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7793f30e BM |
1 | /* crypto/ec/ec2_smpl.c */ |
2 | /* ==================================================================== | |
3 | * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. | |
4 | * | |
5 | * The Elliptic Curve Public-Key Crypto Library (ECC Code) included | |
6 | * herein is developed by SUN MICROSYSTEMS, INC., and is contributed | |
7 | * to the OpenSSL project. | |
8 | * | |
9 | * The ECC Code is licensed pursuant to the OpenSSL open source | |
10 | * license provided below. | |
11 | * | |
7793f30e BM |
12 | * The software is originally written by Sheueling Chang Shantz and |
13 | * Douglas Stebila of Sun Microsystems Laboratories. | |
14 | * | |
15 | */ | |
16 | /* ==================================================================== | |
8dee9f84 | 17 | * Copyright (c) 1998-2005 The OpenSSL Project. All rights reserved. |
7793f30e BM |
18 | * |
19 | * Redistribution and use in source and binary forms, with or without | |
20 | * modification, are permitted provided that the following conditions | |
21 | * are met: | |
22 | * | |
23 | * 1. Redistributions of source code must retain the above copyright | |
24 | * notice, this list of conditions and the following disclaimer. | |
25 | * | |
26 | * 2. Redistributions in binary form must reproduce the above copyright | |
27 | * notice, this list of conditions and the following disclaimer in | |
28 | * the documentation and/or other materials provided with the | |
29 | * distribution. | |
30 | * | |
31 | * 3. All advertising materials mentioning features or use of this | |
32 | * software must display the following acknowledgment: | |
33 | * "This product includes software developed by the OpenSSL Project | |
34 | * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" | |
35 | * | |
36 | * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to | |
37 | * endorse or promote products derived from this software without | |
38 | * prior written permission. For written permission, please contact | |
39 | * openssl-core@openssl.org. | |
40 | * | |
41 | * 5. Products derived from this software may not be called "OpenSSL" | |
42 | * nor may "OpenSSL" appear in their names without prior written | |
43 | * permission of the OpenSSL Project. | |
44 | * | |
45 | * 6. Redistributions of any form whatsoever must retain the following | |
46 | * acknowledgment: | |
47 | * "This product includes software developed by the OpenSSL Project | |
48 | * for use in the OpenSSL Toolkit (http://www.openssl.org/)" | |
49 | * | |
50 | * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY | |
51 | * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE | |
52 | * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR | |
53 | * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR | |
54 | * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, | |
55 | * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT | |
56 | * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; | |
57 | * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) | |
58 | * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, | |
59 | * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) | |
60 | * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED | |
61 | * OF THE POSSIBILITY OF SUCH DAMAGE. | |
62 | * ==================================================================== | |
63 | * | |
64 | * This product includes cryptographic software written by Eric Young | |
65 | * (eay@cryptsoft.com). This product includes software written by Tim | |
66 | * Hudson (tjh@cryptsoft.com). | |
67 | * | |
68 | */ | |
69 | ||
70 | #include <openssl/err.h> | |
71 | ||
72 | #include "ec_lcl.h" | |
73 | ||
74 | ||
75 | const EC_METHOD *EC_GF2m_simple_method(void) | |
76 | { | |
77 | static const EC_METHOD ret = { | |
78 | NID_X9_62_characteristic_two_field, | |
79 | ec_GF2m_simple_group_init, | |
80 | ec_GF2m_simple_group_finish, | |
81 | ec_GF2m_simple_group_clear_finish, | |
82 | ec_GF2m_simple_group_copy, | |
35b73a1f BM |
83 | ec_GF2m_simple_group_set_curve, |
84 | ec_GF2m_simple_group_get_curve, | |
7793f30e BM |
85 | ec_GF2m_simple_group_get_degree, |
86 | ec_GF2m_simple_group_check_discriminant, | |
87 | ec_GF2m_simple_point_init, | |
88 | ec_GF2m_simple_point_finish, | |
89 | ec_GF2m_simple_point_clear_finish, | |
90 | ec_GF2m_simple_point_copy, | |
91 | ec_GF2m_simple_point_set_to_infinity, | |
35b73a1f BM |
92 | 0 /* set_Jprojective_coordinates_GFp */, |
93 | 0 /* get_Jprojective_coordinates_GFp */, | |
94 | ec_GF2m_simple_point_set_affine_coordinates, | |
95 | ec_GF2m_simple_point_get_affine_coordinates, | |
96 | ec_GF2m_simple_set_compressed_coordinates, | |
7793f30e BM |
97 | ec_GF2m_simple_point2oct, |
98 | ec_GF2m_simple_oct2point, | |
99 | ec_GF2m_simple_add, | |
100 | ec_GF2m_simple_dbl, | |
101 | ec_GF2m_simple_invert, | |
7793f30e BM |
102 | ec_GF2m_simple_is_at_infinity, |
103 | ec_GF2m_simple_is_on_curve, | |
104 | ec_GF2m_simple_cmp, | |
105 | ec_GF2m_simple_make_affine, | |
106 | ec_GF2m_simple_points_make_affine, | |
37c660ff BM |
107 | |
108 | /* the following three method functions are defined in ec2_mult.c */ | |
109 | ec_GF2m_simple_mul, | |
110 | ec_GF2m_precompute_mult, | |
111 | ec_GF2m_have_precompute_mult, | |
112 | ||
7793f30e BM |
113 | ec_GF2m_simple_field_mul, |
114 | ec_GF2m_simple_field_sqr, | |
115 | ec_GF2m_simple_field_div, | |
116 | 0 /* field_encode */, | |
117 | 0 /* field_decode */, | |
118 | 0 /* field_set_to_one */ }; | |
119 | ||
120 | return &ret; | |
121 | } | |
122 | ||
123 | ||
124 | /* Initialize a GF(2^m)-based EC_GROUP structure. | |
125 | * Note that all other members are handled by EC_GROUP_new. | |
126 | */ | |
127 | int ec_GF2m_simple_group_init(EC_GROUP *group) | |
128 | { | |
129 | BN_init(&group->field); | |
130 | BN_init(&group->a); | |
131 | BN_init(&group->b); | |
132 | return 1; | |
133 | } | |
134 | ||
135 | ||
136 | /* Free a GF(2^m)-based EC_GROUP structure. | |
137 | * Note that all other members are handled by EC_GROUP_free. | |
138 | */ | |
139 | void ec_GF2m_simple_group_finish(EC_GROUP *group) | |
140 | { | |
141 | BN_free(&group->field); | |
142 | BN_free(&group->a); | |
143 | BN_free(&group->b); | |
144 | } | |
145 | ||
146 | ||
147 | /* Clear and free a GF(2^m)-based EC_GROUP structure. | |
148 | * Note that all other members are handled by EC_GROUP_clear_free. | |
149 | */ | |
150 | void ec_GF2m_simple_group_clear_finish(EC_GROUP *group) | |
151 | { | |
152 | BN_clear_free(&group->field); | |
153 | BN_clear_free(&group->a); | |
154 | BN_clear_free(&group->b); | |
155 | group->poly[0] = 0; | |
156 | group->poly[1] = 0; | |
157 | group->poly[2] = 0; | |
158 | group->poly[3] = 0; | |
159 | group->poly[4] = 0; | |
c4e7870a | 160 | group->poly[5] = -1; |
7793f30e BM |
161 | } |
162 | ||
163 | ||
164 | /* Copy a GF(2^m)-based EC_GROUP structure. | |
165 | * Note that all other members are handled by EC_GROUP_copy. | |
166 | */ | |
167 | int ec_GF2m_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src) | |
168 | { | |
169 | int i; | |
170 | if (!BN_copy(&dest->field, &src->field)) return 0; | |
171 | if (!BN_copy(&dest->a, &src->a)) return 0; | |
172 | if (!BN_copy(&dest->b, &src->b)) return 0; | |
173 | dest->poly[0] = src->poly[0]; | |
174 | dest->poly[1] = src->poly[1]; | |
175 | dest->poly[2] = src->poly[2]; | |
176 | dest->poly[3] = src->poly[3]; | |
177 | dest->poly[4] = src->poly[4]; | |
c4e7870a | 178 | dest->poly[5] = src->poly[5]; |
2d9dcd4f BM |
179 | if (bn_wexpand(&dest->a, (int)(dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) return 0; |
180 | if (bn_wexpand(&dest->b, (int)(dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) return 0; | |
7793f30e BM |
181 | for (i = dest->a.top; i < dest->a.dmax; i++) dest->a.d[i] = 0; |
182 | for (i = dest->b.top; i < dest->b.dmax; i++) dest->b.d[i] = 0; | |
183 | return 1; | |
184 | } | |
185 | ||
186 | ||
187 | /* Set the curve parameters of an EC_GROUP structure. */ | |
35b73a1f | 188 | int ec_GF2m_simple_group_set_curve(EC_GROUP *group, |
7793f30e BM |
189 | const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) |
190 | { | |
191 | int ret = 0, i; | |
192 | ||
193 | /* group->field */ | |
194 | if (!BN_copy(&group->field, p)) goto err; | |
c4e7870a | 195 | i = BN_GF2m_poly2arr(&group->field, group->poly, 6) - 1; |
34f1f2a8 BM |
196 | if ((i != 5) && (i != 3)) |
197 | { | |
198 | ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_SET_CURVE, EC_R_UNSUPPORTED_FIELD); | |
199 | goto err; | |
200 | } | |
7793f30e BM |
201 | |
202 | /* group->a */ | |
203 | if (!BN_GF2m_mod_arr(&group->a, a, group->poly)) goto err; | |
2d9dcd4f | 204 | if(bn_wexpand(&group->a, (int)(group->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) goto err; |
7793f30e BM |
205 | for (i = group->a.top; i < group->a.dmax; i++) group->a.d[i] = 0; |
206 | ||
207 | /* group->b */ | |
208 | if (!BN_GF2m_mod_arr(&group->b, b, group->poly)) goto err; | |
2d9dcd4f | 209 | if(bn_wexpand(&group->b, (int)(group->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) goto err; |
7793f30e BM |
210 | for (i = group->b.top; i < group->b.dmax; i++) group->b.d[i] = 0; |
211 | ||
212 | ret = 1; | |
213 | err: | |
214 | return ret; | |
215 | } | |
216 | ||
217 | ||
218 | /* Get the curve parameters of an EC_GROUP structure. | |
219 | * If p, a, or b are NULL then there values will not be set but the method will return with success. | |
220 | */ | |
35b73a1f | 221 | int ec_GF2m_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx) |
7793f30e BM |
222 | { |
223 | int ret = 0; | |
224 | ||
225 | if (p != NULL) | |
226 | { | |
227 | if (!BN_copy(p, &group->field)) return 0; | |
228 | } | |
229 | ||
f72ed615 | 230 | if (a != NULL) |
7793f30e | 231 | { |
f72ed615 BM |
232 | if (!BN_copy(a, &group->a)) goto err; |
233 | } | |
234 | ||
235 | if (b != NULL) | |
236 | { | |
237 | if (!BN_copy(b, &group->b)) goto err; | |
7793f30e BM |
238 | } |
239 | ||
240 | ret = 1; | |
241 | ||
242 | err: | |
243 | return ret; | |
244 | } | |
245 | ||
246 | ||
247 | /* Gets the degree of the field. For a curve over GF(2^m) this is the value m. */ | |
248 | int ec_GF2m_simple_group_get_degree(const EC_GROUP *group) | |
249 | { | |
250 | return BN_num_bits(&group->field)-1; | |
251 | } | |
252 | ||
253 | ||
254 | /* Checks the discriminant of the curve. | |
255 | * y^2 + x*y = x^3 + a*x^2 + b is an elliptic curve <=> b != 0 (mod p) | |
256 | */ | |
257 | int ec_GF2m_simple_group_check_discriminant(const EC_GROUP *group, BN_CTX *ctx) | |
258 | { | |
259 | int ret = 0; | |
260 | BIGNUM *b; | |
261 | BN_CTX *new_ctx = NULL; | |
262 | ||
263 | if (ctx == NULL) | |
264 | { | |
265 | ctx = new_ctx = BN_CTX_new(); | |
266 | if (ctx == NULL) | |
267 | { | |
268 | ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_CHECK_DISCRIMINANT, ERR_R_MALLOC_FAILURE); | |
269 | goto err; | |
270 | } | |
271 | } | |
272 | BN_CTX_start(ctx); | |
273 | b = BN_CTX_get(ctx); | |
274 | if (b == NULL) goto err; | |
275 | ||
276 | if (!BN_GF2m_mod_arr(b, &group->b, group->poly)) goto err; | |
277 | ||
278 | /* check the discriminant: | |
279 | * y^2 + x*y = x^3 + a*x^2 + b is an elliptic curve <=> b != 0 (mod p) | |
280 | */ | |
281 | if (BN_is_zero(b)) goto err; | |
282 | ||
283 | ret = 1; | |
284 | ||
285 | err: | |
47d55666 NL |
286 | if (ctx != NULL) |
287 | BN_CTX_end(ctx); | |
7793f30e BM |
288 | if (new_ctx != NULL) |
289 | BN_CTX_free(new_ctx); | |
290 | return ret; | |
291 | } | |
292 | ||
293 | ||
294 | /* Initializes an EC_POINT. */ | |
295 | int ec_GF2m_simple_point_init(EC_POINT *point) | |
296 | { | |
297 | BN_init(&point->X); | |
298 | BN_init(&point->Y); | |
299 | BN_init(&point->Z); | |
300 | return 1; | |
301 | } | |
302 | ||
303 | ||
304 | /* Frees an EC_POINT. */ | |
305 | void ec_GF2m_simple_point_finish(EC_POINT *point) | |
306 | { | |
307 | BN_free(&point->X); | |
308 | BN_free(&point->Y); | |
309 | BN_free(&point->Z); | |
310 | } | |
311 | ||
312 | ||
313 | /* Clears and frees an EC_POINT. */ | |
314 | void ec_GF2m_simple_point_clear_finish(EC_POINT *point) | |
315 | { | |
316 | BN_clear_free(&point->X); | |
317 | BN_clear_free(&point->Y); | |
318 | BN_clear_free(&point->Z); | |
319 | point->Z_is_one = 0; | |
320 | } | |
321 | ||
322 | ||
323 | /* Copy the contents of one EC_POINT into another. Assumes dest is initialized. */ | |
324 | int ec_GF2m_simple_point_copy(EC_POINT *dest, const EC_POINT *src) | |
325 | { | |
326 | if (!BN_copy(&dest->X, &src->X)) return 0; | |
327 | if (!BN_copy(&dest->Y, &src->Y)) return 0; | |
328 | if (!BN_copy(&dest->Z, &src->Z)) return 0; | |
329 | dest->Z_is_one = src->Z_is_one; | |
330 | ||
331 | return 1; | |
332 | } | |
333 | ||
334 | ||
335 | /* Set an EC_POINT to the point at infinity. | |
336 | * A point at infinity is represented by having Z=0. | |
337 | */ | |
338 | int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *group, EC_POINT *point) | |
339 | { | |
340 | point->Z_is_one = 0; | |
b6358c89 GT |
341 | BN_zero(&point->Z); |
342 | return 1; | |
7793f30e BM |
343 | } |
344 | ||
345 | ||
346 | /* Set the coordinates of an EC_POINT using affine coordinates. | |
347 | * Note that the simple implementation only uses affine coordinates. | |
348 | */ | |
35b73a1f | 349 | int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *group, EC_POINT *point, |
7793f30e BM |
350 | const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx) |
351 | { | |
352 | int ret = 0; | |
353 | if (x == NULL || y == NULL) | |
354 | { | |
35b73a1f | 355 | ECerr(EC_F_EC_GF2M_SIMPLE_POINT_SET_AFFINE_COORDINATES, ERR_R_PASSED_NULL_PARAMETER); |
7793f30e BM |
356 | return 0; |
357 | } | |
358 | ||
359 | if (!BN_copy(&point->X, x)) goto err; | |
ff22e913 | 360 | BN_set_negative(&point->X, 0); |
7793f30e | 361 | if (!BN_copy(&point->Y, y)) goto err; |
ff22e913 | 362 | BN_set_negative(&point->Y, 0); |
7793f30e | 363 | if (!BN_copy(&point->Z, BN_value_one())) goto err; |
ff22e913 | 364 | BN_set_negative(&point->Z, 0); |
7793f30e | 365 | point->Z_is_one = 1; |
dd616752 | 366 | ret = 1; |
7793f30e BM |
367 | |
368 | err: | |
369 | return ret; | |
370 | } | |
371 | ||
372 | ||
373 | /* Gets the affine coordinates of an EC_POINT. | |
374 | * Note that the simple implementation only uses affine coordinates. | |
375 | */ | |
35b73a1f | 376 | int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point, |
7793f30e BM |
377 | BIGNUM *x, BIGNUM *y, BN_CTX *ctx) |
378 | { | |
379 | int ret = 0; | |
380 | ||
381 | if (EC_POINT_is_at_infinity(group, point)) | |
382 | { | |
35b73a1f | 383 | ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES, EC_R_POINT_AT_INFINITY); |
7793f30e BM |
384 | return 0; |
385 | } | |
386 | ||
387 | if (BN_cmp(&point->Z, BN_value_one())) | |
388 | { | |
35b73a1f | 389 | ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); |
7793f30e BM |
390 | return 0; |
391 | } | |
392 | if (x != NULL) | |
393 | { | |
394 | if (!BN_copy(x, &point->X)) goto err; | |
ff22e913 | 395 | BN_set_negative(x, 0); |
7793f30e BM |
396 | } |
397 | if (y != NULL) | |
398 | { | |
399 | if (!BN_copy(y, &point->Y)) goto err; | |
ff22e913 | 400 | BN_set_negative(y, 0); |
7793f30e BM |
401 | } |
402 | ret = 1; | |
403 | ||
404 | err: | |
405 | return ret; | |
406 | } | |
407 | ||
408 | ||
8dee9f84 BM |
409 | /* Calculates and sets the affine coordinates of an EC_POINT from the given |
410 | * compressed coordinates. Uses algorithm 2.3.4 of SEC 1. | |
411 | * Note that the simple implementation only uses affine coordinates. | |
412 | * | |
413 | * The method is from the following publication: | |
414 | * | |
415 | * Harper, Menezes, Vanstone: | |
416 | * "Public-Key Cryptosystems with Very Small Key Lengths", | |
417 | * EUROCRYPT '92, Springer-Verlag LNCS 658, | |
418 | * published February 1993 | |
419 | * | |
420 | * US Patents 6,141,420 and 6,618,483 (Vanstone, Mullin, Agnew) describe | |
421 | * the same method, but claim no priority date earlier than July 29, 1994 | |
422 | * (and additionally fail to cite the EUROCRYPT '92 publication as prior art). | |
423 | */ | |
424 | int ec_GF2m_simple_set_compressed_coordinates(const EC_GROUP *group, EC_POINT *point, | |
425 | const BIGNUM *x_, int y_bit, BN_CTX *ctx) | |
426 | { | |
427 | BN_CTX *new_ctx = NULL; | |
428 | BIGNUM *tmp, *x, *y, *z; | |
429 | int ret = 0, z0; | |
430 | ||
431 | /* clear error queue */ | |
432 | ERR_clear_error(); | |
433 | ||
434 | if (ctx == NULL) | |
435 | { | |
436 | ctx = new_ctx = BN_CTX_new(); | |
437 | if (ctx == NULL) | |
438 | return 0; | |
439 | } | |
440 | ||
441 | y_bit = (y_bit != 0) ? 1 : 0; | |
442 | ||
443 | BN_CTX_start(ctx); | |
444 | tmp = BN_CTX_get(ctx); | |
445 | x = BN_CTX_get(ctx); | |
446 | y = BN_CTX_get(ctx); | |
447 | z = BN_CTX_get(ctx); | |
448 | if (z == NULL) goto err; | |
449 | ||
450 | if (!BN_GF2m_mod_arr(x, x_, group->poly)) goto err; | |
451 | if (BN_is_zero(x)) | |
452 | { | |
453 | if (!BN_GF2m_mod_sqrt_arr(y, &group->b, group->poly, ctx)) goto err; | |
454 | } | |
455 | else | |
456 | { | |
457 | if (!group->meth->field_sqr(group, tmp, x, ctx)) goto err; | |
458 | if (!group->meth->field_div(group, tmp, &group->b, tmp, ctx)) goto err; | |
459 | if (!BN_GF2m_add(tmp, &group->a, tmp)) goto err; | |
460 | if (!BN_GF2m_add(tmp, x, tmp)) goto err; | |
461 | if (!BN_GF2m_mod_solve_quad_arr(z, tmp, group->poly, ctx)) | |
462 | { | |
463 | unsigned long err = ERR_peek_last_error(); | |
464 | ||
465 | if (ERR_GET_LIB(err) == ERR_LIB_BN && ERR_GET_REASON(err) == BN_R_NO_SOLUTION) | |
466 | { | |
467 | ERR_clear_error(); | |
468 | ECerr(EC_F_EC_GF2M_SIMPLE_SET_COMPRESSED_COORDINATES, EC_R_INVALID_COMPRESSED_POINT); | |
469 | } | |
470 | else | |
471 | ECerr(EC_F_EC_GF2M_SIMPLE_SET_COMPRESSED_COORDINATES, ERR_R_BN_LIB); | |
472 | goto err; | |
473 | } | |
474 | z0 = (BN_is_odd(z)) ? 1 : 0; | |
475 | if (!group->meth->field_mul(group, y, x, z, ctx)) goto err; | |
476 | if (z0 != y_bit) | |
477 | { | |
478 | if (!BN_GF2m_add(y, y, x)) goto err; | |
479 | } | |
480 | } | |
481 | ||
482 | if (!EC_POINT_set_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err; | |
483 | ||
484 | ret = 1; | |
485 | ||
486 | err: | |
487 | BN_CTX_end(ctx); | |
488 | if (new_ctx != NULL) | |
489 | BN_CTX_free(new_ctx); | |
490 | return ret; | |
491 | } | |
7793f30e BM |
492 | |
493 | ||
494 | /* Converts an EC_POINT to an octet string. | |
495 | * If buf is NULL, the encoded length will be returned. | |
496 | * If the length len of buf is smaller than required an error will be returned. | |
7793f30e BM |
497 | */ |
498 | size_t ec_GF2m_simple_point2oct(const EC_GROUP *group, const EC_POINT *point, point_conversion_form_t form, | |
499 | unsigned char *buf, size_t len, BN_CTX *ctx) | |
500 | { | |
501 | size_t ret; | |
502 | BN_CTX *new_ctx = NULL; | |
503 | int used_ctx = 0; | |
504 | BIGNUM *x, *y, *yxi; | |
505 | size_t field_len, i, skip; | |
506 | ||
7793f30e BM |
507 | if ((form != POINT_CONVERSION_COMPRESSED) |
508 | && (form != POINT_CONVERSION_UNCOMPRESSED) | |
509 | && (form != POINT_CONVERSION_HYBRID)) | |
510 | { | |
511 | ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_INVALID_FORM); | |
512 | goto err; | |
513 | } | |
514 | ||
515 | if (EC_POINT_is_at_infinity(group, point)) | |
516 | { | |
517 | /* encodes to a single 0 octet */ | |
518 | if (buf != NULL) | |
519 | { | |
520 | if (len < 1) | |
521 | { | |
522 | ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL); | |
523 | return 0; | |
524 | } | |
525 | buf[0] = 0; | |
526 | } | |
527 | return 1; | |
528 | } | |
529 | ||
530 | ||
531 | /* ret := required output buffer length */ | |
532 | field_len = (EC_GROUP_get_degree(group) + 7) / 8; | |
533 | ret = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len; | |
534 | ||
535 | /* if 'buf' is NULL, just return required length */ | |
536 | if (buf != NULL) | |
537 | { | |
538 | if (len < ret) | |
539 | { | |
540 | ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL); | |
541 | goto err; | |
542 | } | |
543 | ||
544 | if (ctx == NULL) | |
545 | { | |
546 | ctx = new_ctx = BN_CTX_new(); | |
547 | if (ctx == NULL) | |
548 | return 0; | |
549 | } | |
550 | ||
551 | BN_CTX_start(ctx); | |
552 | used_ctx = 1; | |
553 | x = BN_CTX_get(ctx); | |
554 | y = BN_CTX_get(ctx); | |
555 | yxi = BN_CTX_get(ctx); | |
556 | if (yxi == NULL) goto err; | |
557 | ||
558 | if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err; | |
559 | ||
560 | buf[0] = form; | |
7793f30e BM |
561 | if ((form != POINT_CONVERSION_UNCOMPRESSED) && !BN_is_zero(x)) |
562 | { | |
563 | if (!group->meth->field_div(group, yxi, y, x, ctx)) goto err; | |
564 | if (BN_is_odd(yxi)) buf[0]++; | |
565 | } | |
7793f30e BM |
566 | |
567 | i = 1; | |
568 | ||
569 | skip = field_len - BN_num_bytes(x); | |
570 | if (skip > field_len) | |
571 | { | |
572 | ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); | |
573 | goto err; | |
574 | } | |
575 | while (skip > 0) | |
576 | { | |
577 | buf[i++] = 0; | |
578 | skip--; | |
579 | } | |
580 | skip = BN_bn2bin(x, buf + i); | |
581 | i += skip; | |
582 | if (i != 1 + field_len) | |
583 | { | |
584 | ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); | |
585 | goto err; | |
586 | } | |
587 | ||
588 | if (form == POINT_CONVERSION_UNCOMPRESSED || form == POINT_CONVERSION_HYBRID) | |
589 | { | |
590 | skip = field_len - BN_num_bytes(y); | |
591 | if (skip > field_len) | |
592 | { | |
593 | ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); | |
594 | goto err; | |
595 | } | |
596 | while (skip > 0) | |
597 | { | |
598 | buf[i++] = 0; | |
599 | skip--; | |
600 | } | |
601 | skip = BN_bn2bin(y, buf + i); | |
602 | i += skip; | |
603 | } | |
604 | ||
605 | if (i != ret) | |
606 | { | |
607 | ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); | |
608 | goto err; | |
609 | } | |
610 | } | |
611 | ||
612 | if (used_ctx) | |
613 | BN_CTX_end(ctx); | |
614 | if (new_ctx != NULL) | |
615 | BN_CTX_free(new_ctx); | |
616 | return ret; | |
617 | ||
618 | err: | |
619 | if (used_ctx) | |
620 | BN_CTX_end(ctx); | |
621 | if (new_ctx != NULL) | |
622 | BN_CTX_free(new_ctx); | |
623 | return 0; | |
624 | } | |
625 | ||
626 | ||
627 | /* Converts an octet string representation to an EC_POINT. | |
628 | * Note that the simple implementation only uses affine coordinates. | |
629 | */ | |
630 | int ec_GF2m_simple_oct2point(const EC_GROUP *group, EC_POINT *point, | |
631 | const unsigned char *buf, size_t len, BN_CTX *ctx) | |
632 | { | |
633 | point_conversion_form_t form; | |
634 | int y_bit; | |
635 | BN_CTX *new_ctx = NULL; | |
636 | BIGNUM *x, *y, *yxi; | |
637 | size_t field_len, enc_len; | |
638 | int ret = 0; | |
639 | ||
640 | if (len == 0) | |
641 | { | |
642 | ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_BUFFER_TOO_SMALL); | |
643 | return 0; | |
644 | } | |
645 | form = buf[0]; | |
646 | y_bit = form & 1; | |
560f7abb | 647 | form = form & ~1U; |
7793f30e BM |
648 | if ((form != 0) && (form != POINT_CONVERSION_COMPRESSED) |
649 | && (form != POINT_CONVERSION_UNCOMPRESSED) | |
650 | && (form != POINT_CONVERSION_HYBRID)) | |
651 | { | |
652 | ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); | |
653 | return 0; | |
654 | } | |
655 | if ((form == 0 || form == POINT_CONVERSION_UNCOMPRESSED) && y_bit) | |
656 | { | |
657 | ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); | |
658 | return 0; | |
659 | } | |
660 | ||
661 | if (form == 0) | |
662 | { | |
663 | if (len != 1) | |
664 | { | |
665 | ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); | |
666 | return 0; | |
667 | } | |
668 | ||
669 | return EC_POINT_set_to_infinity(group, point); | |
670 | } | |
671 | ||
672 | field_len = (EC_GROUP_get_degree(group) + 7) / 8; | |
673 | enc_len = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len; | |
674 | ||
675 | if (len != enc_len) | |
676 | { | |
677 | ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); | |
678 | return 0; | |
679 | } | |
680 | ||
681 | if (ctx == NULL) | |
682 | { | |
683 | ctx = new_ctx = BN_CTX_new(); | |
684 | if (ctx == NULL) | |
685 | return 0; | |
686 | } | |
687 | ||
688 | BN_CTX_start(ctx); | |
689 | x = BN_CTX_get(ctx); | |
690 | y = BN_CTX_get(ctx); | |
691 | yxi = BN_CTX_get(ctx); | |
692 | if (yxi == NULL) goto err; | |
693 | ||
694 | if (!BN_bin2bn(buf + 1, field_len, x)) goto err; | |
695 | if (BN_ucmp(x, &group->field) >= 0) | |
696 | { | |
697 | ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); | |
698 | goto err; | |
699 | } | |
700 | ||
701 | if (form == POINT_CONVERSION_COMPRESSED) | |
702 | { | |
703 | if (!EC_POINT_set_compressed_coordinates_GF2m(group, point, x, y_bit, ctx)) goto err; | |
704 | } | |
705 | else | |
706 | { | |
707 | if (!BN_bin2bn(buf + 1 + field_len, field_len, y)) goto err; | |
708 | if (BN_ucmp(y, &group->field) >= 0) | |
709 | { | |
710 | ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); | |
711 | goto err; | |
712 | } | |
713 | if (form == POINT_CONVERSION_HYBRID) | |
714 | { | |
715 | if (!group->meth->field_div(group, yxi, y, x, ctx)) goto err; | |
716 | if (y_bit != BN_is_odd(yxi)) | |
717 | { | |
718 | ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); | |
719 | goto err; | |
720 | } | |
721 | } | |
722 | ||
723 | if (!EC_POINT_set_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err; | |
724 | } | |
725 | ||
726 | if (!EC_POINT_is_on_curve(group, point, ctx)) /* test required by X9.62 */ | |
727 | { | |
728 | ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_POINT_IS_NOT_ON_CURVE); | |
729 | goto err; | |
730 | } | |
731 | ||
732 | ret = 1; | |
733 | ||
734 | err: | |
735 | BN_CTX_end(ctx); | |
736 | if (new_ctx != NULL) | |
737 | BN_CTX_free(new_ctx); | |
738 | return ret; | |
739 | } | |
740 | ||
741 | ||
742 | /* Computes a + b and stores the result in r. r could be a or b, a could be b. | |
743 | * Uses algorithm A.10.2 of IEEE P1363. | |
744 | */ | |
745 | int ec_GF2m_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx) | |
746 | { | |
747 | BN_CTX *new_ctx = NULL; | |
748 | BIGNUM *x0, *y0, *x1, *y1, *x2, *y2, *s, *t; | |
749 | int ret = 0; | |
750 | ||
751 | if (EC_POINT_is_at_infinity(group, a)) | |
752 | { | |
753 | if (!EC_POINT_copy(r, b)) return 0; | |
754 | return 1; | |
755 | } | |
756 | ||
757 | if (EC_POINT_is_at_infinity(group, b)) | |
758 | { | |
759 | if (!EC_POINT_copy(r, a)) return 0; | |
760 | return 1; | |
761 | } | |
762 | ||
763 | if (ctx == NULL) | |
764 | { | |
765 | ctx = new_ctx = BN_CTX_new(); | |
766 | if (ctx == NULL) | |
767 | return 0; | |
768 | } | |
769 | ||
770 | BN_CTX_start(ctx); | |
771 | x0 = BN_CTX_get(ctx); | |
772 | y0 = BN_CTX_get(ctx); | |
773 | x1 = BN_CTX_get(ctx); | |
774 | y1 = BN_CTX_get(ctx); | |
775 | x2 = BN_CTX_get(ctx); | |
776 | y2 = BN_CTX_get(ctx); | |
777 | s = BN_CTX_get(ctx); | |
778 | t = BN_CTX_get(ctx); | |
779 | if (t == NULL) goto err; | |
780 | ||
781 | if (a->Z_is_one) | |
782 | { | |
783 | if (!BN_copy(x0, &a->X)) goto err; | |
784 | if (!BN_copy(y0, &a->Y)) goto err; | |
785 | } | |
786 | else | |
787 | { | |
788 | if (!EC_POINT_get_affine_coordinates_GF2m(group, a, x0, y0, ctx)) goto err; | |
789 | } | |
790 | if (b->Z_is_one) | |
791 | { | |
792 | if (!BN_copy(x1, &b->X)) goto err; | |
793 | if (!BN_copy(y1, &b->Y)) goto err; | |
794 | } | |
795 | else | |
796 | { | |
797 | if (!EC_POINT_get_affine_coordinates_GF2m(group, b, x1, y1, ctx)) goto err; | |
798 | } | |
799 | ||
800 | ||
801 | if (BN_GF2m_cmp(x0, x1)) | |
802 | { | |
803 | if (!BN_GF2m_add(t, x0, x1)) goto err; | |
804 | if (!BN_GF2m_add(s, y0, y1)) goto err; | |
805 | if (!group->meth->field_div(group, s, s, t, ctx)) goto err; | |
806 | if (!group->meth->field_sqr(group, x2, s, ctx)) goto err; | |
807 | if (!BN_GF2m_add(x2, x2, &group->a)) goto err; | |
808 | if (!BN_GF2m_add(x2, x2, s)) goto err; | |
809 | if (!BN_GF2m_add(x2, x2, t)) goto err; | |
810 | } | |
811 | else | |
812 | { | |
813 | if (BN_GF2m_cmp(y0, y1) || BN_is_zero(x1)) | |
814 | { | |
815 | if (!EC_POINT_set_to_infinity(group, r)) goto err; | |
816 | ret = 1; | |
817 | goto err; | |
818 | } | |
819 | if (!group->meth->field_div(group, s, y1, x1, ctx)) goto err; | |
820 | if (!BN_GF2m_add(s, s, x1)) goto err; | |
821 | ||
822 | if (!group->meth->field_sqr(group, x2, s, ctx)) goto err; | |
823 | if (!BN_GF2m_add(x2, x2, s)) goto err; | |
824 | if (!BN_GF2m_add(x2, x2, &group->a)) goto err; | |
825 | } | |
826 | ||
827 | if (!BN_GF2m_add(y2, x1, x2)) goto err; | |
828 | if (!group->meth->field_mul(group, y2, y2, s, ctx)) goto err; | |
829 | if (!BN_GF2m_add(y2, y2, x2)) goto err; | |
830 | if (!BN_GF2m_add(y2, y2, y1)) goto err; | |
831 | ||
832 | if (!EC_POINT_set_affine_coordinates_GF2m(group, r, x2, y2, ctx)) goto err; | |
833 | ||
834 | ret = 1; | |
835 | ||
836 | err: | |
837 | BN_CTX_end(ctx); | |
838 | if (new_ctx != NULL) | |
839 | BN_CTX_free(new_ctx); | |
840 | return ret; | |
841 | } | |
842 | ||
843 | ||
844 | /* Computes 2 * a and stores the result in r. r could be a. | |
845 | * Uses algorithm A.10.2 of IEEE P1363. | |
846 | */ | |
847 | int ec_GF2m_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_CTX *ctx) | |
848 | { | |
849 | return ec_GF2m_simple_add(group, r, a, a, ctx); | |
850 | } | |
851 | ||
852 | ||
853 | int ec_GF2m_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx) | |
854 | { | |
855 | if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(&point->Y)) | |
856 | /* point is its own inverse */ | |
857 | return 1; | |
858 | ||
859 | if (!EC_POINT_make_affine(group, point, ctx)) return 0; | |
860 | return BN_GF2m_add(&point->Y, &point->X, &point->Y); | |
861 | } | |
862 | ||
863 | ||
864 | /* Indicates whether the given point is the point at infinity. */ | |
865 | int ec_GF2m_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point) | |
866 | { | |
867 | return BN_is_zero(&point->Z); | |
868 | } | |
869 | ||
870 | ||
871 | /* Determines whether the given EC_POINT is an actual point on the curve defined | |
872 | * in the EC_GROUP. A point is valid if it satisfies the Weierstrass equation: | |
873 | * y^2 + x*y = x^3 + a*x^2 + b. | |
874 | */ | |
875 | int ec_GF2m_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx) | |
876 | { | |
7793f30e | 877 | int ret = -1; |
7f5b4dd1 GT |
878 | BN_CTX *new_ctx = NULL; |
879 | BIGNUM *lh, *y2; | |
880 | int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *); | |
881 | int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); | |
7793f30e BM |
882 | |
883 | if (EC_POINT_is_at_infinity(group, point)) | |
884 | return 1; | |
7f5b4dd1 GT |
885 | |
886 | field_mul = group->meth->field_mul; | |
887 | field_sqr = group->meth->field_sqr; | |
888 | ||
7793f30e BM |
889 | /* only support affine coordinates */ |
890 | if (!point->Z_is_one) goto err; | |
891 | ||
892 | if (ctx == NULL) | |
893 | { | |
894 | ctx = new_ctx = BN_CTX_new(); | |
895 | if (ctx == NULL) | |
896 | return -1; | |
897 | } | |
898 | ||
899 | BN_CTX_start(ctx); | |
7f5b4dd1 | 900 | y2 = BN_CTX_get(ctx); |
7793f30e | 901 | lh = BN_CTX_get(ctx); |
7f5b4dd1 | 902 | if (lh == NULL) goto err; |
7793f30e BM |
903 | |
904 | /* We have a curve defined by a Weierstrass equation | |
905 | * y^2 + x*y = x^3 + a*x^2 + b. | |
7f5b4dd1 GT |
906 | * <=> x^3 + a*x^2 + x*y + b + y^2 = 0 |
907 | * <=> ((x + a) * x + y ) * x + b + y^2 = 0 | |
7793f30e | 908 | */ |
7f5b4dd1 GT |
909 | if (!BN_GF2m_add(lh, &point->X, &group->a)) goto err; |
910 | if (!field_mul(group, lh, lh, &point->X, ctx)) goto err; | |
911 | if (!BN_GF2m_add(lh, lh, &point->Y)) goto err; | |
912 | if (!field_mul(group, lh, lh, &point->X, ctx)) goto err; | |
913 | if (!BN_GF2m_add(lh, lh, &group->b)) goto err; | |
914 | if (!field_sqr(group, y2, &point->Y, ctx)) goto err; | |
915 | if (!BN_GF2m_add(lh, lh, y2)) goto err; | |
916 | ret = BN_is_zero(lh); | |
7793f30e BM |
917 | err: |
918 | if (ctx) BN_CTX_end(ctx); | |
919 | if (new_ctx) BN_CTX_free(new_ctx); | |
920 | return ret; | |
921 | } | |
922 | ||
923 | ||
924 | /* Indicates whether two points are equal. | |
925 | * Return values: | |
926 | * -1 error | |
927 | * 0 equal (in affine coordinates) | |
928 | * 1 not equal | |
929 | */ | |
930 | int ec_GF2m_simple_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx) | |
931 | { | |
932 | BIGNUM *aX, *aY, *bX, *bY; | |
933 | BN_CTX *new_ctx = NULL; | |
934 | int ret = -1; | |
935 | ||
936 | if (EC_POINT_is_at_infinity(group, a)) | |
937 | { | |
938 | return EC_POINT_is_at_infinity(group, b) ? 0 : 1; | |
939 | } | |
0aa1aedb DSH |
940 | |
941 | if (EC_POINT_is_at_infinity(group, b)) | |
942 | return 1; | |
7793f30e BM |
943 | |
944 | if (a->Z_is_one && b->Z_is_one) | |
945 | { | |
946 | return ((BN_cmp(&a->X, &b->X) == 0) && BN_cmp(&a->Y, &b->Y) == 0) ? 0 : 1; | |
947 | } | |
948 | ||
949 | if (ctx == NULL) | |
950 | { | |
951 | ctx = new_ctx = BN_CTX_new(); | |
952 | if (ctx == NULL) | |
953 | return -1; | |
954 | } | |
955 | ||
956 | BN_CTX_start(ctx); | |
957 | aX = BN_CTX_get(ctx); | |
958 | aY = BN_CTX_get(ctx); | |
959 | bX = BN_CTX_get(ctx); | |
960 | bY = BN_CTX_get(ctx); | |
961 | if (bY == NULL) goto err; | |
962 | ||
963 | if (!EC_POINT_get_affine_coordinates_GF2m(group, a, aX, aY, ctx)) goto err; | |
964 | if (!EC_POINT_get_affine_coordinates_GF2m(group, b, bX, bY, ctx)) goto err; | |
965 | ret = ((BN_cmp(aX, bX) == 0) && BN_cmp(aY, bY) == 0) ? 0 : 1; | |
966 | ||
967 | err: | |
968 | if (ctx) BN_CTX_end(ctx); | |
969 | if (new_ctx) BN_CTX_free(new_ctx); | |
970 | return ret; | |
971 | } | |
972 | ||
973 | ||
974 | /* Forces the given EC_POINT to internally use affine coordinates. */ | |
975 | int ec_GF2m_simple_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx) | |
976 | { | |
977 | BN_CTX *new_ctx = NULL; | |
978 | BIGNUM *x, *y; | |
979 | int ret = 0; | |
980 | ||
981 | if (point->Z_is_one || EC_POINT_is_at_infinity(group, point)) | |
982 | return 1; | |
983 | ||
984 | if (ctx == NULL) | |
985 | { | |
986 | ctx = new_ctx = BN_CTX_new(); | |
987 | if (ctx == NULL) | |
988 | return 0; | |
989 | } | |
990 | ||
991 | BN_CTX_start(ctx); | |
992 | x = BN_CTX_get(ctx); | |
993 | y = BN_CTX_get(ctx); | |
994 | if (y == NULL) goto err; | |
995 | ||
996 | if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err; | |
997 | if (!BN_copy(&point->X, x)) goto err; | |
998 | if (!BN_copy(&point->Y, y)) goto err; | |
999 | if (!BN_one(&point->Z)) goto err; | |
1000 | ||
1001 | ret = 1; | |
1002 | ||
1003 | err: | |
1004 | if (ctx) BN_CTX_end(ctx); | |
1005 | if (new_ctx) BN_CTX_free(new_ctx); | |
1006 | return ret; | |
1007 | } | |
1008 | ||
1009 | ||
1010 | /* Forces each of the EC_POINTs in the given array to use affine coordinates. */ | |
1011 | int ec_GF2m_simple_points_make_affine(const EC_GROUP *group, size_t num, EC_POINT *points[], BN_CTX *ctx) | |
1012 | { | |
1013 | size_t i; | |
1014 | ||
1015 | for (i = 0; i < num; i++) | |
1016 | { | |
1017 | if (!group->meth->make_affine(group, points[i], ctx)) return 0; | |
1018 | } | |
1019 | ||
1020 | return 1; | |
1021 | } | |
1022 | ||
1023 | ||
1024 | /* Wrapper to simple binary polynomial field multiplication implementation. */ | |
1025 | int ec_GF2m_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) | |
1026 | { | |
1027 | return BN_GF2m_mod_mul_arr(r, a, b, group->poly, ctx); | |
1028 | } | |
1029 | ||
1030 | ||
1031 | /* Wrapper to simple binary polynomial field squaring implementation. */ | |
1032 | int ec_GF2m_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx) | |
1033 | { | |
1034 | return BN_GF2m_mod_sqr_arr(r, a, group->poly, ctx); | |
1035 | } | |
1036 | ||
1037 | ||
1038 | /* Wrapper to simple binary polynomial field division implementation. */ | |
1039 | int ec_GF2m_simple_field_div(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) | |
1040 | { | |
1041 | return BN_GF2m_mod_div(r, a, b, &group->field, ctx); | |
1042 | } |