | |
264 | if (!BN_copy(a, group->a)) | |
265 | goto err; | |
266 | } | |
267 | if (b != NULL) { | |
268 | if (!BN_copy(b, group->b)) | |
269 | goto err; | |
270 | } | |
271 | } | |
272 | } | |
273 | ||
274 | ret = 1; | |
60428dbf | 275 | |
0f113f3e MC |
276 | err: |
277 | if (new_ctx) | |
278 | BN_CTX_free(new_ctx); | |
279 | return ret; | |
280 | } | |
60428dbf | 281 | |
7793f30e | 282 | int ec_GFp_simple_group_get_degree(const EC_GROUP *group) |
0f113f3e MC |
283 | { |
284 | return BN_num_bits(group->field); | |
285 | } | |
7793f30e | 286 | |
17d6bb81 | 287 | int ec_GFp_simple_group_check_discriminant(const EC_GROUP *group, BN_CTX *ctx) |
0f113f3e MC |
288 | { |
289 | int ret = 0; | |
290 | BIGNUM *a, *b, *order, *tmp_1, *tmp_2; | |
291 | const BIGNUM *p = group->field; | |
292 | BN_CTX *new_ctx = NULL; | |
293 | ||
294 | if (ctx == NULL) { | |
295 | ctx = new_ctx = BN_CTX_new(); | |
296 | if (ctx == NULL) { | |
297 | ECerr(EC_F_EC_GFP_SIMPLE_GROUP_CHECK_DISCRIMINANT, | |
298 | ERR_R_MALLOC_FAILURE); | |
299 | goto err; | |
300 | } | |
301 | } | |
302 | BN_CTX_start(ctx); | |
303 | a = BN_CTX_get(ctx); | |
304 | b = BN_CTX_get(ctx); | |
305 | tmp_1 = BN_CTX_get(ctx); | |
306 | tmp_2 = BN_CTX_get(ctx); | |
307 | order = BN_CTX_get(ctx); | |
308 | if (order == NULL) | |
309 | goto err; | |
310 | ||
311 | if (group->meth->field_decode) { | |
312 | if (!group->meth->field_decode(group, a, group->a, ctx)) | |
313 | goto err; | |
314 | if (!group->meth->field_decode(group, b, group->b, ctx)) | |
315 | goto err; | |
316 | } else { | |
317 | if (!BN_copy(a, group->a)) | |
318 | goto err; | |
319 | if (!BN_copy(b, group->b)) | |
320 | goto err; | |
321 | } | |
322 | ||
50e735f9 MC |
323 | /*- |
324 | * check the discriminant: | |
325 | * y^2 = x^3 + a*x + b is an elliptic curve <=> 4*a^3 + 27*b^2 != 0 (mod p) | |
326 | * 0 =< a, b < p | |
327 | */ | |
0f113f3e MC |
328 | if (BN_is_zero(a)) { |
329 | if (BN_is_zero(b)) | |
330 | goto err; | |
331 | } else if (!BN_is_zero(b)) { | |
332 | if (!BN_mod_sqr(tmp_1, a, p, ctx)) | |
333 | goto err; | |
334 | if (!BN_mod_mul(tmp_2, tmp_1, a, p, ctx)) | |
335 | goto err; | |
336 | if (!BN_lshift(tmp_1, tmp_2, 2)) | |
337 | goto err; | |
338 | /* tmp_1 = 4*a^3 */ | |
339 | ||
340 | if (!BN_mod_sqr(tmp_2, b, p, ctx)) | |
341 | goto err; | |
342 | if (!BN_mul_word(tmp_2, 27)) | |
343 | goto err; | |
344 | /* tmp_2 = 27*b^2 */ | |
345 | ||
346 | if (!BN_mod_add(a, tmp_1, tmp_2, p, ctx)) | |
347 | goto err; | |
348 | if (BN_is_zero(a)) | |
349 | goto err; | |
350 | } | |
351 | ret = 1; | |
af28dd6c | 352 | |
0f113f3e MC |
353 | err: |
354 | if (ctx != NULL) | |
355 | BN_CTX_end(ctx); | |
356 | if (new_ctx != NULL) | |
357 | BN_CTX_free(new_ctx); | |
358 | return ret; | |
359 | } | |
af28dd6c | 360 | |
60428dbf | 361 | int ec_GFp_simple_point_init(EC_POINT *point) |
0f113f3e MC |
362 | { |
363 | point->X = BN_new(); | |
364 | point->Y = BN_new(); | |
365 | point->Z = BN_new(); | |
366 | point->Z_is_one = 0; | |
367 | ||
368 | if (!point->X || !point->Y || !point->Z) { | |
369 | if (point->X) | |
370 | BN_free(point->X); | |
371 | if (point->Y) | |
372 | BN_free(point->Y); | |
373 | if (point->Z) | |
374 | BN_free(point->Z); | |
375 | return 0; | |
376 | } | |
377 | return 1; | |
378 | } | |
60428dbf BM |
379 | |
380 | void ec_GFp_simple_point_finish(EC_POINT *point) | |
0f113f3e MC |
381 | { |
382 | BN_free(point->X); | |
383 | BN_free(point->Y); | |
384 | BN_free(point->Z); | |
385 | } | |
60428dbf BM |
386 | |
387 | void ec_GFp_simple_point_clear_finish(EC_POINT *point) | |
0f113f3e MC |
388 | { |
389 | BN_clear_free(point->X); | |
390 | BN_clear_free(point->Y); | |
391 | BN_clear_free(point->Z); | |
392 | point->Z_is_one = 0; | |
393 | } | |
60428dbf BM |
394 | |
395 | int ec_GFp_simple_point_copy(EC_POINT *dest, const EC_POINT *src) | |
0f113f3e MC |
396 | { |
397 | if (!BN_copy(dest->X, src->X)) | |
398 | return 0; | |
399 | if (!BN_copy(dest->Y, src->Y)) | |
400 | return 0; | |
401 | if (!BN_copy(dest->Z, src->Z)) | |
402 | return 0; | |
403 | dest->Z_is_one = src->Z_is_one; | |
404 | ||
405 | return 1; | |
406 | } | |
407 | ||
408 | int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *group, | |
409 | EC_POINT *point) | |
410 | { | |
411 | point->Z_is_one = 0; | |
412 | BN_zero(point->Z); | |
413 | return 1; | |
414 | } | |
415 | ||
416 | int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *group, | |
417 | EC_POINT *point, | |
418 | const BIGNUM *x, | |
419 | const BIGNUM *y, | |
420 | const BIGNUM *z, | |
421 | BN_CTX *ctx) | |
422 | { | |
423 | BN_CTX *new_ctx = NULL; | |
424 | int ret = 0; | |
425 | ||
426 | if (ctx == NULL) { | |
427 | ctx = new_ctx = BN_CTX_new(); | |
428 | if (ctx == NULL) | |
429 | return 0; | |
430 | } | |
431 | ||
432 | if (x != NULL) { | |
433 | if (!BN_nnmod(point->X, x, group->field, ctx)) | |
434 | goto err; | |
435 | if (group->meth->field_encode) { | |
436 | if (!group->meth->field_encode(group, point->X, point->X, ctx)) | |
437 | goto err; | |
438 | } | |
439 | } | |
440 | ||
441 | if (y != NULL) { | |
442 | if (!BN_nnmod(point->Y, y, group->field, ctx)) | |
443 | goto err; | |
444 | if (group->meth->field_encode) { | |
445 | if (!group->meth->field_encode(group, point->Y, point->Y, ctx)) | |
446 | goto err; | |
447 | } | |
448 | } | |
449 | ||
450 | if (z != NULL) { | |
451 | int Z_is_one; | |
452 | ||
453 | if (!BN_nnmod(point->Z, z, group->field, ctx)) | |
454 | goto err; | |
455 | Z_is_one = BN_is_one(point->Z); | |
456 | if (group->meth->field_encode) { | |
457 | if (Z_is_one && (group->meth->field_set_to_one != 0)) { | |
458 | if (!group->meth->field_set_to_one(group, point->Z, ctx)) | |
459 | goto err; | |
460 | } else { | |
461 | if (!group-> | |
462 | meth->field_encode(group, point->Z, point->Z, ctx)) | |
463 | goto err; | |
464 | } | |
465 | } | |
466 | point->Z_is_one = Z_is_one; | |
467 | } | |
468 | ||
469 | ret = 1; | |
470 | ||
bb62a8b0 | 471 | err: |
0f113f3e MC |
472 | if (new_ctx != NULL) |
473 | BN_CTX_free(new_ctx); | |
474 | return ret; | |
475 | } | |
476 | ||
477 | int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *group, | |
478 | const EC_POINT *point, | |
479 | BIGNUM *x, BIGNUM *y, | |
480 | BIGNUM *z, BN_CTX *ctx) | |
481 | { | |
482 | BN_CTX *new_ctx = NULL; | |
483 | int ret = 0; | |
484 | ||
485 | if (group->meth->field_decode != 0) { | |
486 | if (ctx == NULL) { | |
487 | ctx = new_ctx = BN_CTX_new(); | |
488 | if (ctx == NULL) | |
489 | return 0; | |
490 | } | |
491 | ||
492 | if (x != NULL) { | |
493 | if (!group->meth->field_decode(group, x, point->X, ctx)) | |
494 | goto err; | |
495 | } | |
496 | if (y != NULL) { | |
497 | if (!group->meth->field_decode(group, y, point->Y, ctx)) | |
498 | goto err; | |
499 | } | |
500 | if (z != NULL) { | |
501 | if (!group->meth->field_decode(group, z, point->Z, ctx)) | |
502 | goto err; | |
503 | } | |
504 | } else { | |
505 | if (x != NULL) { | |
506 | if (!BN_copy(x, point->X)) | |
507 | goto err; | |
508 | } | |
509 | if (y != NULL) { | |
510 | if (!BN_copy(y, point->Y)) | |
511 | goto err; | |
512 | } | |
513 | if (z != NULL) { | |
514 | if (!BN_copy(z, point->Z)) | |
515 | goto err; | |
516 | } | |
517 | } | |
518 | ||
519 | ret = 1; | |
bb62a8b0 | 520 | |
226cc7de | 521 | err: |
0f113f3e MC |
522 | if (new_ctx != NULL) |
523 | BN_CTX_free(new_ctx); | |
524 | return ret; | |
525 | } | |
526 | ||
527 | int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *group, | |
528 | EC_POINT *point, | |
529 | const BIGNUM *x, | |
530 | const BIGNUM *y, BN_CTX *ctx) | |
531 | { | |
532 | if (x == NULL || y == NULL) { | |
533 | /* | |
534 | * unlike for projective coordinates, we do not tolerate this | |
535 | */ | |
536 | ECerr(EC_F_EC_GFP_SIMPLE_POINT_SET_AFFINE_COORDINATES, | |
537 | ERR_R_PASSED_NULL_PARAMETER); | |
538 | return 0; | |
539 | } | |
540 | ||
541 | return EC_POINT_set_Jprojective_coordinates_GFp(group, point, x, y, | |
542 | BN_value_one(), ctx); | |
543 | } | |
544 | ||
545 | int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *group, | |
546 | const EC_POINT *point, | |
547 | BIGNUM *x, BIGNUM *y, | |
548 | BN_CTX *ctx) | |
549 | { | |
550 | BN_CTX *new_ctx = NULL; | |
551 | BIGNUM *Z, *Z_1, *Z_2, *Z_3; | |
552 | const BIGNUM *Z_; | |
553 | int ret = 0; | |
554 | ||
555 | if (EC_POINT_is_at_infinity(group, point)) { | |
556 | ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES, | |
557 | EC_R_POINT_AT_INFINITY); | |
558 | return 0; | |
559 | } | |
560 | ||
561 | if (ctx == NULL) { | |
562 | ctx = new_ctx = BN_CTX_new(); | |
563 | if (ctx == NULL) | |
564 | return 0; | |
565 | } | |
566 | ||
567 | BN_CTX_start(ctx); | |
568 | Z = BN_CTX_get(ctx); | |
569 | Z_1 = BN_CTX_get(ctx); | |
570 | Z_2 = BN_CTX_get(ctx); | |
571 | Z_3 = BN_CTX_get(ctx); | |
572 | if (Z_3 == NULL) | |
573 | goto err; | |
574 | ||
575 | /* transform (X, Y, Z) into (x, y) := (X/Z^2, Y/Z^3) */ | |
576 | ||
577 | if (group->meth->field_decode) { | |
578 | if (!group->meth->field_decode(group, Z, point->Z, ctx)) | |
579 | goto err; | |
580 | Z_ = Z; | |
581 | } else { | |
582 | Z_ = point->Z; | |
583 | } | |
584 | ||
585 | if (BN_is_one(Z_)) { | |
586 | if (group->meth->field_decode) { | |
587 | if (x != NULL) { | |
588 | if (!group->meth->field_decode(group, x, point->X, ctx)) | |
589 | goto err; | |
590 | } | |
591 | if (y != NULL) { | |
592 | if (!group->meth->field_decode(group, y, point->Y, ctx)) | |
593 | goto err; | |
594 | } | |
595 | } else { | |
596 | if (x != NULL) { | |
597 | if (!BN_copy(x, point->X)) | |
598 | goto err; | |
599 | } | |
600 | if (y != NULL) { | |
601 | if (!BN_copy(y, point->Y)) | |
602 | goto err; | |
603 | } | |
604 | } | |
605 | } else { | |
606 | if (!BN_mod_inverse(Z_1, Z_, group->field, ctx)) { | |
607 | ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES, | |
608 | ERR_R_BN_LIB); | |
609 | goto err; | |
610 | } | |
611 | ||
612 | if (group->meth->field_encode == 0) { | |
613 | /* field_sqr works on standard representation */ | |
614 | if (!group->meth->field_sqr(group, Z_2, Z_1, ctx)) | |
615 | goto err; | |
616 | } else { | |
617 | if (!BN_mod_sqr(Z_2, Z_1, group->field, ctx)) | |
618 | goto err; | |
619 | } | |
620 | ||
621 | if (x != NULL) { | |
622 | /* | |
623 | * in the Montgomery case, field_mul will cancel out Montgomery | |
624 | * factor in X: | |
625 | */ | |
626 | if (!group->meth->field_mul(group, x, point->X, Z_2, ctx)) | |
627 | goto err; | |
628 | } | |
629 | ||
630 | if (y != NULL) { | |
631 | if (group->meth->field_encode == 0) { | |
632 | /* | |
633 | * field_mul works on standard representation | |
634 | */ | |
635 | if (!group->meth->field_mul(group, Z_3, Z_2, Z_1, ctx)) | |
636 | goto err; | |
637 | } else { | |
638 | if (!BN_mod_mul(Z_3, Z_2, Z_1, group->field, ctx)) | |
639 | goto err; | |
640 | } | |
641 | ||
642 | /* | |
643 | * in the Montgomery case, field_mul will cancel out Montgomery | |
644 | * factor in Y: | |
645 | */ | |
646 | if (!group->meth->field_mul(group, y, point->Y, Z_3, ctx)) | |
647 | goto err; | |
648 | } | |
649 | } | |
650 | ||
651 | ret = 1; | |
226cc7de BM |
652 | |
653 | err: | |
0f113f3e MC |
654 | BN_CTX_end(ctx); |
655 | if (new_ctx != NULL) | |
656 | BN_CTX_free(new_ctx); | |
657 | return ret; | |
658 | } | |
659 | ||
660 | int ec_GFp_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, | |
661 | const EC_POINT *b, BN_CTX *ctx) | |
662 | { | |
663 | int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *, | |
664 | const BIGNUM *, BN_CTX *); | |
665 | int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); | |
666 | const BIGNUM *p; | |
667 | BN_CTX *new_ctx = NULL; | |
668 | BIGNUM *n0, *n1, *n2, *n3, *n4, *n5, *n6; | |
669 | int ret = 0; | |
670 | ||
671 | if (a == b) | |
672 | return EC_POINT_dbl(group, r, a, ctx); | |
673 | if (EC_POINT_is_at_infinity(group, a)) | |
674 | return EC_POINT_copy(r, b); | |
675 | if (EC_POINT_is_at_infinity(group, b)) | |
676 | return EC_POINT_copy(r, a); | |
677 | ||
678 | field_mul = group->meth->field_mul; | |
679 | field_sqr = group->meth->field_sqr; | |
680 | p = group->field; | |
681 | ||
682 | if (ctx == NULL) { | |
683 | ctx = new_ctx = BN_CTX_new(); | |
684 | if (ctx == NULL) | |
685 | return 0; | |
686 | } | |
687 | ||
688 | BN_CTX_start(ctx); | |
689 | n0 = BN_CTX_get(ctx); | |
690 | n1 = BN_CTX_get(ctx); | |
691 | n2 = BN_CTX_get(ctx); | |
692 | n3 = BN_CTX_get(ctx); | |
693 | n4 = BN_CTX_get(ctx); | |
694 | n5 = BN_CTX_get(ctx); | |
695 | n6 = BN_CTX_get(ctx); | |
696 | if (n6 == NULL) | |
697 | goto end; | |
698 | ||
699 | /* | |
700 | * Note that in this function we must not read components of 'a' or 'b' | |
701 | * once we have written the corresponding components of 'r'. ('r' might | |
702 | * be one of 'a' or 'b'.) | |
703 | */ | |
704 | ||
705 | /* n1, n2 */ | |
706 | if (b->Z_is_one) { | |
707 | if (!BN_copy(n1, a->X)) | |
708 | goto end; | |
709 | if (!BN_copy(n2, a->Y)) | |
710 | goto end; | |
711 | /* n1 = X_a */ | |
712 | /* n2 = Y_a */ | |
713 | } else { | |
714 | if (!field_sqr(group, n0, b->Z, ctx)) | |
715 | goto end; | |
716 | if (!field_mul(group, n1, a->X, n0, ctx)) | |
717 | goto end; | |
718 | /* n1 = X_a * Z_b^2 */ | |
719 | ||
720 | if (!field_mul(group, n0, n0, b->Z, ctx)) | |
721 | goto end; | |
722 | if (!field_mul(group, n2, a->Y, n0, ctx)) | |
723 | goto end; | |
724 | /* n2 = Y_a * Z_b^3 */ | |
725 | } | |
726 | ||
727 | /* n3, n4 */ | |
728 | if (a->Z_is_one) { | |
729 | if (!BN_copy(n3, b->X)) | |
730 | goto end; | |
731 | if (!BN_copy(n4, b->Y)) | |
732 | goto end; | |
733 | /* n3 = X_b */ | |
734 | /* n4 = Y_b */ | |
735 | } else { | |
736 | if (!field_sqr(group, n0, a->Z, ctx)) | |
737 | goto end; | |
738 | if (!field_mul(group, n3, b->X, n0, ctx)) | |
739 | goto end; | |
740 | /* n3 = X_b * Z_a^2 */ | |
741 | ||
742 | if (!field_mul(group, n0, n0, a->Z, ctx)) | |
743 | goto end; | |
744 | if (!field_mul(group, n4, b->Y, n0, ctx)) | |
745 | goto end; | |
746 | /* n4 = Y_b * Z_a^3 */ | |
747 | } | |
748 | ||
749 | /* n5, n6 */ | |
750 | if (!BN_mod_sub_quick(n5, n1, n3, p)) | |
751 | goto end; | |
752 | if (!BN_mod_sub_quick(n6, n2, n4, p)) | |
753 | goto end; | |
754 | /* n5 = n1 - n3 */ | |
755 | /* n6 = n2 - n4 */ | |
756 | ||
757 | if (BN_is_zero(n5)) { | |
758 | if (BN_is_zero(n6)) { | |
759 | /* a is the same point as b */ | |
760 | BN_CTX_end(ctx); | |
761 | ret = EC_POINT_dbl(group, r, a, ctx); | |
762 | ctx = NULL; | |
763 | goto end; | |
764 | } else { | |
765 | /* a is the inverse of b */ | |
766 | BN_zero(r->Z); | |
767 | r->Z_is_one = 0; | |
768 | ret = 1; | |
769 | goto end; | |
770 | } | |
771 | } | |
772 | ||
773 | /* 'n7', 'n8' */ | |
774 | if (!BN_mod_add_quick(n1, n1, n3, p)) | |
775 | goto end; | |
776 | if (!BN_mod_add_quick(n2, n2, n4, p)) | |
777 | goto end; | |
778 | /* 'n7' = n1 + n3 */ | |
779 | /* 'n8' = n2 + n4 */ | |
780 | ||
781 | /* Z_r */ | |
782 | if (a->Z_is_one && b->Z_is_one) { | |
783 | if (!BN_copy(r->Z, n5)) | |
784 | goto end; | |
785 | } else { | |
786 | if (a->Z_is_one) { | |
787 | if (!BN_copy(n0, b->Z)) | |
788 | goto end; | |
789 | } else if (b->Z_is_one) { | |
790 | if (!BN_copy(n0, a->Z)) | |
791 | goto end; | |
792 | } else { | |
793 | if (!field_mul(group, n0, a->Z, b->Z, ctx)) | |
794 | goto end; | |
795 | } | |
796 | if (!field_mul(group, r->Z, n0, n5, ctx)) | |
797 | goto end; | |
798 | } | |
799 | r->Z_is_one = 0; | |
800 | /* Z_r = Z_a * Z_b * n5 */ | |
801 | ||
802 | /* X_r */ | |
803 | if (!field_sqr(group, n0, n6, ctx)) | |
804 | goto end; | |
805 | if (!field_sqr(group, n4, n5, ctx)) | |
806 | goto end; | |
807 | if (!field_mul(group, n3, n1, n4, ctx)) | |
808 | goto end; | |
809 | if (!BN_mod_sub_quick(r->X, n0, n3, p)) | |
810 | goto end; | |
811 | /* X_r = n6^2 - n5^2 * 'n7' */ | |
812 | ||
813 | /* 'n9' */ | |
814 | if (!BN_mod_lshift1_quick(n0, r->X, p)) | |
815 | goto end; | |
816 | if (!BN_mod_sub_quick(n0, n3, n0, p)) | |
817 | goto end; | |
818 | /* n9 = n5^2 * 'n7' - 2 * X_r */ | |
819 | ||
820 | /* Y_r */ | |
821 | if (!field_mul(group, n0, n0, n6, ctx)) | |
822 | goto end; | |
823 | if (!field_mul(group, n5, n4, n5, ctx)) | |
824 | goto end; /* now n5 is n5^3 */ | |
825 | if (!field_mul(group, n1, n2, n5, ctx)) | |
826 | goto end; | |
827 | if (!BN_mod_sub_quick(n0, n0, n1, p)) | |
828 | goto end; | |
829 | if (BN_is_odd(n0)) | |
830 | if (!BN_add(n0, n0, p)) | |
831 | goto end; | |
832 | /* now 0 <= n0 < 2*p, and n0 is even */ | |
833 | if (!BN_rshift1(r->Y, n0)) | |
834 | goto end; | |
835 | /* Y_r = (n6 * 'n9' - 'n8' * 'n5^3') / 2 */ | |
836 | ||
837 | ret = 1; | |
60428dbf BM |
838 | |
839 | end: | |
0f113f3e MC |
840 | if (ctx) /* otherwise we already called BN_CTX_end */ |
841 | BN_CTX_end(ctx); | |
842 | if (new_ctx != NULL) | |
843 | BN_CTX_free(new_ctx); | |
844 | return ret; | |
845 | } | |
846 | ||
847 | int ec_GFp_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, | |
848 | BN_CTX *ctx) | |
849 | { | |
850 | int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *, | |
851 | const BIGNUM *, BN_CTX *); | |
852 | int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); | |
853 | const BIGNUM *p; | |
854 | BN_CTX *new_ctx = NULL; | |
855 | BIGNUM *n0, *n1, *n2, *n3; | |
856 | int ret = 0; | |
857 | ||
858 | if (EC_POINT_is_at_infinity(group, a)) { | |
859 | BN_zero(r->Z); | |
860 | r->Z_is_one = 0; | |
861 | return 1; | |
862 | } | |
863 | ||
864 | field_mul = group->meth->field_mul; | |
865 | field_sqr = group->meth->field_sqr; | |
866 | p = group->field; | |
867 | ||
868 | if (ctx == NULL) { | |
869 | ctx = new_ctx = BN_CTX_new(); | |
870 | if (ctx == NULL) | |
871 | return 0; | |
872 | } | |
873 | ||
874 | BN_CTX_start(ctx); | |
875 | n0 = BN_CTX_get(ctx); | |
876 | n1 = BN_CTX_get(ctx); | |
877 | n2 = BN_CTX_get(ctx); | |
878 | n3 = BN_CTX_get(ctx); | |
879 | if (n3 == NULL) | |
880 | goto err; | |
881 | ||
882 | /* | |
883 | * Note that in this function we must not read components of 'a' once we | |
884 | * have written the corresponding components of 'r'. ('r' might the same | |
885 | * as 'a'.) | |
886 | */ | |
887 | ||
888 | /* n1 */ | |
889 | if (a->Z_is_one) { | |
890 | if (!field_sqr(group, n0, a->X, ctx)) | |
891 | goto err; | |
892 | if (!BN_mod_lshift1_quick(n1, n0, p)) | |
893 | goto err; | |
894 | if (!BN_mod_add_quick(n0, n0, n1, p)) | |
895 | goto err; | |
896 | if (!BN_mod_add_quick(n1, n0, group->a, p)) | |
897 | goto err; | |
898 | /* n1 = 3 * X_a^2 + a_curve */ | |
899 | } else if (group->a_is_minus3) { | |
900 | if (!field_sqr(group, n1, a->Z, ctx)) | |
901 | goto err; | |
902 | if (!BN_mod_add_quick(n0, a->X, n1, p)) | |
903 | goto err; | |
904 | if (!BN_mod_sub_quick(n2, a->X, n1, p)) | |
905 | goto err; | |
906 | if (!field_mul(group, n1, n0, n2, ctx)) | |
907 | goto err; | |
908 | if (!BN_mod_lshift1_quick(n0, n1, p)) | |
909 | goto err; | |
910 | if (!BN_mod_add_quick(n1, n0, n1, p)) | |
911 | goto err; | |
35a1cc90 MC |
912 | /*- |
913 | * n1 = 3 * (X_a + Z_a^2) * (X_a - Z_a^2) | |
914 | * = 3 * X_a^2 - 3 * Z_a^4 | |
915 | */ | |
0f113f3e MC |
916 | } else { |
917 | if (!field_sqr(group, n0, a->X, ctx)) | |
918 | goto err; | |
919 | if (!BN_mod_lshift1_quick(n1, n0, p)) | |
920 | goto err; | |
921 | if (!BN_mod_add_quick(n0, n0, n1, p)) | |
922 | goto err; | |
923 | if (!field_sqr(group, n1, a->Z, ctx)) | |
924 | goto err; | |
925 | if (!field_sqr(group, n1, n1, ctx)) | |
926 | goto err; | |
927 | if (!field_mul(group, n1, n1, group->a, ctx)) | |
928 | goto err; | |
929 | if (!BN_mod_add_quick(n1, n1, n0, p)) | |
930 | goto err; | |
931 | /* n1 = 3 * X_a^2 + a_curve * Z_a^4 */ | |
932 | } | |
933 | ||
934 | /* Z_r */ | |
935 | if (a->Z_is_one) { | |
936 | if (!BN_copy(n0, a->Y)) | |
937 | goto err; | |
938 | } else { | |
939 | if (!field_mul(group, n0, a->Y, a->Z, ctx)) | |
940 | goto err; | |
941 | } | |
942 | if (!BN_mod_lshift1_quick(r->Z, n0, p)) | |
943 | goto err; | |
944 | r->Z_is_one = 0; | |
945 | /* Z_r = 2 * Y_a * Z_a */ | |
946 | ||
947 | /* n2 */ | |
948 | if (!field_sqr(group, n3, a->Y, ctx)) | |
949 | goto err; | |
950 | if (!field_mul(group, n2, a->X, n3, ctx)) | |
951 | goto err; | |
952 | if (!BN_mod_lshift_quick(n2, n2, 2, p)) | |
953 | goto err; | |
954 | /* n2 = 4 * X_a * Y_a^2 */ | |
955 | ||
956 | /* X_r */ | |
957 | if (!BN_mod_lshift1_quick(n0, n2, p)) | |
958 | goto err; | |
959 | if (!field_sqr(group, r->X, n1, ctx)) | |
960 | goto err; | |
961 | if (!BN_mod_sub_quick(r->X, r->X, n0, p)) | |
962 | goto err; | |
963 | /* X_r = n1^2 - 2 * n2 */ | |
964 | ||
965 | /* n3 */ | |
966 | if (!field_sqr(group, n0, n3, ctx)) | |
967 | goto err; | |
968 | if (!BN_mod_lshift_quick(n3, n0, 3, p)) | |
969 | goto err; | |
970 | /* n3 = 8 * Y_a^4 */ | |
971 | ||
972 | /* Y_r */ | |
973 | if (!BN_mod_sub_quick(n0, n2, r->X, p)) | |
974 | goto err; | |
975 | if (!field_mul(group, n0, n1, n0, ctx)) | |
976 | goto err; | |
977 | if (!BN_mod_sub_quick(r->Y, n0, n3, p)) | |
978 | goto err; | |
979 | /* Y_r = n1 * (n2 - X_r) - n3 */ | |
980 | ||
981 | ret = 1; | |
60428dbf BM |
982 | |
983 | err: | |
0f113f3e MC |
984 | BN_CTX_end(ctx); |
985 | if (new_ctx != NULL) | |
986 | BN_CTX_free(new_ctx); | |
987 | return ret; | |
988 | } | |
60428dbf | 989 | |
bb62a8b0 | 990 | int ec_GFp_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx) |
0f113f3e MC |
991 | { |
992 | if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(point->Y)) | |
993 | /* point is its own inverse */ | |
994 | return 1; | |
1d5bd6cf | 995 | |
0f113f3e MC |
996 | return BN_usub(point->Y, group->field, point->Y); |
997 | } | |
1d5bd6cf | 998 | |
60428dbf | 999 | int ec_GFp_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point) |
0f113f3e MC |
1000 | { |
1001 | return BN_is_zero(point->Z); | |
1002 | } | |
1003 | ||
1004 | int ec_GFp_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, | |
1005 | BN_CTX *ctx) | |
1006 | { | |
1007 | int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *, | |
1008 | const BIGNUM *, BN_CTX *); | |
1009 | int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); | |
1010 | const BIGNUM *p; | |
1011 | BN_CTX *new_ctx = NULL; | |
1012 | BIGNUM *rh, *tmp, *Z4, *Z6; | |
1013 | int ret = -1; | |
1014 | ||
1015 | if (EC_POINT_is_at_infinity(group, point)) | |
1016 | return 1; | |
1017 | ||
1018 | field_mul = group->meth->field_mul; | |
1019 | field_sqr = group->meth->field_sqr; | |
1020 | p = group->field; | |
1021 | ||
1022 | if (ctx == NULL) { | |
1023 | ctx = new_ctx = BN_CTX_new(); | |
1024 | if (ctx == NULL) | |
1025 | return -1; | |
1026 | } | |
1027 | ||
1028 | BN_CTX_start(ctx); | |
1029 | rh = BN_CTX_get(ctx); | |
1030 | tmp = BN_CTX_get(ctx); | |
1031 | Z4 = BN_CTX_get(ctx); | |
1032 | Z6 = BN_CTX_get(ctx); | |
1033 | if (Z6 == NULL) | |
1034 | goto err; | |
1035 | ||
35a1cc90 MC |
1036 | /*- |
1037 | * We have a curve defined by a Weierstrass equation | |
1038 | * y^2 = x^3 + a*x + b. | |
1039 | * The point to consider is given in Jacobian projective coordinates | |
1040 | * where (X, Y, Z) represents (x, y) = (X/Z^2, Y/Z^3). | |
1041 | * Substituting this and multiplying by Z^6 transforms the above equation into | |
1042 | * Y^2 = X^3 + a*X*Z^4 + b*Z^6. | |
1043 | * To test this, we add up the right-hand side in 'rh'. | |
1044 | */ | |
0f113f3e MC |
1045 | |
1046 | /* rh := X^2 */ | |
1047 | if (!field_sqr(group, rh, point->X, ctx)) | |
1048 | goto err; | |
1049 | ||
1050 | if (!point->Z_is_one) { | |
1051 | if (!field_sqr(group, tmp, point->Z, ctx)) | |
1052 | goto err; | |
1053 | if (!field_sqr(group, Z4, tmp, ctx)) | |
1054 | goto err; | |
1055 | if (!field_mul(group, Z6, Z4, tmp, ctx)) | |
1056 | goto err; | |
1057 | ||
1058 | /* rh := (rh + a*Z^4)*X */ | |
1059 | if (group->a_is_minus3) { | |
1060 | if (!BN_mod_lshift1_quick(tmp, Z4, p)) | |
1061 | goto err; | |
1062 | if (!BN_mod_add_quick(tmp, tmp, Z4, p)) | |
1063 | goto err; | |
1064 | if (!BN_mod_sub_quick(rh, rh, tmp, p)) | |
1065 | goto err; | |
1066 | if (!field_mul(group, rh, rh, point->X, ctx)) | |
1067 | goto err; | |
1068 | } else { | |
1069 | if (!field_mul(group, tmp, Z4, group->a, ctx)) | |
1070 | goto err; | |
1071 | if (!BN_mod_add_quick(rh, rh, tmp, p)) | |
1072 | goto err; | |
1073 | if (!field_mul(group, rh, rh, point->X, ctx)) | |
1074 | goto err; | |
1075 | } | |
1076 | ||
1077 | /* rh := rh + b*Z^6 */ | |
1078 | if (!field_mul(group, tmp, group->b, Z6, ctx)) | |
1079 | goto err; | |
1080 | if (!BN_mod_add_quick(rh, rh, tmp, p)) | |
1081 | goto err; | |
1082 | } else { | |
1083 | /* point->Z_is_one */ | |
1084 | ||
1085 | /* rh := (rh + a)*X */ | |
1086 | if (!BN_mod_add_quick(rh, rh, group->a, p)) | |
1087 | goto err; | |
1088 | if (!field_mul(group, rh, rh, point->X, ctx)) | |
1089 | goto err; | |
1090 | /* rh := rh + b */ | |
1091 | if (!BN_mod_add_quick(rh, rh, group->b, p)) | |
1092 | goto err; | |
1093 | } | |
1094 | ||
1095 | /* 'lh' := Y^2 */ | |
1096 | if (!field_sqr(group, tmp, point->Y, ctx)) | |
1097 | goto err; | |
1098 | ||
1099 | ret = (0 == BN_ucmp(tmp, rh)); | |
e869d4bd BM |
1100 | |
1101 | err: | |
0f113f3e MC |
1102 | BN_CTX_end(ctx); |
1103 | if (new_ctx != NULL) | |
1104 | BN_CTX_free(new_ctx); | |
1105 | return ret; | |
1106 | } | |
1107 | ||
1108 | int ec_GFp_simple_cmp(const EC_GROUP *group, const EC_POINT *a, | |
1109 | const EC_POINT *b, BN_CTX *ctx) | |
1110 | { | |
35a1cc90 MC |
1111 | /*- |
1112 | * return values: | |
1113 | * -1 error | |
1114 | * 0 equal (in affine coordinates) | |
1115 | * 1 not equal | |
1116 | */ | |
0f113f3e MC |
1117 | |
1118 | int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *, | |
1119 | const BIGNUM *, BN_CTX *); | |
1120 | int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); | |
1121 | BN_CTX *new_ctx = NULL; | |
1122 | BIGNUM *tmp1, *tmp2, *Za23, *Zb23; | |
1123 | const BIGNUM *tmp1_, *tmp2_; | |
1124 | int ret = -1; | |
1125 | ||
1126 | if (EC_POINT_is_at_infinity(group, a)) { | |
1127 | return EC_POINT_is_at_infinity(group, b) ? 0 : 1; | |
1128 | } | |
1129 | ||
1130 | if (EC_POINT_is_at_infinity(group, b)) | |
1131 | return 1; | |
1132 | ||
1133 | if (a->Z_is_one && b->Z_is_one) { | |
1134 | return ((BN_cmp(a->X, b->X) == 0) && BN_cmp(a->Y, b->Y) == 0) ? 0 : 1; | |
1135 | } | |
1136 | ||
1137 | field_mul = group->meth->field_mul; | |
1138 | field_sqr = group->meth->field_sqr; | |
1139 | ||
1140 | if (ctx == NULL) { | |
1141 | ctx = new_ctx = BN_CTX_new(); | |
1142 | if (ctx == NULL) | |
1143 | return -1; | |
1144 | } | |
1145 | ||
1146 | BN_CTX_start(ctx); | |
1147 | tmp1 = BN_CTX_get(ctx); | |
1148 | tmp2 = BN_CTX_get(ctx); | |
1149 | Za23 = BN_CTX_get(ctx); | |
1150 | Zb23 = BN_CTX_get(ctx); | |
1151 | if (Zb23 == NULL) | |
1152 | goto end; | |
1153 | ||
35a1cc90 MC |
1154 | /*- |
1155 | * We have to decide whether | |
1156 | * (X_a/Z_a^2, Y_a/Z_a^3) = (X_b/Z_b^2, Y_b/Z_b^3), | |
1157 | * or equivalently, whether | |
1158 | * (X_a*Z_b^2, Y_a*Z_b^3) = (X_b*Z_a^2, Y_b*Z_a^3). | |
1159 | */ | |
0f113f3e MC |
1160 | |
1161 | if (!b->Z_is_one) { | |
1162 | if (!field_sqr(group, Zb23, b->Z, ctx)) | |
1163 | goto end; | |
1164 | if (!field_mul(group, tmp1, a->X, Zb23, ctx)) | |
1165 | goto end; | |
1166 | tmp1_ = tmp1; | |
1167 | } else | |
1168 | tmp1_ = a->X; | |
1169 | if (!a->Z_is_one) { | |
1170 | if (!field_sqr(group, Za23, a->Z, ctx)) | |
1171 | goto end; | |
1172 | if (!field_mul(group, tmp2, b->X, Za23, ctx)) | |
1173 | goto end; | |
1174 | tmp2_ = tmp2; | |
1175 | } else | |
1176 | tmp2_ = b->X; | |
1177 | ||
1178 | /* compare X_a*Z_b^2 with X_b*Z_a^2 */ | |
1179 | if (BN_cmp(tmp1_, tmp2_) != 0) { | |
1180 | ret = 1; /* points differ */ | |
1181 | goto end; | |
1182 | } | |
1183 | ||
1184 | if (!b->Z_is_one) { | |
1185 | if (!field_mul(group, Zb23, Zb23, b->Z, ctx)) | |
1186 | goto end; | |
1187 | if (!field_mul(group, tmp1, a->Y, Zb23, ctx)) | |
1188 | goto end; | |
1189 | /* tmp1_ = tmp1 */ | |
1190 | } else | |
1191 | tmp1_ = a->Y; | |
1192 | if (!a->Z_is_one) { | |
1193 | if (!field_mul(group, Za23, Za23, a->Z, ctx)) | |
1194 | goto end; | |
1195 | if (!field_mul(group, tmp2, b->Y, Za23, ctx)) | |
1196 | goto end; | |
1197 | /* tmp2_ = tmp2 */ | |
1198 | } else | |
1199 | tmp2_ = b->Y; | |
1200 | ||
1201 | /* compare Y_a*Z_b^3 with Y_b*Z_a^3 */ | |
1202 | if (BN_cmp(tmp1_, tmp2_) != 0) { | |
1203 | ret = 1; /* points differ */ | |
1204 | goto end; | |
1205 | } | |
1206 | ||
1207 | /* points are equal */ | |
1208 | ret = 0; | |
bb62a8b0 BM |
1209 | |
1210 | end: | |
0f113f3e MC |
1211 | BN_CTX_end(ctx); |
1212 | if (new_ctx != NULL) | |
1213 | BN_CTX_free(new_ctx); | |
1214 | return ret; | |
1215 | } | |
1216 | ||
1217 | int ec_GFp_simple_make_affine(const EC_GROUP *group, EC_POINT *point, | |
1218 | BN_CTX *ctx) | |
1219 | { | |
1220 | BN_CTX *new_ctx = NULL; | |
1221 | BIGNUM *x, *y; | |
1222 | int ret = 0; | |
1223 | ||
1224 | if (point->Z_is_one || EC_POINT_is_at_infinity(group, point)) | |
1225 | return 1; | |
1226 | ||
1227 | if (ctx == NULL) { | |
1228 | ctx = new_ctx = BN_CTX_new(); | |
1229 | if (ctx == NULL) | |
1230 | return 0; | |
1231 | } | |
1232 | ||
1233 | BN_CTX_start(ctx); | |
1234 | x = BN_CTX_get(ctx); | |
1235 | y = BN_CTX_get(ctx); | |
1236 | if (y == NULL) | |
1237 | goto err; | |
1238 | ||
1239 | if (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx)) | |
1240 | goto err; | |
1241 | if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) | |
1242 | goto err; | |
1243 | if (!point->Z_is_one) { | |
1244 | ECerr(EC_F_EC_GFP_SIMPLE_MAKE_AFFINE, ERR_R_INTERNAL_ERROR); | |
1245 | goto err; | |
1246 | } | |
1247 | ||
1248 | ret = 1; | |
e869d4bd | 1249 | |
226cc7de | 1250 | err: |
0f113f3e MC |
1251 | BN_CTX_end(ctx); |
1252 | if (new_ctx != NULL) | |
1253 | BN_CTX_free(new_ctx); | |
1254 | return ret; | |
1255 | } | |
1256 | ||
1257 | int ec_GFp_simple_points_make_affine(const EC_GROUP *group, size_t num, | |
1258 | EC_POINT *points[], BN_CTX *ctx) | |
1259 | { | |
1260 | BN_CTX *new_ctx = NULL; | |
1261 | BIGNUM *tmp, *tmp_Z; | |
1262 | BIGNUM **prod_Z = NULL; | |
1263 | size_t i; | |
1264 | int ret = 0; | |
1265 | ||
1266 | if (num == 0) | |
1267 | return 1; | |
1268 | ||
1269 | if (ctx == NULL) { | |
1270 | ctx = new_ctx = BN_CTX_new(); | |
1271 | if (ctx == NULL) | |
1272 | return 0; | |
1273 | } | |
1274 | ||
1275 | BN_CTX_start(ctx); | |
1276 | tmp = BN_CTX_get(ctx); | |
1277 | tmp_Z = BN_CTX_get(ctx); | |
1278 | if (tmp == NULL || tmp_Z == NULL) | |
1279 | goto err; | |
1280 | ||
1281 | prod_Z = OPENSSL_malloc(num * sizeof prod_Z[0]); | |
1282 | if (prod_Z == NULL) | |
1283 | goto err; | |
1284 | for (i = 0; i < num; i++) { | |
1285 | prod_Z[i] = BN_new(); | |
1286 | if (prod_Z[i] == NULL) | |
1287 | goto err; | |
1288 | } | |
1289 | ||
1290 | /* | |
1291 | * Set each prod_Z[i] to the product of points[0]->Z .. points[i]->Z, | |
1292 | * skipping any zero-valued inputs (pretend that they're 1). | |
1293 | */ | |
1294 | ||
1295 | if (!BN_is_zero(points[0]->Z)) { | |
1296 | if (!BN_copy(prod_Z[0], points[0]->Z)) | |
1297 | goto err; | |
1298 | } else { | |
1299 | if (group->meth->field_set_to_one != 0) { | |
1300 | if (!group->meth->field_set_to_one(group, prod_Z[0], ctx)) | |
1301 | goto err; | |
1302 | } else { | |
1303 | if (!BN_one(prod_Z[0])) | |
1304 | goto err; | |
1305 | } | |
1306 | } | |
1307 | ||
1308 | for (i = 1; i < num; i++) { | |
1309 | if (!BN_is_zero(points[i]->Z)) { | |
1310 | if (!group-> | |
1311 | meth->field_mul(group, prod_Z[i], prod_Z[i - 1], points[i]->Z, | |
1312 | ctx)) | |
1313 | goto err; | |
1314 | } else { | |
1315 | if (!BN_copy(prod_Z[i], prod_Z[i - 1])) | |
1316 | goto err; | |
1317 | } | |
1318 | } | |
1319 | ||
1320 | /* | |
1321 | * Now use a single explicit inversion to replace every non-zero | |
1322 | * points[i]->Z by its inverse. | |
1323 | */ | |
1324 | ||
1325 | if (!BN_mod_inverse(tmp, prod_Z[num - 1], group->field, ctx)) { | |
1326 | ECerr(EC_F_EC_GFP_SIMPLE_POINTS_MAKE_AFFINE, ERR_R_BN_LIB); | |
1327 | goto err; | |
1328 | } | |
1329 | if (group->meth->field_encode != 0) { | |
1330 | /* | |
1331 | * In the Montgomery case, we just turned R*H (representing H) into | |
1332 | * 1/(R*H), but we need R*(1/H) (representing 1/H); i.e. we need to | |
1333 | * multiply by the Montgomery factor twice. | |
1334 | */ | |
1335 | if (!group->meth->field_encode(group, tmp, tmp, ctx)) | |
1336 | goto err; | |
1337 | if (!group->meth->field_encode(group, tmp, tmp, ctx)) | |
1338 | goto err; | |
1339 | } | |
1340 | ||
1341 | for (i = num - 1; i > 0; --i) { | |
1342 | /* | |
1343 | * Loop invariant: tmp is the product of the inverses of points[0]->Z | |
1344 | * .. points[i]->Z (zero-valued inputs skipped). | |
1345 | */ | |
1346 | if (!BN_is_zero(points[i]->Z)) { | |
1347 | /* | |
1348 | * Set tmp_Z to the inverse of points[i]->Z (as product of Z | |
1349 | * inverses 0 .. i, Z values 0 .. i - 1). | |
1350 | */ | |
1351 | if (!group-> | |
1352 | meth->field_mul(group, tmp_Z, prod_Z[i - 1], tmp, ctx)) | |
1353 | goto err; | |
1354 | /* | |
1355 | * Update tmp to satisfy the loop invariant for i - 1. | |
1356 | */ | |
1357 | if (!group->meth->field_mul(group, tmp, tmp, points[i]->Z, ctx)) | |
1358 | goto err; | |
1359 | /* Replace points[i]->Z by its inverse. */ | |
1360 | if (!BN_copy(points[i]->Z, tmp_Z)) | |
1361 | goto err; | |
1362 | } | |
1363 | } | |
1364 | ||
1365 | if (!BN_is_zero(points[0]->Z)) { | |
1366 | /* Replace points[0]->Z by its inverse. */ | |
1367 | if (!BN_copy(points[0]->Z, tmp)) | |
1368 | goto err; | |
1369 | } | |
1370 | ||
1371 | /* Finally, fix up the X and Y coordinates for all points. */ | |
1372 | ||
1373 | for (i = 0; i < num; i++) { | |
1374 | EC_POINT *p = points[i]; | |
1375 | ||
1376 | if (!BN_is_zero(p->Z)) { | |
1377 | /* turn (X, Y, 1/Z) into (X/Z^2, Y/Z^3, 1) */ | |
1378 | ||
1379 | if (!group->meth->field_sqr(group, tmp, p->Z, ctx)) | |
1380 | goto err; | |
1381 | if (!group->meth->field_mul(group, p->X, p->X, tmp, ctx)) | |
1382 | goto err; | |
1383 | ||
1384 | if (!group->meth->field_mul(group, tmp, tmp, p->Z, ctx)) | |
1385 | goto err; | |
1386 | if (!group->meth->field_mul(group, p->Y, p->Y, tmp, ctx)) | |
1387 | goto err; | |
1388 | ||
1389 | if (group->meth->field_set_to_one != 0) { | |
1390 | if (!group->meth->field_set_to_one(group, p->Z, ctx)) | |
1391 | goto err; | |
1392 | } else { | |
1393 | if (!BN_one(p->Z)) | |
1394 | goto err; | |
1395 | } | |
1396 | p->Z_is_one = 1; | |
1397 | } | |
1398 | } | |
1399 | ||
1400 | ret = 1; | |
0fe73d6c | 1401 | |
48fe4d62 | 1402 | err: |
0f113f3e MC |
1403 | BN_CTX_end(ctx); |
1404 | if (new_ctx != NULL) | |
1405 | BN_CTX_free(new_ctx); | |
1406 | if (prod_Z != NULL) { | |
1407 | for (i = 0; i < num; i++) { | |
1408 | if (prod_Z[i] == NULL) | |
1409 | break; | |
1410 | BN_clear_free(prod_Z[i]); | |
1411 | } | |
1412 | OPENSSL_free(prod_Z); | |
1413 | } | |
1414 | return ret; | |
1415 | } | |
1416 | ||
1417 | int ec_GFp_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, | |
1418 | const BIGNUM *b, BN_CTX *ctx) | |
1419 | { | |
1420 | return BN_mod_mul(r, a, b, group->field, ctx); | |
1421 | } | |
1422 | ||
1423 | int ec_GFp_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, | |
1424 | BN_CTX *ctx) | |
1425 | { | |
1426 | return BN_mod_sqr(r, a, group->field, ctx); | |
1427 | } |