]>
Commit | Line | Data |
---|---|---|
0f113f3e | 1 | /* |
aa6bb135 | 2 | * Copyright 2001-2016 The OpenSSL Project Authors. All Rights Reserved. |
f8fe20e0 | 3 | * |
aa6bb135 RS |
4 | * Licensed under the OpenSSL license (the "License"). You may not use |
5 | * this file except in compliance with the License. You can obtain a copy | |
6 | * in the file LICENSE in the source distribution or at | |
7 | * https://www.openssl.org/source/license.html | |
f8fe20e0 | 8 | */ |
aa6bb135 | 9 | |
7793f30e BM |
10 | /* ==================================================================== |
11 | * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. | |
12 | * Portions of this software developed by SUN MICROSYSTEMS, INC., | |
13 | * and contributed to the OpenSSL project. | |
14 | */ | |
f8fe20e0 | 15 | |
60428dbf | 16 | #include <openssl/err.h> |
02cbedc3 | 17 | #include <openssl/symhacks.h> |
60428dbf | 18 | |
f8fe20e0 | 19 | #include "ec_lcl.h" |
0657bf9c | 20 | |
0657bf9c | 21 | const EC_METHOD *EC_GFp_simple_method(void) |
0f113f3e MC |
22 | { |
23 | static const EC_METHOD ret = { | |
24 | EC_FLAGS_DEFAULT_OCT, | |
25 | NID_X9_62_prime_field, | |
26 | ec_GFp_simple_group_init, | |
27 | ec_GFp_simple_group_finish, | |
28 | ec_GFp_simple_group_clear_finish, | |
29 | ec_GFp_simple_group_copy, | |
30 | ec_GFp_simple_group_set_curve, | |
31 | ec_GFp_simple_group_get_curve, | |
32 | ec_GFp_simple_group_get_degree, | |
9ff9bccc | 33 | ec_group_simple_order_bits, |
0f113f3e MC |
34 | ec_GFp_simple_group_check_discriminant, |
35 | ec_GFp_simple_point_init, | |
36 | ec_GFp_simple_point_finish, | |
37 | ec_GFp_simple_point_clear_finish, | |
38 | ec_GFp_simple_point_copy, | |
39 | ec_GFp_simple_point_set_to_infinity, | |
40 | ec_GFp_simple_set_Jprojective_coordinates_GFp, | |
41 | ec_GFp_simple_get_Jprojective_coordinates_GFp, | |
42 | ec_GFp_simple_point_set_affine_coordinates, | |
43 | ec_GFp_simple_point_get_affine_coordinates, | |
44 | 0, 0, 0, | |
45 | ec_GFp_simple_add, | |
46 | ec_GFp_simple_dbl, | |
47 | ec_GFp_simple_invert, | |
48 | ec_GFp_simple_is_at_infinity, | |
49 | ec_GFp_simple_is_on_curve, | |
50 | ec_GFp_simple_cmp, | |
51 | ec_GFp_simple_make_affine, | |
52 | ec_GFp_simple_points_make_affine, | |
53 | 0 /* mul */ , | |
54 | 0 /* precompute_mult */ , | |
55 | 0 /* have_precompute_mult */ , | |
56 | ec_GFp_simple_field_mul, | |
57 | ec_GFp_simple_field_sqr, | |
58 | 0 /* field_div */ , | |
59 | 0 /* field_encode */ , | |
60 | 0 /* field_decode */ , | |
9ff9bccc DSH |
61 | 0, /* field_set_to_one */ |
62 | ec_key_simple_priv2oct, | |
63 | ec_key_simple_oct2priv, | |
64 | 0, /* set private */ | |
65 | ec_key_simple_generate_key, | |
66 | ec_key_simple_check_key, | |
67 | ec_key_simple_generate_public_key, | |
68 | 0, /* keycopy */ | |
69 | 0, /* keyfinish */ | |
70 | ecdh_simple_compute_key | |
0f113f3e MC |
71 | }; |
72 | ||
73 | return &ret; | |
74 | } | |
60428dbf | 75 | |
3a83462d MC |
76 | /* |
77 | * Most method functions in this file are designed to work with | |
922fa76e BM |
78 | * non-trivial representations of field elements if necessary |
79 | * (see ecp_mont.c): while standard modular addition and subtraction | |
80 | * are used, the field_mul and field_sqr methods will be used for | |
81 | * multiplication, and field_encode and field_decode (if defined) | |
82 | * will be used for converting between representations. | |
3a83462d | 83 | * |
922fa76e BM |
84 | * Functions ec_GFp_simple_points_make_affine() and |
85 | * ec_GFp_simple_point_get_affine_coordinates() specifically assume | |
86 | * that if a non-trivial representation is used, it is a Montgomery | |
87 | * representation (i.e. 'encoding' means multiplying by some factor R). | |
88 | */ | |
89 | ||
60428dbf | 90 | int ec_GFp_simple_group_init(EC_GROUP *group) |
0f113f3e MC |
91 | { |
92 | group->field = BN_new(); | |
93 | group->a = BN_new(); | |
94 | group->b = BN_new(); | |
90945fa3 | 95 | if (group->field == NULL || group->a == NULL || group->b == NULL) { |
a3853772 RS |
96 | BN_free(group->field); |
97 | BN_free(group->a); | |
98 | BN_free(group->b); | |
0f113f3e MC |
99 | return 0; |
100 | } | |
101 | group->a_is_minus3 = 0; | |
102 | return 1; | |
103 | } | |
60428dbf | 104 | |
bb62a8b0 | 105 | void ec_GFp_simple_group_finish(EC_GROUP *group) |
0f113f3e MC |
106 | { |
107 | BN_free(group->field); | |
108 | BN_free(group->a); | |
109 | BN_free(group->b); | |
110 | } | |
bb62a8b0 BM |
111 | |
112 | void ec_GFp_simple_group_clear_finish(EC_GROUP *group) | |
0f113f3e MC |
113 | { |
114 | BN_clear_free(group->field); | |
115 | BN_clear_free(group->a); | |
116 | BN_clear_free(group->b); | |
117 | } | |
bb62a8b0 BM |
118 | |
119 | int ec_GFp_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src) | |
0f113f3e MC |
120 | { |
121 | if (!BN_copy(dest->field, src->field)) | |
122 | return 0; | |
123 | if (!BN_copy(dest->a, src->a)) | |
124 | return 0; | |
125 | if (!BN_copy(dest->b, src->b)) | |
126 | return 0; | |
bb62a8b0 | 127 | |
0f113f3e | 128 | dest->a_is_minus3 = src->a_is_minus3; |
bb62a8b0 | 129 | |
0f113f3e MC |
130 | return 1; |
131 | } | |
bb62a8b0 | 132 | |
35b73a1f | 133 | int ec_GFp_simple_group_set_curve(EC_GROUP *group, |
0f113f3e MC |
134 | const BIGNUM *p, const BIGNUM *a, |
135 | const BIGNUM *b, BN_CTX *ctx) | |
136 | { | |
137 | int ret = 0; | |
138 | BN_CTX *new_ctx = NULL; | |
139 | BIGNUM *tmp_a; | |
140 | ||
141 | /* p must be a prime > 3 */ | |
142 | if (BN_num_bits(p) <= 2 || !BN_is_odd(p)) { | |
143 | ECerr(EC_F_EC_GFP_SIMPLE_GROUP_SET_CURVE, EC_R_INVALID_FIELD); | |
144 | return 0; | |
145 | } | |
146 | ||
147 | if (ctx == NULL) { | |
148 | ctx = new_ctx = BN_CTX_new(); | |
149 | if (ctx == NULL) | |
150 | return 0; | |
151 | } | |
152 | ||
153 | BN_CTX_start(ctx); | |
154 | tmp_a = BN_CTX_get(ctx); | |
155 | if (tmp_a == NULL) | |
156 | goto err; | |
157 | ||
158 | /* group->field */ | |
159 | if (!BN_copy(group->field, p)) | |
160 | goto err; | |
161 | BN_set_negative(group->field, 0); | |
162 | ||
163 | /* group->a */ | |
164 | if (!BN_nnmod(tmp_a, a, p, ctx)) | |
165 | goto err; | |
166 | if (group->meth->field_encode) { | |
167 | if (!group->meth->field_encode(group, group->a, tmp_a, ctx)) | |
168 | goto err; | |
169 | } else if (!BN_copy(group->a, tmp_a)) | |
170 | goto err; | |
171 | ||
172 | /* group->b */ | |
173 | if (!BN_nnmod(group->b, b, p, ctx)) | |
174 | goto err; | |
175 | if (group->meth->field_encode) | |
176 | if (!group->meth->field_encode(group, group->b, group->b, ctx)) | |
177 | goto err; | |
178 | ||
179 | /* group->a_is_minus3 */ | |
180 | if (!BN_add_word(tmp_a, 3)) | |
181 | goto err; | |
182 | group->a_is_minus3 = (0 == BN_cmp(tmp_a, group->field)); | |
183 | ||
184 | ret = 1; | |
60428dbf BM |
185 | |
186 | err: | |
0f113f3e | 187 | BN_CTX_end(ctx); |
23a1d5e9 | 188 | BN_CTX_free(new_ctx); |
0f113f3e MC |
189 | return ret; |
190 | } | |
191 | ||
192 | int ec_GFp_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, | |
193 | BIGNUM *b, BN_CTX *ctx) | |
194 | { | |
195 | int ret = 0; | |
196 | BN_CTX *new_ctx = NULL; | |
197 | ||
198 | if (p != NULL) { | |
199 | if (!BN_copy(p, group->field)) | |
200 | return 0; | |
201 | } | |
202 | ||
203 | if (a != NULL || b != NULL) { | |
204 | if (group->meth->field_decode) { | |
205 | if (ctx == NULL) { | |
206 | ctx = new_ctx = BN_CTX_new(); | |
207 | if (ctx == NULL) | |
208 | return 0; | |
209 | } | |
210 | if (a != NULL) { | |
211 | if (!group->meth->field_decode(group, a, group->a, ctx)) | |
212 | goto err; | |
213 | } | |
214 | if (b != NULL) { | |
215 | if (!group->meth->field_decode(group, b, group->b, ctx)) | |
216 | goto err; | |
217 | } | |
218 | } else { | |
219 | if (a != NULL) { | |
220 | if (!BN_copy(a, group->a)) | |
221 | goto err; | |
222 | } | |
223 | if (b != NULL) { | |
224 | if (!BN_copy(b, group->b)) | |
225 | goto err; | |
226 | } | |
227 | } | |
228 | } | |
229 | ||
230 | ret = 1; | |
60428dbf | 231 | |
0f113f3e | 232 | err: |
23a1d5e9 | 233 | BN_CTX_free(new_ctx); |
0f113f3e MC |
234 | return ret; |
235 | } | |
60428dbf | 236 | |
7793f30e | 237 | int ec_GFp_simple_group_get_degree(const EC_GROUP *group) |
0f113f3e MC |
238 | { |
239 | return BN_num_bits(group->field); | |
240 | } | |
7793f30e | 241 | |
17d6bb81 | 242 | int ec_GFp_simple_group_check_discriminant(const EC_GROUP *group, BN_CTX *ctx) |
0f113f3e MC |
243 | { |
244 | int ret = 0; | |
245 | BIGNUM *a, *b, *order, *tmp_1, *tmp_2; | |
246 | const BIGNUM *p = group->field; | |
247 | BN_CTX *new_ctx = NULL; | |
248 | ||
249 | if (ctx == NULL) { | |
250 | ctx = new_ctx = BN_CTX_new(); | |
251 | if (ctx == NULL) { | |
252 | ECerr(EC_F_EC_GFP_SIMPLE_GROUP_CHECK_DISCRIMINANT, | |
253 | ERR_R_MALLOC_FAILURE); | |
254 | goto err; | |
255 | } | |
256 | } | |
257 | BN_CTX_start(ctx); | |
258 | a = BN_CTX_get(ctx); | |
259 | b = BN_CTX_get(ctx); | |
260 | tmp_1 = BN_CTX_get(ctx); | |
261 | tmp_2 = BN_CTX_get(ctx); | |
262 | order = BN_CTX_get(ctx); | |
263 | if (order == NULL) | |
264 | goto err; | |
265 | ||
266 | if (group->meth->field_decode) { | |
267 | if (!group->meth->field_decode(group, a, group->a, ctx)) | |
268 | goto err; | |
269 | if (!group->meth->field_decode(group, b, group->b, ctx)) | |
270 | goto err; | |
271 | } else { | |
272 | if (!BN_copy(a, group->a)) | |
273 | goto err; | |
274 | if (!BN_copy(b, group->b)) | |
275 | goto err; | |
276 | } | |
277 | ||
50e735f9 MC |
278 | /*- |
279 | * check the discriminant: | |
280 | * y^2 = x^3 + a*x + b is an elliptic curve <=> 4*a^3 + 27*b^2 != 0 (mod p) | |
281 | * 0 =< a, b < p | |
282 | */ | |
0f113f3e MC |
283 | if (BN_is_zero(a)) { |
284 | if (BN_is_zero(b)) | |
285 | goto err; | |
286 | } else if (!BN_is_zero(b)) { | |
287 | if (!BN_mod_sqr(tmp_1, a, p, ctx)) | |
288 | goto err; | |
289 | if (!BN_mod_mul(tmp_2, tmp_1, a, p, ctx)) | |
290 | goto err; | |
291 | if (!BN_lshift(tmp_1, tmp_2, 2)) | |
292 | goto err; | |
293 | /* tmp_1 = 4*a^3 */ | |
294 | ||
295 | if (!BN_mod_sqr(tmp_2, b, p, ctx)) | |
296 | goto err; | |
297 | if (!BN_mul_word(tmp_2, 27)) | |
298 | goto err; | |
299 | /* tmp_2 = 27*b^2 */ | |
300 | ||
301 | if (!BN_mod_add(a, tmp_1, tmp_2, p, ctx)) | |
302 | goto err; | |
303 | if (BN_is_zero(a)) | |
304 | goto err; | |
305 | } | |
306 | ret = 1; | |
af28dd6c | 307 | |
0f113f3e MC |
308 | err: |
309 | if (ctx != NULL) | |
310 | BN_CTX_end(ctx); | |
23a1d5e9 | 311 | BN_CTX_free(new_ctx); |
0f113f3e MC |
312 | return ret; |
313 | } | |
af28dd6c | 314 | |
60428dbf | 315 | int ec_GFp_simple_point_init(EC_POINT *point) |
0f113f3e MC |
316 | { |
317 | point->X = BN_new(); | |
318 | point->Y = BN_new(); | |
319 | point->Z = BN_new(); | |
320 | point->Z_is_one = 0; | |
321 | ||
90945fa3 | 322 | if (point->X == NULL || point->Y == NULL || point->Z == NULL) { |
23a1d5e9 RS |
323 | BN_free(point->X); |
324 | BN_free(point->Y); | |
325 | BN_free(point->Z); | |
0f113f3e MC |
326 | return 0; |
327 | } | |
328 | return 1; | |
329 | } | |
60428dbf BM |
330 | |
331 | void ec_GFp_simple_point_finish(EC_POINT *point) | |
0f113f3e MC |
332 | { |
333 | BN_free(point->X); | |
334 | BN_free(point->Y); | |
335 | BN_free(point->Z); | |
336 | } | |
60428dbf BM |
337 | |
338 | void ec_GFp_simple_point_clear_finish(EC_POINT *point) | |
0f113f3e MC |
339 | { |
340 | BN_clear_free(point->X); | |
341 | BN_clear_free(point->Y); | |
342 | BN_clear_free(point->Z); | |
343 | point->Z_is_one = 0; | |
344 | } | |
60428dbf BM |
345 | |
346 | int ec_GFp_simple_point_copy(EC_POINT *dest, const EC_POINT *src) | |
0f113f3e MC |
347 | { |
348 | if (!BN_copy(dest->X, src->X)) | |
349 | return 0; | |
350 | if (!BN_copy(dest->Y, src->Y)) | |
351 | return 0; | |
352 | if (!BN_copy(dest->Z, src->Z)) | |
353 | return 0; | |
354 | dest->Z_is_one = src->Z_is_one; | |
355 | ||
356 | return 1; | |
357 | } | |
358 | ||
359 | int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *group, | |
360 | EC_POINT *point) | |
361 | { | |
362 | point->Z_is_one = 0; | |
363 | BN_zero(point->Z); | |
364 | return 1; | |
365 | } | |
366 | ||
367 | int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *group, | |
368 | EC_POINT *point, | |
369 | const BIGNUM *x, | |
370 | const BIGNUM *y, | |
371 | const BIGNUM *z, | |
372 | BN_CTX *ctx) | |
373 | { | |
374 | BN_CTX *new_ctx = NULL; | |
375 | int ret = 0; | |
376 | ||
377 | if (ctx == NULL) { | |
378 | ctx = new_ctx = BN_CTX_new(); | |
379 | if (ctx == NULL) | |
380 | return 0; | |
381 | } | |
382 | ||
383 | if (x != NULL) { | |
384 | if (!BN_nnmod(point->X, x, group->field, ctx)) | |
385 | goto err; | |
386 | if (group->meth->field_encode) { | |
387 | if (!group->meth->field_encode(group, point->X, point->X, ctx)) | |
388 | goto err; | |
389 | } | |
390 | } | |
391 | ||
392 | if (y != NULL) { | |
393 | if (!BN_nnmod(point->Y, y, group->field, ctx)) | |
394 | goto err; | |
395 | if (group->meth->field_encode) { | |
396 | if (!group->meth->field_encode(group, point->Y, point->Y, ctx)) | |
397 | goto err; | |
398 | } | |
399 | } | |
400 | ||
401 | if (z != NULL) { | |
402 | int Z_is_one; | |
403 | ||
404 | if (!BN_nnmod(point->Z, z, group->field, ctx)) | |
405 | goto err; | |
406 | Z_is_one = BN_is_one(point->Z); | |
407 | if (group->meth->field_encode) { | |
408 | if (Z_is_one && (group->meth->field_set_to_one != 0)) { | |
409 | if (!group->meth->field_set_to_one(group, point->Z, ctx)) | |
410 | goto err; | |
411 | } else { | |
412 | if (!group-> | |
413 | meth->field_encode(group, point->Z, point->Z, ctx)) | |
414 | goto err; | |
415 | } | |
416 | } | |
417 | point->Z_is_one = Z_is_one; | |
418 | } | |
419 | ||
420 | ret = 1; | |
421 | ||
bb62a8b0 | 422 | err: |
23a1d5e9 | 423 | BN_CTX_free(new_ctx); |
0f113f3e MC |
424 | return ret; |
425 | } | |
426 | ||
427 | int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *group, | |
428 | const EC_POINT *point, | |
429 | BIGNUM *x, BIGNUM *y, | |
430 | BIGNUM *z, BN_CTX *ctx) | |
431 | { | |
432 | BN_CTX *new_ctx = NULL; | |
433 | int ret = 0; | |
434 | ||
435 | if (group->meth->field_decode != 0) { | |
436 | if (ctx == NULL) { | |
437 | ctx = new_ctx = BN_CTX_new(); | |
438 | if (ctx == NULL) | |
439 | return 0; | |
440 | } | |
441 | ||
442 | if (x != NULL) { | |
443 | if (!group->meth->field_decode(group, x, point->X, ctx)) | |
444 | goto err; | |
445 | } | |
446 | if (y != NULL) { | |
447 | if (!group->meth->field_decode(group, y, point->Y, ctx)) | |
448 | goto err; | |
449 | } | |
450 | if (z != NULL) { | |
451 | if (!group->meth->field_decode(group, z, point->Z, ctx)) | |
452 | goto err; | |
453 | } | |
454 | } else { | |
455 | if (x != NULL) { | |
456 | if (!BN_copy(x, point->X)) | |
457 | goto err; | |
458 | } | |
459 | if (y != NULL) { | |
460 | if (!BN_copy(y, point->Y)) | |
461 | goto err; | |
462 | } | |
463 | if (z != NULL) { | |
464 | if (!BN_copy(z, point->Z)) | |
465 | goto err; | |
466 | } | |
467 | } | |
468 | ||
469 | ret = 1; | |
bb62a8b0 | 470 | |
226cc7de | 471 | err: |
23a1d5e9 | 472 | BN_CTX_free(new_ctx); |
0f113f3e MC |
473 | return ret; |
474 | } | |
475 | ||
476 | int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *group, | |
477 | EC_POINT *point, | |
478 | const BIGNUM *x, | |
479 | const BIGNUM *y, BN_CTX *ctx) | |
480 | { | |
481 | if (x == NULL || y == NULL) { | |
482 | /* | |
483 | * unlike for projective coordinates, we do not tolerate this | |
484 | */ | |
485 | ECerr(EC_F_EC_GFP_SIMPLE_POINT_SET_AFFINE_COORDINATES, | |
486 | ERR_R_PASSED_NULL_PARAMETER); | |
487 | return 0; | |
488 | } | |
489 | ||
490 | return EC_POINT_set_Jprojective_coordinates_GFp(group, point, x, y, | |
491 | BN_value_one(), ctx); | |
492 | } | |
493 | ||
494 | int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *group, | |
495 | const EC_POINT *point, | |
496 | BIGNUM *x, BIGNUM *y, | |
497 | BN_CTX *ctx) | |
498 | { | |
499 | BN_CTX *new_ctx = NULL; | |
500 | BIGNUM *Z, *Z_1, *Z_2, *Z_3; | |
501 | const BIGNUM *Z_; | |
502 | int ret = 0; | |
503 | ||
504 | if (EC_POINT_is_at_infinity(group, point)) { | |
505 | ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES, | |
506 | EC_R_POINT_AT_INFINITY); | |
507 | return 0; | |
508 | } | |
509 | ||
510 | if (ctx == NULL) { | |
511 | ctx = new_ctx = BN_CTX_new(); | |
512 | if (ctx == NULL) | |
513 | return 0; | |
514 | } | |
515 | ||
516 | BN_CTX_start(ctx); | |
517 | Z = BN_CTX_get(ctx); | |
518 | Z_1 = BN_CTX_get(ctx); | |
519 | Z_2 = BN_CTX_get(ctx); | |
520 | Z_3 = BN_CTX_get(ctx); | |
521 | if (Z_3 == NULL) | |
522 | goto err; | |
523 | ||
524 | /* transform (X, Y, Z) into (x, y) := (X/Z^2, Y/Z^3) */ | |
525 | ||
526 | if (group->meth->field_decode) { | |
527 | if (!group->meth->field_decode(group, Z, point->Z, ctx)) | |
528 | goto err; | |
529 | Z_ = Z; | |
530 | } else { | |
531 | Z_ = point->Z; | |
532 | } | |
533 | ||
534 | if (BN_is_one(Z_)) { | |
535 | if (group->meth->field_decode) { | |
536 | if (x != NULL) { | |
537 | if (!group->meth->field_decode(group, x, point->X, ctx)) | |
538 | goto err; | |
539 | } | |
540 | if (y != NULL) { | |
541 | if (!group->meth->field_decode(group, y, point->Y, ctx)) | |
542 | goto err; | |
543 | } | |
544 | } else { | |
545 | if (x != NULL) { | |
546 | if (!BN_copy(x, point->X)) | |
547 | goto err; | |
548 | } | |
549 | if (y != NULL) { | |
550 | if (!BN_copy(y, point->Y)) | |
551 | goto err; | |
552 | } | |
553 | } | |
554 | } else { | |
555 | if (!BN_mod_inverse(Z_1, Z_, group->field, ctx)) { | |
556 | ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES, | |
557 | ERR_R_BN_LIB); | |
558 | goto err; | |
559 | } | |
560 | ||
561 | if (group->meth->field_encode == 0) { | |
562 | /* field_sqr works on standard representation */ | |
563 | if (!group->meth->field_sqr(group, Z_2, Z_1, ctx)) | |
564 | goto err; | |
565 | } else { | |
566 | if (!BN_mod_sqr(Z_2, Z_1, group->field, ctx)) | |
567 | goto err; | |
568 | } | |
569 | ||
570 | if (x != NULL) { | |
571 | /* | |
572 | * in the Montgomery case, field_mul will cancel out Montgomery | |
573 | * factor in X: | |
574 | */ | |
575 | if (!group->meth->field_mul(group, x, point->X, Z_2, ctx)) | |
576 | goto err; | |
577 | } | |
578 | ||
579 | if (y != NULL) { | |
580 | if (group->meth->field_encode == 0) { | |
581 | /* | |
582 | * field_mul works on standard representation | |
583 | */ | |
584 | if (!group->meth->field_mul(group, Z_3, Z_2, Z_1, ctx)) | |
585 | goto err; | |
586 | } else { | |
587 | if (!BN_mod_mul(Z_3, Z_2, Z_1, group->field, ctx)) | |
588 | goto err; | |
589 | } | |
590 | ||
591 | /* | |
592 | * in the Montgomery case, field_mul will cancel out Montgomery | |
593 | * factor in Y: | |
594 | */ | |
595 | if (!group->meth->field_mul(group, y, point->Y, Z_3, ctx)) | |
596 | goto err; | |
597 | } | |
598 | } | |
599 | ||
600 | ret = 1; | |
226cc7de BM |
601 | |
602 | err: | |
0f113f3e | 603 | BN_CTX_end(ctx); |
23a1d5e9 | 604 | BN_CTX_free(new_ctx); |
0f113f3e MC |
605 | return ret; |
606 | } | |
607 | ||
608 | int ec_GFp_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, | |
609 | const EC_POINT *b, BN_CTX *ctx) | |
610 | { | |
611 | int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *, | |
612 | const BIGNUM *, BN_CTX *); | |
613 | int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); | |
614 | const BIGNUM *p; | |
615 | BN_CTX *new_ctx = NULL; | |
616 | BIGNUM *n0, *n1, *n2, *n3, *n4, *n5, *n6; | |
617 | int ret = 0; | |
618 | ||
619 | if (a == b) | |
620 | return EC_POINT_dbl(group, r, a, ctx); | |
621 | if (EC_POINT_is_at_infinity(group, a)) | |
622 | return EC_POINT_copy(r, b); | |
623 | if (EC_POINT_is_at_infinity(group, b)) | |
624 | return EC_POINT_copy(r, a); | |
625 | ||
626 | field_mul = group->meth->field_mul; | |
627 | field_sqr = group->meth->field_sqr; | |
628 | p = group->field; | |
629 | ||
630 | if (ctx == NULL) { | |
631 | ctx = new_ctx = BN_CTX_new(); | |
632 | if (ctx == NULL) | |
633 | return 0; | |
634 | } | |
635 | ||
636 | BN_CTX_start(ctx); | |
637 | n0 = BN_CTX_get(ctx); | |
638 | n1 = BN_CTX_get(ctx); | |
639 | n2 = BN_CTX_get(ctx); | |
640 | n3 = BN_CTX_get(ctx); | |
641 | n4 = BN_CTX_get(ctx); | |
642 | n5 = BN_CTX_get(ctx); | |
643 | n6 = BN_CTX_get(ctx); | |
644 | if (n6 == NULL) | |
645 | goto end; | |
646 | ||
647 | /* | |
648 | * Note that in this function we must not read components of 'a' or 'b' | |
649 | * once we have written the corresponding components of 'r'. ('r' might | |
650 | * be one of 'a' or 'b'.) | |
651 | */ | |
652 | ||
653 | /* n1, n2 */ | |
654 | if (b->Z_is_one) { | |
655 | if (!BN_copy(n1, a->X)) | |
656 | goto end; | |
657 | if (!BN_copy(n2, a->Y)) | |
658 | goto end; | |
659 | /* n1 = X_a */ | |
660 | /* n2 = Y_a */ | |
661 | } else { | |
662 | if (!field_sqr(group, n0, b->Z, ctx)) | |
663 | goto end; | |
664 | if (!field_mul(group, n1, a->X, n0, ctx)) | |
665 | goto end; | |
666 | /* n1 = X_a * Z_b^2 */ | |
667 | ||
668 | if (!field_mul(group, n0, n0, b->Z, ctx)) | |
669 | goto end; | |
670 | if (!field_mul(group, n2, a->Y, n0, ctx)) | |
671 | goto end; | |
672 | /* n2 = Y_a * Z_b^3 */ | |
673 | } | |
674 | ||
675 | /* n3, n4 */ | |
676 | if (a->Z_is_one) { | |
677 | if (!BN_copy(n3, b->X)) | |
678 | goto end; | |
679 | if (!BN_copy(n4, b->Y)) | |
680 | goto end; | |
681 | /* n3 = X_b */ | |
682 | /* n4 = Y_b */ | |
683 | } else { | |
684 | if (!field_sqr(group, n0, a->Z, ctx)) | |
685 | goto end; | |
686 | if (!field_mul(group, n3, b->X, n0, ctx)) | |
687 | goto end; | |
688 | /* n3 = X_b * Z_a^2 */ | |
689 | ||
690 | if (!field_mul(group, n0, n0, a->Z, ctx)) | |
691 | goto end; | |
692 | if (!field_mul(group, n4, b->Y, n0, ctx)) | |
693 | goto end; | |
694 | /* n4 = Y_b * Z_a^3 */ | |
695 | } | |
696 | ||
697 | /* n5, n6 */ | |
698 | if (!BN_mod_sub_quick(n5, n1, n3, p)) | |
699 | goto end; | |
700 | if (!BN_mod_sub_quick(n6, n2, n4, p)) | |
701 | goto end; | |
702 | /* n5 = n1 - n3 */ | |
703 | /* n6 = n2 - n4 */ | |
704 | ||
705 | if (BN_is_zero(n5)) { | |
706 | if (BN_is_zero(n6)) { | |
707 | /* a is the same point as b */ | |
708 | BN_CTX_end(ctx); | |
709 | ret = EC_POINT_dbl(group, r, a, ctx); | |
710 | ctx = NULL; | |
711 | goto end; | |
712 | } else { | |
713 | /* a is the inverse of b */ | |
714 | BN_zero(r->Z); | |
715 | r->Z_is_one = 0; | |
716 | ret = 1; | |
717 | goto end; | |
718 | } | |
719 | } | |
720 | ||
721 | /* 'n7', 'n8' */ | |
722 | if (!BN_mod_add_quick(n1, n1, n3, p)) | |
723 | goto end; | |
724 | if (!BN_mod_add_quick(n2, n2, n4, p)) | |
725 | goto end; | |
726 | /* 'n7' = n1 + n3 */ | |
727 | /* 'n8' = n2 + n4 */ | |
728 | ||
729 | /* Z_r */ | |
730 | if (a->Z_is_one && b->Z_is_one) { | |
731 | if (!BN_copy(r->Z, n5)) | |
732 | goto end; | |
733 | } else { | |
734 | if (a->Z_is_one) { | |
735 | if (!BN_copy(n0, b->Z)) | |
736 | goto end; | |
737 | } else if (b->Z_is_one) { | |
738 | if (!BN_copy(n0, a->Z)) | |
739 | goto end; | |
740 | } else { | |
741 | if (!field_mul(group, n0, a->Z, b->Z, ctx)) | |
742 | goto end; | |
743 | } | |
744 | if (!field_mul(group, r->Z, n0, n5, ctx)) | |
745 | goto end; | |
746 | } | |
747 | r->Z_is_one = 0; | |
748 | /* Z_r = Z_a * Z_b * n5 */ | |
749 | ||
750 | /* X_r */ | |
751 | if (!field_sqr(group, n0, n6, ctx)) | |
752 | goto end; | |
753 | if (!field_sqr(group, n4, n5, ctx)) | |
754 | goto end; | |
755 | if (!field_mul(group, n3, n1, n4, ctx)) | |
756 | goto end; | |
757 | if (!BN_mod_sub_quick(r->X, n0, n3, p)) | |
758 | goto end; | |
759 | /* X_r = n6^2 - n5^2 * 'n7' */ | |
760 | ||
761 | /* 'n9' */ | |
762 | if (!BN_mod_lshift1_quick(n0, r->X, p)) | |
763 | goto end; | |
764 | if (!BN_mod_sub_quick(n0, n3, n0, p)) | |
765 | goto end; | |
766 | /* n9 = n5^2 * 'n7' - 2 * X_r */ | |
767 | ||
768 | /* Y_r */ | |
769 | if (!field_mul(group, n0, n0, n6, ctx)) | |
770 | goto end; | |
771 | if (!field_mul(group, n5, n4, n5, ctx)) | |
772 | goto end; /* now n5 is n5^3 */ | |
773 | if (!field_mul(group, n1, n2, n5, ctx)) | |
774 | goto end; | |
775 | if (!BN_mod_sub_quick(n0, n0, n1, p)) | |
776 | goto end; | |
777 | if (BN_is_odd(n0)) | |
778 | if (!BN_add(n0, n0, p)) | |
779 | goto end; | |
780 | /* now 0 <= n0 < 2*p, and n0 is even */ | |
781 | if (!BN_rshift1(r->Y, n0)) | |
782 | goto end; | |
783 | /* Y_r = (n6 * 'n9' - 'n8' * 'n5^3') / 2 */ | |
784 | ||
785 | ret = 1; | |
60428dbf BM |
786 | |
787 | end: | |
0f113f3e MC |
788 | if (ctx) /* otherwise we already called BN_CTX_end */ |
789 | BN_CTX_end(ctx); | |
23a1d5e9 | 790 | BN_CTX_free(new_ctx); |
0f113f3e MC |
791 | return ret; |
792 | } | |
793 | ||
794 | int ec_GFp_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, | |
795 | BN_CTX *ctx) | |
796 | { | |
797 | int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *, | |
798 | const BIGNUM *, BN_CTX *); | |
799 | int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); | |
800 | const BIGNUM *p; | |
801 | BN_CTX *new_ctx = NULL; | |
802 | BIGNUM *n0, *n1, *n2, *n3; | |
803 | int ret = 0; | |
804 | ||
805 | if (EC_POINT_is_at_infinity(group, a)) { | |
806 | BN_zero(r->Z); | |
807 | r->Z_is_one = 0; | |
808 | return 1; | |
809 | } | |
810 | ||
811 | field_mul = group->meth->field_mul; | |
812 | field_sqr = group->meth->field_sqr; | |
813 | p = group->field; | |
814 | ||
815 | if (ctx == NULL) { | |
816 | ctx = new_ctx = BN_CTX_new(); | |
817 | if (ctx == NULL) | |
818 | return 0; | |
819 | } | |
820 | ||
821 | BN_CTX_start(ctx); | |
822 | n0 = BN_CTX_get(ctx); | |
823 | n1 = BN_CTX_get(ctx); | |
824 | n2 = BN_CTX_get(ctx); | |
825 | n3 = BN_CTX_get(ctx); | |
826 | if (n3 == NULL) | |
827 | goto err; | |
828 | ||
829 | /* | |
830 | * Note that in this function we must not read components of 'a' once we | |
831 | * have written the corresponding components of 'r'. ('r' might the same | |
832 | * as 'a'.) | |
833 | */ | |
834 | ||
835 | /* n1 */ | |
836 | if (a->Z_is_one) { | |
837 | if (!field_sqr(group, n0, a->X, ctx)) | |
838 | goto err; | |
839 | if (!BN_mod_lshift1_quick(n1, n0, p)) | |
840 | goto err; | |
841 | if (!BN_mod_add_quick(n0, n0, n1, p)) | |
842 | goto err; | |
843 | if (!BN_mod_add_quick(n1, n0, group->a, p)) | |
844 | goto err; | |
845 | /* n1 = 3 * X_a^2 + a_curve */ | |
846 | } else if (group->a_is_minus3) { | |
847 | if (!field_sqr(group, n1, a->Z, ctx)) | |
848 | goto err; | |
849 | if (!BN_mod_add_quick(n0, a->X, n1, p)) | |
850 | goto err; | |
851 | if (!BN_mod_sub_quick(n2, a->X, n1, p)) | |
852 | goto err; | |
853 | if (!field_mul(group, n1, n0, n2, ctx)) | |
854 | goto err; | |
855 | if (!BN_mod_lshift1_quick(n0, n1, p)) | |
856 | goto err; | |
857 | if (!BN_mod_add_quick(n1, n0, n1, p)) | |
858 | goto err; | |
35a1cc90 MC |
859 | /*- |
860 | * n1 = 3 * (X_a + Z_a^2) * (X_a - Z_a^2) | |
861 | * = 3 * X_a^2 - 3 * Z_a^4 | |
862 | */ | |
0f113f3e MC |
863 | } else { |
864 | if (!field_sqr(group, n0, a->X, ctx)) | |
865 | goto err; | |
866 | if (!BN_mod_lshift1_quick(n1, n0, p)) | |
867 | goto err; | |
868 | if (!BN_mod_add_quick(n0, n0, n1, p)) | |
869 | goto err; | |
870 | if (!field_sqr(group, n1, a->Z, ctx)) | |
871 | goto err; | |
872 | if (!field_sqr(group, n1, n1, ctx)) | |
873 | goto err; | |
874 | if (!field_mul(group, n1, n1, group->a, ctx)) | |
875 | goto err; | |
876 | if (!BN_mod_add_quick(n1, n1, n0, p)) | |
877 | goto err; | |
878 | /* n1 = 3 * X_a^2 + a_curve * Z_a^4 */ | |
879 | } | |
880 | ||
881 | /* Z_r */ | |
882 | if (a->Z_is_one) { | |
883 | if (!BN_copy(n0, a->Y)) | |
884 | goto err; | |
885 | } else { | |
886 | if (!field_mul(group, n0, a->Y, a->Z, ctx)) | |
887 | goto err; | |
888 | } | |
889 | if (!BN_mod_lshift1_quick(r->Z, n0, p)) | |
890 | goto err; | |
891 | r->Z_is_one = 0; | |
892 | /* Z_r = 2 * Y_a * Z_a */ | |
893 | ||
894 | /* n2 */ | |
895 | if (!field_sqr(group, n3, a->Y, ctx)) | |
896 | goto err; | |
897 | if (!field_mul(group, n2, a->X, n3, ctx)) | |
898 | goto err; | |
899 | if (!BN_mod_lshift_quick(n2, n2, 2, p)) | |
900 | goto err; | |
901 | /* n2 = 4 * X_a * Y_a^2 */ | |
902 | ||
903 | /* X_r */ | |
904 | if (!BN_mod_lshift1_quick(n0, n2, p)) | |
905 | goto err; | |
906 | if (!field_sqr(group, r->X, n1, ctx)) | |
907 | goto err; | |
908 | if (!BN_mod_sub_quick(r->X, r->X, n0, p)) | |
909 | goto err; | |
910 | /* X_r = n1^2 - 2 * n2 */ | |
911 | ||
912 | /* n3 */ | |
913 | if (!field_sqr(group, n0, n3, ctx)) | |
914 | goto err; | |
915 | if (!BN_mod_lshift_quick(n3, n0, 3, p)) | |
916 | goto err; | |
917 | /* n3 = 8 * Y_a^4 */ | |
918 | ||
919 | /* Y_r */ | |
920 | if (!BN_mod_sub_quick(n0, n2, r->X, p)) | |
921 | goto err; | |
922 | if (!field_mul(group, n0, n1, n0, ctx)) | |
923 | goto err; | |
924 | if (!BN_mod_sub_quick(r->Y, n0, n3, p)) | |
925 | goto err; | |
926 | /* Y_r = n1 * (n2 - X_r) - n3 */ | |
927 | ||
928 | ret = 1; | |
60428dbf BM |
929 | |
930 | err: | |
0f113f3e | 931 | BN_CTX_end(ctx); |
23a1d5e9 | 932 | BN_CTX_free(new_ctx); |
0f113f3e MC |
933 | return ret; |
934 | } | |
60428dbf | 935 | |
bb62a8b0 | 936 | int ec_GFp_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx) |
0f113f3e MC |
937 | { |
938 | if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(point->Y)) | |
939 | /* point is its own inverse */ | |
940 | return 1; | |
1d5bd6cf | 941 | |
0f113f3e MC |
942 | return BN_usub(point->Y, group->field, point->Y); |
943 | } | |
1d5bd6cf | 944 | |
60428dbf | 945 | int ec_GFp_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point) |
0f113f3e MC |
946 | { |
947 | return BN_is_zero(point->Z); | |
948 | } | |
949 | ||
950 | int ec_GFp_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, | |
951 | BN_CTX *ctx) | |
952 | { | |
953 | int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *, | |
954 | const BIGNUM *, BN_CTX *); | |
955 | int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); | |
956 | const BIGNUM *p; | |
957 | BN_CTX *new_ctx = NULL; | |
958 | BIGNUM *rh, *tmp, *Z4, *Z6; | |
959 | int ret = -1; | |
960 | ||
961 | if (EC_POINT_is_at_infinity(group, point)) | |
962 | return 1; | |
963 | ||
964 | field_mul = group->meth->field_mul; | |
965 | field_sqr = group->meth->field_sqr; | |
966 | p = group->field; | |
967 | ||
968 | if (ctx == NULL) { | |
969 | ctx = new_ctx = BN_CTX_new(); | |
970 | if (ctx == NULL) | |
971 | return -1; | |
972 | } | |
973 | ||
974 | BN_CTX_start(ctx); | |
975 | rh = BN_CTX_get(ctx); | |
976 | tmp = BN_CTX_get(ctx); | |
977 | Z4 = BN_CTX_get(ctx); | |
978 | Z6 = BN_CTX_get(ctx); | |
979 | if (Z6 == NULL) | |
980 | goto err; | |
981 | ||
35a1cc90 MC |
982 | /*- |
983 | * We have a curve defined by a Weierstrass equation | |
984 | * y^2 = x^3 + a*x + b. | |
985 | * The point to consider is given in Jacobian projective coordinates | |
986 | * where (X, Y, Z) represents (x, y) = (X/Z^2, Y/Z^3). | |
987 | * Substituting this and multiplying by Z^6 transforms the above equation into | |
988 | * Y^2 = X^3 + a*X*Z^4 + b*Z^6. | |
989 | * To test this, we add up the right-hand side in 'rh'. | |
990 | */ | |
0f113f3e MC |
991 | |
992 | /* rh := X^2 */ | |
993 | if (!field_sqr(group, rh, point->X, ctx)) | |
994 | goto err; | |
995 | ||
996 | if (!point->Z_is_one) { | |
997 | if (!field_sqr(group, tmp, point->Z, ctx)) | |
998 | goto err; | |
999 | if (!field_sqr(group, Z4, tmp, ctx)) | |
1000 | goto err; | |
1001 | if (!field_mul(group, Z6, Z4, tmp, ctx)) | |
1002 | goto err; | |
1003 | ||
1004 | /* rh := (rh + a*Z^4)*X */ | |
1005 | if (group->a_is_minus3) { | |
1006 | if (!BN_mod_lshift1_quick(tmp, Z4, p)) | |
1007 | goto err; | |
1008 | if (!BN_mod_add_quick(tmp, tmp, Z4, p)) | |
1009 | goto err; | |
1010 | if (!BN_mod_sub_quick(rh, rh, tmp, p)) | |
1011 | goto err; | |
1012 | if (!field_mul(group, rh, rh, point->X, ctx)) | |
1013 | goto err; | |
1014 | } else { | |
1015 | if (!field_mul(group, tmp, Z4, group->a, ctx)) | |
1016 | goto err; | |
1017 | if (!BN_mod_add_quick(rh, rh, tmp, p)) | |
1018 | goto err; | |
1019 | if (!field_mul(group, rh, rh, point->X, ctx)) | |
1020 | goto err; | |
1021 | } | |
1022 | ||
1023 | /* rh := rh + b*Z^6 */ | |
1024 | if (!field_mul(group, tmp, group->b, Z6, ctx)) | |
1025 | goto err; | |
1026 | if (!BN_mod_add_quick(rh, rh, tmp, p)) | |
1027 | goto err; | |
1028 | } else { | |
1029 | /* point->Z_is_one */ | |
1030 | ||
1031 | /* rh := (rh + a)*X */ | |
1032 | if (!BN_mod_add_quick(rh, rh, group->a, p)) | |
1033 | goto err; | |
1034 | if (!field_mul(group, rh, rh, point->X, ctx)) | |
1035 | goto err; | |
1036 | /* rh := rh + b */ | |
1037 | if (!BN_mod_add_quick(rh, rh, group->b, p)) | |
1038 | goto err; | |
1039 | } | |
1040 | ||
1041 | /* 'lh' := Y^2 */ | |
1042 | if (!field_sqr(group, tmp, point->Y, ctx)) | |
1043 | goto err; | |
1044 | ||
1045 | ret = (0 == BN_ucmp(tmp, rh)); | |
e869d4bd BM |
1046 | |
1047 | err: | |
0f113f3e | 1048 | BN_CTX_end(ctx); |
23a1d5e9 | 1049 | BN_CTX_free(new_ctx); |
0f113f3e MC |
1050 | return ret; |
1051 | } | |
1052 | ||
1053 | int ec_GFp_simple_cmp(const EC_GROUP *group, const EC_POINT *a, | |
1054 | const EC_POINT *b, BN_CTX *ctx) | |
1055 | { | |
35a1cc90 MC |
1056 | /*- |
1057 | * return values: | |
1058 | * -1 error | |
1059 | * 0 equal (in affine coordinates) | |
1060 | * 1 not equal | |
1061 | */ | |
0f113f3e MC |
1062 | |
1063 | int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *, | |
1064 | const BIGNUM *, BN_CTX *); | |
1065 | int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); | |
1066 | BN_CTX *new_ctx = NULL; | |
1067 | BIGNUM *tmp1, *tmp2, *Za23, *Zb23; | |
1068 | const BIGNUM *tmp1_, *tmp2_; | |
1069 | int ret = -1; | |
1070 | ||
1071 | if (EC_POINT_is_at_infinity(group, a)) { | |
1072 | return EC_POINT_is_at_infinity(group, b) ? 0 : 1; | |
1073 | } | |
1074 | ||
1075 | if (EC_POINT_is_at_infinity(group, b)) | |
1076 | return 1; | |
1077 | ||
1078 | if (a->Z_is_one && b->Z_is_one) { | |
1079 | return ((BN_cmp(a->X, b->X) == 0) && BN_cmp(a->Y, b->Y) == 0) ? 0 : 1; | |
1080 | } | |
1081 | ||
1082 | field_mul = group->meth->field_mul; | |
1083 | field_sqr = group->meth->field_sqr; | |
1084 | ||
1085 | if (ctx == NULL) { | |
1086 | ctx = new_ctx = BN_CTX_new(); | |
1087 | if (ctx == NULL) | |
1088 | return -1; | |
1089 | } | |
1090 | ||
1091 | BN_CTX_start(ctx); | |
1092 | tmp1 = BN_CTX_get(ctx); | |
1093 | tmp2 = BN_CTX_get(ctx); | |
1094 | Za23 = BN_CTX_get(ctx); | |
1095 | Zb23 = BN_CTX_get(ctx); | |
1096 | if (Zb23 == NULL) | |
1097 | goto end; | |
1098 | ||
35a1cc90 MC |
1099 | /*- |
1100 | * We have to decide whether | |
1101 | * (X_a/Z_a^2, Y_a/Z_a^3) = (X_b/Z_b^2, Y_b/Z_b^3), | |
1102 | * or equivalently, whether | |
1103 | * (X_a*Z_b^2, Y_a*Z_b^3) = (X_b*Z_a^2, Y_b*Z_a^3). | |
1104 | */ | |
0f113f3e MC |
1105 | |
1106 | if (!b->Z_is_one) { | |
1107 | if (!field_sqr(group, Zb23, b->Z, ctx)) | |
1108 | goto end; | |
1109 | if (!field_mul(group, tmp1, a->X, Zb23, ctx)) | |
1110 | goto end; | |
1111 | tmp1_ = tmp1; | |
1112 | } else | |
1113 | tmp1_ = a->X; | |
1114 | if (!a->Z_is_one) { | |
1115 | if (!field_sqr(group, Za23, a->Z, ctx)) | |
1116 | goto end; | |
1117 | if (!field_mul(group, tmp2, b->X, Za23, ctx)) | |
1118 | goto end; | |
1119 | tmp2_ = tmp2; | |
1120 | } else | |
1121 | tmp2_ = b->X; | |
1122 | ||
1123 | /* compare X_a*Z_b^2 with X_b*Z_a^2 */ | |
1124 | if (BN_cmp(tmp1_, tmp2_) != 0) { | |
1125 | ret = 1; /* points differ */ | |
1126 | goto end; | |
1127 | } | |
1128 | ||
1129 | if (!b->Z_is_one) { | |
1130 | if (!field_mul(group, Zb23, Zb23, b->Z, ctx)) | |
1131 | goto end; | |
1132 | if (!field_mul(group, tmp1, a->Y, Zb23, ctx)) | |
1133 | goto end; | |
1134 | /* tmp1_ = tmp1 */ | |
1135 | } else | |
1136 | tmp1_ = a->Y; | |
1137 | if (!a->Z_is_one) { | |
1138 | if (!field_mul(group, Za23, Za23, a->Z, ctx)) | |
1139 | goto end; | |
1140 | if (!field_mul(group, tmp2, b->Y, Za23, ctx)) | |
1141 | goto end; | |
1142 | /* tmp2_ = tmp2 */ | |
1143 | } else | |
1144 | tmp2_ = b->Y; | |
1145 | ||
1146 | /* compare Y_a*Z_b^3 with Y_b*Z_a^3 */ | |
1147 | if (BN_cmp(tmp1_, tmp2_) != 0) { | |
1148 | ret = 1; /* points differ */ | |
1149 | goto end; | |
1150 | } | |
1151 | ||
1152 | /* points are equal */ | |
1153 | ret = 0; | |
bb62a8b0 BM |
1154 | |
1155 | end: | |
0f113f3e | 1156 | BN_CTX_end(ctx); |
23a1d5e9 | 1157 | BN_CTX_free(new_ctx); |
0f113f3e MC |
1158 | return ret; |
1159 | } | |
1160 | ||
1161 | int ec_GFp_simple_make_affine(const EC_GROUP *group, EC_POINT *point, | |
1162 | BN_CTX *ctx) | |
1163 | { | |
1164 | BN_CTX *new_ctx = NULL; | |
1165 | BIGNUM *x, *y; | |
1166 | int ret = 0; | |
1167 | ||
1168 | if (point->Z_is_one || EC_POINT_is_at_infinity(group, point)) | |
1169 | return 1; | |
1170 | ||
1171 | if (ctx == NULL) { | |
1172 | ctx = new_ctx = BN_CTX_new(); | |
1173 | if (ctx == NULL) | |
1174 | return 0; | |
1175 | } | |
1176 | ||
1177 | BN_CTX_start(ctx); | |
1178 | x = BN_CTX_get(ctx); | |
1179 | y = BN_CTX_get(ctx); | |
1180 | if (y == NULL) | |
1181 | goto err; | |
1182 | ||
1183 | if (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx)) | |
1184 | goto err; | |
1185 | if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) | |
1186 | goto err; | |
1187 | if (!point->Z_is_one) { | |
1188 | ECerr(EC_F_EC_GFP_SIMPLE_MAKE_AFFINE, ERR_R_INTERNAL_ERROR); | |
1189 | goto err; | |
1190 | } | |
1191 | ||
1192 | ret = 1; | |
e869d4bd | 1193 | |
226cc7de | 1194 | err: |
0f113f3e | 1195 | BN_CTX_end(ctx); |
23a1d5e9 | 1196 | BN_CTX_free(new_ctx); |
0f113f3e MC |
1197 | return ret; |
1198 | } | |
1199 | ||
1200 | int ec_GFp_simple_points_make_affine(const EC_GROUP *group, size_t num, | |
1201 | EC_POINT *points[], BN_CTX *ctx) | |
1202 | { | |
1203 | BN_CTX *new_ctx = NULL; | |
1204 | BIGNUM *tmp, *tmp_Z; | |
1205 | BIGNUM **prod_Z = NULL; | |
1206 | size_t i; | |
1207 | int ret = 0; | |
1208 | ||
1209 | if (num == 0) | |
1210 | return 1; | |
1211 | ||
1212 | if (ctx == NULL) { | |
1213 | ctx = new_ctx = BN_CTX_new(); | |
1214 | if (ctx == NULL) | |
1215 | return 0; | |
1216 | } | |
1217 | ||
1218 | BN_CTX_start(ctx); | |
1219 | tmp = BN_CTX_get(ctx); | |
1220 | tmp_Z = BN_CTX_get(ctx); | |
1221 | if (tmp == NULL || tmp_Z == NULL) | |
1222 | goto err; | |
1223 | ||
1224 | prod_Z = OPENSSL_malloc(num * sizeof prod_Z[0]); | |
1225 | if (prod_Z == NULL) | |
1226 | goto err; | |
1227 | for (i = 0; i < num; i++) { | |
1228 | prod_Z[i] = BN_new(); | |
1229 | if (prod_Z[i] == NULL) | |
1230 | goto err; | |
1231 | } | |
1232 | ||
1233 | /* | |
1234 | * Set each prod_Z[i] to the product of points[0]->Z .. points[i]->Z, | |
1235 | * skipping any zero-valued inputs (pretend that they're 1). | |
1236 | */ | |
1237 | ||
1238 | if (!BN_is_zero(points[0]->Z)) { | |
1239 | if (!BN_copy(prod_Z[0], points[0]->Z)) | |
1240 | goto err; | |
1241 | } else { | |
1242 | if (group->meth->field_set_to_one != 0) { | |
1243 | if (!group->meth->field_set_to_one(group, prod_Z[0], ctx)) | |
1244 | goto err; | |
1245 | } else { | |
1246 | if (!BN_one(prod_Z[0])) | |
1247 | goto err; | |
1248 | } | |
1249 | } | |
1250 | ||
1251 | for (i = 1; i < num; i++) { | |
1252 | if (!BN_is_zero(points[i]->Z)) { | |
1253 | if (!group-> | |
1254 | meth->field_mul(group, prod_Z[i], prod_Z[i - 1], points[i]->Z, | |
1255 | ctx)) | |
1256 | goto err; | |
1257 | } else { | |
1258 | if (!BN_copy(prod_Z[i], prod_Z[i - 1])) | |
1259 | goto err; | |
1260 | } | |
1261 | } | |
1262 | ||
1263 | /* | |
1264 | * Now use a single explicit inversion to replace every non-zero | |
1265 | * points[i]->Z by its inverse. | |
1266 | */ | |
1267 | ||
1268 | if (!BN_mod_inverse(tmp, prod_Z[num - 1], group->field, ctx)) { | |
1269 | ECerr(EC_F_EC_GFP_SIMPLE_POINTS_MAKE_AFFINE, ERR_R_BN_LIB); | |
1270 | goto err; | |
1271 | } | |
1272 | if (group->meth->field_encode != 0) { | |
1273 | /* | |
1274 | * In the Montgomery case, we just turned R*H (representing H) into | |
1275 | * 1/(R*H), but we need R*(1/H) (representing 1/H); i.e. we need to | |
1276 | * multiply by the Montgomery factor twice. | |
1277 | */ | |
1278 | if (!group->meth->field_encode(group, tmp, tmp, ctx)) | |
1279 | goto err; | |
1280 | if (!group->meth->field_encode(group, tmp, tmp, ctx)) | |
1281 | goto err; | |
1282 | } | |
1283 | ||
1284 | for (i = num - 1; i > 0; --i) { | |
1285 | /* | |
1286 | * Loop invariant: tmp is the product of the inverses of points[0]->Z | |
1287 | * .. points[i]->Z (zero-valued inputs skipped). | |
1288 | */ | |
1289 | if (!BN_is_zero(points[i]->Z)) { | |
1290 | /* | |
1291 | * Set tmp_Z to the inverse of points[i]->Z (as product of Z | |
1292 | * inverses 0 .. i, Z values 0 .. i - 1). | |
1293 | */ | |
1294 | if (!group-> | |
1295 | meth->field_mul(group, tmp_Z, prod_Z[i - 1], tmp, ctx)) | |
1296 | goto err; | |
1297 | /* | |
1298 | * Update tmp to satisfy the loop invariant for i - 1. | |
1299 | */ | |
1300 | if (!group->meth->field_mul(group, tmp, tmp, points[i]->Z, ctx)) | |
1301 | goto err; | |
1302 | /* Replace points[i]->Z by its inverse. */ | |
1303 | if (!BN_copy(points[i]->Z, tmp_Z)) | |
1304 | goto err; | |
1305 | } | |
1306 | } | |
1307 | ||
1308 | if (!BN_is_zero(points[0]->Z)) { | |
1309 | /* Replace points[0]->Z by its inverse. */ | |
1310 | if (!BN_copy(points[0]->Z, tmp)) | |
1311 | goto err; | |
1312 | } | |
1313 | ||
1314 | /* Finally, fix up the X and Y coordinates for all points. */ | |
1315 | ||
1316 | for (i = 0; i < num; i++) { | |
1317 | EC_POINT *p = points[i]; | |
1318 | ||
1319 | if (!BN_is_zero(p->Z)) { | |
1320 | /* turn (X, Y, 1/Z) into (X/Z^2, Y/Z^3, 1) */ | |
1321 | ||
1322 | if (!group->meth->field_sqr(group, tmp, p->Z, ctx)) | |
1323 | goto err; | |
1324 | if (!group->meth->field_mul(group, p->X, p->X, tmp, ctx)) | |
1325 | goto err; | |
1326 | ||
1327 | if (!group->meth->field_mul(group, tmp, tmp, p->Z, ctx)) | |
1328 | goto err; | |
1329 | if (!group->meth->field_mul(group, p->Y, p->Y, tmp, ctx)) | |
1330 | goto err; | |
1331 | ||
1332 | if (group->meth->field_set_to_one != 0) { | |
1333 | if (!group->meth->field_set_to_one(group, p->Z, ctx)) | |
1334 | goto err; | |
1335 | } else { | |
1336 | if (!BN_one(p->Z)) | |
1337 | goto err; | |
1338 | } | |
1339 | p->Z_is_one = 1; | |
1340 | } | |
1341 | } | |
1342 | ||
1343 | ret = 1; | |
0fe73d6c | 1344 | |
48fe4d62 | 1345 | err: |
0f113f3e | 1346 | BN_CTX_end(ctx); |
23a1d5e9 | 1347 | BN_CTX_free(new_ctx); |
0f113f3e MC |
1348 | if (prod_Z != NULL) { |
1349 | for (i = 0; i < num; i++) { | |
1350 | if (prod_Z[i] == NULL) | |
1351 | break; | |
1352 | BN_clear_free(prod_Z[i]); | |
1353 | } | |
1354 | OPENSSL_free(prod_Z); | |
1355 | } | |
1356 | return ret; | |
1357 | } | |
1358 | ||
1359 | int ec_GFp_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, | |
1360 | const BIGNUM *b, BN_CTX *ctx) | |
1361 | { | |
1362 | return BN_mod_mul(r, a, b, group->field, ctx); | |
1363 | } | |
1364 | ||
1365 | int ec_GFp_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, | |
1366 | BN_CTX *ctx) | |
1367 | { | |
1368 | return BN_mod_sqr(r, a, group->field, ctx); | |
1369 | } |