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Commit | Line | Data |
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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) { | |
a3853772 RS |
136 | BN_free(group->field); |
137 | BN_free(group->a); | |
138 | BN_free(group->b); | |
0f113f3e MC |
139 | return 0; |
140 | } | |
141 | group->a_is_minus3 = 0; | |
142 | return 1; | |
143 | } | |
60428dbf | 144 | |
bb62a8b0 | 145 | void ec_GFp_simple_group_finish(EC_GROUP *group) |
0f113f3e MC |
146 | { |
147 | BN_free(group->field); | |
148 | BN_free(group->a); | |
149 | BN_free(group->b); | |
150 | } | |
bb62a8b0 BM |
151 | |
152 | void ec_GFp_simple_group_clear_finish(EC_GROUP *group) | |
0f113f3e MC |
153 | { |
154 | BN_clear_free(group->field); | |
155 | BN_clear_free(group->a); | |
156 | BN_clear_free(group->b); | |
157 | } | |
bb62a8b0 BM |
158 | |
159 | int ec_GFp_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src) | |
0f113f3e MC |
160 | { |
161 | if (!BN_copy(dest->field, src->field)) | |
162 | return 0; | |
163 | if (!BN_copy(dest->a, src->a)) | |
164 | return 0; | |
165 | if (!BN_copy(dest->b, src->b)) | |
166 | return 0; | |
bb62a8b0 | 167 | |
0f113f3e | 168 | dest->a_is_minus3 = src->a_is_minus3; |
bb62a8b0 | 169 | |
0f113f3e MC |
170 | return 1; |
171 | } | |
bb62a8b0 | 172 | |
35b73a1f | 173 | int ec_GFp_simple_group_set_curve(EC_GROUP *group, |
0f113f3e MC |
174 | const BIGNUM *p, const BIGNUM *a, |
175 | const BIGNUM *b, BN_CTX *ctx) | |
176 | { | |
177 | int ret = 0; | |
178 | BN_CTX *new_ctx = NULL; | |
179 | BIGNUM *tmp_a; | |
180 | ||
181 | /* p must be a prime > 3 */ | |
182 | if (BN_num_bits(p) <= 2 || !BN_is_odd(p)) { | |
183 | ECerr(EC_F_EC_GFP_SIMPLE_GROUP_SET_CURVE, EC_R_INVALID_FIELD); | |
184 | return 0; | |
185 | } | |
186 | ||
187 | if (ctx == NULL) { | |
188 | ctx = new_ctx = BN_CTX_new(); | |
189 | if (ctx == NULL) | |
190 | return 0; | |
191 | } | |
192 | ||
193 | BN_CTX_start(ctx); | |
194 | tmp_a = BN_CTX_get(ctx); | |
195 | if (tmp_a == NULL) | |
196 | goto err; | |
197 | ||
198 | /* group->field */ | |
199 | if (!BN_copy(group->field, p)) | |
200 | goto err; | |
201 | BN_set_negative(group->field, 0); | |
202 | ||
203 | /* group->a */ | |
204 | if (!BN_nnmod(tmp_a, a, p, ctx)) | |
205 | goto err; | |
206 | if (group->meth->field_encode) { | |
207 | if (!group->meth->field_encode(group, group->a, tmp_a, ctx)) | |
208 | goto err; | |
209 | } else if (!BN_copy(group->a, tmp_a)) | |
210 | goto err; | |
211 | ||
212 | /* group->b */ | |
213 | if (!BN_nnmod(group->b, b, p, ctx)) | |
214 | goto err; | |
215 | if (group->meth->field_encode) | |
216 | if (!group->meth->field_encode(group, group->b, group->b, ctx)) | |
217 | goto err; | |
218 | ||
219 | /* group->a_is_minus3 */ | |
220 | if (!BN_add_word(tmp_a, 3)) | |
221 | goto err; | |
222 | group->a_is_minus3 = (0 == BN_cmp(tmp_a, group->field)); | |
223 | ||
224 | ret = 1; | |
60428dbf BM |
225 | |
226 | err: | |
0f113f3e MC |
227 | BN_CTX_end(ctx); |
228 | if (new_ctx != NULL) | |
229 | BN_CTX_free(new_ctx); | |
230 | return ret; | |
231 | } | |
232 | ||
233 | int ec_GFp_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, | |
234 | BIGNUM *b, BN_CTX *ctx) | |
235 | { | |
236 | int ret = 0; | |
237 | BN_CTX *new_ctx = NULL; | |
238 | ||
239 | if (p != NULL) { | |
240 | if (!BN_copy(p, group->field)) | |
241 | return 0; | |
242 | } | |
243 | ||
244 | if (a != NULL || b != NULL) { | |
245 | if (group->meth->field_decode) { | |
246 | if (ctx == NULL) { | |
247 | ctx = new_ctx = BN_CTX_new(); | |
248 | if (ctx == NULL) | |
249 | return 0; | |
250 | } | |
251 | if (a != NULL) { | |
252 | if (!group->meth->field_decode(group, a, group->a, ctx)) | |
253 | goto err; | |
254 | } | |
255 | if (b != NULL) { | |
256 | if (!group->meth->field_decode(group, b, group->b, ctx)) | |
257 | goto err; | |
258 | } | |
259 | } else { | |
260 | if (a != NULL) { | |
261 | if (!BN_copy(a, group->a)) | |
262 | goto err; | |
263 | } | |
264 | if (b != NULL) { | |
265 | if (!BN_copy(b, group->b)) | |
266 | goto err; | |
267 | } | |
268 | } | |
269 | } | |
270 | ||
271 | ret = 1; | |
60428dbf | 272 | |
0f113f3e MC |
273 | err: |
274 | if (new_ctx) | |
275 | BN_CTX_free(new_ctx); | |
276 | return ret; | |
277 | } | |
60428dbf | 278 | |
7793f30e | 279 | int ec_GFp_simple_group_get_degree(const EC_GROUP *group) |
0f113f3e MC |
280 | { |
281 | return BN_num_bits(group->field); | |
282 | } | |
7793f30e | 283 | |
17d6bb81 | 284 | int ec_GFp_simple_group_check_discriminant(const EC_GROUP *group, BN_CTX *ctx) |
0f113f3e MC |
285 | { |
286 | int ret = 0; | |
287 | BIGNUM *a, *b, *order, *tmp_1, *tmp_2; | |
288 | const BIGNUM *p = group->field; | |
289 | BN_CTX *new_ctx = NULL; | |
290 | ||
291 | if (ctx == NULL) { | |
292 | ctx = new_ctx = BN_CTX_new(); | |
293 | if (ctx == NULL) { | |
294 | ECerr(EC_F_EC_GFP_SIMPLE_GROUP_CHECK_DISCRIMINANT, | |
295 | ERR_R_MALLOC_FAILURE); | |
296 | goto err; | |
297 | } | |
298 | } | |
299 | BN_CTX_start(ctx); | |
300 | a = BN_CTX_get(ctx); | |
301 | b = BN_CTX_get(ctx); | |
302 | tmp_1 = BN_CTX_get(ctx); | |
303 | tmp_2 = BN_CTX_get(ctx); | |
304 | order = BN_CTX_get(ctx); | |
305 | if (order == NULL) | |
306 | goto err; | |
307 | ||
308 | if (group->meth->field_decode) { | |
309 | if (!group->meth->field_decode(group, a, group->a, ctx)) | |
310 | goto err; | |
311 | if (!group->meth->field_decode(group, b, group->b, ctx)) | |
312 | goto err; | |
313 | } else { | |
314 | if (!BN_copy(a, group->a)) | |
315 | goto err; | |
316 | if (!BN_copy(b, group->b)) | |
317 | goto err; | |
318 | } | |
319 | ||
50e735f9 MC |
320 | /*- |
321 | * check the discriminant: | |
322 | * y^2 = x^3 + a*x + b is an elliptic curve <=> 4*a^3 + 27*b^2 != 0 (mod p) | |
323 | * 0 =< a, b < p | |
324 | */ | |
0f113f3e MC |
325 | if (BN_is_zero(a)) { |
326 | if (BN_is_zero(b)) | |
327 | goto err; | |
328 | } else if (!BN_is_zero(b)) { | |
329 | if (!BN_mod_sqr(tmp_1, a, p, ctx)) | |
330 | goto err; | |
331 | if (!BN_mod_mul(tmp_2, tmp_1, a, p, ctx)) | |
332 | goto err; | |
333 | if (!BN_lshift(tmp_1, tmp_2, 2)) | |
334 | goto err; | |
335 | /* tmp_1 = 4*a^3 */ | |
336 | ||
337 | if (!BN_mod_sqr(tmp_2, b, p, ctx)) | |
338 | goto err; | |
339 | if (!BN_mul_word(tmp_2, 27)) | |
340 | goto err; | |
341 | /* tmp_2 = 27*b^2 */ | |
342 | ||
343 | if (!BN_mod_add(a, tmp_1, tmp_2, p, ctx)) | |
344 | goto err; | |
345 | if (BN_is_zero(a)) | |
346 | goto err; | |
347 | } | |
348 | ret = 1; | |
af28dd6c | 349 | |
0f113f3e MC |
350 | err: |
351 | if (ctx != NULL) | |
352 | BN_CTX_end(ctx); | |
353 | if (new_ctx != NULL) | |
354 | BN_CTX_free(new_ctx); | |
355 | return ret; | |
356 | } | |
af28dd6c | 357 | |
60428dbf | 358 | int ec_GFp_simple_point_init(EC_POINT *point) |
0f113f3e MC |
359 | { |
360 | point->X = BN_new(); | |
361 | point->Y = BN_new(); | |
362 | point->Z = BN_new(); | |
363 | point->Z_is_one = 0; | |
364 | ||
365 | if (!point->X || !point->Y || !point->Z) { | |
366 | if (point->X) | |
367 | BN_free(point->X); | |
368 | if (point->Y) | |
369 | BN_free(point->Y); | |
370 | if (point->Z) | |
371 | BN_free(point->Z); | |
372 | return 0; | |
373 | } | |
374 | return 1; | |
375 | } | |
60428dbf BM |
376 | |
377 | void ec_GFp_simple_point_finish(EC_POINT *point) | |
0f113f3e MC |
378 | { |
379 | BN_free(point->X); | |
380 | BN_free(point->Y); | |
381 | BN_free(point->Z); | |
382 | } | |
60428dbf BM |
383 | |
384 | void ec_GFp_simple_point_clear_finish(EC_POINT *point) | |
0f113f3e MC |
385 | { |
386 | BN_clear_free(point->X); | |
387 | BN_clear_free(point->Y); | |
388 | BN_clear_free(point->Z); | |
389 | point->Z_is_one = 0; | |
390 | } | |
60428dbf BM |
391 | |
392 | int ec_GFp_simple_point_copy(EC_POINT *dest, const EC_POINT *src) | |
0f113f3e MC |
393 | { |
394 | if (!BN_copy(dest->X, src->X)) | |
395 | return 0; | |
396 | if (!BN_copy(dest->Y, src->Y)) | |
397 | return 0; | |
398 | if (!BN_copy(dest->Z, src->Z)) | |
399 | return 0; | |
400 | dest->Z_is_one = src->Z_is_one; | |
401 | ||
402 | return 1; | |
403 | } | |
404 | ||
405 | int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *group, | |
406 | EC_POINT *point) | |
407 | { | |
408 | point->Z_is_one = 0; | |
409 | BN_zero(point->Z); | |
410 | return 1; | |
411 | } | |
412 | ||
413 | int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *group, | |
414 | EC_POINT *point, | |
415 | const BIGNUM *x, | |
416 | const BIGNUM *y, | |
417 | const BIGNUM *z, | |
418 | BN_CTX *ctx) | |
419 | { | |
420 | BN_CTX *new_ctx = NULL; | |
421 | int ret = 0; | |
422 | ||
423 | if (ctx == NULL) { | |
424 | ctx = new_ctx = BN_CTX_new(); | |
425 | if (ctx == NULL) | |
426 | return 0; | |
427 | } | |
428 | ||
429 | if (x != NULL) { | |
430 | if (!BN_nnmod(point->X, x, group->field, ctx)) | |
431 | goto err; | |
432 | if (group->meth->field_encode) { | |
433 | if (!group->meth->field_encode(group, point->X, point->X, ctx)) | |
434 | goto err; | |
435 | } | |
436 | } | |
437 | ||
438 | if (y != NULL) { | |
439 | if (!BN_nnmod(point->Y, y, group->field, ctx)) | |
440 | goto err; | |
441 | if (group->meth->field_encode) { | |
442 | if (!group->meth->field_encode(group, point->Y, point->Y, ctx)) | |
443 | goto err; | |
444 | } | |
445 | } | |
446 | ||
447 | if (z != NULL) { | |
448 | int Z_is_one; | |
449 | ||
450 | if (!BN_nnmod(point->Z, z, group->field, ctx)) | |
451 | goto err; | |
452 | Z_is_one = BN_is_one(point->Z); | |
453 | if (group->meth->field_encode) { | |
454 | if (Z_is_one && (group->meth->field_set_to_one != 0)) { | |
455 | if (!group->meth->field_set_to_one(group, point->Z, ctx)) | |
456 | goto err; | |
457 | } else { | |
458 | if (!group-> | |
459 | meth->field_encode(group, point->Z, point->Z, ctx)) | |
460 | goto err; | |
461 | } | |
462 | } | |
463 | point->Z_is_one = Z_is_one; | |
464 | } | |
465 | ||
466 | ret = 1; | |
467 | ||
bb62a8b0 | 468 | err: |
0f113f3e MC |
469 | if (new_ctx != NULL) |
470 | BN_CTX_free(new_ctx); | |
471 | return ret; | |
472 | } | |
473 | ||
474 | int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *group, | |
475 | const EC_POINT *point, | |
476 | BIGNUM *x, BIGNUM *y, | |
477 | BIGNUM *z, BN_CTX *ctx) | |
478 | { | |
479 | BN_CTX *new_ctx = NULL; | |
480 | int ret = 0; | |
481 | ||
482 | if (group->meth->field_decode != 0) { | |
483 | if (ctx == NULL) { | |
484 | ctx = new_ctx = BN_CTX_new(); | |
485 | if (ctx == NULL) | |
486 | return 0; | |
487 | } | |
488 | ||
489 | if (x != NULL) { | |
490 | if (!group->meth->field_decode(group, x, point->X, ctx)) | |
491 | goto err; | |
492 | } | |
493 | if (y != NULL) { | |
494 | if (!group->meth->field_decode(group, y, point->Y, ctx)) | |
495 | goto err; | |
496 | } | |
497 | if (z != NULL) { | |
498 | if (!group->meth->field_decode(group, z, point->Z, ctx)) | |
499 | goto err; | |
500 | } | |
501 | } else { | |
502 | if (x != NULL) { | |
503 | if (!BN_copy(x, point->X)) | |
504 | goto err; | |
505 | } | |
506 | if (y != NULL) { | |
507 | if (!BN_copy(y, point->Y)) | |
508 | goto err; | |
509 | } | |
510 | if (z != NULL) { | |
511 | if (!BN_copy(z, point->Z)) | |
512 | goto err; | |
513 | } | |
514 | } | |
515 | ||
516 | ret = 1; | |
bb62a8b0 | 517 | |
226cc7de | 518 | err: |
0f113f3e MC |
519 | if (new_ctx != NULL) |
520 | BN_CTX_free(new_ctx); | |
521 | return ret; | |
522 | } | |
523 | ||
524 | int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *group, | |
525 | EC_POINT *point, | |
526 | const BIGNUM *x, | |
527 | const BIGNUM *y, BN_CTX *ctx) | |
528 | { | |
529 | if (x == NULL || y == NULL) { | |
530 | /* | |
531 | * unlike for projective coordinates, we do not tolerate this | |
532 | */ | |
533 | ECerr(EC_F_EC_GFP_SIMPLE_POINT_SET_AFFINE_COORDINATES, | |
534 | ERR_R_PASSED_NULL_PARAMETER); | |
535 | return 0; | |
536 | } | |
537 | ||
538 | return EC_POINT_set_Jprojective_coordinates_GFp(group, point, x, y, | |
539 | BN_value_one(), ctx); | |
540 | } | |
541 | ||
542 | int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *group, | |
543 | const EC_POINT *point, | |
544 | BIGNUM *x, BIGNUM *y, | |
545 | BN_CTX *ctx) | |
546 | { | |
547 | BN_CTX *new_ctx = NULL; | |
548 | BIGNUM *Z, *Z_1, *Z_2, *Z_3; | |
549 | const BIGNUM *Z_; | |
550 | int ret = 0; | |
551 | ||
552 | if (EC_POINT_is_at_infinity(group, point)) { | |
553 | ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES, | |
554 | EC_R_POINT_AT_INFINITY); | |
555 | return 0; | |
556 | } | |
557 | ||
558 | if (ctx == NULL) { | |
559 | ctx = new_ctx = BN_CTX_new(); | |
560 | if (ctx == NULL) | |
561 | return 0; | |
562 | } | |
563 | ||
564 | BN_CTX_start(ctx); | |
565 | Z = BN_CTX_get(ctx); | |
566 | Z_1 = BN_CTX_get(ctx); | |
567 | Z_2 = BN_CTX_get(ctx); | |
568 | Z_3 = BN_CTX_get(ctx); | |
569 | if (Z_3 == NULL) | |
570 | goto err; | |
571 | ||
572 | /* transform (X, Y, Z) into (x, y) := (X/Z^2, Y/Z^3) */ | |
573 | ||
574 | if (group->meth->field_decode) { | |
575 | if (!group->meth->field_decode(group, Z, point->Z, ctx)) | |
576 | goto err; | |
577 | Z_ = Z; | |
578 | } else { | |
579 | Z_ = point->Z; | |
580 | } | |
581 | ||
582 | if (BN_is_one(Z_)) { | |
583 | if (group->meth->field_decode) { | |
584 | if (x != NULL) { | |
585 | if (!group->meth->field_decode(group, x, point->X, ctx)) | |
586 | goto err; | |
587 | } | |
588 | if (y != NULL) { | |
589 | if (!group->meth->field_decode(group, y, point->Y, ctx)) | |
590 | goto err; | |
591 | } | |
592 | } else { | |
593 | if (x != NULL) { | |
594 | if (!BN_copy(x, point->X)) | |
595 | goto err; | |
596 | } | |
597 | if (y != NULL) { | |
598 | if (!BN_copy(y, point->Y)) | |
599 | goto err; | |
600 | } | |
601 | } | |
602 | } else { | |
603 | if (!BN_mod_inverse(Z_1, Z_, group->field, ctx)) { | |
604 | ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES, | |
605 | ERR_R_BN_LIB); | |
606 | goto err; | |
607 | } | |
608 | ||
609 | if (group->meth->field_encode == 0) { | |
610 | /* field_sqr works on standard representation */ | |
611 | if (!group->meth->field_sqr(group, Z_2, Z_1, ctx)) | |
612 | goto err; | |
613 | } else { | |
614 | if (!BN_mod_sqr(Z_2, Z_1, group->field, ctx)) | |
615 | goto err; | |
616 | } | |
617 | ||
618 | if (x != NULL) { | |
619 | /* | |
620 | * in the Montgomery case, field_mul will cancel out Montgomery | |
621 | * factor in X: | |
622 | */ | |
623 | if (!group->meth->field_mul(group, x, point->X, Z_2, ctx)) | |
624 | goto err; | |
625 | } | |
626 | ||
627 | if (y != NULL) { | |
628 | if (group->meth->field_encode == 0) { | |
629 | /* | |
630 | * field_mul works on standard representation | |
631 | */ | |
632 | if (!group->meth->field_mul(group, Z_3, Z_2, Z_1, ctx)) | |
633 | goto err; | |
634 | } else { | |
635 | if (!BN_mod_mul(Z_3, Z_2, Z_1, group->field, ctx)) | |
636 | goto err; | |
637 | } | |
638 | ||
639 | /* | |
640 | * in the Montgomery case, field_mul will cancel out Montgomery | |
641 | * factor in Y: | |
642 | */ | |
643 | if (!group->meth->field_mul(group, y, point->Y, Z_3, ctx)) | |
644 | goto err; | |
645 | } | |
646 | } | |
647 | ||
648 | ret = 1; | |
226cc7de BM |
649 | |
650 | err: | |
0f113f3e MC |
651 | BN_CTX_end(ctx); |
652 | if (new_ctx != NULL) | |
653 | BN_CTX_free(new_ctx); | |
654 | return ret; | |
655 | } | |
656 | ||
657 | int ec_GFp_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, | |
658 | const EC_POINT *b, BN_CTX *ctx) | |
659 | { | |
660 | int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *, | |
661 | const BIGNUM *, BN_CTX *); | |
662 | int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); | |
663 | const BIGNUM *p; | |
664 | BN_CTX *new_ctx = NULL; | |
665 | BIGNUM *n0, *n1, *n2, *n3, *n4, *n5, *n6; | |
666 | int ret = 0; | |
667 | ||
668 | if (a == b) | |
669 | return EC_POINT_dbl(group, r, a, ctx); | |
670 | if (EC_POINT_is_at_infinity(group, a)) | |
671 | return EC_POINT_copy(r, b); | |
672 | if (EC_POINT_is_at_infinity(group, b)) | |
673 | return EC_POINT_copy(r, a); | |
674 | ||
675 | field_mul = group->meth->field_mul; | |
676 | field_sqr = group->meth->field_sqr; | |
677 | p = group->field; | |
678 | ||
679 | if (ctx == NULL) { | |
680 | ctx = new_ctx = BN_CTX_new(); | |
681 | if (ctx == NULL) | |
682 | return 0; | |
683 | } | |
684 | ||
685 | BN_CTX_start(ctx); | |
686 | n0 = BN_CTX_get(ctx); | |
687 | n1 = BN_CTX_get(ctx); | |
688 | n2 = BN_CTX_get(ctx); | |
689 | n3 = BN_CTX_get(ctx); | |
690 | n4 = BN_CTX_get(ctx); | |
691 | n5 = BN_CTX_get(ctx); | |
692 | n6 = BN_CTX_get(ctx); | |
693 | if (n6 == NULL) | |
694 | goto end; | |
695 | ||
696 | /* | |
697 | * Note that in this function we must not read components of 'a' or 'b' | |
698 | * once we have written the corresponding components of 'r'. ('r' might | |
699 | * be one of 'a' or 'b'.) | |
700 | */ | |
701 | ||
702 | /* n1, n2 */ | |
703 | if (b->Z_is_one) { | |
704 | if (!BN_copy(n1, a->X)) | |
705 | goto end; | |
706 | if (!BN_copy(n2, a->Y)) | |
707 | goto end; | |
708 | /* n1 = X_a */ | |
709 | /* n2 = Y_a */ | |
710 | } else { | |
711 | if (!field_sqr(group, n0, b->Z, ctx)) | |
712 | goto end; | |
713 | if (!field_mul(group, n1, a->X, n0, ctx)) | |
714 | goto end; | |
715 | /* n1 = X_a * Z_b^2 */ | |
716 | ||
717 | if (!field_mul(group, n0, n0, b->Z, ctx)) | |
718 | goto end; | |
719 | if (!field_mul(group, n2, a->Y, n0, ctx)) | |
720 | goto end; | |
721 | /* n2 = Y_a * Z_b^3 */ | |
722 | } | |
723 | ||
724 | /* n3, n4 */ | |
725 | if (a->Z_is_one) { | |
726 | if (!BN_copy(n3, b->X)) | |
727 | goto end; | |
728 | if (!BN_copy(n4, b->Y)) | |
729 | goto end; | |
730 | /* n3 = X_b */ | |
731 | /* n4 = Y_b */ | |
732 | } else { | |
733 | if (!field_sqr(group, n0, a->Z, ctx)) | |
734 | goto end; | |
735 | if (!field_mul(group, n3, b->X, n0, ctx)) | |
736 | goto end; | |
737 | /* n3 = X_b * Z_a^2 */ | |
738 | ||
739 | if (!field_mul(group, n0, n0, a->Z, ctx)) | |
740 | goto end; | |
741 | if (!field_mul(group, n4, b->Y, n0, ctx)) | |
742 | goto end; | |
743 | /* n4 = Y_b * Z_a^3 */ | |
744 | } | |
745 | ||
746 | /* n5, n6 */ | |
747 | if (!BN_mod_sub_quick(n5, n1, n3, p)) | |
748 | goto end; | |
749 | if (!BN_mod_sub_quick(n6, n2, n4, p)) | |
750 | goto end; | |
751 | /* n5 = n1 - n3 */ | |
752 | /* n6 = n2 - n4 */ | |
753 | ||
754 | if (BN_is_zero(n5)) { | |
755 | if (BN_is_zero(n6)) { | |
756 | /* a is the same point as b */ | |
757 | BN_CTX_end(ctx); | |
758 | ret = EC_POINT_dbl(group, r, a, ctx); | |
759 | ctx = NULL; | |
760 | goto end; | |
761 | } else { | |
762 | /* a is the inverse of b */ | |
763 | BN_zero(r->Z); | |
764 | r->Z_is_one = 0; | |
765 | ret = 1; | |
766 | goto end; | |
767 | } | |
768 | } | |
769 | ||
770 | /* 'n7', 'n8' */ | |
771 | if (!BN_mod_add_quick(n1, n1, n3, p)) | |
772 | goto end; | |
773 | if (!BN_mod_add_quick(n2, n2, n4, p)) | |
774 | goto end; | |
775 | /* 'n7' = n1 + n3 */ | |
776 | /* 'n8' = n2 + n4 */ | |
777 | ||
778 | /* Z_r */ | |
779 | if (a->Z_is_one && b->Z_is_one) { | |
780 | if (!BN_copy(r->Z, n5)) | |
781 | goto end; | |
782 | } else { | |
783 | if (a->Z_is_one) { | |
784 | if (!BN_copy(n0, b->Z)) | |
785 | goto end; | |
786 | } else if (b->Z_is_one) { | |
787 | if (!BN_copy(n0, a->Z)) | |
788 | goto end; | |
789 | } else { | |
790 | if (!field_mul(group, n0, a->Z, b->Z, ctx)) | |
791 | goto end; | |
792 | } | |
793 | if (!field_mul(group, r->Z, n0, n5, ctx)) | |
794 | goto end; | |
795 | } | |
796 | r->Z_is_one = 0; | |
797 | /* Z_r = Z_a * Z_b * n5 */ | |
798 | ||
799 | /* X_r */ | |
800 | if (!field_sqr(group, n0, n6, ctx)) | |
801 | goto end; | |
802 | if (!field_sqr(group, n4, n5, ctx)) | |
803 | goto end; | |
804 | if (!field_mul(group, n3, n1, n4, ctx)) | |
805 | goto end; | |
806 | if (!BN_mod_sub_quick(r->X, n0, n3, p)) | |
807 | goto end; | |
808 | /* X_r = n6^2 - n5^2 * 'n7' */ | |
809 | ||
810 | /* 'n9' */ | |
811 | if (!BN_mod_lshift1_quick(n0, r->X, p)) | |
812 | goto end; | |
813 | if (!BN_mod_sub_quick(n0, n3, n0, p)) | |
814 | goto end; | |
815 | /* n9 = n5^2 * 'n7' - 2 * X_r */ | |
816 | ||
817 | /* Y_r */ | |
818 | if (!field_mul(group, n0, n0, n6, ctx)) | |
819 | goto end; | |
820 | if (!field_mul(group, n5, n4, n5, ctx)) | |
821 | goto end; /* now n5 is n5^3 */ | |
822 | if (!field_mul(group, n1, n2, n5, ctx)) | |
823 | goto end; | |
824 | if (!BN_mod_sub_quick(n0, n0, n1, p)) | |
825 | goto end; | |
826 | if (BN_is_odd(n0)) | |
827 | if (!BN_add(n0, n0, p)) | |
828 | goto end; | |
829 | /* now 0 <= n0 < 2*p, and n0 is even */ | |
830 | if (!BN_rshift1(r->Y, n0)) | |
831 | goto end; | |
832 | /* Y_r = (n6 * 'n9' - 'n8' * 'n5^3') / 2 */ | |
833 | ||
834 | ret = 1; | |
60428dbf BM |
835 | |
836 | end: | |
0f113f3e MC |
837 | if (ctx) /* otherwise we already called BN_CTX_end */ |
838 | BN_CTX_end(ctx); | |
839 | if (new_ctx != NULL) | |
840 | BN_CTX_free(new_ctx); | |
841 | return ret; | |
842 | } | |
843 | ||
844 | int ec_GFp_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, | |
845 | BN_CTX *ctx) | |
846 | { | |
847 | int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *, | |
848 | const BIGNUM *, BN_CTX *); | |
849 | int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); | |
850 | const BIGNUM *p; | |
851 | BN_CTX *new_ctx = NULL; | |
852 | BIGNUM *n0, *n1, *n2, *n3; | |
853 | int ret = 0; | |
854 | ||
855 | if (EC_POINT_is_at_infinity(group, a)) { | |
856 | BN_zero(r->Z); | |
857 | r->Z_is_one = 0; | |
858 | return 1; | |
859 | } | |
860 | ||
861 | field_mul = group->meth->field_mul; | |
862 | field_sqr = group->meth->field_sqr; | |
863 | p = group->field; | |
864 | ||
865 | if (ctx == NULL) { | |
866 | ctx = new_ctx = BN_CTX_new(); | |
867 | if (ctx == NULL) | |
868 | return 0; | |
869 | } | |
870 | ||
871 | BN_CTX_start(ctx); | |
872 | n0 = BN_CTX_get(ctx); | |
873 | n1 = BN_CTX_get(ctx); | |
874 | n2 = BN_CTX_get(ctx); | |
875 | n3 = BN_CTX_get(ctx); | |
876 | if (n3 == NULL) | |
877 | goto err; | |
878 | ||
879 | /* | |
880 | * Note that in this function we must not read components of 'a' once we | |
881 | * have written the corresponding components of 'r'. ('r' might the same | |
882 | * as 'a'.) | |
883 | */ | |
884 | ||
885 | /* n1 */ | |
886 | if (a->Z_is_one) { | |
887 | if (!field_sqr(group, n0, a->X, ctx)) | |
888 | goto err; | |
889 | if (!BN_mod_lshift1_quick(n1, n0, p)) | |
890 | goto err; | |
891 | if (!BN_mod_add_quick(n0, n0, n1, p)) | |
892 | goto err; | |
893 | if (!BN_mod_add_quick(n1, n0, group->a, p)) | |
894 | goto err; | |
895 | /* n1 = 3 * X_a^2 + a_curve */ | |
896 | } else if (group->a_is_minus3) { | |
897 | if (!field_sqr(group, n1, a->Z, ctx)) | |
898 | goto err; | |
899 | if (!BN_mod_add_quick(n0, a->X, n1, p)) | |
900 | goto err; | |
901 | if (!BN_mod_sub_quick(n2, a->X, n1, p)) | |
902 | goto err; | |
903 | if (!field_mul(group, n1, n0, n2, ctx)) | |
904 | goto err; | |
905 | if (!BN_mod_lshift1_quick(n0, n1, p)) | |
906 | goto err; | |
907 | if (!BN_mod_add_quick(n1, n0, n1, p)) | |
908 | goto err; | |
35a1cc90 MC |
909 | /*- |
910 | * n1 = 3 * (X_a + Z_a^2) * (X_a - Z_a^2) | |
911 | * = 3 * X_a^2 - 3 * Z_a^4 | |
912 | */ | |
0f113f3e MC |
913 | } else { |
914 | if (!field_sqr(group, n0, a->X, ctx)) | |
915 | goto err; | |
916 | if (!BN_mod_lshift1_quick(n1, n0, p)) | |
917 | goto err; | |
918 | if (!BN_mod_add_quick(n0, n0, n1, p)) | |
919 | goto err; | |
920 | if (!field_sqr(group, n1, a->Z, ctx)) | |
921 | goto err; | |
922 | if (!field_sqr(group, n1, n1, ctx)) | |
923 | goto err; | |
924 | if (!field_mul(group, n1, n1, group->a, ctx)) | |
925 | goto err; | |
926 | if (!BN_mod_add_quick(n1, n1, n0, p)) | |
927 | goto err; | |
928 | /* n1 = 3 * X_a^2 + a_curve * Z_a^4 */ | |
929 | } | |
930 | ||
931 | /* Z_r */ | |
932 | if (a->Z_is_one) { | |
933 | if (!BN_copy(n0, a->Y)) | |
934 | goto err; | |
935 | } else { | |
936 | if (!field_mul(group, n0, a->Y, a->Z, ctx)) | |
937 | goto err; | |
938 | } | |
939 | if (!BN_mod_lshift1_quick(r->Z, n0, p)) | |
940 | goto err; | |
941 | r->Z_is_one = 0; | |
942 | /* Z_r = 2 * Y_a * Z_a */ | |
943 | ||
944 | /* n2 */ | |
945 | if (!field_sqr(group, n3, a->Y, ctx)) | |
946 | goto err; | |
947 | if (!field_mul(group, n2, a->X, n3, ctx)) | |
948 | goto err; | |
949 | if (!BN_mod_lshift_quick(n2, n2, 2, p)) | |
950 | goto err; | |
951 | /* n2 = 4 * X_a * Y_a^2 */ | |
952 | ||
953 | /* X_r */ | |
954 | if (!BN_mod_lshift1_quick(n0, n2, p)) | |
955 | goto err; | |
956 | if (!field_sqr(group, r->X, n1, ctx)) | |
957 | goto err; | |
958 | if (!BN_mod_sub_quick(r->X, r->X, n0, p)) | |
959 | goto err; | |
960 | /* X_r = n1^2 - 2 * n2 */ | |
961 | ||
962 | /* n3 */ | |
963 | if (!field_sqr(group, n0, n3, ctx)) | |
964 | goto err; | |
965 | if (!BN_mod_lshift_quick(n3, n0, 3, p)) | |
966 | goto err; | |
967 | /* n3 = 8 * Y_a^4 */ | |
968 | ||
969 | /* Y_r */ | |
970 | if (!BN_mod_sub_quick(n0, n2, r->X, p)) | |
971 | goto err; | |
972 | if (!field_mul(group, n0, n1, n0, ctx)) | |
973 | goto err; | |
974 | if (!BN_mod_sub_quick(r->Y, n0, n3, p)) | |
975 | goto err; | |
976 | /* Y_r = n1 * (n2 - X_r) - n3 */ | |
977 | ||
978 | ret = 1; | |
60428dbf BM |
979 | |
980 | err: | |
0f113f3e MC |
981 | BN_CTX_end(ctx); |
982 | if (new_ctx != NULL) | |
983 | BN_CTX_free(new_ctx); | |
984 | return ret; | |
985 | } | |
60428dbf | 986 | |
bb62a8b0 | 987 | int ec_GFp_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx) |
0f113f3e MC |
988 | { |
989 | if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(point->Y)) | |
990 | /* point is its own inverse */ | |
991 | return 1; | |
1d5bd6cf | 992 | |
0f113f3e MC |
993 | return BN_usub(point->Y, group->field, point->Y); |
994 | } | |
1d5bd6cf | 995 | |
60428dbf | 996 | int ec_GFp_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point) |
0f113f3e MC |
997 | { |
998 | return BN_is_zero(point->Z); | |
999 | } | |
1000 | ||
1001 | int ec_GFp_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, | |
1002 | BN_CTX *ctx) | |
1003 | { | |
1004 | int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *, | |
1005 | const BIGNUM *, BN_CTX *); | |
1006 | int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); | |
1007 | const BIGNUM *p; | |
1008 | BN_CTX *new_ctx = NULL; | |
1009 | BIGNUM *rh, *tmp, *Z4, *Z6; | |
1010 | int ret = -1; | |
1011 | ||
1012 | if (EC_POINT_is_at_infinity(group, point)) | |
1013 | return 1; | |
1014 | ||
1015 | field_mul = group->meth->field_mul; | |
1016 | field_sqr = group->meth->field_sqr; | |
1017 | p = group->field; | |
1018 | ||
1019 | if (ctx == NULL) { | |
1020 | ctx = new_ctx = BN_CTX_new(); | |
1021 | if (ctx == NULL) | |
1022 | return -1; | |
1023 | } | |
1024 | ||
1025 | BN_CTX_start(ctx); | |
1026 | rh = BN_CTX_get(ctx); | |
1027 | tmp = BN_CTX_get(ctx); | |
1028 | Z4 = BN_CTX_get(ctx); | |
1029 | Z6 = BN_CTX_get(ctx); | |
1030 | if (Z6 == NULL) | |
1031 | goto err; | |
1032 | ||
35a1cc90 MC |
1033 | /*- |
1034 | * We have a curve defined by a Weierstrass equation | |
1035 | * y^2 = x^3 + a*x + b. | |
1036 | * The point to consider is given in Jacobian projective coordinates | |
1037 | * where (X, Y, Z) represents (x, y) = (X/Z^2, Y/Z^3). | |
1038 | * Substituting this and multiplying by Z^6 transforms the above equation into | |
1039 | * Y^2 = X^3 + a*X*Z^4 + b*Z^6. | |
1040 | * To test this, we add up the right-hand side in 'rh'. | |
1041 | */ | |
0f113f3e MC |
1042 | |
1043 | /* rh := X^2 */ | |
1044 | if (!field_sqr(group, rh, point->X, ctx)) | |
1045 | goto err; | |
1046 | ||
1047 | if (!point->Z_is_one) { | |
1048 | if (!field_sqr(group, tmp, point->Z, ctx)) | |
1049 | goto err; | |
1050 | if (!field_sqr(group, Z4, tmp, ctx)) | |
1051 | goto err; | |
1052 | if (!field_mul(group, Z6, Z4, tmp, ctx)) | |
1053 | goto err; | |
1054 | ||
1055 | /* rh := (rh + a*Z^4)*X */ | |
1056 | if (group->a_is_minus3) { | |
1057 | if (!BN_mod_lshift1_quick(tmp, Z4, p)) | |
1058 | goto err; | |
1059 | if (!BN_mod_add_quick(tmp, tmp, Z4, p)) | |
1060 | goto err; | |
1061 | if (!BN_mod_sub_quick(rh, rh, tmp, p)) | |
1062 | goto err; | |
1063 | if (!field_mul(group, rh, rh, point->X, ctx)) | |
1064 | goto err; | |
1065 | } else { | |
1066 | if (!field_mul(group, tmp, Z4, group->a, ctx)) | |
1067 | goto err; | |
1068 | if (!BN_mod_add_quick(rh, rh, tmp, p)) | |
1069 | goto err; | |
1070 | if (!field_mul(group, rh, rh, point->X, ctx)) | |
1071 | goto err; | |
1072 | } | |
1073 | ||
1074 | /* rh := rh + b*Z^6 */ | |
1075 | if (!field_mul(group, tmp, group->b, Z6, ctx)) | |
1076 | goto err; | |
1077 | if (!BN_mod_add_quick(rh, rh, tmp, p)) | |
1078 | goto err; | |
1079 | } else { | |
1080 | /* point->Z_is_one */ | |
1081 | ||
1082 | /* rh := (rh + a)*X */ | |
1083 | if (!BN_mod_add_quick(rh, rh, group->a, p)) | |
1084 | goto err; | |
1085 | if (!field_mul(group, rh, rh, point->X, ctx)) | |
1086 | goto err; | |
1087 | /* rh := rh + b */ | |
1088 | if (!BN_mod_add_quick(rh, rh, group->b, p)) | |
1089 | goto err; | |
1090 | } | |
1091 | ||
1092 | /* 'lh' := Y^2 */ | |
1093 | if (!field_sqr(group, tmp, point->Y, ctx)) | |
1094 | goto err; | |
1095 | ||
1096 | ret = (0 == BN_ucmp(tmp, rh)); | |
e869d4bd BM |
1097 | |
1098 | err: | |
0f113f3e MC |
1099 | BN_CTX_end(ctx); |
1100 | if (new_ctx != NULL) | |
1101 | BN_CTX_free(new_ctx); | |
1102 | return ret; | |
1103 | } | |
1104 | ||
1105 | int ec_GFp_simple_cmp(const EC_GROUP *group, const EC_POINT *a, | |
1106 | const EC_POINT *b, BN_CTX *ctx) | |
1107 | { | |
35a1cc90 MC |
1108 | /*- |
1109 | * return values: | |
1110 | * -1 error | |
1111 | * 0 equal (in affine coordinates) | |
1112 | * 1 not equal | |
1113 | */ | |
0f113f3e MC |
1114 | |
1115 | int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *, | |
1116 | const BIGNUM *, BN_CTX *); | |
1117 | int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); | |
1118 | BN_CTX *new_ctx = NULL; | |
1119 | BIGNUM *tmp1, *tmp2, *Za23, *Zb23; | |
1120 | const BIGNUM *tmp1_, *tmp2_; | |
1121 | int ret = -1; | |
1122 | ||
1123 | if (EC_POINT_is_at_infinity(group, a)) { | |
1124 | return EC_POINT_is_at_infinity(group, b) ? 0 : 1; | |
1125 | } | |
1126 | ||
1127 | if (EC_POINT_is_at_infinity(group, b)) | |
1128 | return 1; | |
1129 | ||
1130 | if (a->Z_is_one && b->Z_is_one) { | |
1131 | return ((BN_cmp(a->X, b->X) == 0) && BN_cmp(a->Y, b->Y) == 0) ? 0 : 1; | |
1132 | } | |
1133 | ||
1134 | field_mul = group->meth->field_mul; | |
1135 | field_sqr = group->meth->field_sqr; | |
1136 | ||
1137 | if (ctx == NULL) { | |
1138 | ctx = new_ctx = BN_CTX_new(); | |
1139 | if (ctx == NULL) | |
1140 | return -1; | |
1141 | } | |
1142 | ||
1143 | BN_CTX_start(ctx); | |
1144 | tmp1 = BN_CTX_get(ctx); | |
1145 | tmp2 = BN_CTX_get(ctx); | |
1146 | Za23 = BN_CTX_get(ctx); | |
1147 | Zb23 = BN_CTX_get(ctx); | |
1148 | if (Zb23 == NULL) | |
1149 | goto end; | |
1150 | ||
35a1cc90 MC |
1151 | /*- |
1152 | * We have to decide whether | |
1153 | * (X_a/Z_a^2, Y_a/Z_a^3) = (X_b/Z_b^2, Y_b/Z_b^3), | |
1154 | * or equivalently, whether | |
1155 | * (X_a*Z_b^2, Y_a*Z_b^3) = (X_b*Z_a^2, Y_b*Z_a^3). | |
1156 | */ | |
0f113f3e MC |
1157 | |
1158 | if (!b->Z_is_one) { | |
1159 | if (!field_sqr(group, Zb23, b->Z, ctx)) | |
1160 | goto end; | |
1161 | if (!field_mul(group, tmp1, a->X, Zb23, ctx)) | |
1162 | goto end; | |
1163 | tmp1_ = tmp1; | |
1164 | } else | |
1165 | tmp1_ = a->X; | |
1166 | if (!a->Z_is_one) { | |
1167 | if (!field_sqr(group, Za23, a->Z, ctx)) | |
1168 | goto end; | |
1169 | if (!field_mul(group, tmp2, b->X, Za23, ctx)) | |
1170 | goto end; | |
1171 | tmp2_ = tmp2; | |
1172 | } else | |
1173 | tmp2_ = b->X; | |
1174 | ||
1175 | /* compare X_a*Z_b^2 with X_b*Z_a^2 */ | |
1176 | if (BN_cmp(tmp1_, tmp2_) != 0) { | |
1177 | ret = 1; /* points differ */ | |
1178 | goto end; | |
1179 | } | |
1180 | ||
1181 | if (!b->Z_is_one) { | |
1182 | if (!field_mul(group, Zb23, Zb23, b->Z, ctx)) | |
1183 | goto end; | |
1184 | if (!field_mul(group, tmp1, a->Y, Zb23, ctx)) | |
1185 | goto end; | |
1186 | /* tmp1_ = tmp1 */ | |
1187 | } else | |
1188 | tmp1_ = a->Y; | |
1189 | if (!a->Z_is_one) { | |
1190 | if (!field_mul(group, Za23, Za23, a->Z, ctx)) | |
1191 | goto end; | |
1192 | if (!field_mul(group, tmp2, b->Y, Za23, ctx)) | |
1193 | goto end; | |
1194 | /* tmp2_ = tmp2 */ | |
1195 | } else | |
1196 | tmp2_ = b->Y; | |
1197 | ||
1198 | /* compare Y_a*Z_b^3 with Y_b*Z_a^3 */ | |
1199 | if (BN_cmp(tmp1_, tmp2_) != 0) { | |
1200 | ret = 1; /* points differ */ | |
1201 | goto end; | |
1202 | } | |
1203 | ||
1204 | /* points are equal */ | |
1205 | ret = 0; | |
bb62a8b0 BM |
1206 | |
1207 | end: | |
0f113f3e MC |
1208 | BN_CTX_end(ctx); |
1209 | if (new_ctx != NULL) | |
1210 | BN_CTX_free(new_ctx); | |
1211 | return ret; | |
1212 | } | |
1213 | ||
1214 | int ec_GFp_simple_make_affine(const EC_GROUP *group, EC_POINT *point, | |
1215 | BN_CTX *ctx) | |
1216 | { | |
1217 | BN_CTX *new_ctx = NULL; | |
1218 | BIGNUM *x, *y; | |
1219 | int ret = 0; | |
1220 | ||
1221 | if (point->Z_is_one || EC_POINT_is_at_infinity(group, point)) | |
1222 | return 1; | |
1223 | ||
1224 | if (ctx == NULL) { | |
1225 | ctx = new_ctx = BN_CTX_new(); | |
1226 | if (ctx == NULL) | |
1227 | return 0; | |
1228 | } | |
1229 | ||
1230 | BN_CTX_start(ctx); | |
1231 | x = BN_CTX_get(ctx); | |
1232 | y = BN_CTX_get(ctx); | |
1233 | if (y == NULL) | |
1234 | goto err; | |
1235 | ||
1236 | if (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx)) | |
1237 | goto err; | |
1238 | if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) | |
1239 | goto err; | |
1240 | if (!point->Z_is_one) { | |
1241 | ECerr(EC_F_EC_GFP_SIMPLE_MAKE_AFFINE, ERR_R_INTERNAL_ERROR); | |
1242 | goto err; | |
1243 | } | |
1244 | ||
1245 | ret = 1; | |
e869d4bd | 1246 | |
226cc7de | 1247 | err: |
0f113f3e MC |
1248 | BN_CTX_end(ctx); |
1249 | if (new_ctx != NULL) | |
1250 | BN_CTX_free(new_ctx); | |
1251 | return ret; | |
1252 | } | |
1253 | ||
1254 | int ec_GFp_simple_points_make_affine(const EC_GROUP *group, size_t num, | |
1255 | EC_POINT *points[], BN_CTX *ctx) | |
1256 | { | |
1257 | BN_CTX *new_ctx = NULL; | |
1258 | BIGNUM *tmp, *tmp_Z; | |
1259 | BIGNUM **prod_Z = NULL; | |
1260 | size_t i; | |
1261 | int ret = 0; | |
1262 | ||
1263 | if (num == 0) | |
1264 | return 1; | |
1265 | ||
1266 | if (ctx == NULL) { | |
1267 | ctx = new_ctx = BN_CTX_new(); | |
1268 | if (ctx == NULL) | |
1269 | return 0; | |
1270 | } | |
1271 | ||
1272 | BN_CTX_start(ctx); | |
1273 | tmp = BN_CTX_get(ctx); | |
1274 | tmp_Z = BN_CTX_get(ctx); | |
1275 | if (tmp == NULL || tmp_Z == NULL) | |
1276 | goto err; | |
1277 | ||
1278 | prod_Z = OPENSSL_malloc(num * sizeof prod_Z[0]); | |
1279 | if (prod_Z == NULL) | |
1280 | goto err; | |
1281 | for (i = 0; i < num; i++) { | |
1282 | prod_Z[i] = BN_new(); | |
1283 | if (prod_Z[i] == NULL) | |
1284 | goto err; | |
1285 | } | |
1286 | ||
1287 | /* | |
1288 | * Set each prod_Z[i] to the product of points[0]->Z .. points[i]->Z, | |
1289 | * skipping any zero-valued inputs (pretend that they're 1). | |
1290 | */ | |
1291 | ||
1292 | if (!BN_is_zero(points[0]->Z)) { | |
1293 | if (!BN_copy(prod_Z[0], points[0]->Z)) | |
1294 | goto err; | |
1295 | } else { | |
1296 | if (group->meth->field_set_to_one != 0) { | |
1297 | if (!group->meth->field_set_to_one(group, prod_Z[0], ctx)) | |
1298 | goto err; | |
1299 | } else { | |
1300 | if (!BN_one(prod_Z[0])) | |
1301 | goto err; | |
1302 | } | |
1303 | } | |
1304 | ||
1305 | for (i = 1; i < num; i++) { | |
1306 | if (!BN_is_zero(points[i]->Z)) { | |
1307 | if (!group-> | |
1308 | meth->field_mul(group, prod_Z[i], prod_Z[i - 1], points[i]->Z, | |
1309 | ctx)) | |
1310 | goto err; | |
1311 | } else { | |
1312 | if (!BN_copy(prod_Z[i], prod_Z[i - 1])) | |
1313 | goto err; | |
1314 | } | |
1315 | } | |
1316 | ||
1317 | /* | |
1318 | * Now use a single explicit inversion to replace every non-zero | |
1319 | * points[i]->Z by its inverse. | |
1320 | */ | |
1321 | ||
1322 | if (!BN_mod_inverse(tmp, prod_Z[num - 1], group->field, ctx)) { | |
1323 | ECerr(EC_F_EC_GFP_SIMPLE_POINTS_MAKE_AFFINE, ERR_R_BN_LIB); | |
1324 | goto err; | |
1325 | } | |
1326 | if (group->meth->field_encode != 0) { | |
1327 | /* | |
1328 | * In the Montgomery case, we just turned R*H (representing H) into | |
1329 | * 1/(R*H), but we need R*(1/H) (representing 1/H); i.e. we need to | |
1330 | * multiply by the Montgomery factor twice. | |
1331 | */ | |
1332 | if (!group->meth->field_encode(group, tmp, tmp, ctx)) | |
1333 | goto err; | |
1334 | if (!group->meth->field_encode(group, tmp, tmp, ctx)) | |
1335 | goto err; | |
1336 | } | |
1337 | ||
1338 | for (i = num - 1; i > 0; --i) { | |
1339 | /* | |
1340 | * Loop invariant: tmp is the product of the inverses of points[0]->Z | |
1341 | * .. points[i]->Z (zero-valued inputs skipped). | |
1342 | */ | |
1343 | if (!BN_is_zero(points[i]->Z)) { | |
1344 | /* | |
1345 | * Set tmp_Z to the inverse of points[i]->Z (as product of Z | |
1346 | * inverses 0 .. i, Z values 0 .. i - 1). | |
1347 | */ | |
1348 | if (!group-> | |
1349 | meth->field_mul(group, tmp_Z, prod_Z[i - 1], tmp, ctx)) | |
1350 | goto err; | |
1351 | /* | |
1352 | * Update tmp to satisfy the loop invariant for i - 1. | |
1353 | */ | |
1354 | if (!group->meth->field_mul(group, tmp, tmp, points[i]->Z, ctx)) | |
1355 | goto err; | |
1356 | /* Replace points[i]->Z by its inverse. */ | |
1357 | if (!BN_copy(points[i]->Z, tmp_Z)) | |
1358 | goto err; | |
1359 | } | |
1360 | } | |
1361 | ||
1362 | if (!BN_is_zero(points[0]->Z)) { | |
1363 | /* Replace points[0]->Z by its inverse. */ | |
1364 | if (!BN_copy(points[0]->Z, tmp)) | |
1365 | goto err; | |
1366 | } | |
1367 | ||
1368 | /* Finally, fix up the X and Y coordinates for all points. */ | |
1369 | ||
1370 | for (i = 0; i < num; i++) { | |
1371 | EC_POINT *p = points[i]; | |
1372 | ||
1373 | if (!BN_is_zero(p->Z)) { | |
1374 | /* turn (X, Y, 1/Z) into (X/Z^2, Y/Z^3, 1) */ | |
1375 | ||
1376 | if (!group->meth->field_sqr(group, tmp, p->Z, ctx)) | |
1377 | goto err; | |
1378 | if (!group->meth->field_mul(group, p->X, p->X, tmp, ctx)) | |
1379 | goto err; | |
1380 | ||
1381 | if (!group->meth->field_mul(group, tmp, tmp, p->Z, ctx)) | |
1382 | goto err; | |
1383 | if (!group->meth->field_mul(group, p->Y, p->Y, tmp, ctx)) | |
1384 | goto err; | |
1385 | ||
1386 | if (group->meth->field_set_to_one != 0) { | |
1387 | if (!group->meth->field_set_to_one(group, p->Z, ctx)) | |
1388 | goto err; | |
1389 | } else { | |
1390 | if (!BN_one(p->Z)) | |
1391 | goto err; | |
1392 | } | |
1393 | p->Z_is_one = 1; | |
1394 | } | |
1395 | } | |
1396 | ||
1397 | ret = 1; | |
0fe73d6c | 1398 | |
48fe4d62 | 1399 | err: |
0f113f3e MC |
1400 | BN_CTX_end(ctx); |
1401 | if (new_ctx != NULL) | |
1402 | BN_CTX_free(new_ctx); | |
1403 | if (prod_Z != NULL) { | |
1404 | for (i = 0; i < num; i++) { | |
1405 | if (prod_Z[i] == NULL) | |
1406 | break; | |
1407 | BN_clear_free(prod_Z[i]); | |
1408 | } | |
1409 | OPENSSL_free(prod_Z); | |
1410 | } | |
1411 | return ret; | |
1412 | } | |
1413 | ||
1414 | int ec_GFp_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, | |
1415 | const BIGNUM *b, BN_CTX *ctx) | |
1416 | { | |
1417 | return BN_mod_mul(r, a, b, group->field, ctx); | |
1418 | } | |
1419 | ||
1420 | int ec_GFp_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, | |
1421 | BN_CTX *ctx) | |
1422 | { | |
1423 | return BN_mod_sqr(r, a, group->field, ctx); | |
1424 | } |