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Commit | Line | Data |
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4f22f405 RS |
1 | /* |
2 | * Copyright 2002-2016 The OpenSSL Project Authors. All Rights Reserved. | |
3 | * | |
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 | |
8 | */ | |
9 | ||
7793f30e BM |
10 | /* ==================================================================== |
11 | * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. | |
12 | * | |
13 | * The Elliptic Curve Public-Key Crypto Library (ECC Code) included | |
14 | * herein is developed by SUN MICROSYSTEMS, INC., and is contributed | |
15 | * to the OpenSSL project. | |
16 | * | |
17 | * The ECC Code is licensed pursuant to the OpenSSL open source | |
18 | * license provided below. | |
19 | * | |
7793f30e BM |
20 | * The software is originally written by Sheueling Chang Shantz and |
21 | * Douglas Stebila of Sun Microsystems Laboratories. | |
22 | * | |
23 | */ | |
7793f30e BM |
24 | |
25 | #include <openssl/err.h> | |
26 | ||
5784a521 | 27 | #include "internal/bn_int.h" |
7793f30e BM |
28 | #include "ec_lcl.h" |
29 | ||
b3310161 DSH |
30 | #ifndef OPENSSL_NO_EC2M |
31 | ||
7793f30e | 32 | const EC_METHOD *EC_GF2m_simple_method(void) |
0f113f3e MC |
33 | { |
34 | static const EC_METHOD ret = { | |
35 | EC_FLAGS_DEFAULT_OCT, | |
36 | NID_X9_62_characteristic_two_field, | |
37 | ec_GF2m_simple_group_init, | |
38 | ec_GF2m_simple_group_finish, | |
39 | ec_GF2m_simple_group_clear_finish, | |
40 | ec_GF2m_simple_group_copy, | |
41 | ec_GF2m_simple_group_set_curve, | |
42 | ec_GF2m_simple_group_get_curve, | |
43 | ec_GF2m_simple_group_get_degree, | |
9ff9bccc | 44 | ec_group_simple_order_bits, |
0f113f3e MC |
45 | ec_GF2m_simple_group_check_discriminant, |
46 | ec_GF2m_simple_point_init, | |
47 | ec_GF2m_simple_point_finish, | |
48 | ec_GF2m_simple_point_clear_finish, | |
49 | ec_GF2m_simple_point_copy, | |
50 | ec_GF2m_simple_point_set_to_infinity, | |
51 | 0 /* set_Jprojective_coordinates_GFp */ , | |
52 | 0 /* get_Jprojective_coordinates_GFp */ , | |
53 | ec_GF2m_simple_point_set_affine_coordinates, | |
54 | ec_GF2m_simple_point_get_affine_coordinates, | |
55 | 0, 0, 0, | |
56 | ec_GF2m_simple_add, | |
57 | ec_GF2m_simple_dbl, | |
58 | ec_GF2m_simple_invert, | |
59 | ec_GF2m_simple_is_at_infinity, | |
60 | ec_GF2m_simple_is_on_curve, | |
61 | ec_GF2m_simple_cmp, | |
62 | ec_GF2m_simple_make_affine, | |
63 | ec_GF2m_simple_points_make_affine, | |
64 | ||
65 | /* | |
66 | * the following three method functions are defined in ec2_mult.c | |
67 | */ | |
68 | ec_GF2m_simple_mul, | |
69 | ec_GF2m_precompute_mult, | |
70 | ec_GF2m_have_precompute_mult, | |
71 | ||
72 | ec_GF2m_simple_field_mul, | |
73 | ec_GF2m_simple_field_sqr, | |
74 | ec_GF2m_simple_field_div, | |
75 | 0 /* field_encode */ , | |
76 | 0 /* field_decode */ , | |
9ff9bccc DSH |
77 | 0, /* field_set_to_one */ |
78 | ec_key_simple_priv2oct, | |
79 | ec_key_simple_oct2priv, | |
80 | 0, /* set private */ | |
81 | ec_key_simple_generate_key, | |
82 | ec_key_simple_check_key, | |
83 | ec_key_simple_generate_public_key, | |
84 | 0, /* keycopy */ | |
85 | 0, /* keyfinish */ | |
86 | ecdh_simple_compute_key | |
0f113f3e MC |
87 | }; |
88 | ||
89 | return &ret; | |
90 | } | |
91 | ||
92 | /* | |
93 | * Initialize a GF(2^m)-based EC_GROUP structure. Note that all other members | |
94 | * are handled by EC_GROUP_new. | |
7793f30e BM |
95 | */ |
96 | int ec_GF2m_simple_group_init(EC_GROUP *group) | |
0f113f3e MC |
97 | { |
98 | group->field = BN_new(); | |
99 | group->a = BN_new(); | |
100 | group->b = BN_new(); | |
101 | ||
90945fa3 | 102 | if (group->field == NULL || group->a == NULL || group->b == NULL) { |
23a1d5e9 RS |
103 | BN_free(group->field); |
104 | BN_free(group->a); | |
105 | BN_free(group->b); | |
0f113f3e MC |
106 | return 0; |
107 | } | |
108 | return 1; | |
109 | } | |
110 | ||
111 | /* | |
112 | * Free a GF(2^m)-based EC_GROUP structure. Note that all other members are | |
113 | * handled by EC_GROUP_free. | |
7793f30e BM |
114 | */ |
115 | void ec_GF2m_simple_group_finish(EC_GROUP *group) | |
0f113f3e MC |
116 | { |
117 | BN_free(group->field); | |
118 | BN_free(group->a); | |
119 | BN_free(group->b); | |
120 | } | |
121 | ||
122 | /* | |
123 | * Clear and free a GF(2^m)-based EC_GROUP structure. Note that all other | |
124 | * members are handled by EC_GROUP_clear_free. | |
7793f30e BM |
125 | */ |
126 | void ec_GF2m_simple_group_clear_finish(EC_GROUP *group) | |
0f113f3e MC |
127 | { |
128 | BN_clear_free(group->field); | |
129 | BN_clear_free(group->a); | |
130 | BN_clear_free(group->b); | |
131 | group->poly[0] = 0; | |
132 | group->poly[1] = 0; | |
133 | group->poly[2] = 0; | |
134 | group->poly[3] = 0; | |
135 | group->poly[4] = 0; | |
136 | group->poly[5] = -1; | |
137 | } | |
138 | ||
139 | /* | |
140 | * Copy a GF(2^m)-based EC_GROUP structure. Note that all other members are | |
141 | * handled by EC_GROUP_copy. | |
7793f30e BM |
142 | */ |
143 | int ec_GF2m_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src) | |
0f113f3e MC |
144 | { |
145 | if (!BN_copy(dest->field, src->field)) | |
146 | return 0; | |
147 | if (!BN_copy(dest->a, src->a)) | |
148 | return 0; | |
149 | if (!BN_copy(dest->b, src->b)) | |
150 | return 0; | |
151 | dest->poly[0] = src->poly[0]; | |
152 | dest->poly[1] = src->poly[1]; | |
153 | dest->poly[2] = src->poly[2]; | |
154 | dest->poly[3] = src->poly[3]; | |
155 | dest->poly[4] = src->poly[4]; | |
156 | dest->poly[5] = src->poly[5]; | |
157 | if (bn_wexpand(dest->a, (int)(dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) == | |
158 | NULL) | |
159 | return 0; | |
160 | if (bn_wexpand(dest->b, (int)(dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) == | |
161 | NULL) | |
162 | return 0; | |
163 | bn_set_all_zero(dest->a); | |
164 | bn_set_all_zero(dest->b); | |
165 | return 1; | |
166 | } | |
7793f30e BM |
167 | |
168 | /* Set the curve parameters of an EC_GROUP structure. */ | |
35b73a1f | 169 | int ec_GF2m_simple_group_set_curve(EC_GROUP *group, |
0f113f3e MC |
170 | const BIGNUM *p, const BIGNUM *a, |
171 | const BIGNUM *b, BN_CTX *ctx) | |
172 | { | |
173 | int ret = 0, i; | |
174 | ||
175 | /* group->field */ | |
176 | if (!BN_copy(group->field, p)) | |
177 | goto err; | |
178 | i = BN_GF2m_poly2arr(group->field, group->poly, 6) - 1; | |
179 | if ((i != 5) && (i != 3)) { | |
180 | ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_SET_CURVE, EC_R_UNSUPPORTED_FIELD); | |
181 | goto err; | |
182 | } | |
183 | ||
184 | /* group->a */ | |
185 | if (!BN_GF2m_mod_arr(group->a, a, group->poly)) | |
186 | goto err; | |
187 | if (bn_wexpand(group->a, (int)(group->poly[0] + BN_BITS2 - 1) / BN_BITS2) | |
188 | == NULL) | |
189 | goto err; | |
190 | bn_set_all_zero(group->a); | |
191 | ||
192 | /* group->b */ | |
193 | if (!BN_GF2m_mod_arr(group->b, b, group->poly)) | |
194 | goto err; | |
195 | if (bn_wexpand(group->b, (int)(group->poly[0] + BN_BITS2 - 1) / BN_BITS2) | |
196 | == NULL) | |
197 | goto err; | |
198 | bn_set_all_zero(group->b); | |
199 | ||
200 | ret = 1; | |
201 | err: | |
202 | return ret; | |
203 | } | |
204 | ||
205 | /* | |
206 | * Get the curve parameters of an EC_GROUP structure. If p, a, or b are NULL | |
207 | * then there values will not be set but the method will return with success. | |
7793f30e | 208 | */ |
0f113f3e MC |
209 | int ec_GF2m_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, |
210 | BIGNUM *a, BIGNUM *b, BN_CTX *ctx) | |
211 | { | |
212 | int ret = 0; | |
213 | ||
214 | if (p != NULL) { | |
215 | if (!BN_copy(p, group->field)) | |
216 | return 0; | |
217 | } | |
218 | ||
219 | if (a != NULL) { | |
220 | if (!BN_copy(a, group->a)) | |
221 | goto err; | |
222 | } | |
7793f30e | 223 | |
0f113f3e MC |
224 | if (b != NULL) { |
225 | if (!BN_copy(b, group->b)) | |
226 | goto err; | |
227 | } | |
7793f30e | 228 | |
0f113f3e MC |
229 | ret = 1; |
230 | ||
231 | err: | |
232 | return ret; | |
233 | } | |
234 | ||
235 | /* | |
236 | * Gets the degree of the field. For a curve over GF(2^m) this is the value | |
237 | * m. | |
238 | */ | |
239 | int ec_GF2m_simple_group_get_degree(const EC_GROUP *group) | |
240 | { | |
241 | return BN_num_bits(group->field) - 1; | |
242 | } | |
243 | ||
244 | /* | |
245 | * Checks the discriminant of the curve. y^2 + x*y = x^3 + a*x^2 + b is an | |
246 | * elliptic curve <=> b != 0 (mod p) | |
7793f30e | 247 | */ |
0f113f3e MC |
248 | int ec_GF2m_simple_group_check_discriminant(const EC_GROUP *group, |
249 | BN_CTX *ctx) | |
250 | { | |
251 | int ret = 0; | |
252 | BIGNUM *b; | |
253 | BN_CTX *new_ctx = NULL; | |
254 | ||
255 | if (ctx == NULL) { | |
256 | ctx = new_ctx = BN_CTX_new(); | |
257 | if (ctx == NULL) { | |
258 | ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_CHECK_DISCRIMINANT, | |
259 | ERR_R_MALLOC_FAILURE); | |
260 | goto err; | |
261 | } | |
262 | } | |
263 | BN_CTX_start(ctx); | |
264 | b = BN_CTX_get(ctx); | |
265 | if (b == NULL) | |
266 | goto err; | |
267 | ||
268 | if (!BN_GF2m_mod_arr(b, group->b, group->poly)) | |
269 | goto err; | |
270 | ||
271 | /* | |
272 | * check the discriminant: y^2 + x*y = x^3 + a*x^2 + b is an elliptic | |
273 | * curve <=> b != 0 (mod p) | |
274 | */ | |
275 | if (BN_is_zero(b)) | |
276 | goto err; | |
277 | ||
278 | ret = 1; | |
7793f30e | 279 | |
0f113f3e MC |
280 | err: |
281 | if (ctx != NULL) | |
282 | BN_CTX_end(ctx); | |
23a1d5e9 | 283 | BN_CTX_free(new_ctx); |
0f113f3e MC |
284 | return ret; |
285 | } | |
7793f30e BM |
286 | |
287 | /* Initializes an EC_POINT. */ | |
288 | int ec_GF2m_simple_point_init(EC_POINT *point) | |
0f113f3e MC |
289 | { |
290 | point->X = BN_new(); | |
291 | point->Y = BN_new(); | |
292 | point->Z = BN_new(); | |
293 | ||
90945fa3 | 294 | if (point->X == NULL || point->Y == NULL || point->Z == NULL) { |
23a1d5e9 RS |
295 | BN_free(point->X); |
296 | BN_free(point->Y); | |
297 | BN_free(point->Z); | |
0f113f3e MC |
298 | return 0; |
299 | } | |
300 | return 1; | |
301 | } | |
7793f30e BM |
302 | |
303 | /* Frees an EC_POINT. */ | |
304 | void ec_GF2m_simple_point_finish(EC_POINT *point) | |
0f113f3e MC |
305 | { |
306 | BN_free(point->X); | |
307 | BN_free(point->Y); | |
308 | BN_free(point->Z); | |
309 | } | |
7793f30e BM |
310 | |
311 | /* Clears and frees an EC_POINT. */ | |
312 | void ec_GF2m_simple_point_clear_finish(EC_POINT *point) | |
0f113f3e MC |
313 | { |
314 | BN_clear_free(point->X); | |
315 | BN_clear_free(point->Y); | |
316 | BN_clear_free(point->Z); | |
317 | point->Z_is_one = 0; | |
318 | } | |
319 | ||
320 | /* | |
321 | * Copy the contents of one EC_POINT into another. Assumes dest is | |
322 | * initialized. | |
7793f30e | 323 | */ |
0f113f3e MC |
324 | int ec_GF2m_simple_point_copy(EC_POINT *dest, const EC_POINT *src) |
325 | { | |
326 | if (!BN_copy(dest->X, src->X)) | |
327 | return 0; | |
328 | if (!BN_copy(dest->Y, src->Y)) | |
329 | return 0; | |
330 | if (!BN_copy(dest->Z, src->Z)) | |
331 | return 0; | |
332 | dest->Z_is_one = src->Z_is_one; | |
333 | ||
334 | return 1; | |
335 | } | |
336 | ||
337 | /* | |
338 | * Set an EC_POINT to the point at infinity. A point at infinity is | |
339 | * represented by having Z=0. | |
7793f30e | 340 | */ |
0f113f3e MC |
341 | int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *group, |
342 | EC_POINT *point) | |
343 | { | |
344 | point->Z_is_one = 0; | |
345 | BN_zero(point->Z); | |
346 | return 1; | |
347 | } | |
348 | ||
349 | /* | |
350 | * Set the coordinates of an EC_POINT using affine coordinates. Note that | |
351 | * the simple implementation only uses affine coordinates. | |
7793f30e | 352 | */ |
0f113f3e MC |
353 | int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *group, |
354 | EC_POINT *point, | |
355 | const BIGNUM *x, | |
356 | const BIGNUM *y, BN_CTX *ctx) | |
357 | { | |
358 | int ret = 0; | |
359 | if (x == NULL || y == NULL) { | |
360 | ECerr(EC_F_EC_GF2M_SIMPLE_POINT_SET_AFFINE_COORDINATES, | |
361 | ERR_R_PASSED_NULL_PARAMETER); | |
362 | return 0; | |
363 | } | |
364 | ||
365 | if (!BN_copy(point->X, x)) | |
366 | goto err; | |
367 | BN_set_negative(point->X, 0); | |
368 | if (!BN_copy(point->Y, y)) | |
369 | goto err; | |
370 | BN_set_negative(point->Y, 0); | |
371 | if (!BN_copy(point->Z, BN_value_one())) | |
372 | goto err; | |
373 | BN_set_negative(point->Z, 0); | |
374 | point->Z_is_one = 1; | |
375 | ret = 1; | |
376 | ||
7793f30e | 377 | err: |
0f113f3e MC |
378 | return ret; |
379 | } | |
7793f30e | 380 | |
0f113f3e MC |
381 | /* |
382 | * Gets the affine coordinates of an EC_POINT. Note that the simple | |
383 | * implementation only uses affine coordinates. | |
7793f30e | 384 | */ |
0f113f3e MC |
385 | int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *group, |
386 | const EC_POINT *point, | |
387 | BIGNUM *x, BIGNUM *y, | |
388 | BN_CTX *ctx) | |
389 | { | |
390 | int ret = 0; | |
391 | ||
392 | if (EC_POINT_is_at_infinity(group, point)) { | |
393 | ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES, | |
394 | EC_R_POINT_AT_INFINITY); | |
395 | return 0; | |
396 | } | |
397 | ||
398 | if (BN_cmp(point->Z, BN_value_one())) { | |
399 | ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES, | |
400 | ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); | |
401 | return 0; | |
402 | } | |
403 | if (x != NULL) { | |
404 | if (!BN_copy(x, point->X)) | |
405 | goto err; | |
406 | BN_set_negative(x, 0); | |
407 | } | |
408 | if (y != NULL) { | |
409 | if (!BN_copy(y, point->Y)) | |
410 | goto err; | |
411 | BN_set_negative(y, 0); | |
412 | } | |
413 | ret = 1; | |
7793f30e BM |
414 | |
415 | err: | |
0f113f3e MC |
416 | return ret; |
417 | } | |
7793f30e | 418 | |
0f113f3e MC |
419 | /* |
420 | * Computes a + b and stores the result in r. r could be a or b, a could be | |
421 | * b. Uses algorithm A.10.2 of IEEE P1363. | |
7793f30e | 422 | */ |
0f113f3e MC |
423 | int ec_GF2m_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, |
424 | const EC_POINT *b, BN_CTX *ctx) | |
425 | { | |
426 | BN_CTX *new_ctx = NULL; | |
427 | BIGNUM *x0, *y0, *x1, *y1, *x2, *y2, *s, *t; | |
428 | int ret = 0; | |
429 | ||
430 | if (EC_POINT_is_at_infinity(group, a)) { | |
431 | if (!EC_POINT_copy(r, b)) | |
432 | return 0; | |
433 | return 1; | |
434 | } | |
435 | ||
436 | if (EC_POINT_is_at_infinity(group, b)) { | |
437 | if (!EC_POINT_copy(r, a)) | |
438 | return 0; | |
439 | return 1; | |
440 | } | |
441 | ||
442 | if (ctx == NULL) { | |
443 | ctx = new_ctx = BN_CTX_new(); | |
444 | if (ctx == NULL) | |
445 | return 0; | |
446 | } | |
447 | ||
448 | BN_CTX_start(ctx); | |
449 | x0 = BN_CTX_get(ctx); | |
450 | y0 = BN_CTX_get(ctx); | |
451 | x1 = BN_CTX_get(ctx); | |
452 | y1 = BN_CTX_get(ctx); | |
453 | x2 = BN_CTX_get(ctx); | |
454 | y2 = BN_CTX_get(ctx); | |
455 | s = BN_CTX_get(ctx); | |
456 | t = BN_CTX_get(ctx); | |
457 | if (t == NULL) | |
458 | goto err; | |
459 | ||
460 | if (a->Z_is_one) { | |
461 | if (!BN_copy(x0, a->X)) | |
462 | goto err; | |
463 | if (!BN_copy(y0, a->Y)) | |
464 | goto err; | |
465 | } else { | |
466 | if (!EC_POINT_get_affine_coordinates_GF2m(group, a, x0, y0, ctx)) | |
467 | goto err; | |
468 | } | |
469 | if (b->Z_is_one) { | |
470 | if (!BN_copy(x1, b->X)) | |
471 | goto err; | |
472 | if (!BN_copy(y1, b->Y)) | |
473 | goto err; | |
474 | } else { | |
475 | if (!EC_POINT_get_affine_coordinates_GF2m(group, b, x1, y1, ctx)) | |
476 | goto err; | |
477 | } | |
478 | ||
479 | if (BN_GF2m_cmp(x0, x1)) { | |
480 | if (!BN_GF2m_add(t, x0, x1)) | |
481 | goto err; | |
482 | if (!BN_GF2m_add(s, y0, y1)) | |
483 | goto err; | |
484 | if (!group->meth->field_div(group, s, s, t, ctx)) | |
485 | goto err; | |
486 | if (!group->meth->field_sqr(group, x2, s, ctx)) | |
487 | goto err; | |
488 | if (!BN_GF2m_add(x2, x2, group->a)) | |
489 | goto err; | |
490 | if (!BN_GF2m_add(x2, x2, s)) | |
491 | goto err; | |
492 | if (!BN_GF2m_add(x2, x2, t)) | |
493 | goto err; | |
494 | } else { | |
495 | if (BN_GF2m_cmp(y0, y1) || BN_is_zero(x1)) { | |
496 | if (!EC_POINT_set_to_infinity(group, r)) | |
497 | goto err; | |
498 | ret = 1; | |
499 | goto err; | |
500 | } | |
501 | if (!group->meth->field_div(group, s, y1, x1, ctx)) | |
502 | goto err; | |
503 | if (!BN_GF2m_add(s, s, x1)) | |
504 | goto err; | |
505 | ||
506 | if (!group->meth->field_sqr(group, x2, s, ctx)) | |
507 | goto err; | |
508 | if (!BN_GF2m_add(x2, x2, s)) | |
509 | goto err; | |
510 | if (!BN_GF2m_add(x2, x2, group->a)) | |
511 | goto err; | |
512 | } | |
513 | ||
514 | if (!BN_GF2m_add(y2, x1, x2)) | |
515 | goto err; | |
516 | if (!group->meth->field_mul(group, y2, y2, s, ctx)) | |
517 | goto err; | |
518 | if (!BN_GF2m_add(y2, y2, x2)) | |
519 | goto err; | |
520 | if (!BN_GF2m_add(y2, y2, y1)) | |
521 | goto err; | |
522 | ||
523 | if (!EC_POINT_set_affine_coordinates_GF2m(group, r, x2, y2, ctx)) | |
524 | goto err; | |
525 | ||
526 | ret = 1; | |
7793f30e | 527 | |
0f113f3e MC |
528 | err: |
529 | BN_CTX_end(ctx); | |
23a1d5e9 | 530 | BN_CTX_free(new_ctx); |
0f113f3e MC |
531 | return ret; |
532 | } | |
533 | ||
534 | /* | |
535 | * Computes 2 * a and stores the result in r. r could be a. Uses algorithm | |
536 | * A.10.2 of IEEE P1363. | |
537 | */ | |
538 | int ec_GF2m_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, | |
539 | BN_CTX *ctx) | |
540 | { | |
541 | return ec_GF2m_simple_add(group, r, a, a, ctx); | |
542 | } | |
7793f30e BM |
543 | |
544 | int ec_GF2m_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx) | |
0f113f3e MC |
545 | { |
546 | if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(point->Y)) | |
547 | /* point is its own inverse */ | |
548 | return 1; | |
7793f30e | 549 | |
0f113f3e MC |
550 | if (!EC_POINT_make_affine(group, point, ctx)) |
551 | return 0; | |
552 | return BN_GF2m_add(point->Y, point->X, point->Y); | |
553 | } | |
7793f30e BM |
554 | |
555 | /* Indicates whether the given point is the point at infinity. */ | |
0f113f3e MC |
556 | int ec_GF2m_simple_is_at_infinity(const EC_GROUP *group, |
557 | const EC_POINT *point) | |
558 | { | |
559 | return BN_is_zero(point->Z); | |
560 | } | |
7793f30e | 561 | |
23a22b4c MC |
562 | /*- |
563 | * Determines whether the given EC_POINT is an actual point on the curve defined | |
7793f30e BM |
564 | * in the EC_GROUP. A point is valid if it satisfies the Weierstrass equation: |
565 | * y^2 + x*y = x^3 + a*x^2 + b. | |
566 | */ | |
0f113f3e MC |
567 | int ec_GF2m_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, |
568 | BN_CTX *ctx) | |
569 | { | |
570 | int ret = -1; | |
571 | BN_CTX *new_ctx = NULL; | |
572 | BIGNUM *lh, *y2; | |
573 | int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *, | |
574 | const BIGNUM *, BN_CTX *); | |
575 | int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); | |
576 | ||
577 | if (EC_POINT_is_at_infinity(group, point)) | |
578 | return 1; | |
579 | ||
580 | field_mul = group->meth->field_mul; | |
581 | field_sqr = group->meth->field_sqr; | |
582 | ||
583 | /* only support affine coordinates */ | |
584 | if (!point->Z_is_one) | |
585 | return -1; | |
586 | ||
587 | if (ctx == NULL) { | |
588 | ctx = new_ctx = BN_CTX_new(); | |
589 | if (ctx == NULL) | |
590 | return -1; | |
591 | } | |
592 | ||
593 | BN_CTX_start(ctx); | |
594 | y2 = BN_CTX_get(ctx); | |
595 | lh = BN_CTX_get(ctx); | |
596 | if (lh == NULL) | |
597 | goto err; | |
598 | ||
50e735f9 MC |
599 | /*- |
600 | * We have a curve defined by a Weierstrass equation | |
601 | * y^2 + x*y = x^3 + a*x^2 + b. | |
602 | * <=> x^3 + a*x^2 + x*y + b + y^2 = 0 | |
603 | * <=> ((x + a) * x + y ) * x + b + y^2 = 0 | |
604 | */ | |
0f113f3e MC |
605 | if (!BN_GF2m_add(lh, point->X, group->a)) |
606 | goto err; | |
607 | if (!field_mul(group, lh, lh, point->X, ctx)) | |
608 | goto err; | |
609 | if (!BN_GF2m_add(lh, lh, point->Y)) | |
610 | goto err; | |
611 | if (!field_mul(group, lh, lh, point->X, ctx)) | |
612 | goto err; | |
613 | if (!BN_GF2m_add(lh, lh, group->b)) | |
614 | goto err; | |
615 | if (!field_sqr(group, y2, point->Y, ctx)) | |
616 | goto err; | |
617 | if (!BN_GF2m_add(lh, lh, y2)) | |
618 | goto err; | |
619 | ret = BN_is_zero(lh); | |
7793f30e | 620 | err: |
0f113f3e MC |
621 | if (ctx) |
622 | BN_CTX_end(ctx); | |
23a1d5e9 | 623 | BN_CTX_free(new_ctx); |
0f113f3e MC |
624 | return ret; |
625 | } | |
7793f30e | 626 | |
1d97c843 TH |
627 | /*- |
628 | * Indicates whether two points are equal. | |
7793f30e BM |
629 | * Return values: |
630 | * -1 error | |
631 | * 0 equal (in affine coordinates) | |
632 | * 1 not equal | |
633 | */ | |
0f113f3e MC |
634 | int ec_GF2m_simple_cmp(const EC_GROUP *group, const EC_POINT *a, |
635 | const EC_POINT *b, BN_CTX *ctx) | |
636 | { | |
637 | BIGNUM *aX, *aY, *bX, *bY; | |
638 | BN_CTX *new_ctx = NULL; | |
639 | int ret = -1; | |
640 | ||
641 | if (EC_POINT_is_at_infinity(group, a)) { | |
642 | return EC_POINT_is_at_infinity(group, b) ? 0 : 1; | |
643 | } | |
644 | ||
645 | if (EC_POINT_is_at_infinity(group, b)) | |
646 | return 1; | |
647 | ||
648 | if (a->Z_is_one && b->Z_is_one) { | |
649 | return ((BN_cmp(a->X, b->X) == 0) && BN_cmp(a->Y, b->Y) == 0) ? 0 : 1; | |
650 | } | |
651 | ||
652 | if (ctx == NULL) { | |
653 | ctx = new_ctx = BN_CTX_new(); | |
654 | if (ctx == NULL) | |
655 | return -1; | |
656 | } | |
657 | ||
658 | BN_CTX_start(ctx); | |
659 | aX = BN_CTX_get(ctx); | |
660 | aY = BN_CTX_get(ctx); | |
661 | bX = BN_CTX_get(ctx); | |
662 | bY = BN_CTX_get(ctx); | |
663 | if (bY == NULL) | |
664 | goto err; | |
665 | ||
666 | if (!EC_POINT_get_affine_coordinates_GF2m(group, a, aX, aY, ctx)) | |
667 | goto err; | |
668 | if (!EC_POINT_get_affine_coordinates_GF2m(group, b, bX, bY, ctx)) | |
669 | goto err; | |
670 | ret = ((BN_cmp(aX, bX) == 0) && BN_cmp(aY, bY) == 0) ? 0 : 1; | |
7793f30e | 671 | |
0f113f3e MC |
672 | err: |
673 | if (ctx) | |
674 | BN_CTX_end(ctx); | |
23a1d5e9 | 675 | BN_CTX_free(new_ctx); |
0f113f3e MC |
676 | return ret; |
677 | } | |
7793f30e BM |
678 | |
679 | /* Forces the given EC_POINT to internally use affine coordinates. */ | |
0f113f3e MC |
680 | int ec_GF2m_simple_make_affine(const EC_GROUP *group, EC_POINT *point, |
681 | BN_CTX *ctx) | |
682 | { | |
683 | BN_CTX *new_ctx = NULL; | |
684 | BIGNUM *x, *y; | |
685 | int ret = 0; | |
686 | ||
687 | if (point->Z_is_one || EC_POINT_is_at_infinity(group, point)) | |
688 | return 1; | |
689 | ||
690 | if (ctx == NULL) { | |
691 | ctx = new_ctx = BN_CTX_new(); | |
692 | if (ctx == NULL) | |
693 | return 0; | |
694 | } | |
695 | ||
696 | BN_CTX_start(ctx); | |
697 | x = BN_CTX_get(ctx); | |
698 | y = BN_CTX_get(ctx); | |
699 | if (y == NULL) | |
700 | goto err; | |
701 | ||
702 | if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx)) | |
703 | goto err; | |
704 | if (!BN_copy(point->X, x)) | |
705 | goto err; | |
706 | if (!BN_copy(point->Y, y)) | |
707 | goto err; | |
708 | if (!BN_one(point->Z)) | |
709 | goto err; | |
dd67493c | 710 | point->Z_is_one = 1; |
0f113f3e MC |
711 | |
712 | ret = 1; | |
713 | ||
714 | err: | |
715 | if (ctx) | |
716 | BN_CTX_end(ctx); | |
23a1d5e9 | 717 | BN_CTX_free(new_ctx); |
0f113f3e MC |
718 | return ret; |
719 | } | |
720 | ||
721 | /* | |
722 | * Forces each of the EC_POINTs in the given array to use affine coordinates. | |
723 | */ | |
724 | int ec_GF2m_simple_points_make_affine(const EC_GROUP *group, size_t num, | |
725 | EC_POINT *points[], BN_CTX *ctx) | |
726 | { | |
727 | size_t i; | |
7793f30e | 728 | |
0f113f3e MC |
729 | for (i = 0; i < num; i++) { |
730 | if (!group->meth->make_affine(group, points[i], ctx)) | |
731 | return 0; | |
732 | } | |
7793f30e | 733 | |
0f113f3e MC |
734 | return 1; |
735 | } | |
7793f30e | 736 | |
0f113f3e MC |
737 | /* Wrapper to simple binary polynomial field multiplication implementation. */ |
738 | int ec_GF2m_simple_field_mul(const EC_GROUP *group, BIGNUM *r, | |
739 | const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) | |
740 | { | |
741 | return BN_GF2m_mod_mul_arr(r, a, b, group->poly, ctx); | |
742 | } | |
7793f30e BM |
743 | |
744 | /* Wrapper to simple binary polynomial field squaring implementation. */ | |
0f113f3e MC |
745 | int ec_GF2m_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, |
746 | const BIGNUM *a, BN_CTX *ctx) | |
747 | { | |
748 | return BN_GF2m_mod_sqr_arr(r, a, group->poly, ctx); | |
749 | } | |
7793f30e BM |
750 | |
751 | /* Wrapper to simple binary polynomial field division implementation. */ | |
0f113f3e MC |
752 | int ec_GF2m_simple_field_div(const EC_GROUP *group, BIGNUM *r, |
753 | const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) | |
754 | { | |
755 | return BN_GF2m_mod_div(r, a, b, group->field, ctx); | |
756 | } | |
b3310161 DSH |
757 | |
758 | #endif |