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Commit | Line | Data |
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f8fe20e0 | 1 | /* crypto/ec/ecp_smpl.c */ |
60428dbf | 2 | /* Includes code written by Lenka Fibikova <fibikova@exp-math.uni-essen.de> |
35b73a1f BM |
3 | * for the OpenSSL project. |
4 | * Includes code written by Bodo Moeller for the OpenSSL project. | |
5 | */ | |
f8fe20e0 | 6 | /* ==================================================================== |
af28dd6c | 7 | * Copyright (c) 1998-2002 The OpenSSL Project. All rights reserved. |
f8fe20e0 BM |
8 | * |
9 | * Redistribution and use in source and binary forms, with or without | |
10 | * modification, are permitted provided that the following conditions | |
11 | * are met: | |
12 | * | |
13 | * 1. Redistributions of source code must retain the above copyright | |
14 | * notice, this list of conditions and the following disclaimer. | |
15 | * | |
16 | * 2. Redistributions in binary form must reproduce the above copyright | |
17 | * notice, this list of conditions and the following disclaimer in | |
18 | * the documentation and/or other materials provided with the | |
19 | * distribution. | |
20 | * | |
21 | * 3. All advertising materials mentioning features or use of this | |
22 | * software must display the following acknowledgment: | |
23 | * "This product includes software developed by the OpenSSL Project | |
24 | * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" | |
25 | * | |
26 | * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to | |
27 | * endorse or promote products derived from this software without | |
28 | * prior written permission. For written permission, please contact | |
29 | * openssl-core@openssl.org. | |
30 | * | |
31 | * 5. Products derived from this software may not be called "OpenSSL" | |
32 | * nor may "OpenSSL" appear in their names without prior written | |
33 | * permission of the OpenSSL Project. | |
34 | * | |
35 | * 6. Redistributions of any form whatsoever must retain the following | |
36 | * acknowledgment: | |
37 | * "This product includes software developed by the OpenSSL Project | |
38 | * for use in the OpenSSL Toolkit (http://www.openssl.org/)" | |
39 | * | |
40 | * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY | |
41 | * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE | |
42 | * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR | |
43 | * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR | |
44 | * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, | |
45 | * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT | |
46 | * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; | |
47 | * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) | |
48 | * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, | |
49 | * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) | |
50 | * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED | |
51 | * OF THE POSSIBILITY OF SUCH DAMAGE. | |
52 | * ==================================================================== | |
53 | * | |
54 | * This product includes cryptographic software written by Eric Young | |
55 | * (eay@cryptsoft.com). This product includes software written by Tim | |
56 | * Hudson (tjh@cryptsoft.com). | |
57 | * | |
58 | */ | |
7793f30e BM |
59 | /* ==================================================================== |
60 | * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. | |
61 | * Portions of this software developed by SUN MICROSYSTEMS, INC., | |
62 | * and contributed to the OpenSSL project. | |
63 | */ | |
f8fe20e0 | 64 | |
73e45b2d | 65 | |
84b08eee | 66 | |
60428dbf | 67 | #include <openssl/err.h> |
02cbedc3 | 68 | #include <openssl/symhacks.h> |
60428dbf | 69 | |
f8fe20e0 | 70 | #include "ec_lcl.h" |
0657bf9c | 71 | |
0657bf9c BM |
72 | const EC_METHOD *EC_GFp_simple_method(void) |
73 | { | |
58fc6229 | 74 | static const EC_METHOD ret = { |
84b08eee | 75 | EC_FLAGS_DEFAULT_OCT, |
458c2917 | 76 | NID_X9_62_prime_field, |
58fc6229 | 77 | ec_GFp_simple_group_init, |
58fc6229 BM |
78 | ec_GFp_simple_group_finish, |
79 | ec_GFp_simple_group_clear_finish, | |
80 | ec_GFp_simple_group_copy, | |
35b73a1f BM |
81 | ec_GFp_simple_group_set_curve, |
82 | ec_GFp_simple_group_get_curve, | |
7793f30e | 83 | ec_GFp_simple_group_get_degree, |
17d6bb81 | 84 | ec_GFp_simple_group_check_discriminant, |
58fc6229 BM |
85 | ec_GFp_simple_point_init, |
86 | ec_GFp_simple_point_finish, | |
87 | ec_GFp_simple_point_clear_finish, | |
88 | ec_GFp_simple_point_copy, | |
226cc7de | 89 | ec_GFp_simple_point_set_to_infinity, |
1d5bd6cf BM |
90 | ec_GFp_simple_set_Jprojective_coordinates_GFp, |
91 | ec_GFp_simple_get_Jprojective_coordinates_GFp, | |
35b73a1f BM |
92 | ec_GFp_simple_point_set_affine_coordinates, |
93 | ec_GFp_simple_point_get_affine_coordinates, | |
84b08eee | 94 | 0,0,0, |
58fc6229 BM |
95 | ec_GFp_simple_add, |
96 | ec_GFp_simple_dbl, | |
1d5bd6cf | 97 | ec_GFp_simple_invert, |
58fc6229 BM |
98 | ec_GFp_simple_is_at_infinity, |
99 | ec_GFp_simple_is_on_curve, | |
1d5bd6cf | 100 | ec_GFp_simple_cmp, |
58fc6229 | 101 | ec_GFp_simple_make_affine, |
48fe4d62 | 102 | ec_GFp_simple_points_make_affine, |
37c660ff BM |
103 | 0 /* mul */, |
104 | 0 /* precompute_mult */, | |
105 | 0 /* have_precompute_mult */, | |
60428dbf | 106 | ec_GFp_simple_field_mul, |
58fc6229 | 107 | ec_GFp_simple_field_sqr, |
7793f30e | 108 | 0 /* field_div */, |
58fc6229 | 109 | 0 /* field_encode */, |
48fe4d62 BM |
110 | 0 /* field_decode */, |
111 | 0 /* field_set_to_one */ }; | |
0657bf9c BM |
112 | |
113 | return &ret; | |
114 | } | |
60428dbf BM |
115 | |
116 | ||
922fa76e BM |
117 | /* Most method functions in this file are designed to work with |
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. | |
123 | ||
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 | ||
130 | ||
60428dbf BM |
131 | int ec_GFp_simple_group_init(EC_GROUP *group) |
132 | { | |
5784a521 MC |
133 | group->field = BN_new(); |
134 | group->a = BN_new(); | |
135 | group->b = BN_new(); | |
136 | if(!group->field || !group->a || !group->b) | |
137 | { | |
138 | if(!group->field) BN_free(group->field); | |
139 | if(!group->a) BN_free(group->a); | |
140 | if(!group->b) BN_free(group->b); | |
141 | return 0; | |
142 | } | |
60428dbf | 143 | group->a_is_minus3 = 0; |
60428dbf BM |
144 | return 1; |
145 | } | |
146 | ||
147 | ||
bb62a8b0 BM |
148 | void ec_GFp_simple_group_finish(EC_GROUP *group) |
149 | { | |
5784a521 MC |
150 | BN_free(group->field); |
151 | BN_free(group->a); | |
152 | BN_free(group->b); | |
bb62a8b0 BM |
153 | } |
154 | ||
155 | ||
156 | void ec_GFp_simple_group_clear_finish(EC_GROUP *group) | |
157 | { | |
5784a521 MC |
158 | BN_clear_free(group->field); |
159 | BN_clear_free(group->a); | |
160 | BN_clear_free(group->b); | |
bb62a8b0 BM |
161 | } |
162 | ||
163 | ||
164 | int ec_GFp_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src) | |
165 | { | |
5784a521 MC |
166 | if (!BN_copy(dest->field, src->field)) return 0; |
167 | if (!BN_copy(dest->a, src->a)) return 0; | |
168 | if (!BN_copy(dest->b, src->b)) return 0; | |
bb62a8b0 BM |
169 | |
170 | dest->a_is_minus3 = src->a_is_minus3; | |
171 | ||
bb62a8b0 BM |
172 | return 1; |
173 | } | |
174 | ||
175 | ||
35b73a1f | 176 | int ec_GFp_simple_group_set_curve(EC_GROUP *group, |
60428dbf BM |
177 | const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) |
178 | { | |
179 | int ret = 0; | |
180 | BN_CTX *new_ctx = NULL; | |
181 | BIGNUM *tmp_a; | |
182 | ||
1d5bd6cf BM |
183 | /* p must be a prime > 3 */ |
184 | if (BN_num_bits(p) <= 2 || !BN_is_odd(p)) | |
185 | { | |
35b73a1f | 186 | ECerr(EC_F_EC_GFP_SIMPLE_GROUP_SET_CURVE, EC_R_INVALID_FIELD); |
1d5bd6cf BM |
187 | return 0; |
188 | } | |
189 | ||
60428dbf BM |
190 | if (ctx == NULL) |
191 | { | |
192 | ctx = new_ctx = BN_CTX_new(); | |
193 | if (ctx == NULL) | |
194 | return 0; | |
195 | } | |
60428dbf | 196 | |
226cc7de | 197 | BN_CTX_start(ctx); |
60428dbf BM |
198 | tmp_a = BN_CTX_get(ctx); |
199 | if (tmp_a == NULL) goto err; | |
200 | ||
201 | /* group->field */ | |
5784a521 MC |
202 | if (!BN_copy(group->field, p)) goto err; |
203 | BN_set_negative(group->field, 0); | |
60428dbf BM |
204 | |
205 | /* group->a */ | |
206 | if (!BN_nnmod(tmp_a, a, p, ctx)) goto err; | |
207 | if (group->meth->field_encode) | |
5784a521 | 208 | { if (!group->meth->field_encode(group, group->a, tmp_a, ctx)) goto err; } |
60428dbf | 209 | else |
5784a521 | 210 | if (!BN_copy(group->a, tmp_a)) goto err; |
60428dbf BM |
211 | |
212 | /* group->b */ | |
5784a521 | 213 | if (!BN_nnmod(group->b, b, p, ctx)) goto err; |
60428dbf | 214 | if (group->meth->field_encode) |
5784a521 | 215 | if (!group->meth->field_encode(group, group->b, group->b, ctx)) goto err; |
60428dbf BM |
216 | |
217 | /* group->a_is_minus3 */ | |
218 | if (!BN_add_word(tmp_a, 3)) goto err; | |
5784a521 | 219 | group->a_is_minus3 = (0 == BN_cmp(tmp_a, group->field)); |
60428dbf BM |
220 | |
221 | ret = 1; | |
222 | ||
223 | err: | |
224 | BN_CTX_end(ctx); | |
225 | if (new_ctx != NULL) | |
226 | BN_CTX_free(new_ctx); | |
227 | return ret; | |
228 | } | |
229 | ||
230 | ||
35b73a1f | 231 | int ec_GFp_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx) |
60428dbf | 232 | { |
bb62a8b0 BM |
233 | int ret = 0; |
234 | BN_CTX *new_ctx = NULL; | |
235 | ||
236 | if (p != NULL) | |
60428dbf | 237 | { |
5784a521 | 238 | if (!BN_copy(p, group->field)) return 0; |
60428dbf | 239 | } |
60428dbf | 240 | |
bb62a8b0 | 241 | if (a != NULL || b != NULL) |
60428dbf | 242 | { |
bb62a8b0 | 243 | if (group->meth->field_decode) |
60428dbf | 244 | { |
bb62a8b0 BM |
245 | if (ctx == NULL) |
246 | { | |
247 | ctx = new_ctx = BN_CTX_new(); | |
248 | if (ctx == NULL) | |
249 | return 0; | |
250 | } | |
251 | if (a != NULL) | |
252 | { | |
5784a521 | 253 | if (!group->meth->field_decode(group, a, group->a, ctx)) goto err; |
bb62a8b0 BM |
254 | } |
255 | if (b != NULL) | |
256 | { | |
5784a521 | 257 | if (!group->meth->field_decode(group, b, group->b, ctx)) goto err; |
bb62a8b0 | 258 | } |
60428dbf | 259 | } |
bb62a8b0 | 260 | else |
60428dbf | 261 | { |
bb62a8b0 BM |
262 | if (a != NULL) |
263 | { | |
5784a521 | 264 | if (!BN_copy(a, group->a)) goto err; |
bb62a8b0 BM |
265 | } |
266 | if (b != NULL) | |
267 | { | |
5784a521 | 268 | if (!BN_copy(b, group->b)) goto err; |
bb62a8b0 | 269 | } |
60428dbf BM |
270 | } |
271 | } | |
bb62a8b0 BM |
272 | |
273 | ret = 1; | |
274 | ||
275 | err: | |
276 | if (new_ctx) | |
277 | BN_CTX_free(new_ctx); | |
278 | return ret; | |
60428dbf BM |
279 | } |
280 | ||
281 | ||
7793f30e BM |
282 | int ec_GFp_simple_group_get_degree(const EC_GROUP *group) |
283 | { | |
5784a521 | 284 | return BN_num_bits(group->field); |
7793f30e BM |
285 | } |
286 | ||
287 | ||
17d6bb81 | 288 | int ec_GFp_simple_group_check_discriminant(const EC_GROUP *group, BN_CTX *ctx) |
af28dd6c BM |
289 | { |
290 | int ret = 0; | |
291 | BIGNUM *a,*b,*order,*tmp_1,*tmp_2; | |
5784a521 | 292 | const BIGNUM *p = group->field; |
af28dd6c | 293 | BN_CTX *new_ctx = NULL; |
af28dd6c BM |
294 | |
295 | if (ctx == NULL) | |
296 | { | |
297 | ctx = new_ctx = BN_CTX_new(); | |
298 | if (ctx == NULL) | |
299 | { | |
17d6bb81 | 300 | ECerr(EC_F_EC_GFP_SIMPLE_GROUP_CHECK_DISCRIMINANT, ERR_R_MALLOC_FAILURE); |
af28dd6c BM |
301 | goto err; |
302 | } | |
303 | } | |
304 | BN_CTX_start(ctx); | |
305 | a = BN_CTX_get(ctx); | |
306 | b = BN_CTX_get(ctx); | |
307 | tmp_1 = BN_CTX_get(ctx); | |
308 | tmp_2 = BN_CTX_get(ctx); | |
309 | order = BN_CTX_get(ctx); | |
310 | if (order == NULL) goto err; | |
311 | ||
312 | if (group->meth->field_decode) | |
313 | { | |
5784a521 MC |
314 | if (!group->meth->field_decode(group, a, group->a, ctx)) goto err; |
315 | if (!group->meth->field_decode(group, b, group->b, ctx)) goto err; | |
af28dd6c BM |
316 | } |
317 | else | |
318 | { | |
5784a521 MC |
319 | if (!BN_copy(a, group->a)) goto err; |
320 | if (!BN_copy(b, group->b)) goto err; | |
af28dd6c BM |
321 | } |
322 | ||
323 | /* check the discriminant: | |
324 | * y^2 = x^3 + a*x + b is an elliptic curve <=> 4*a^3 + 27*b^2 != 0 (mod p) | |
325 | * 0 =< a, b < p */ | |
326 | if (BN_is_zero(a)) | |
327 | { | |
17d6bb81 | 328 | if (BN_is_zero(b)) goto err; |
af28dd6c BM |
329 | } |
330 | else if (!BN_is_zero(b)) | |
331 | { | |
332 | if (!BN_mod_sqr(tmp_1, a, p, ctx)) goto err; | |
333 | if (!BN_mod_mul(tmp_2, tmp_1, a, p, ctx)) goto err; | |
334 | if (!BN_lshift(tmp_1, tmp_2, 2)) goto err; | |
335 | /* tmp_1 = 4*a^3 */ | |
336 | ||
337 | if (!BN_mod_sqr(tmp_2, b, p, ctx)) goto err; | |
338 | if (!BN_mul_word(tmp_2, 27)) goto err; | |
339 | /* tmp_2 = 27*b^2 */ | |
340 | ||
341 | if (!BN_mod_add(a, tmp_1, tmp_2, p, ctx)) goto err; | |
17d6bb81 | 342 | if (BN_is_zero(a)) goto err; |
af28dd6c | 343 | } |
af28dd6c BM |
344 | ret = 1; |
345 | ||
346 | err: | |
47d55666 NL |
347 | if (ctx != NULL) |
348 | BN_CTX_end(ctx); | |
af28dd6c BM |
349 | if (new_ctx != NULL) |
350 | BN_CTX_free(new_ctx); | |
af28dd6c BM |
351 | return ret; |
352 | } | |
353 | ||
354 | ||
60428dbf BM |
355 | int ec_GFp_simple_point_init(EC_POINT *point) |
356 | { | |
5784a521 MC |
357 | point->X = BN_new(); |
358 | point->Y = BN_new(); | |
359 | point->Z = BN_new(); | |
60428dbf BM |
360 | point->Z_is_one = 0; |
361 | ||
5784a521 MC |
362 | if(!point->X || !point->Y || !point->Z) |
363 | { | |
364 | if(point->X) BN_free(point->X); | |
365 | if(point->Y) BN_free(point->Y); | |
366 | if(point->Z) BN_free(point->Z); | |
367 | return 0; | |
368 | } | |
60428dbf BM |
369 | return 1; |
370 | } | |
371 | ||
372 | ||
373 | void ec_GFp_simple_point_finish(EC_POINT *point) | |
374 | { | |
5784a521 MC |
375 | BN_free(point->X); |
376 | BN_free(point->Y); | |
377 | BN_free(point->Z); | |
60428dbf BM |
378 | } |
379 | ||
380 | ||
381 | void ec_GFp_simple_point_clear_finish(EC_POINT *point) | |
382 | { | |
5784a521 MC |
383 | BN_clear_free(point->X); |
384 | BN_clear_free(point->Y); | |
385 | BN_clear_free(point->Z); | |
60428dbf BM |
386 | point->Z_is_one = 0; |
387 | } | |
388 | ||
389 | ||
390 | int ec_GFp_simple_point_copy(EC_POINT *dest, const EC_POINT *src) | |
391 | { | |
5784a521 MC |
392 | if (!BN_copy(dest->X, src->X)) return 0; |
393 | if (!BN_copy(dest->Y, src->Y)) return 0; | |
394 | if (!BN_copy(dest->Z, src->Z)) return 0; | |
60428dbf BM |
395 | dest->Z_is_one = src->Z_is_one; |
396 | ||
397 | return 1; | |
398 | } | |
399 | ||
400 | ||
226cc7de BM |
401 | int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *group, EC_POINT *point) |
402 | { | |
403 | point->Z_is_one = 0; | |
5784a521 | 404 | BN_zero(point->Z); |
b6358c89 | 405 | return 1; |
226cc7de BM |
406 | } |
407 | ||
408 | ||
1d5bd6cf | 409 | int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *group, EC_POINT *point, |
bb62a8b0 BM |
410 | const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *ctx) |
411 | { | |
412 | BN_CTX *new_ctx = NULL; | |
413 | int ret = 0; | |
414 | ||
415 | if (ctx == NULL) | |
416 | { | |
417 | ctx = new_ctx = BN_CTX_new(); | |
418 | if (ctx == NULL) | |
419 | return 0; | |
420 | } | |
1d5bd6cf | 421 | |
bb62a8b0 BM |
422 | if (x != NULL) |
423 | { | |
5784a521 | 424 | if (!BN_nnmod(point->X, x, group->field, ctx)) goto err; |
bb62a8b0 BM |
425 | if (group->meth->field_encode) |
426 | { | |
5784a521 | 427 | if (!group->meth->field_encode(group, point->X, point->X, ctx)) goto err; |
bb62a8b0 BM |
428 | } |
429 | } | |
430 | ||
431 | if (y != NULL) | |
432 | { | |
5784a521 | 433 | if (!BN_nnmod(point->Y, y, group->field, ctx)) goto err; |
bb62a8b0 BM |
434 | if (group->meth->field_encode) |
435 | { | |
5784a521 | 436 | if (!group->meth->field_encode(group, point->Y, point->Y, ctx)) goto err; |
bb62a8b0 BM |
437 | } |
438 | } | |
439 | ||
440 | if (z != NULL) | |
441 | { | |
442 | int Z_is_one; | |
1d5bd6cf | 443 | |
5784a521 MC |
444 | if (!BN_nnmod(point->Z, z, group->field, ctx)) goto err; |
445 | Z_is_one = BN_is_one(point->Z); | |
bb62a8b0 BM |
446 | if (group->meth->field_encode) |
447 | { | |
48fe4d62 BM |
448 | if (Z_is_one && (group->meth->field_set_to_one != 0)) |
449 | { | |
5784a521 | 450 | if (!group->meth->field_set_to_one(group, point->Z, ctx)) goto err; |
48fe4d62 BM |
451 | } |
452 | else | |
453 | { | |
5784a521 | 454 | if (!group->meth->field_encode(group, point->Z, point->Z, ctx)) goto err; |
48fe4d62 | 455 | } |
bb62a8b0 BM |
456 | } |
457 | point->Z_is_one = Z_is_one; | |
458 | } | |
dd616752 DSH |
459 | |
460 | ret = 1; | |
bb62a8b0 BM |
461 | |
462 | err: | |
463 | if (new_ctx != NULL) | |
464 | BN_CTX_free(new_ctx); | |
465 | return ret; | |
466 | } | |
1d5bd6cf BM |
467 | |
468 | ||
bb62a8b0 BM |
469 | int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *group, const EC_POINT *point, |
470 | BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *ctx) | |
226cc7de BM |
471 | { |
472 | BN_CTX *new_ctx = NULL; | |
473 | int ret = 0; | |
bb62a8b0 BM |
474 | |
475 | if (group->meth->field_decode != 0) | |
226cc7de BM |
476 | { |
477 | if (ctx == NULL) | |
478 | { | |
479 | ctx = new_ctx = BN_CTX_new(); | |
480 | if (ctx == NULL) | |
481 | return 0; | |
482 | } | |
226cc7de | 483 | |
bb62a8b0 BM |
484 | if (x != NULL) |
485 | { | |
5784a521 | 486 | if (!group->meth->field_decode(group, x, point->X, ctx)) goto err; |
bb62a8b0 BM |
487 | } |
488 | if (y != NULL) | |
489 | { | |
5784a521 | 490 | if (!group->meth->field_decode(group, y, point->Y, ctx)) goto err; |
bb62a8b0 BM |
491 | } |
492 | if (z != NULL) | |
493 | { | |
5784a521 | 494 | if (!group->meth->field_decode(group, z, point->Z, ctx)) goto err; |
bb62a8b0 BM |
495 | } |
496 | } | |
497 | else | |
498 | { | |
499 | if (x != NULL) | |
500 | { | |
5784a521 | 501 | if (!BN_copy(x, point->X)) goto err; |
bb62a8b0 BM |
502 | } |
503 | if (y != NULL) | |
504 | { | |
5784a521 | 505 | if (!BN_copy(y, point->Y)) goto err; |
bb62a8b0 BM |
506 | } |
507 | if (z != NULL) | |
508 | { | |
5784a521 | 509 | if (!BN_copy(z, point->Z)) goto err; |
bb62a8b0 BM |
510 | } |
511 | } | |
226cc7de | 512 | |
bb62a8b0 BM |
513 | ret = 1; |
514 | ||
226cc7de BM |
515 | err: |
516 | if (new_ctx != NULL) | |
517 | BN_CTX_free(new_ctx); | |
518 | return ret; | |
519 | } | |
520 | ||
521 | ||
35b73a1f | 522 | int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *group, EC_POINT *point, |
bb62a8b0 BM |
523 | const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx) |
524 | { | |
525 | if (x == NULL || y == NULL) | |
526 | { | |
527 | /* unlike for projective coordinates, we do not tolerate this */ | |
35b73a1f | 528 | ECerr(EC_F_EC_GFP_SIMPLE_POINT_SET_AFFINE_COORDINATES, ERR_R_PASSED_NULL_PARAMETER); |
bb62a8b0 BM |
529 | return 0; |
530 | } | |
531 | ||
532 | return EC_POINT_set_Jprojective_coordinates_GFp(group, point, x, y, BN_value_one(), ctx); | |
533 | } | |
534 | ||
535 | ||
35b73a1f | 536 | int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point, |
226cc7de BM |
537 | BIGNUM *x, BIGNUM *y, BN_CTX *ctx) |
538 | { | |
539 | BN_CTX *new_ctx = NULL; | |
13744514 BM |
540 | BIGNUM *Z, *Z_1, *Z_2, *Z_3; |
541 | const BIGNUM *Z_; | |
226cc7de BM |
542 | int ret = 0; |
543 | ||
544 | if (EC_POINT_is_at_infinity(group, point)) | |
545 | { | |
35b73a1f | 546 | ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES, EC_R_POINT_AT_INFINITY); |
226cc7de BM |
547 | return 0; |
548 | } | |
549 | ||
550 | if (ctx == NULL) | |
551 | { | |
552 | ctx = new_ctx = BN_CTX_new(); | |
553 | if (ctx == NULL) | |
554 | return 0; | |
555 | } | |
556 | ||
557 | BN_CTX_start(ctx); | |
226cc7de BM |
558 | Z = BN_CTX_get(ctx); |
559 | Z_1 = BN_CTX_get(ctx); | |
560 | Z_2 = BN_CTX_get(ctx); | |
561 | Z_3 = BN_CTX_get(ctx); | |
562 | if (Z_3 == NULL) goto err; | |
563 | ||
564 | /* transform (X, Y, Z) into (x, y) := (X/Z^2, Y/Z^3) */ | |
565 | ||
566 | if (group->meth->field_decode) | |
567 | { | |
5784a521 | 568 | if (!group->meth->field_decode(group, Z, point->Z, ctx)) goto err; |
13744514 | 569 | Z_ = Z; |
226cc7de BM |
570 | } |
571 | else | |
572 | { | |
5784a521 | 573 | Z_ = point->Z; |
226cc7de BM |
574 | } |
575 | ||
576 | if (BN_is_one(Z_)) | |
577 | { | |
13744514 | 578 | if (group->meth->field_decode) |
1d5bd6cf | 579 | { |
13744514 BM |
580 | if (x != NULL) |
581 | { | |
5784a521 | 582 | if (!group->meth->field_decode(group, x, point->X, ctx)) goto err; |
13744514 BM |
583 | } |
584 | if (y != NULL) | |
585 | { | |
5784a521 | 586 | if (!group->meth->field_decode(group, y, point->Y, ctx)) goto err; |
13744514 | 587 | } |
1d5bd6cf | 588 | } |
13744514 | 589 | else |
1d5bd6cf | 590 | { |
13744514 BM |
591 | if (x != NULL) |
592 | { | |
5784a521 | 593 | if (!BN_copy(x, point->X)) goto err; |
13744514 BM |
594 | } |
595 | if (y != NULL) | |
596 | { | |
5784a521 | 597 | if (!BN_copy(y, point->Y)) goto err; |
13744514 | 598 | } |
1d5bd6cf | 599 | } |
226cc7de BM |
600 | } |
601 | else | |
602 | { | |
5784a521 | 603 | if (!BN_mod_inverse(Z_1, Z_, group->field, ctx)) |
226cc7de | 604 | { |
35b73a1f | 605 | ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES, ERR_R_BN_LIB); |
226cc7de BM |
606 | goto err; |
607 | } | |
48fe4d62 BM |
608 | |
609 | if (group->meth->field_encode == 0) | |
610 | { | |
611 | /* field_sqr works on standard representation */ | |
612 | if (!group->meth->field_sqr(group, Z_2, Z_1, ctx)) goto err; | |
613 | } | |
614 | else | |
615 | { | |
5784a521 | 616 | if (!BN_mod_sqr(Z_2, Z_1, group->field, ctx)) goto err; |
48fe4d62 | 617 | } |
226cc7de | 618 | |
1d5bd6cf BM |
619 | if (x != NULL) |
620 | { | |
13744514 | 621 | /* in the Montgomery case, field_mul will cancel out Montgomery factor in X: */ |
5784a521 | 622 | if (!group->meth->field_mul(group, x, point->X, Z_2, ctx)) goto err; |
1d5bd6cf BM |
623 | } |
624 | ||
625 | if (y != NULL) | |
626 | { | |
48fe4d62 BM |
627 | if (group->meth->field_encode == 0) |
628 | { | |
629 | /* field_mul works on standard representation */ | |
630 | if (!group->meth->field_mul(group, Z_3, Z_2, Z_1, ctx)) goto err; | |
48fe4d62 BM |
631 | } |
632 | else | |
633 | { | |
5784a521 | 634 | if (!BN_mod_mul(Z_3, Z_2, Z_1, group->field, ctx)) goto err; |
48fe4d62 | 635 | } |
13744514 BM |
636 | |
637 | /* in the Montgomery case, field_mul will cancel out Montgomery factor in Y: */ | |
5784a521 | 638 | if (!group->meth->field_mul(group, y, point->Y, Z_3, ctx)) goto err; |
1d5bd6cf | 639 | } |
226cc7de BM |
640 | } |
641 | ||
642 | ret = 1; | |
643 | ||
644 | err: | |
645 | BN_CTX_end(ctx); | |
646 | if (new_ctx != NULL) | |
647 | BN_CTX_free(new_ctx); | |
648 | return ret; | |
649 | } | |
650 | ||
60428dbf BM |
651 | int ec_GFp_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx) |
652 | { | |
653 | int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *); | |
654 | int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); | |
655 | const BIGNUM *p; | |
656 | BN_CTX *new_ctx = NULL; | |
657 | BIGNUM *n0, *n1, *n2, *n3, *n4, *n5, *n6; | |
658 | int ret = 0; | |
659 | ||
660 | if (a == b) | |
661 | return EC_POINT_dbl(group, r, a, ctx); | |
662 | if (EC_POINT_is_at_infinity(group, a)) | |
663 | return EC_POINT_copy(r, b); | |
664 | if (EC_POINT_is_at_infinity(group, b)) | |
665 | return EC_POINT_copy(r, a); | |
666 | ||
667 | field_mul = group->meth->field_mul; | |
668 | field_sqr = group->meth->field_sqr; | |
5784a521 | 669 | p = group->field; |
60428dbf BM |
670 | |
671 | if (ctx == NULL) | |
672 | { | |
673 | ctx = new_ctx = BN_CTX_new(); | |
674 | if (ctx == NULL) | |
675 | return 0; | |
676 | } | |
60428dbf | 677 | |
226cc7de | 678 | BN_CTX_start(ctx); |
60428dbf BM |
679 | n0 = BN_CTX_get(ctx); |
680 | n1 = BN_CTX_get(ctx); | |
681 | n2 = BN_CTX_get(ctx); | |
682 | n3 = BN_CTX_get(ctx); | |
683 | n4 = BN_CTX_get(ctx); | |
684 | n5 = BN_CTX_get(ctx); | |
685 | n6 = BN_CTX_get(ctx); | |
686 | if (n6 == NULL) goto end; | |
687 | ||
1d5bd6cf BM |
688 | /* Note that in this function we must not read components of 'a' or 'b' |
689 | * once we have written the corresponding components of 'r'. | |
690 | * ('r' might be one of 'a' or 'b'.) | |
691 | */ | |
692 | ||
60428dbf BM |
693 | /* n1, n2 */ |
694 | if (b->Z_is_one) | |
695 | { | |
5784a521 MC |
696 | if (!BN_copy(n1, a->X)) goto end; |
697 | if (!BN_copy(n2, a->Y)) goto end; | |
60428dbf BM |
698 | /* n1 = X_a */ |
699 | /* n2 = Y_a */ | |
700 | } | |
701 | else | |
702 | { | |
5784a521 MC |
703 | if (!field_sqr(group, n0, b->Z, ctx)) goto end; |
704 | if (!field_mul(group, n1, a->X, n0, ctx)) goto end; | |
60428dbf BM |
705 | /* n1 = X_a * Z_b^2 */ |
706 | ||
5784a521 MC |
707 | if (!field_mul(group, n0, n0, b->Z, ctx)) goto end; |
708 | if (!field_mul(group, n2, a->Y, n0, ctx)) goto end; | |
60428dbf BM |
709 | /* n2 = Y_a * Z_b^3 */ |
710 | } | |
711 | ||
712 | /* n3, n4 */ | |
713 | if (a->Z_is_one) | |
714 | { | |
5784a521 MC |
715 | if (!BN_copy(n3, b->X)) goto end; |
716 | if (!BN_copy(n4, b->Y)) goto end; | |
60428dbf BM |
717 | /* n3 = X_b */ |
718 | /* n4 = Y_b */ | |
719 | } | |
720 | else | |
721 | { | |
5784a521 MC |
722 | if (!field_sqr(group, n0, a->Z, ctx)) goto end; |
723 | if (!field_mul(group, n3, b->X, n0, ctx)) goto end; | |
60428dbf BM |
724 | /* n3 = X_b * Z_a^2 */ |
725 | ||
5784a521 MC |
726 | if (!field_mul(group, n0, n0, a->Z, ctx)) goto end; |
727 | if (!field_mul(group, n4, b->Y, n0, ctx)) goto end; | |
60428dbf BM |
728 | /* n4 = Y_b * Z_a^3 */ |
729 | } | |
730 | ||
731 | /* n5, n6 */ | |
732 | if (!BN_mod_sub_quick(n5, n1, n3, p)) goto end; | |
733 | if (!BN_mod_sub_quick(n6, n2, n4, p)) goto end; | |
734 | /* n5 = n1 - n3 */ | |
735 | /* n6 = n2 - n4 */ | |
736 | ||
737 | if (BN_is_zero(n5)) | |
738 | { | |
739 | if (BN_is_zero(n6)) | |
740 | { | |
741 | /* a is the same point as b */ | |
742 | BN_CTX_end(ctx); | |
60428dbf | 743 | ret = EC_POINT_dbl(group, r, a, ctx); |
e869d4bd | 744 | ctx = NULL; |
60428dbf BM |
745 | goto end; |
746 | } | |
747 | else | |
748 | { | |
749 | /* a is the inverse of b */ | |
5784a521 | 750 | BN_zero(r->Z); |
60428dbf BM |
751 | r->Z_is_one = 0; |
752 | ret = 1; | |
753 | goto end; | |
754 | } | |
755 | } | |
756 | ||
757 | /* 'n7', 'n8' */ | |
758 | if (!BN_mod_add_quick(n1, n1, n3, p)) goto end; | |
759 | if (!BN_mod_add_quick(n2, n2, n4, p)) goto end; | |
760 | /* 'n7' = n1 + n3 */ | |
761 | /* 'n8' = n2 + n4 */ | |
762 | ||
763 | /* Z_r */ | |
764 | if (a->Z_is_one && b->Z_is_one) | |
765 | { | |
5784a521 | 766 | if (!BN_copy(r->Z, n5)) goto end; |
60428dbf BM |
767 | } |
768 | else | |
769 | { | |
770 | if (a->Z_is_one) | |
5784a521 | 771 | { if (!BN_copy(n0, b->Z)) goto end; } |
60428dbf | 772 | else if (b->Z_is_one) |
5784a521 | 773 | { if (!BN_copy(n0, a->Z)) goto end; } |
60428dbf | 774 | else |
5784a521 MC |
775 | { if (!field_mul(group, n0, a->Z, b->Z, ctx)) goto end; } |
776 | if (!field_mul(group, r->Z, n0, n5, ctx)) goto end; | |
60428dbf BM |
777 | } |
778 | r->Z_is_one = 0; | |
779 | /* Z_r = Z_a * Z_b * n5 */ | |
780 | ||
781 | /* X_r */ | |
782 | if (!field_sqr(group, n0, n6, ctx)) goto end; | |
783 | if (!field_sqr(group, n4, n5, ctx)) goto end; | |
784 | if (!field_mul(group, n3, n1, n4, ctx)) goto end; | |
5784a521 | 785 | if (!BN_mod_sub_quick(r->X, n0, n3, p)) goto end; |
60428dbf BM |
786 | /* X_r = n6^2 - n5^2 * 'n7' */ |
787 | ||
788 | /* 'n9' */ | |
5784a521 | 789 | if (!BN_mod_lshift1_quick(n0, r->X, p)) goto end; |
60428dbf BM |
790 | if (!BN_mod_sub_quick(n0, n3, n0, p)) goto end; |
791 | /* n9 = n5^2 * 'n7' - 2 * X_r */ | |
792 | ||
793 | /* Y_r */ | |
794 | if (!field_mul(group, n0, n0, n6, ctx)) goto end; | |
795 | if (!field_mul(group, n5, n4, n5, ctx)) goto end; /* now n5 is n5^3 */ | |
796 | if (!field_mul(group, n1, n2, n5, ctx)) goto end; | |
797 | if (!BN_mod_sub_quick(n0, n0, n1, p)) goto end; | |
798 | if (BN_is_odd(n0)) | |
799 | if (!BN_add(n0, n0, p)) goto end; | |
800 | /* now 0 <= n0 < 2*p, and n0 is even */ | |
5784a521 | 801 | if (!BN_rshift1(r->Y, n0)) goto end; |
60428dbf BM |
802 | /* Y_r = (n6 * 'n9' - 'n8' * 'n5^3') / 2 */ |
803 | ||
804 | ret = 1; | |
805 | ||
806 | end: | |
807 | if (ctx) /* otherwise we already called BN_CTX_end */ | |
808 | BN_CTX_end(ctx); | |
809 | if (new_ctx != NULL) | |
810 | BN_CTX_free(new_ctx); | |
811 | return ret; | |
812 | } | |
813 | ||
814 | ||
815 | int ec_GFp_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_CTX *ctx) | |
816 | { | |
817 | int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *); | |
818 | int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); | |
819 | const BIGNUM *p; | |
820 | BN_CTX *new_ctx = NULL; | |
821 | BIGNUM *n0, *n1, *n2, *n3; | |
822 | int ret = 0; | |
823 | ||
824 | if (EC_POINT_is_at_infinity(group, a)) | |
825 | { | |
5784a521 | 826 | BN_zero(r->Z); |
60428dbf BM |
827 | r->Z_is_one = 0; |
828 | return 1; | |
829 | } | |
830 | ||
831 | field_mul = group->meth->field_mul; | |
832 | field_sqr = group->meth->field_sqr; | |
5784a521 | 833 | p = group->field; |
60428dbf BM |
834 | |
835 | if (ctx == NULL) | |
836 | { | |
837 | ctx = new_ctx = BN_CTX_new(); | |
838 | if (ctx == NULL) | |
839 | return 0; | |
840 | } | |
60428dbf | 841 | |
226cc7de | 842 | BN_CTX_start(ctx); |
60428dbf BM |
843 | n0 = BN_CTX_get(ctx); |
844 | n1 = BN_CTX_get(ctx); | |
845 | n2 = BN_CTX_get(ctx); | |
846 | n3 = BN_CTX_get(ctx); | |
847 | if (n3 == NULL) goto err; | |
848 | ||
1d5bd6cf BM |
849 | /* Note that in this function we must not read components of 'a' |
850 | * once we have written the corresponding components of 'r'. | |
851 | * ('r' might the same as 'a'.) | |
852 | */ | |
853 | ||
60428dbf BM |
854 | /* n1 */ |
855 | if (a->Z_is_one) | |
856 | { | |
5784a521 | 857 | if (!field_sqr(group, n0, a->X, ctx)) goto err; |
60428dbf BM |
858 | if (!BN_mod_lshift1_quick(n1, n0, p)) goto err; |
859 | if (!BN_mod_add_quick(n0, n0, n1, p)) goto err; | |
5784a521 | 860 | if (!BN_mod_add_quick(n1, n0, group->a, p)) goto err; |
60428dbf BM |
861 | /* n1 = 3 * X_a^2 + a_curve */ |
862 | } | |
863 | else if (group->a_is_minus3) | |
864 | { | |
5784a521 MC |
865 | if (!field_sqr(group, n1, a->Z, ctx)) goto err; |
866 | if (!BN_mod_add_quick(n0, a->X, n1, p)) goto err; | |
867 | if (!BN_mod_sub_quick(n2, a->X, n1, p)) goto err; | |
60428dbf BM |
868 | if (!field_mul(group, n1, n0, n2, ctx)) goto err; |
869 | if (!BN_mod_lshift1_quick(n0, n1, p)) goto err; | |
870 | if (!BN_mod_add_quick(n1, n0, n1, p)) goto err; | |
871 | /* n1 = 3 * (X_a + Z_a^2) * (X_a - Z_a^2) | |
872 | * = 3 * X_a^2 - 3 * Z_a^4 */ | |
873 | } | |
874 | else | |
875 | { | |
5784a521 | 876 | if (!field_sqr(group, n0, a->X, ctx)) goto err; |
60428dbf BM |
877 | if (!BN_mod_lshift1_quick(n1, n0, p)) goto err; |
878 | if (!BN_mod_add_quick(n0, n0, n1, p)) goto err; | |
5784a521 | 879 | if (!field_sqr(group, n1, a->Z, ctx)) goto err; |
60428dbf | 880 | if (!field_sqr(group, n1, n1, ctx)) goto err; |
5784a521 | 881 | if (!field_mul(group, n1, n1, group->a, ctx)) goto err; |
60428dbf BM |
882 | if (!BN_mod_add_quick(n1, n1, n0, p)) goto err; |
883 | /* n1 = 3 * X_a^2 + a_curve * Z_a^4 */ | |
884 | } | |
885 | ||
886 | /* Z_r */ | |
887 | if (a->Z_is_one) | |
888 | { | |
5784a521 | 889 | if (!BN_copy(n0, a->Y)) goto err; |
60428dbf BM |
890 | } |
891 | else | |
892 | { | |
5784a521 | 893 | if (!field_mul(group, n0, a->Y, a->Z, ctx)) goto err; |
60428dbf | 894 | } |
5784a521 | 895 | if (!BN_mod_lshift1_quick(r->Z, n0, p)) goto err; |
60428dbf BM |
896 | r->Z_is_one = 0; |
897 | /* Z_r = 2 * Y_a * Z_a */ | |
898 | ||
899 | /* n2 */ | |
5784a521 MC |
900 | if (!field_sqr(group, n3, a->Y, ctx)) goto err; |
901 | if (!field_mul(group, n2, a->X, n3, ctx)) goto err; | |
60428dbf BM |
902 | if (!BN_mod_lshift_quick(n2, n2, 2, p)) goto err; |
903 | /* n2 = 4 * X_a * Y_a^2 */ | |
904 | ||
905 | /* X_r */ | |
906 | if (!BN_mod_lshift1_quick(n0, n2, p)) goto err; | |
5784a521 MC |
907 | if (!field_sqr(group, r->X, n1, ctx)) goto err; |
908 | if (!BN_mod_sub_quick(r->X, r->X, n0, p)) goto err; | |
60428dbf BM |
909 | /* X_r = n1^2 - 2 * n2 */ |
910 | ||
911 | /* n3 */ | |
912 | if (!field_sqr(group, n0, n3, ctx)) goto err; | |
913 | if (!BN_mod_lshift_quick(n3, n0, 3, p)) goto err; | |
914 | /* n3 = 8 * Y_a^4 */ | |
915 | ||
916 | /* Y_r */ | |
5784a521 | 917 | if (!BN_mod_sub_quick(n0, n2, r->X, p)) goto err; |
60428dbf | 918 | if (!field_mul(group, n0, n1, n0, ctx)) goto err; |
5784a521 | 919 | if (!BN_mod_sub_quick(r->Y, n0, n3, p)) goto err; |
60428dbf BM |
920 | /* Y_r = n1 * (n2 - X_r) - n3 */ |
921 | ||
922 | ret = 1; | |
923 | ||
924 | err: | |
925 | BN_CTX_end(ctx); | |
926 | if (new_ctx != NULL) | |
927 | BN_CTX_free(new_ctx); | |
928 | return ret; | |
929 | } | |
930 | ||
931 | ||
bb62a8b0 BM |
932 | int ec_GFp_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx) |
933 | { | |
5784a521 | 934 | if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(point->Y)) |
bb62a8b0 BM |
935 | /* point is its own inverse */ |
936 | return 1; | |
937 | ||
5784a521 | 938 | return BN_usub(point->Y, group->field, point->Y); |
bb62a8b0 | 939 | } |
1d5bd6cf BM |
940 | |
941 | ||
60428dbf BM |
942 | int ec_GFp_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point) |
943 | { | |
5784a521 | 944 | return BN_is_zero(point->Z); |
60428dbf BM |
945 | } |
946 | ||
947 | ||
e869d4bd BM |
948 | int ec_GFp_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx) |
949 | { | |
950 | int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *); | |
951 | int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); | |
952 | const BIGNUM *p; | |
953 | BN_CTX *new_ctx = NULL; | |
7f5b4dd1 | 954 | BIGNUM *rh, *tmp, *Z4, *Z6; |
e869d4bd | 955 | int ret = -1; |
60428dbf | 956 | |
e869d4bd BM |
957 | if (EC_POINT_is_at_infinity(group, point)) |
958 | return 1; | |
959 | ||
960 | field_mul = group->meth->field_mul; | |
961 | field_sqr = group->meth->field_sqr; | |
5784a521 | 962 | p = group->field; |
60428dbf | 963 | |
e869d4bd BM |
964 | if (ctx == NULL) |
965 | { | |
966 | ctx = new_ctx = BN_CTX_new(); | |
967 | if (ctx == NULL) | |
226cc7de | 968 | return -1; |
e869d4bd | 969 | } |
e869d4bd | 970 | |
226cc7de | 971 | BN_CTX_start(ctx); |
e869d4bd | 972 | rh = BN_CTX_get(ctx); |
7f5b4dd1 | 973 | tmp = BN_CTX_get(ctx); |
e869d4bd BM |
974 | Z4 = BN_CTX_get(ctx); |
975 | Z6 = BN_CTX_get(ctx); | |
976 | if (Z6 == NULL) goto err; | |
977 | ||
978 | /* We have a curve defined by a Weierstrass equation | |
979 | * y^2 = x^3 + a*x + b. | |
980 | * The point to consider is given in Jacobian projective coordinates | |
981 | * where (X, Y, Z) represents (x, y) = (X/Z^2, Y/Z^3). | |
982 | * Substituting this and multiplying by Z^6 transforms the above equation into | |
983 | * Y^2 = X^3 + a*X*Z^4 + b*Z^6. | |
984 | * To test this, we add up the right-hand side in 'rh'. | |
985 | */ | |
986 | ||
7f5b4dd1 | 987 | /* rh := X^2 */ |
5784a521 | 988 | if (!field_sqr(group, rh, point->X, ctx)) goto err; |
e869d4bd BM |
989 | |
990 | if (!point->Z_is_one) | |
991 | { | |
5784a521 | 992 | if (!field_sqr(group, tmp, point->Z, ctx)) goto err; |
7f5b4dd1 GT |
993 | if (!field_sqr(group, Z4, tmp, ctx)) goto err; |
994 | if (!field_mul(group, Z6, Z4, tmp, ctx)) goto err; | |
e869d4bd | 995 | |
7f5b4dd1 | 996 | /* rh := (rh + a*Z^4)*X */ |
bb62a8b0 | 997 | if (group->a_is_minus3) |
e869d4bd | 998 | { |
7f5b4dd1 GT |
999 | if (!BN_mod_lshift1_quick(tmp, Z4, p)) goto err; |
1000 | if (!BN_mod_add_quick(tmp, tmp, Z4, p)) goto err; | |
1001 | if (!BN_mod_sub_quick(rh, rh, tmp, p)) goto err; | |
5784a521 | 1002 | if (!field_mul(group, rh, rh, point->X, ctx)) goto err; |
e869d4bd BM |
1003 | } |
1004 | else | |
1005 | { | |
5784a521 | 1006 | if (!field_mul(group, tmp, Z4, group->a, ctx)) goto err; |
7f5b4dd1 | 1007 | if (!BN_mod_add_quick(rh, rh, tmp, p)) goto err; |
5784a521 | 1008 | if (!field_mul(group, rh, rh, point->X, ctx)) goto err; |
e869d4bd BM |
1009 | } |
1010 | ||
1011 | /* rh := rh + b*Z^6 */ | |
5784a521 | 1012 | if (!field_mul(group, tmp, group->b, Z6, ctx)) goto err; |
7f5b4dd1 | 1013 | if (!BN_mod_add_quick(rh, rh, tmp, p)) goto err; |
e869d4bd BM |
1014 | } |
1015 | else | |
1016 | { | |
1017 | /* point->Z_is_one */ | |
1018 | ||
7f5b4dd1 | 1019 | /* rh := (rh + a)*X */ |
5784a521 MC |
1020 | if (!BN_mod_add_quick(rh, rh, group->a, p)) goto err; |
1021 | if (!field_mul(group, rh, rh, point->X, ctx)) goto err; | |
e869d4bd | 1022 | /* rh := rh + b */ |
5784a521 | 1023 | if (!BN_mod_add_quick(rh, rh, group->b, p)) goto err; |
e869d4bd BM |
1024 | } |
1025 | ||
1026 | /* 'lh' := Y^2 */ | |
5784a521 | 1027 | if (!field_sqr(group, tmp, point->Y, ctx)) goto err; |
e869d4bd | 1028 | |
7f5b4dd1 | 1029 | ret = (0 == BN_ucmp(tmp, rh)); |
e869d4bd BM |
1030 | |
1031 | err: | |
1032 | BN_CTX_end(ctx); | |
1033 | if (new_ctx != NULL) | |
1034 | BN_CTX_free(new_ctx); | |
1035 | return ret; | |
1036 | } | |
1037 | ||
1038 | ||
bb62a8b0 BM |
1039 | int ec_GFp_simple_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx) |
1040 | { | |
1041 | /* return values: | |
1042 | * -1 error | |
1043 | * 0 equal (in affine coordinates) | |
1044 | * 1 not equal | |
1045 | */ | |
1046 | ||
1047 | int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *); | |
1048 | int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); | |
1049 | BN_CTX *new_ctx = NULL; | |
1050 | BIGNUM *tmp1, *tmp2, *Za23, *Zb23; | |
1051 | const BIGNUM *tmp1_, *tmp2_; | |
1052 | int ret = -1; | |
1053 | ||
1054 | if (EC_POINT_is_at_infinity(group, a)) | |
1055 | { | |
1056 | return EC_POINT_is_at_infinity(group, b) ? 0 : 1; | |
1057 | } | |
0aa1aedb DSH |
1058 | |
1059 | if (EC_POINT_is_at_infinity(group, b)) | |
1060 | return 1; | |
bb62a8b0 BM |
1061 | |
1062 | if (a->Z_is_one && b->Z_is_one) | |
1063 | { | |
5784a521 | 1064 | return ((BN_cmp(a->X, b->X) == 0) && BN_cmp(a->Y, b->Y) == 0) ? 0 : 1; |
bb62a8b0 BM |
1065 | } |
1066 | ||
1067 | field_mul = group->meth->field_mul; | |
1068 | field_sqr = group->meth->field_sqr; | |
1069 | ||
1070 | if (ctx == NULL) | |
1071 | { | |
1072 | ctx = new_ctx = BN_CTX_new(); | |
1073 | if (ctx == NULL) | |
1074 | return -1; | |
1075 | } | |
1076 | ||
1077 | BN_CTX_start(ctx); | |
1078 | tmp1 = BN_CTX_get(ctx); | |
1079 | tmp2 = BN_CTX_get(ctx); | |
1080 | Za23 = BN_CTX_get(ctx); | |
1081 | Zb23 = BN_CTX_get(ctx); | |
1082 | if (Zb23 == NULL) goto end; | |
1083 | ||
1084 | /* We have to decide whether | |
1085 | * (X_a/Z_a^2, Y_a/Z_a^3) = (X_b/Z_b^2, Y_b/Z_b^3), | |
1086 | * or equivalently, whether | |
1087 | * (X_a*Z_b^2, Y_a*Z_b^3) = (X_b*Z_a^2, Y_b*Z_a^3). | |
1088 | */ | |
1089 | ||
1090 | if (!b->Z_is_one) | |
1091 | { | |
5784a521 MC |
1092 | if (!field_sqr(group, Zb23, b->Z, ctx)) goto end; |
1093 | if (!field_mul(group, tmp1, a->X, Zb23, ctx)) goto end; | |
bb62a8b0 BM |
1094 | tmp1_ = tmp1; |
1095 | } | |
1096 | else | |
5784a521 | 1097 | tmp1_ = a->X; |
bb62a8b0 BM |
1098 | if (!a->Z_is_one) |
1099 | { | |
5784a521 MC |
1100 | if (!field_sqr(group, Za23, a->Z, ctx)) goto end; |
1101 | if (!field_mul(group, tmp2, b->X, Za23, ctx)) goto end; | |
bb62a8b0 BM |
1102 | tmp2_ = tmp2; |
1103 | } | |
1104 | else | |
5784a521 | 1105 | tmp2_ = b->X; |
bb62a8b0 BM |
1106 | |
1107 | /* compare X_a*Z_b^2 with X_b*Z_a^2 */ | |
1108 | if (BN_cmp(tmp1_, tmp2_) != 0) | |
1109 | { | |
1110 | ret = 1; /* points differ */ | |
1111 | goto end; | |
1112 | } | |
1113 | ||
1114 | ||
1115 | if (!b->Z_is_one) | |
1116 | { | |
5784a521 MC |
1117 | if (!field_mul(group, Zb23, Zb23, b->Z, ctx)) goto end; |
1118 | if (!field_mul(group, tmp1, a->Y, Zb23, ctx)) goto end; | |
42909e39 | 1119 | /* tmp1_ = tmp1 */ |
bb62a8b0 | 1120 | } |
42909e39 | 1121 | else |
5784a521 | 1122 | tmp1_ = a->Y; |
bb62a8b0 BM |
1123 | if (!a->Z_is_one) |
1124 | { | |
5784a521 MC |
1125 | if (!field_mul(group, Za23, Za23, a->Z, ctx)) goto end; |
1126 | if (!field_mul(group, tmp2, b->Y, Za23, ctx)) goto end; | |
42909e39 | 1127 | /* tmp2_ = tmp2 */ |
bb62a8b0 | 1128 | } |
42909e39 | 1129 | else |
5784a521 | 1130 | tmp2_ = b->Y; |
bb62a8b0 BM |
1131 | |
1132 | /* compare Y_a*Z_b^3 with Y_b*Z_a^3 */ | |
1133 | if (BN_cmp(tmp1_, tmp2_) != 0) | |
1134 | { | |
1135 | ret = 1; /* points differ */ | |
1136 | goto end; | |
1137 | } | |
1138 | ||
1139 | /* points are equal */ | |
1140 | ret = 0; | |
1141 | ||
1142 | end: | |
1143 | BN_CTX_end(ctx); | |
1144 | if (new_ctx != NULL) | |
1145 | BN_CTX_free(new_ctx); | |
1146 | return ret; | |
1147 | } | |
1d5bd6cf | 1148 | |
dd616752 | 1149 | |
e869d4bd BM |
1150 | int ec_GFp_simple_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx) |
1151 | { | |
1152 | BN_CTX *new_ctx = NULL; | |
226cc7de | 1153 | BIGNUM *x, *y; |
e869d4bd BM |
1154 | int ret = 0; |
1155 | ||
1156 | if (point->Z_is_one || EC_POINT_is_at_infinity(group, point)) | |
1157 | return 1; | |
1158 | ||
1159 | if (ctx == NULL) | |
1160 | { | |
1161 | ctx = new_ctx = BN_CTX_new(); | |
1162 | if (ctx == NULL) | |
1163 | return 0; | |
1164 | } | |
e869d4bd | 1165 | |
226cc7de BM |
1166 | BN_CTX_start(ctx); |
1167 | x = BN_CTX_get(ctx); | |
1168 | y = BN_CTX_get(ctx); | |
1169 | if (y == NULL) goto err; | |
e869d4bd | 1170 | |
226cc7de BM |
1171 | if (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx)) goto err; |
1172 | if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) goto err; | |
1173 | if (!point->Z_is_one) | |
e869d4bd | 1174 | { |
226cc7de BM |
1175 | ECerr(EC_F_EC_GFP_SIMPLE_MAKE_AFFINE, ERR_R_INTERNAL_ERROR); |
1176 | goto err; | |
e869d4bd | 1177 | } |
e869d4bd | 1178 | |
e869d4bd BM |
1179 | ret = 1; |
1180 | ||
226cc7de | 1181 | err: |
e869d4bd BM |
1182 | BN_CTX_end(ctx); |
1183 | if (new_ctx != NULL) | |
1184 | BN_CTX_free(new_ctx); | |
1185 | return ret; | |
1186 | } | |
60428dbf BM |
1187 | |
1188 | ||
48fe4d62 BM |
1189 | int ec_GFp_simple_points_make_affine(const EC_GROUP *group, size_t num, EC_POINT *points[], BN_CTX *ctx) |
1190 | { | |
1191 | BN_CTX *new_ctx = NULL; | |
0fe73d6c BM |
1192 | BIGNUM *tmp, *tmp_Z; |
1193 | BIGNUM **prod_Z = NULL; | |
48fe4d62 BM |
1194 | size_t i; |
1195 | int ret = 0; | |
1196 | ||
1197 | if (num == 0) | |
1198 | return 1; | |
1199 | ||
1200 | if (ctx == NULL) | |
1201 | { | |
1202 | ctx = new_ctx = BN_CTX_new(); | |
1203 | if (ctx == NULL) | |
1204 | return 0; | |
1205 | } | |
1206 | ||
1207 | BN_CTX_start(ctx); | |
0fe73d6c BM |
1208 | tmp = BN_CTX_get(ctx); |
1209 | tmp_Z = BN_CTX_get(ctx); | |
1210 | if (tmp == NULL || tmp_Z == NULL) goto err; | |
48fe4d62 | 1211 | |
0fe73d6c BM |
1212 | prod_Z = OPENSSL_malloc(num * sizeof prod_Z[0]); |
1213 | if (prod_Z == NULL) goto err; | |
1214 | for (i = 0; i < num; i++) | |
1215 | { | |
1216 | prod_Z[i] = BN_new(); | |
1217 | if (prod_Z[i] == NULL) goto err; | |
1218 | } | |
48fe4d62 | 1219 | |
0fe73d6c BM |
1220 | /* Set each prod_Z[i] to the product of points[0]->Z .. points[i]->Z, |
1221 | * skipping any zero-valued inputs (pretend that they're 1). */ | |
48fe4d62 | 1222 | |
5784a521 | 1223 | if (!BN_is_zero(points[0]->Z)) |
48fe4d62 | 1224 | { |
5784a521 | 1225 | if (!BN_copy(prod_Z[0], points[0]->Z)) goto err; |
0fe73d6c BM |
1226 | } |
1227 | else | |
1228 | { | |
1229 | if (group->meth->field_set_to_one != 0) | |
48fe4d62 | 1230 | { |
0fe73d6c BM |
1231 | if (!group->meth->field_set_to_one(group, prod_Z[0], ctx)) goto err; |
1232 | } | |
1233 | else | |
1234 | { | |
1235 | if (!BN_one(prod_Z[0])) goto err; | |
48fe4d62 BM |
1236 | } |
1237 | } | |
1238 | ||
0fe73d6c | 1239 | for (i = 1; i < num; i++) |
48fe4d62 | 1240 | { |
5784a521 | 1241 | if (!BN_is_zero(points[i]->Z)) |
48fe4d62 | 1242 | { |
5784a521 | 1243 | if (!group->meth->field_mul(group, prod_Z[i], prod_Z[i - 1], points[i]->Z, ctx)) goto err; |
0fe73d6c BM |
1244 | } |
1245 | else | |
1246 | { | |
1247 | if (!BN_copy(prod_Z[i], prod_Z[i - 1])) goto err; | |
48fe4d62 BM |
1248 | } |
1249 | } | |
0fe73d6c BM |
1250 | |
1251 | /* Now use a single explicit inversion to replace every | |
1252 | * non-zero points[i]->Z by its inverse. */ | |
1253 | ||
5784a521 | 1254 | if (!BN_mod_inverse(tmp, prod_Z[num - 1], group->field, ctx)) |
0fe73d6c BM |
1255 | { |
1256 | ECerr(EC_F_EC_GFP_SIMPLE_POINTS_MAKE_AFFINE, ERR_R_BN_LIB); | |
1257 | goto err; | |
1258 | } | |
48fe4d62 BM |
1259 | if (group->meth->field_encode != 0) |
1260 | { | |
0fe73d6c | 1261 | /* In the Montgomery case, we just turned R*H (representing H) |
48fe4d62 | 1262 | * into 1/(R*H), but we need R*(1/H) (representing 1/H); |
0fe73d6c BM |
1263 | * i.e. we need to multiply by the Montgomery factor twice. */ |
1264 | if (!group->meth->field_encode(group, tmp, tmp, ctx)) goto err; | |
1265 | if (!group->meth->field_encode(group, tmp, tmp, ctx)) goto err; | |
48fe4d62 BM |
1266 | } |
1267 | ||
0fe73d6c | 1268 | for (i = num - 1; i > 0; --i) |
48fe4d62 | 1269 | { |
0fe73d6c BM |
1270 | /* Loop invariant: tmp is the product of the inverses of |
1271 | * points[0]->Z .. points[i]->Z (zero-valued inputs skipped). */ | |
5784a521 | 1272 | if (!BN_is_zero(points[i]->Z)) |
48fe4d62 | 1273 | { |
0fe73d6c BM |
1274 | /* Set tmp_Z to the inverse of points[i]->Z (as product |
1275 | * of Z inverses 0 .. i, Z values 0 .. i - 1). */ | |
1276 | if (!group->meth->field_mul(group, tmp_Z, prod_Z[i - 1], tmp, ctx)) goto err; | |
1277 | /* Update tmp to satisfy the loop invariant for i - 1. */ | |
5784a521 | 1278 | if (!group->meth->field_mul(group, tmp, tmp, points[i]->Z, ctx)) goto err; |
0fe73d6c | 1279 | /* Replace points[i]->Z by its inverse. */ |
5784a521 | 1280 | if (!BN_copy(points[i]->Z, tmp_Z)) goto err; |
48fe4d62 BM |
1281 | } |
1282 | } | |
1283 | ||
5784a521 | 1284 | if (!BN_is_zero(points[0]->Z)) |
0fe73d6c BM |
1285 | { |
1286 | /* Replace points[0]->Z by its inverse. */ | |
5784a521 | 1287 | if (!BN_copy(points[0]->Z, tmp)) goto err; |
0fe73d6c BM |
1288 | } |
1289 | ||
1290 | /* Finally, fix up the X and Y coordinates for all points. */ | |
1291 | ||
48fe4d62 BM |
1292 | for (i = 0; i < num; i++) |
1293 | { | |
1294 | EC_POINT *p = points[i]; | |
0fe73d6c | 1295 | |
5784a521 | 1296 | if (!BN_is_zero(p->Z)) |
48fe4d62 BM |
1297 | { |
1298 | /* turn (X, Y, 1/Z) into (X/Z^2, Y/Z^3, 1) */ | |
1299 | ||
5784a521 MC |
1300 | if (!group->meth->field_sqr(group, tmp, p->Z, ctx)) goto err; |
1301 | if (!group->meth->field_mul(group, p->X, p->X, tmp, ctx)) goto err; | |
0fe73d6c | 1302 | |
5784a521 MC |
1303 | if (!group->meth->field_mul(group, tmp, tmp, p->Z, ctx)) goto err; |
1304 | if (!group->meth->field_mul(group, p->Y, p->Y, tmp, ctx)) goto err; | |
48fe4d62 | 1305 | |
48fe4d62 BM |
1306 | if (group->meth->field_set_to_one != 0) |
1307 | { | |
5784a521 | 1308 | if (!group->meth->field_set_to_one(group, p->Z, ctx)) goto err; |
48fe4d62 BM |
1309 | } |
1310 | else | |
1311 | { | |
5784a521 | 1312 | if (!BN_one(p->Z)) goto err; |
48fe4d62 BM |
1313 | } |
1314 | p->Z_is_one = 1; | |
1315 | } | |
1316 | } | |
1317 | ||
1318 | ret = 1; | |
0fe73d6c | 1319 | |
48fe4d62 BM |
1320 | err: |
1321 | BN_CTX_end(ctx); | |
1322 | if (new_ctx != NULL) | |
1323 | BN_CTX_free(new_ctx); | |
0fe73d6c | 1324 | if (prod_Z != NULL) |
48fe4d62 | 1325 | { |
0fe73d6c | 1326 | for (i = 0; i < num; i++) |
48fe4d62 | 1327 | { |
16602b5c BM |
1328 | if (prod_Z[i] == NULL) break; |
1329 | BN_clear_free(prod_Z[i]); | |
48fe4d62 | 1330 | } |
0fe73d6c | 1331 | OPENSSL_free(prod_Z); |
48fe4d62 BM |
1332 | } |
1333 | return ret; | |
1334 | } | |
1335 | ||
1336 | ||
60428dbf BM |
1337 | int ec_GFp_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) |
1338 | { | |
5784a521 | 1339 | return BN_mod_mul(r, a, b, group->field, ctx); |
60428dbf BM |
1340 | } |
1341 | ||
1342 | ||
1343 | int ec_GFp_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx) | |
1344 | { | |
5784a521 | 1345 | return BN_mod_sqr(r, a, group->field, ctx); |
60428dbf | 1346 | } |