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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 | /* ==================================================================== | |
17 | * Copyright (c) 1998-2002 The OpenSSL Project. All rights reserved. | |
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, | |
102 | ec_GF2m_mont_mul, | |
103 | ec_GF2m_mont_precompute_mult, | |
104 | ec_GF2m_simple_is_at_infinity, | |
105 | ec_GF2m_simple_is_on_curve, | |
106 | ec_GF2m_simple_cmp, | |
107 | ec_GF2m_simple_make_affine, | |
108 | ec_GF2m_simple_points_make_affine, | |
109 | ec_GF2m_simple_field_mul, | |
110 | ec_GF2m_simple_field_sqr, | |
111 | ec_GF2m_simple_field_div, | |
112 | 0 /* field_encode */, | |
113 | 0 /* field_decode */, | |
114 | 0 /* field_set_to_one */ }; | |
115 | ||
116 | return &ret; | |
117 | } | |
118 | ||
119 | ||
120 | /* Initialize a GF(2^m)-based EC_GROUP structure. | |
121 | * Note that all other members are handled by EC_GROUP_new. | |
122 | */ | |
123 | int ec_GF2m_simple_group_init(EC_GROUP *group) | |
124 | { | |
125 | BN_init(&group->field); | |
126 | BN_init(&group->a); | |
127 | BN_init(&group->b); | |
128 | return 1; | |
129 | } | |
130 | ||
131 | ||
132 | /* Free a GF(2^m)-based EC_GROUP structure. | |
133 | * Note that all other members are handled by EC_GROUP_free. | |
134 | */ | |
135 | void ec_GF2m_simple_group_finish(EC_GROUP *group) | |
136 | { | |
137 | BN_free(&group->field); | |
138 | BN_free(&group->a); | |
139 | BN_free(&group->b); | |
140 | } | |
141 | ||
142 | ||
143 | /* Clear and free a GF(2^m)-based EC_GROUP structure. | |
144 | * Note that all other members are handled by EC_GROUP_clear_free. | |
145 | */ | |
146 | void ec_GF2m_simple_group_clear_finish(EC_GROUP *group) | |
147 | { | |
148 | BN_clear_free(&group->field); | |
149 | BN_clear_free(&group->a); | |
150 | BN_clear_free(&group->b); | |
151 | group->poly[0] = 0; | |
152 | group->poly[1] = 0; | |
153 | group->poly[2] = 0; | |
154 | group->poly[3] = 0; | |
155 | group->poly[4] = 0; | |
156 | } | |
157 | ||
158 | ||
159 | /* Copy a GF(2^m)-based EC_GROUP structure. | |
160 | * Note that all other members are handled by EC_GROUP_copy. | |
161 | */ | |
162 | int ec_GF2m_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src) | |
163 | { | |
164 | int i; | |
165 | if (!BN_copy(&dest->field, &src->field)) return 0; | |
166 | if (!BN_copy(&dest->a, &src->a)) return 0; | |
167 | if (!BN_copy(&dest->b, &src->b)) return 0; | |
168 | dest->poly[0] = src->poly[0]; | |
169 | dest->poly[1] = src->poly[1]; | |
170 | dest->poly[2] = src->poly[2]; | |
171 | dest->poly[3] = src->poly[3]; | |
172 | dest->poly[4] = src->poly[4]; | |
173 | bn_wexpand(&dest->a, (dest->poly[0] + BN_BITS2 - 1) / BN_BITS2); | |
174 | bn_wexpand(&dest->b, (dest->poly[0] + BN_BITS2 - 1) / BN_BITS2); | |
175 | for (i = dest->a.top; i < dest->a.dmax; i++) dest->a.d[i] = 0; | |
176 | for (i = dest->b.top; i < dest->b.dmax; i++) dest->b.d[i] = 0; | |
177 | return 1; | |
178 | } | |
179 | ||
180 | ||
181 | /* Set the curve parameters of an EC_GROUP structure. */ | |
35b73a1f | 182 | int ec_GF2m_simple_group_set_curve(EC_GROUP *group, |
7793f30e BM |
183 | const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) |
184 | { | |
185 | int ret = 0, i; | |
186 | ||
187 | /* group->field */ | |
188 | if (!BN_copy(&group->field, p)) goto err; | |
189 | i = BN_GF2m_poly2arr(&group->field, group->poly, 5); | |
34f1f2a8 BM |
190 | if ((i != 5) && (i != 3)) |
191 | { | |
192 | ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_SET_CURVE, EC_R_UNSUPPORTED_FIELD); | |
193 | goto err; | |
194 | } | |
7793f30e BM |
195 | |
196 | /* group->a */ | |
197 | if (!BN_GF2m_mod_arr(&group->a, a, group->poly)) goto err; | |
198 | bn_wexpand(&group->a, (group->poly[0] + BN_BITS2 - 1) / BN_BITS2); | |
199 | for (i = group->a.top; i < group->a.dmax; i++) group->a.d[i] = 0; | |
200 | ||
201 | /* group->b */ | |
202 | if (!BN_GF2m_mod_arr(&group->b, b, group->poly)) goto err; | |
203 | bn_wexpand(&group->b, (group->poly[0] + BN_BITS2 - 1) / BN_BITS2); | |
204 | for (i = group->b.top; i < group->b.dmax; i++) group->b.d[i] = 0; | |
205 | ||
206 | ret = 1; | |
207 | err: | |
208 | return ret; | |
209 | } | |
210 | ||
211 | ||
212 | /* Get the curve parameters of an EC_GROUP structure. | |
213 | * If p, a, or b are NULL then there values will not be set but the method will return with success. | |
214 | */ | |
35b73a1f | 215 | int ec_GF2m_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx) |
7793f30e BM |
216 | { |
217 | int ret = 0; | |
218 | ||
219 | if (p != NULL) | |
220 | { | |
221 | if (!BN_copy(p, &group->field)) return 0; | |
222 | } | |
223 | ||
f72ed615 | 224 | if (a != NULL) |
7793f30e | 225 | { |
f72ed615 BM |
226 | if (!BN_copy(a, &group->a)) goto err; |
227 | } | |
228 | ||
229 | if (b != NULL) | |
230 | { | |
231 | if (!BN_copy(b, &group->b)) goto err; | |
7793f30e BM |
232 | } |
233 | ||
234 | ret = 1; | |
235 | ||
236 | err: | |
237 | return ret; | |
238 | } | |
239 | ||
240 | ||
241 | /* Gets the degree of the field. For a curve over GF(2^m) this is the value m. */ | |
242 | int ec_GF2m_simple_group_get_degree(const EC_GROUP *group) | |
243 | { | |
244 | return BN_num_bits(&group->field)-1; | |
245 | } | |
246 | ||
247 | ||
248 | /* Checks the discriminant of the curve. | |
249 | * y^2 + x*y = x^3 + a*x^2 + b is an elliptic curve <=> b != 0 (mod p) | |
250 | */ | |
251 | int ec_GF2m_simple_group_check_discriminant(const EC_GROUP *group, BN_CTX *ctx) | |
252 | { | |
253 | int ret = 0; | |
254 | BIGNUM *b; | |
255 | BN_CTX *new_ctx = NULL; | |
256 | ||
257 | if (ctx == NULL) | |
258 | { | |
259 | ctx = new_ctx = BN_CTX_new(); | |
260 | if (ctx == NULL) | |
261 | { | |
262 | ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_CHECK_DISCRIMINANT, ERR_R_MALLOC_FAILURE); | |
263 | goto err; | |
264 | } | |
265 | } | |
266 | BN_CTX_start(ctx); | |
267 | b = BN_CTX_get(ctx); | |
268 | if (b == NULL) goto err; | |
269 | ||
270 | if (!BN_GF2m_mod_arr(b, &group->b, group->poly)) goto err; | |
271 | ||
272 | /* check the discriminant: | |
273 | * y^2 + x*y = x^3 + a*x^2 + b is an elliptic curve <=> b != 0 (mod p) | |
274 | */ | |
275 | if (BN_is_zero(b)) goto err; | |
276 | ||
277 | ret = 1; | |
278 | ||
279 | err: | |
280 | BN_CTX_end(ctx); | |
281 | if (new_ctx != NULL) | |
282 | BN_CTX_free(new_ctx); | |
283 | return ret; | |
284 | } | |
285 | ||
286 | ||
287 | /* Initializes an EC_POINT. */ | |
288 | int ec_GF2m_simple_point_init(EC_POINT *point) | |
289 | { | |
290 | BN_init(&point->X); | |
291 | BN_init(&point->Y); | |
292 | BN_init(&point->Z); | |
293 | return 1; | |
294 | } | |
295 | ||
296 | ||
297 | /* Frees an EC_POINT. */ | |
298 | void ec_GF2m_simple_point_finish(EC_POINT *point) | |
299 | { | |
300 | BN_free(&point->X); | |
301 | BN_free(&point->Y); | |
302 | BN_free(&point->Z); | |
303 | } | |
304 | ||
305 | ||
306 | /* Clears and frees an EC_POINT. */ | |
307 | void ec_GF2m_simple_point_clear_finish(EC_POINT *point) | |
308 | { | |
309 | BN_clear_free(&point->X); | |
310 | BN_clear_free(&point->Y); | |
311 | BN_clear_free(&point->Z); | |
312 | point->Z_is_one = 0; | |
313 | } | |
314 | ||
315 | ||
316 | /* Copy the contents of one EC_POINT into another. Assumes dest is initialized. */ | |
317 | int ec_GF2m_simple_point_copy(EC_POINT *dest, const EC_POINT *src) | |
318 | { | |
319 | if (!BN_copy(&dest->X, &src->X)) return 0; | |
320 | if (!BN_copy(&dest->Y, &src->Y)) return 0; | |
321 | if (!BN_copy(&dest->Z, &src->Z)) return 0; | |
322 | dest->Z_is_one = src->Z_is_one; | |
323 | ||
324 | return 1; | |
325 | } | |
326 | ||
327 | ||
328 | /* Set an EC_POINT to the point at infinity. | |
329 | * A point at infinity is represented by having Z=0. | |
330 | */ | |
331 | int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *group, EC_POINT *point) | |
332 | { | |
333 | point->Z_is_one = 0; | |
334 | return (BN_zero(&point->Z)); | |
335 | } | |
336 | ||
337 | ||
338 | /* Set the coordinates of an EC_POINT using affine coordinates. | |
339 | * Note that the simple implementation only uses affine coordinates. | |
340 | */ | |
35b73a1f | 341 | int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *group, EC_POINT *point, |
7793f30e BM |
342 | const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx) |
343 | { | |
344 | int ret = 0; | |
345 | if (x == NULL || y == NULL) | |
346 | { | |
35b73a1f | 347 | ECerr(EC_F_EC_GF2M_SIMPLE_POINT_SET_AFFINE_COORDINATES, ERR_R_PASSED_NULL_PARAMETER); |
7793f30e BM |
348 | return 0; |
349 | } | |
350 | ||
351 | if (!BN_copy(&point->X, x)) goto err; | |
b53e44e5 | 352 | BN_set_sign(&point->X, 0); |
7793f30e | 353 | if (!BN_copy(&point->Y, y)) goto err; |
b53e44e5 | 354 | BN_set_sign(&point->Y, 0); |
7793f30e | 355 | if (!BN_copy(&point->Z, BN_value_one())) goto err; |
b53e44e5 | 356 | BN_set_sign(&point->Z, 0); |
7793f30e BM |
357 | point->Z_is_one = 1; |
358 | ret = 1; | |
359 | ||
360 | err: | |
361 | return ret; | |
362 | } | |
363 | ||
364 | ||
365 | /* Gets the affine coordinates of an EC_POINT. | |
366 | * Note that the simple implementation only uses affine coordinates. | |
367 | */ | |
35b73a1f | 368 | int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point, |
7793f30e BM |
369 | BIGNUM *x, BIGNUM *y, BN_CTX *ctx) |
370 | { | |
371 | int ret = 0; | |
372 | ||
373 | if (EC_POINT_is_at_infinity(group, point)) | |
374 | { | |
35b73a1f | 375 | ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES, EC_R_POINT_AT_INFINITY); |
7793f30e BM |
376 | return 0; |
377 | } | |
378 | ||
379 | if (BN_cmp(&point->Z, BN_value_one())) | |
380 | { | |
35b73a1f | 381 | ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); |
7793f30e BM |
382 | return 0; |
383 | } | |
384 | if (x != NULL) | |
385 | { | |
386 | if (!BN_copy(x, &point->X)) goto err; | |
b53e44e5 | 387 | BN_set_sign(x, 0); |
7793f30e BM |
388 | } |
389 | if (y != NULL) | |
390 | { | |
391 | if (!BN_copy(y, &point->Y)) goto err; | |
b53e44e5 | 392 | BN_set_sign(y, 0); |
7793f30e BM |
393 | } |
394 | ret = 1; | |
395 | ||
396 | err: | |
397 | return ret; | |
398 | } | |
399 | ||
400 | ||
401 | /* Include patented algorithms. */ | |
402 | #include "ec2_smpt.c" | |
403 | ||
404 | ||
405 | /* Converts an EC_POINT to an octet string. | |
406 | * If buf is NULL, the encoded length will be returned. | |
407 | * If the length len of buf is smaller than required an error will be returned. | |
408 | * | |
409 | * The point compression section of this function is patented by Certicom Corp. | |
410 | * under US Patent 6,141,420. Point compression is disabled by default and can | |
411 | * be enabled by defining the preprocessor macro OPENSSL_EC_BIN_PT_COMP at | |
412 | * Configure-time. | |
413 | */ | |
414 | size_t ec_GF2m_simple_point2oct(const EC_GROUP *group, const EC_POINT *point, point_conversion_form_t form, | |
415 | unsigned char *buf, size_t len, BN_CTX *ctx) | |
416 | { | |
417 | size_t ret; | |
418 | BN_CTX *new_ctx = NULL; | |
419 | int used_ctx = 0; | |
420 | BIGNUM *x, *y, *yxi; | |
421 | size_t field_len, i, skip; | |
422 | ||
423 | #ifndef OPENSSL_EC_BIN_PT_COMP | |
424 | if ((form == POINT_CONVERSION_COMPRESSED) || (form == POINT_CONVERSION_HYBRID)) | |
425 | { | |
426 | ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_DISABLED); | |
427 | goto err; | |
428 | } | |
429 | #endif | |
430 | ||
431 | if ((form != POINT_CONVERSION_COMPRESSED) | |
432 | && (form != POINT_CONVERSION_UNCOMPRESSED) | |
433 | && (form != POINT_CONVERSION_HYBRID)) | |
434 | { | |
435 | ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_INVALID_FORM); | |
436 | goto err; | |
437 | } | |
438 | ||
439 | if (EC_POINT_is_at_infinity(group, point)) | |
440 | { | |
441 | /* encodes to a single 0 octet */ | |
442 | if (buf != NULL) | |
443 | { | |
444 | if (len < 1) | |
445 | { | |
446 | ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL); | |
447 | return 0; | |
448 | } | |
449 | buf[0] = 0; | |
450 | } | |
451 | return 1; | |
452 | } | |
453 | ||
454 | ||
455 | /* ret := required output buffer length */ | |
456 | field_len = (EC_GROUP_get_degree(group) + 7) / 8; | |
457 | ret = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len; | |
458 | ||
459 | /* if 'buf' is NULL, just return required length */ | |
460 | if (buf != NULL) | |
461 | { | |
462 | if (len < ret) | |
463 | { | |
464 | ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL); | |
465 | goto err; | |
466 | } | |
467 | ||
468 | if (ctx == NULL) | |
469 | { | |
470 | ctx = new_ctx = BN_CTX_new(); | |
471 | if (ctx == NULL) | |
472 | return 0; | |
473 | } | |
474 | ||
475 | BN_CTX_start(ctx); | |
476 | used_ctx = 1; | |
477 | x = BN_CTX_get(ctx); | |
478 | y = BN_CTX_get(ctx); | |
479 | yxi = BN_CTX_get(ctx); | |
480 | if (yxi == NULL) goto err; | |
481 | ||
482 | if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err; | |
483 | ||
484 | buf[0] = form; | |
485 | #ifdef OPENSSL_EC_BIN_PT_COMP | |
486 | if ((form != POINT_CONVERSION_UNCOMPRESSED) && !BN_is_zero(x)) | |
487 | { | |
488 | if (!group->meth->field_div(group, yxi, y, x, ctx)) goto err; | |
489 | if (BN_is_odd(yxi)) buf[0]++; | |
490 | } | |
491 | #endif | |
492 | ||
493 | i = 1; | |
494 | ||
495 | skip = field_len - BN_num_bytes(x); | |
496 | if (skip > field_len) | |
497 | { | |
498 | ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); | |
499 | goto err; | |
500 | } | |
501 | while (skip > 0) | |
502 | { | |
503 | buf[i++] = 0; | |
504 | skip--; | |
505 | } | |
506 | skip = BN_bn2bin(x, buf + i); | |
507 | i += skip; | |
508 | if (i != 1 + field_len) | |
509 | { | |
510 | ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); | |
511 | goto err; | |
512 | } | |
513 | ||
514 | if (form == POINT_CONVERSION_UNCOMPRESSED || form == POINT_CONVERSION_HYBRID) | |
515 | { | |
516 | skip = field_len - BN_num_bytes(y); | |
517 | if (skip > field_len) | |
518 | { | |
519 | ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); | |
520 | goto err; | |
521 | } | |
522 | while (skip > 0) | |
523 | { | |
524 | buf[i++] = 0; | |
525 | skip--; | |
526 | } | |
527 | skip = BN_bn2bin(y, buf + i); | |
528 | i += skip; | |
529 | } | |
530 | ||
531 | if (i != ret) | |
532 | { | |
533 | ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); | |
534 | goto err; | |
535 | } | |
536 | } | |
537 | ||
538 | if (used_ctx) | |
539 | BN_CTX_end(ctx); | |
540 | if (new_ctx != NULL) | |
541 | BN_CTX_free(new_ctx); | |
542 | return ret; | |
543 | ||
544 | err: | |
545 | if (used_ctx) | |
546 | BN_CTX_end(ctx); | |
547 | if (new_ctx != NULL) | |
548 | BN_CTX_free(new_ctx); | |
549 | return 0; | |
550 | } | |
551 | ||
552 | ||
553 | /* Converts an octet string representation to an EC_POINT. | |
554 | * Note that the simple implementation only uses affine coordinates. | |
555 | */ | |
556 | int ec_GF2m_simple_oct2point(const EC_GROUP *group, EC_POINT *point, | |
557 | const unsigned char *buf, size_t len, BN_CTX *ctx) | |
558 | { | |
559 | point_conversion_form_t form; | |
560 | int y_bit; | |
561 | BN_CTX *new_ctx = NULL; | |
562 | BIGNUM *x, *y, *yxi; | |
563 | size_t field_len, enc_len; | |
564 | int ret = 0; | |
565 | ||
566 | if (len == 0) | |
567 | { | |
568 | ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_BUFFER_TOO_SMALL); | |
569 | return 0; | |
570 | } | |
571 | form = buf[0]; | |
572 | y_bit = form & 1; | |
573 | form = form & ~1; | |
574 | if ((form != 0) && (form != POINT_CONVERSION_COMPRESSED) | |
575 | && (form != POINT_CONVERSION_UNCOMPRESSED) | |
576 | && (form != POINT_CONVERSION_HYBRID)) | |
577 | { | |
578 | ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); | |
579 | return 0; | |
580 | } | |
581 | if ((form == 0 || form == POINT_CONVERSION_UNCOMPRESSED) && y_bit) | |
582 | { | |
583 | ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); | |
584 | return 0; | |
585 | } | |
586 | ||
587 | if (form == 0) | |
588 | { | |
589 | if (len != 1) | |
590 | { | |
591 | ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); | |
592 | return 0; | |
593 | } | |
594 | ||
595 | return EC_POINT_set_to_infinity(group, point); | |
596 | } | |
597 | ||
598 | field_len = (EC_GROUP_get_degree(group) + 7) / 8; | |
599 | enc_len = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len; | |
600 | ||
601 | if (len != enc_len) | |
602 | { | |
603 | ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); | |
604 | return 0; | |
605 | } | |
606 | ||
607 | if (ctx == NULL) | |
608 | { | |
609 | ctx = new_ctx = BN_CTX_new(); | |
610 | if (ctx == NULL) | |
611 | return 0; | |
612 | } | |
613 | ||
614 | BN_CTX_start(ctx); | |
615 | x = BN_CTX_get(ctx); | |
616 | y = BN_CTX_get(ctx); | |
617 | yxi = BN_CTX_get(ctx); | |
618 | if (yxi == NULL) goto err; | |
619 | ||
620 | if (!BN_bin2bn(buf + 1, field_len, x)) goto err; | |
621 | if (BN_ucmp(x, &group->field) >= 0) | |
622 | { | |
623 | ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); | |
624 | goto err; | |
625 | } | |
626 | ||
627 | if (form == POINT_CONVERSION_COMPRESSED) | |
628 | { | |
629 | if (!EC_POINT_set_compressed_coordinates_GF2m(group, point, x, y_bit, ctx)) goto err; | |
630 | } | |
631 | else | |
632 | { | |
633 | if (!BN_bin2bn(buf + 1 + field_len, field_len, y)) goto err; | |
634 | if (BN_ucmp(y, &group->field) >= 0) | |
635 | { | |
636 | ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); | |
637 | goto err; | |
638 | } | |
639 | if (form == POINT_CONVERSION_HYBRID) | |
640 | { | |
641 | if (!group->meth->field_div(group, yxi, y, x, ctx)) goto err; | |
642 | if (y_bit != BN_is_odd(yxi)) | |
643 | { | |
644 | ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); | |
645 | goto err; | |
646 | } | |
647 | } | |
648 | ||
649 | if (!EC_POINT_set_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err; | |
650 | } | |
651 | ||
652 | if (!EC_POINT_is_on_curve(group, point, ctx)) /* test required by X9.62 */ | |
653 | { | |
654 | ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_POINT_IS_NOT_ON_CURVE); | |
655 | goto err; | |
656 | } | |
657 | ||
658 | ret = 1; | |
659 | ||
660 | err: | |
661 | BN_CTX_end(ctx); | |
662 | if (new_ctx != NULL) | |
663 | BN_CTX_free(new_ctx); | |
664 | return ret; | |
665 | } | |
666 | ||
667 | ||
668 | /* Computes a + b and stores the result in r. r could be a or b, a could be b. | |
669 | * Uses algorithm A.10.2 of IEEE P1363. | |
670 | */ | |
671 | int ec_GF2m_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx) | |
672 | { | |
673 | BN_CTX *new_ctx = NULL; | |
674 | BIGNUM *x0, *y0, *x1, *y1, *x2, *y2, *s, *t; | |
675 | int ret = 0; | |
676 | ||
677 | if (EC_POINT_is_at_infinity(group, a)) | |
678 | { | |
679 | if (!EC_POINT_copy(r, b)) return 0; | |
680 | return 1; | |
681 | } | |
682 | ||
683 | if (EC_POINT_is_at_infinity(group, b)) | |
684 | { | |
685 | if (!EC_POINT_copy(r, a)) return 0; | |
686 | return 1; | |
687 | } | |
688 | ||
689 | if (ctx == NULL) | |
690 | { | |
691 | ctx = new_ctx = BN_CTX_new(); | |
692 | if (ctx == NULL) | |
693 | return 0; | |
694 | } | |
695 | ||
696 | BN_CTX_start(ctx); | |
697 | x0 = BN_CTX_get(ctx); | |
698 | y0 = BN_CTX_get(ctx); | |
699 | x1 = BN_CTX_get(ctx); | |
700 | y1 = BN_CTX_get(ctx); | |
701 | x2 = BN_CTX_get(ctx); | |
702 | y2 = BN_CTX_get(ctx); | |
703 | s = BN_CTX_get(ctx); | |
704 | t = BN_CTX_get(ctx); | |
705 | if (t == NULL) goto err; | |
706 | ||
707 | if (a->Z_is_one) | |
708 | { | |
709 | if (!BN_copy(x0, &a->X)) goto err; | |
710 | if (!BN_copy(y0, &a->Y)) goto err; | |
711 | } | |
712 | else | |
713 | { | |
714 | if (!EC_POINT_get_affine_coordinates_GF2m(group, a, x0, y0, ctx)) goto err; | |
715 | } | |
716 | if (b->Z_is_one) | |
717 | { | |
718 | if (!BN_copy(x1, &b->X)) goto err; | |
719 | if (!BN_copy(y1, &b->Y)) goto err; | |
720 | } | |
721 | else | |
722 | { | |
723 | if (!EC_POINT_get_affine_coordinates_GF2m(group, b, x1, y1, ctx)) goto err; | |
724 | } | |
725 | ||
726 | ||
727 | if (BN_GF2m_cmp(x0, x1)) | |
728 | { | |
729 | if (!BN_GF2m_add(t, x0, x1)) goto err; | |
730 | if (!BN_GF2m_add(s, y0, y1)) goto err; | |
731 | if (!group->meth->field_div(group, s, s, t, ctx)) goto err; | |
732 | if (!group->meth->field_sqr(group, x2, s, ctx)) goto err; | |
733 | if (!BN_GF2m_add(x2, x2, &group->a)) goto err; | |
734 | if (!BN_GF2m_add(x2, x2, s)) goto err; | |
735 | if (!BN_GF2m_add(x2, x2, t)) goto err; | |
736 | } | |
737 | else | |
738 | { | |
739 | if (BN_GF2m_cmp(y0, y1) || BN_is_zero(x1)) | |
740 | { | |
741 | if (!EC_POINT_set_to_infinity(group, r)) goto err; | |
742 | ret = 1; | |
743 | goto err; | |
744 | } | |
745 | if (!group->meth->field_div(group, s, y1, x1, ctx)) goto err; | |
746 | if (!BN_GF2m_add(s, s, x1)) goto err; | |
747 | ||
748 | if (!group->meth->field_sqr(group, x2, s, ctx)) goto err; | |
749 | if (!BN_GF2m_add(x2, x2, s)) goto err; | |
750 | if (!BN_GF2m_add(x2, x2, &group->a)) goto err; | |
751 | } | |
752 | ||
753 | if (!BN_GF2m_add(y2, x1, x2)) goto err; | |
754 | if (!group->meth->field_mul(group, y2, y2, s, ctx)) goto err; | |
755 | if (!BN_GF2m_add(y2, y2, x2)) goto err; | |
756 | if (!BN_GF2m_add(y2, y2, y1)) goto err; | |
757 | ||
758 | if (!EC_POINT_set_affine_coordinates_GF2m(group, r, x2, y2, ctx)) goto err; | |
759 | ||
760 | ret = 1; | |
761 | ||
762 | err: | |
763 | BN_CTX_end(ctx); | |
764 | if (new_ctx != NULL) | |
765 | BN_CTX_free(new_ctx); | |
766 | return ret; | |
767 | } | |
768 | ||
769 | ||
770 | /* Computes 2 * a and stores the result in r. r could be a. | |
771 | * Uses algorithm A.10.2 of IEEE P1363. | |
772 | */ | |
773 | int ec_GF2m_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_CTX *ctx) | |
774 | { | |
775 | return ec_GF2m_simple_add(group, r, a, a, ctx); | |
776 | } | |
777 | ||
778 | ||
779 | int ec_GF2m_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx) | |
780 | { | |
781 | if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(&point->Y)) | |
782 | /* point is its own inverse */ | |
783 | return 1; | |
784 | ||
785 | if (!EC_POINT_make_affine(group, point, ctx)) return 0; | |
786 | return BN_GF2m_add(&point->Y, &point->X, &point->Y); | |
787 | } | |
788 | ||
789 | ||
790 | /* Indicates whether the given point is the point at infinity. */ | |
791 | int ec_GF2m_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point) | |
792 | { | |
793 | return BN_is_zero(&point->Z); | |
794 | } | |
795 | ||
796 | ||
797 | /* Determines whether the given EC_POINT is an actual point on the curve defined | |
798 | * in the EC_GROUP. A point is valid if it satisfies the Weierstrass equation: | |
799 | * y^2 + x*y = x^3 + a*x^2 + b. | |
800 | */ | |
801 | int ec_GF2m_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx) | |
802 | { | |
803 | BN_CTX *new_ctx = NULL; | |
804 | BIGNUM *rh, *lh, *tmp1; | |
805 | int ret = -1; | |
806 | ||
807 | if (EC_POINT_is_at_infinity(group, point)) | |
808 | return 1; | |
809 | ||
810 | /* only support affine coordinates */ | |
811 | if (!point->Z_is_one) goto err; | |
812 | ||
813 | if (ctx == NULL) | |
814 | { | |
815 | ctx = new_ctx = BN_CTX_new(); | |
816 | if (ctx == NULL) | |
817 | return -1; | |
818 | } | |
819 | ||
820 | BN_CTX_start(ctx); | |
821 | rh = BN_CTX_get(ctx); | |
822 | lh = BN_CTX_get(ctx); | |
823 | tmp1 = BN_CTX_get(ctx); | |
824 | if (tmp1 == NULL) goto err; | |
825 | ||
826 | /* We have a curve defined by a Weierstrass equation | |
827 | * y^2 + x*y = x^3 + a*x^2 + b. | |
828 | * To test this, we add up the right-hand side in 'rh' | |
829 | * and the left-hand side in 'lh'. | |
830 | */ | |
831 | ||
832 | /* rh := X^3 */ | |
833 | if (!group->meth->field_sqr(group, tmp1, &point->X, ctx)) goto err; | |
834 | if (!group->meth->field_mul(group, rh, tmp1, &point->X, ctx)) goto err; | |
835 | ||
836 | /* rh := rh + a*X^2 */ | |
837 | if (!group->meth->field_mul(group, tmp1, tmp1, &group->a, ctx)) goto err; | |
838 | if (!BN_GF2m_add(rh, rh, tmp1)) goto err; | |
839 | ||
840 | /* rh := rh + b */ | |
841 | if (!BN_GF2m_add(rh, rh, &group->b)) goto err; | |
842 | ||
843 | /* lh := Y^2 */ | |
844 | if (!group->meth->field_sqr(group, lh, &point->Y, ctx)) goto err; | |
845 | ||
846 | /* lh := lh + x*y */ | |
847 | if (!group->meth->field_mul(group, tmp1, &point->X, &point->Y, ctx)) goto err; | |
848 | if (!BN_GF2m_add(lh, lh, tmp1)) goto err; | |
849 | ||
850 | ret = (0 == BN_GF2m_cmp(lh, rh)); | |
851 | ||
852 | err: | |
853 | if (ctx) BN_CTX_end(ctx); | |
854 | if (new_ctx) BN_CTX_free(new_ctx); | |
855 | return ret; | |
856 | } | |
857 | ||
858 | ||
859 | /* Indicates whether two points are equal. | |
860 | * Return values: | |
861 | * -1 error | |
862 | * 0 equal (in affine coordinates) | |
863 | * 1 not equal | |
864 | */ | |
865 | int ec_GF2m_simple_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx) | |
866 | { | |
867 | BIGNUM *aX, *aY, *bX, *bY; | |
868 | BN_CTX *new_ctx = NULL; | |
869 | int ret = -1; | |
870 | ||
871 | if (EC_POINT_is_at_infinity(group, a)) | |
872 | { | |
873 | return EC_POINT_is_at_infinity(group, b) ? 0 : 1; | |
874 | } | |
875 | ||
876 | if (a->Z_is_one && b->Z_is_one) | |
877 | { | |
878 | return ((BN_cmp(&a->X, &b->X) == 0) && BN_cmp(&a->Y, &b->Y) == 0) ? 0 : 1; | |
879 | } | |
880 | ||
881 | if (ctx == NULL) | |
882 | { | |
883 | ctx = new_ctx = BN_CTX_new(); | |
884 | if (ctx == NULL) | |
885 | return -1; | |
886 | } | |
887 | ||
888 | BN_CTX_start(ctx); | |
889 | aX = BN_CTX_get(ctx); | |
890 | aY = BN_CTX_get(ctx); | |
891 | bX = BN_CTX_get(ctx); | |
892 | bY = BN_CTX_get(ctx); | |
893 | if (bY == NULL) goto err; | |
894 | ||
895 | if (!EC_POINT_get_affine_coordinates_GF2m(group, a, aX, aY, ctx)) goto err; | |
896 | if (!EC_POINT_get_affine_coordinates_GF2m(group, b, bX, bY, ctx)) goto err; | |
897 | ret = ((BN_cmp(aX, bX) == 0) && BN_cmp(aY, bY) == 0) ? 0 : 1; | |
898 | ||
899 | err: | |
900 | if (ctx) BN_CTX_end(ctx); | |
901 | if (new_ctx) BN_CTX_free(new_ctx); | |
902 | return ret; | |
903 | } | |
904 | ||
905 | ||
906 | /* Forces the given EC_POINT to internally use affine coordinates. */ | |
907 | int ec_GF2m_simple_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx) | |
908 | { | |
909 | BN_CTX *new_ctx = NULL; | |
910 | BIGNUM *x, *y; | |
911 | int ret = 0; | |
912 | ||
913 | if (point->Z_is_one || EC_POINT_is_at_infinity(group, point)) | |
914 | return 1; | |
915 | ||
916 | if (ctx == NULL) | |
917 | { | |
918 | ctx = new_ctx = BN_CTX_new(); | |
919 | if (ctx == NULL) | |
920 | return 0; | |
921 | } | |
922 | ||
923 | BN_CTX_start(ctx); | |
924 | x = BN_CTX_get(ctx); | |
925 | y = BN_CTX_get(ctx); | |
926 | if (y == NULL) goto err; | |
927 | ||
928 | if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err; | |
929 | if (!BN_copy(&point->X, x)) goto err; | |
930 | if (!BN_copy(&point->Y, y)) goto err; | |
931 | if (!BN_one(&point->Z)) goto err; | |
932 | ||
933 | ret = 1; | |
934 | ||
935 | err: | |
936 | if (ctx) BN_CTX_end(ctx); | |
937 | if (new_ctx) BN_CTX_free(new_ctx); | |
938 | return ret; | |
939 | } | |
940 | ||
941 | ||
942 | /* Forces each of the EC_POINTs in the given array to use affine coordinates. */ | |
943 | int ec_GF2m_simple_points_make_affine(const EC_GROUP *group, size_t num, EC_POINT *points[], BN_CTX *ctx) | |
944 | { | |
945 | size_t i; | |
946 | ||
947 | for (i = 0; i < num; i++) | |
948 | { | |
949 | if (!group->meth->make_affine(group, points[i], ctx)) return 0; | |
950 | } | |
951 | ||
952 | return 1; | |
953 | } | |
954 | ||
955 | ||
956 | /* Wrapper to simple binary polynomial field multiplication implementation. */ | |
957 | int ec_GF2m_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) | |
958 | { | |
959 | return BN_GF2m_mod_mul_arr(r, a, b, group->poly, ctx); | |
960 | } | |
961 | ||
962 | ||
963 | /* Wrapper to simple binary polynomial field squaring implementation. */ | |
964 | int ec_GF2m_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx) | |
965 | { | |
966 | return BN_GF2m_mod_sqr_arr(r, a, group->poly, ctx); | |
967 | } | |
968 | ||
969 | ||
970 | /* Wrapper to simple binary polynomial field division implementation. */ | |
971 | int ec_GF2m_simple_field_div(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) | |
972 | { | |
973 | return BN_GF2m_mod_div(r, a, b, &group->field, ctx); | |
974 | } |