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 *
12 * The software is originally written by Sheueling Chang Shantz and
13 * Douglas Stebila of Sun Microsystems Laboratories.
14 *
15 */
16 /* ====================================================================
17 * Copyright (c) 1998-2005 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 #ifndef OPENSSL_NO_EC2M
75
76 #ifdef OPENSSL_FIPS
77 #include <openssl/fips.h>
78 #endif
79
80
EC_GF2m_simple_method(void)81 const EC_METHOD *EC_GF2m_simple_method(void)
82 {
83 static const EC_METHOD ret = {
84 EC_FLAGS_DEFAULT_OCT,
85 NID_X9_62_characteristic_two_field,
86 ec_GF2m_simple_group_init,
87 ec_GF2m_simple_group_finish,
88 ec_GF2m_simple_group_clear_finish,
89 ec_GF2m_simple_group_copy,
90 ec_GF2m_simple_group_set_curve,
91 ec_GF2m_simple_group_get_curve,
92 ec_GF2m_simple_group_get_degree,
93 ec_GF2m_simple_group_check_discriminant,
94 ec_GF2m_simple_point_init,
95 ec_GF2m_simple_point_finish,
96 ec_GF2m_simple_point_clear_finish,
97 ec_GF2m_simple_point_copy,
98 ec_GF2m_simple_point_set_to_infinity,
99 0 /* set_Jprojective_coordinates_GFp */,
100 0 /* get_Jprojective_coordinates_GFp */,
101 ec_GF2m_simple_point_set_affine_coordinates,
102 ec_GF2m_simple_point_get_affine_coordinates,
103 0,0,0,
104 ec_GF2m_simple_add,
105 ec_GF2m_simple_dbl,
106 ec_GF2m_simple_invert,
107 ec_GF2m_simple_is_at_infinity,
108 ec_GF2m_simple_is_on_curve,
109 ec_GF2m_simple_cmp,
110 ec_GF2m_simple_make_affine,
111 ec_GF2m_simple_points_make_affine,
112
113 /* the following three method functions are defined in ec2_mult.c */
114 ec_GF2m_simple_mul,
115 ec_GF2m_precompute_mult,
116 ec_GF2m_have_precompute_mult,
117
118 ec_GF2m_simple_field_mul,
119 ec_GF2m_simple_field_sqr,
120 ec_GF2m_simple_field_div,
121 0 /* field_encode */,
122 0 /* field_decode */,
123 0 /* field_set_to_one */ };
124
125 #ifdef OPENSSL_FIPS
126 if (FIPS_mode())
127 return fips_ec_gf2m_simple_method();
128 #endif
129
130 return &ret;
131 }
132
133
134 /* Initialize a GF(2^m)-based EC_GROUP structure.
135 * Note that all other members are handled by EC_GROUP_new.
136 */
ec_GF2m_simple_group_init(EC_GROUP * group)137 int ec_GF2m_simple_group_init(EC_GROUP *group)
138 {
139 BN_init(&group->field);
140 BN_init(&group->a);
141 BN_init(&group->b);
142 return 1;
143 }
144
145
146 /* Free a GF(2^m)-based EC_GROUP structure.
147 * Note that all other members are handled by EC_GROUP_free.
148 */
ec_GF2m_simple_group_finish(EC_GROUP * group)149 void ec_GF2m_simple_group_finish(EC_GROUP *group)
150 {
151 BN_free(&group->field);
152 BN_free(&group->a);
153 BN_free(&group->b);
154 }
155
156
157 /* Clear and free a GF(2^m)-based EC_GROUP structure.
158 * Note that all other members are handled by EC_GROUP_clear_free.
159 */
ec_GF2m_simple_group_clear_finish(EC_GROUP * group)160 void ec_GF2m_simple_group_clear_finish(EC_GROUP *group)
161 {
162 BN_clear_free(&group->field);
163 BN_clear_free(&group->a);
164 BN_clear_free(&group->b);
165 group->poly[0] = 0;
166 group->poly[1] = 0;
167 group->poly[2] = 0;
168 group->poly[3] = 0;
169 group->poly[4] = 0;
170 group->poly[5] = -1;
171 }
172
173
174 /* Copy a GF(2^m)-based EC_GROUP structure.
175 * Note that all other members are handled by EC_GROUP_copy.
176 */
ec_GF2m_simple_group_copy(EC_GROUP * dest,const EC_GROUP * src)177 int ec_GF2m_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src)
178 {
179 int i;
180 if (!BN_copy(&dest->field, &src->field)) return 0;
181 if (!BN_copy(&dest->a, &src->a)) return 0;
182 if (!BN_copy(&dest->b, &src->b)) return 0;
183 dest->poly[0] = src->poly[0];
184 dest->poly[1] = src->poly[1];
185 dest->poly[2] = src->poly[2];
186 dest->poly[3] = src->poly[3];
187 dest->poly[4] = src->poly[4];
188 dest->poly[5] = src->poly[5];
189 if (bn_wexpand(&dest->a, (int)(dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) return 0;
190 if (bn_wexpand(&dest->b, (int)(dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) return 0;
191 for (i = dest->a.top; i < dest->a.dmax; i++) dest->a.d[i] = 0;
192 for (i = dest->b.top; i < dest->b.dmax; i++) dest->b.d[i] = 0;
193 return 1;
194 }
195
196
197 /* Set the curve parameters of an EC_GROUP structure. */
ec_GF2m_simple_group_set_curve(EC_GROUP * group,const BIGNUM * p,const BIGNUM * a,const BIGNUM * b,BN_CTX * ctx)198 int ec_GF2m_simple_group_set_curve(EC_GROUP *group,
199 const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
200 {
201 int ret = 0, i;
202
203 /* group->field */
204 if (!BN_copy(&group->field, p)) goto err;
205 i = BN_GF2m_poly2arr(&group->field, group->poly, 6) - 1;
206 if ((i != 5) && (i != 3))
207 {
208 ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_SET_CURVE, EC_R_UNSUPPORTED_FIELD);
209 goto err;
210 }
211
212 /* group->a */
213 if (!BN_GF2m_mod_arr(&group->a, a, group->poly)) goto err;
214 if(bn_wexpand(&group->a, (int)(group->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) goto err;
215 for (i = group->a.top; i < group->a.dmax; i++) group->a.d[i] = 0;
216
217 /* group->b */
218 if (!BN_GF2m_mod_arr(&group->b, b, group->poly)) goto err;
219 if(bn_wexpand(&group->b, (int)(group->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) goto err;
220 for (i = group->b.top; i < group->b.dmax; i++) group->b.d[i] = 0;
221
222 ret = 1;
223 err:
224 return ret;
225 }
226
227
228 /* Get the curve parameters of an EC_GROUP structure.
229 * If p, a, or b are NULL then there values will not be set but the method will return with success.
230 */
ec_GF2m_simple_group_get_curve(const EC_GROUP * group,BIGNUM * p,BIGNUM * a,BIGNUM * b,BN_CTX * ctx)231 int ec_GF2m_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx)
232 {
233 int ret = 0;
234
235 if (p != NULL)
236 {
237 if (!BN_copy(p, &group->field)) return 0;
238 }
239
240 if (a != NULL)
241 {
242 if (!BN_copy(a, &group->a)) goto err;
243 }
244
245 if (b != NULL)
246 {
247 if (!BN_copy(b, &group->b)) goto err;
248 }
249
250 ret = 1;
251
252 err:
253 return ret;
254 }
255
256
257 /* Gets the degree of the field. For a curve over GF(2^m) this is the value m. */
ec_GF2m_simple_group_get_degree(const EC_GROUP * group)258 int ec_GF2m_simple_group_get_degree(const EC_GROUP *group)
259 {
260 return BN_num_bits(&group->field)-1;
261 }
262
263
264 /* Checks the discriminant of the curve.
265 * y^2 + x*y = x^3 + a*x^2 + b is an elliptic curve <=> b != 0 (mod p)
266 */
ec_GF2m_simple_group_check_discriminant(const EC_GROUP * group,BN_CTX * ctx)267 int ec_GF2m_simple_group_check_discriminant(const EC_GROUP *group, BN_CTX *ctx)
268 {
269 int ret = 0;
270 BIGNUM *b;
271 BN_CTX *new_ctx = NULL;
272
273 if (ctx == NULL)
274 {
275 ctx = new_ctx = BN_CTX_new();
276 if (ctx == NULL)
277 {
278 ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_CHECK_DISCRIMINANT, ERR_R_MALLOC_FAILURE);
279 goto err;
280 }
281 }
282 BN_CTX_start(ctx);
283 b = BN_CTX_get(ctx);
284 if (b == NULL) goto err;
285
286 if (!BN_GF2m_mod_arr(b, &group->b, group->poly)) goto err;
287
288 /* check the discriminant:
289 * y^2 + x*y = x^3 + a*x^2 + b is an elliptic curve <=> b != 0 (mod p)
290 */
291 if (BN_is_zero(b)) goto err;
292
293 ret = 1;
294
295 err:
296 if (ctx != NULL)
297 BN_CTX_end(ctx);
298 if (new_ctx != NULL)
299 BN_CTX_free(new_ctx);
300 return ret;
301 }
302
303
304 /* Initializes an EC_POINT. */
ec_GF2m_simple_point_init(EC_POINT * point)305 int ec_GF2m_simple_point_init(EC_POINT *point)
306 {
307 BN_init(&point->X);
308 BN_init(&point->Y);
309 BN_init(&point->Z);
310 return 1;
311 }
312
313
314 /* Frees an EC_POINT. */
ec_GF2m_simple_point_finish(EC_POINT * point)315 void ec_GF2m_simple_point_finish(EC_POINT *point)
316 {
317 BN_free(&point->X);
318 BN_free(&point->Y);
319 BN_free(&point->Z);
320 }
321
322
323 /* Clears and frees an EC_POINT. */
ec_GF2m_simple_point_clear_finish(EC_POINT * point)324 void ec_GF2m_simple_point_clear_finish(EC_POINT *point)
325 {
326 BN_clear_free(&point->X);
327 BN_clear_free(&point->Y);
328 BN_clear_free(&point->Z);
329 point->Z_is_one = 0;
330 }
331
332
333 /* Copy the contents of one EC_POINT into another. Assumes dest is initialized. */
ec_GF2m_simple_point_copy(EC_POINT * dest,const EC_POINT * src)334 int ec_GF2m_simple_point_copy(EC_POINT *dest, const EC_POINT *src)
335 {
336 if (!BN_copy(&dest->X, &src->X)) return 0;
337 if (!BN_copy(&dest->Y, &src->Y)) return 0;
338 if (!BN_copy(&dest->Z, &src->Z)) return 0;
339 dest->Z_is_one = src->Z_is_one;
340
341 return 1;
342 }
343
344
345 /* Set an EC_POINT to the point at infinity.
346 * A point at infinity is represented by having Z=0.
347 */
ec_GF2m_simple_point_set_to_infinity(const EC_GROUP * group,EC_POINT * point)348 int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *group, EC_POINT *point)
349 {
350 point->Z_is_one = 0;
351 BN_zero(&point->Z);
352 return 1;
353 }
354
355
356 /* Set the coordinates of an EC_POINT using affine coordinates.
357 * Note that the simple implementation only uses affine coordinates.
358 */
ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP * group,EC_POINT * point,const BIGNUM * x,const BIGNUM * y,BN_CTX * ctx)359 int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *group, EC_POINT *point,
360 const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx)
361 {
362 int ret = 0;
363 if (x == NULL || y == NULL)
364 {
365 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_SET_AFFINE_COORDINATES, ERR_R_PASSED_NULL_PARAMETER);
366 return 0;
367 }
368
369 if (!BN_copy(&point->X, x)) goto err;
370 BN_set_negative(&point->X, 0);
371 if (!BN_copy(&point->Y, y)) goto err;
372 BN_set_negative(&point->Y, 0);
373 if (!BN_copy(&point->Z, BN_value_one())) goto err;
374 BN_set_negative(&point->Z, 0);
375 point->Z_is_one = 1;
376 ret = 1;
377
378 err:
379 return ret;
380 }
381
382
383 /* Gets the affine coordinates of an EC_POINT.
384 * Note that the simple implementation only uses affine coordinates.
385 */
ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP * group,const EC_POINT * point,BIGNUM * x,BIGNUM * y,BN_CTX * ctx)386 int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point,
387 BIGNUM *x, BIGNUM *y, BN_CTX *ctx)
388 {
389 int ret = 0;
390
391 if (EC_POINT_is_at_infinity(group, point))
392 {
393 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES, EC_R_POINT_AT_INFINITY);
394 return 0;
395 }
396
397 if (BN_cmp(&point->Z, BN_value_one()))
398 {
399 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
400 return 0;
401 }
402 if (x != NULL)
403 {
404 if (!BN_copy(x, &point->X)) goto err;
405 BN_set_negative(x, 0);
406 }
407 if (y != NULL)
408 {
409 if (!BN_copy(y, &point->Y)) goto err;
410 BN_set_negative(y, 0);
411 }
412 ret = 1;
413
414 err:
415 return ret;
416 }
417
418 /* Computes a + b and stores the result in r. r could be a or b, a could be b.
419 * Uses algorithm A.10.2 of IEEE P1363.
420 */
ec_GF2m_simple_add(const EC_GROUP * group,EC_POINT * r,const EC_POINT * a,const EC_POINT * b,BN_CTX * ctx)421 int ec_GF2m_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
422 {
423 BN_CTX *new_ctx = NULL;
424 BIGNUM *x0, *y0, *x1, *y1, *x2, *y2, *s, *t;
425 int ret = 0;
426
427 if (EC_POINT_is_at_infinity(group, a))
428 {
429 if (!EC_POINT_copy(r, b)) return 0;
430 return 1;
431 }
432
433 if (EC_POINT_is_at_infinity(group, b))
434 {
435 if (!EC_POINT_copy(r, a)) return 0;
436 return 1;
437 }
438
439 if (ctx == NULL)
440 {
441 ctx = new_ctx = BN_CTX_new();
442 if (ctx == NULL)
443 return 0;
444 }
445
446 BN_CTX_start(ctx);
447 x0 = BN_CTX_get(ctx);
448 y0 = BN_CTX_get(ctx);
449 x1 = BN_CTX_get(ctx);
450 y1 = BN_CTX_get(ctx);
451 x2 = BN_CTX_get(ctx);
452 y2 = BN_CTX_get(ctx);
453 s = BN_CTX_get(ctx);
454 t = BN_CTX_get(ctx);
455 if (t == NULL) goto err;
456
457 if (a->Z_is_one)
458 {
459 if (!BN_copy(x0, &a->X)) goto err;
460 if (!BN_copy(y0, &a->Y)) goto err;
461 }
462 else
463 {
464 if (!EC_POINT_get_affine_coordinates_GF2m(group, a, x0, y0, ctx)) goto err;
465 }
466 if (b->Z_is_one)
467 {
468 if (!BN_copy(x1, &b->X)) goto err;
469 if (!BN_copy(y1, &b->Y)) goto err;
470 }
471 else
472 {
473 if (!EC_POINT_get_affine_coordinates_GF2m(group, b, x1, y1, ctx)) goto err;
474 }
475
476
477 if (BN_GF2m_cmp(x0, x1))
478 {
479 if (!BN_GF2m_add(t, x0, x1)) goto err;
480 if (!BN_GF2m_add(s, y0, y1)) goto err;
481 if (!group->meth->field_div(group, s, s, t, ctx)) goto err;
482 if (!group->meth->field_sqr(group, x2, s, ctx)) goto err;
483 if (!BN_GF2m_add(x2, x2, &group->a)) goto err;
484 if (!BN_GF2m_add(x2, x2, s)) goto err;
485 if (!BN_GF2m_add(x2, x2, t)) goto err;
486 }
487 else
488 {
489 if (BN_GF2m_cmp(y0, y1) || BN_is_zero(x1))
490 {
491 if (!EC_POINT_set_to_infinity(group, r)) goto err;
492 ret = 1;
493 goto err;
494 }
495 if (!group->meth->field_div(group, s, y1, x1, ctx)) goto err;
496 if (!BN_GF2m_add(s, s, x1)) goto err;
497
498 if (!group->meth->field_sqr(group, x2, s, ctx)) goto err;
499 if (!BN_GF2m_add(x2, x2, s)) goto err;
500 if (!BN_GF2m_add(x2, x2, &group->a)) goto err;
501 }
502
503 if (!BN_GF2m_add(y2, x1, x2)) goto err;
504 if (!group->meth->field_mul(group, y2, y2, s, ctx)) goto err;
505 if (!BN_GF2m_add(y2, y2, x2)) goto err;
506 if (!BN_GF2m_add(y2, y2, y1)) goto err;
507
508 if (!EC_POINT_set_affine_coordinates_GF2m(group, r, x2, y2, ctx)) goto err;
509
510 ret = 1;
511
512 err:
513 BN_CTX_end(ctx);
514 if (new_ctx != NULL)
515 BN_CTX_free(new_ctx);
516 return ret;
517 }
518
519
520 /* Computes 2 * a and stores the result in r. r could be a.
521 * Uses algorithm A.10.2 of IEEE P1363.
522 */
ec_GF2m_simple_dbl(const EC_GROUP * group,EC_POINT * r,const EC_POINT * a,BN_CTX * ctx)523 int ec_GF2m_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_CTX *ctx)
524 {
525 return ec_GF2m_simple_add(group, r, a, a, ctx);
526 }
527
528
ec_GF2m_simple_invert(const EC_GROUP * group,EC_POINT * point,BN_CTX * ctx)529 int ec_GF2m_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
530 {
531 if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(&point->Y))
532 /* point is its own inverse */
533 return 1;
534
535 if (!EC_POINT_make_affine(group, point, ctx)) return 0;
536 return BN_GF2m_add(&point->Y, &point->X, &point->Y);
537 }
538
539
540 /* Indicates whether the given point is the point at infinity. */
ec_GF2m_simple_is_at_infinity(const EC_GROUP * group,const EC_POINT * point)541 int ec_GF2m_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point)
542 {
543 return BN_is_zero(&point->Z);
544 }
545
546
547 /* Determines whether the given EC_POINT is an actual point on the curve defined
548 * in the EC_GROUP. A point is valid if it satisfies the Weierstrass equation:
549 * y^2 + x*y = x^3 + a*x^2 + b.
550 */
ec_GF2m_simple_is_on_curve(const EC_GROUP * group,const EC_POINT * point,BN_CTX * ctx)551 int ec_GF2m_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx)
552 {
553 int ret = -1;
554 BN_CTX *new_ctx = NULL;
555 BIGNUM *lh, *y2;
556 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
557 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
558
559 if (EC_POINT_is_at_infinity(group, point))
560 return 1;
561
562 field_mul = group->meth->field_mul;
563 field_sqr = group->meth->field_sqr;
564
565 /* only support affine coordinates */
566 if (!point->Z_is_one) return -1;
567
568 if (ctx == NULL)
569 {
570 ctx = new_ctx = BN_CTX_new();
571 if (ctx == NULL)
572 return -1;
573 }
574
575 BN_CTX_start(ctx);
576 y2 = BN_CTX_get(ctx);
577 lh = BN_CTX_get(ctx);
578 if (lh == NULL) goto err;
579
580 /* We have a curve defined by a Weierstrass equation
581 * y^2 + x*y = x^3 + a*x^2 + b.
582 * <=> x^3 + a*x^2 + x*y + b + y^2 = 0
583 * <=> ((x + a) * x + y ) * x + b + y^2 = 0
584 */
585 if (!BN_GF2m_add(lh, &point->X, &group->a)) goto err;
586 if (!field_mul(group, lh, lh, &point->X, ctx)) goto err;
587 if (!BN_GF2m_add(lh, lh, &point->Y)) goto err;
588 if (!field_mul(group, lh, lh, &point->X, ctx)) goto err;
589 if (!BN_GF2m_add(lh, lh, &group->b)) goto err;
590 if (!field_sqr(group, y2, &point->Y, ctx)) goto err;
591 if (!BN_GF2m_add(lh, lh, y2)) goto err;
592 ret = BN_is_zero(lh);
593 err:
594 if (ctx) BN_CTX_end(ctx);
595 if (new_ctx) BN_CTX_free(new_ctx);
596 return ret;
597 }
598
599
600 /* Indicates whether two points are equal.
601 * Return values:
602 * -1 error
603 * 0 equal (in affine coordinates)
604 * 1 not equal
605 */
ec_GF2m_simple_cmp(const EC_GROUP * group,const EC_POINT * a,const EC_POINT * b,BN_CTX * ctx)606 int ec_GF2m_simple_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
607 {
608 BIGNUM *aX, *aY, *bX, *bY;
609 BN_CTX *new_ctx = NULL;
610 int ret = -1;
611
612 if (EC_POINT_is_at_infinity(group, a))
613 {
614 return EC_POINT_is_at_infinity(group, b) ? 0 : 1;
615 }
616
617 if (EC_POINT_is_at_infinity(group, b))
618 return 1;
619
620 if (a->Z_is_one && b->Z_is_one)
621 {
622 return ((BN_cmp(&a->X, &b->X) == 0) && BN_cmp(&a->Y, &b->Y) == 0) ? 0 : 1;
623 }
624
625 if (ctx == NULL)
626 {
627 ctx = new_ctx = BN_CTX_new();
628 if (ctx == NULL)
629 return -1;
630 }
631
632 BN_CTX_start(ctx);
633 aX = BN_CTX_get(ctx);
634 aY = BN_CTX_get(ctx);
635 bX = BN_CTX_get(ctx);
636 bY = BN_CTX_get(ctx);
637 if (bY == NULL) goto err;
638
639 if (!EC_POINT_get_affine_coordinates_GF2m(group, a, aX, aY, ctx)) goto err;
640 if (!EC_POINT_get_affine_coordinates_GF2m(group, b, bX, bY, ctx)) goto err;
641 ret = ((BN_cmp(aX, bX) == 0) && BN_cmp(aY, bY) == 0) ? 0 : 1;
642
643 err:
644 if (ctx) BN_CTX_end(ctx);
645 if (new_ctx) BN_CTX_free(new_ctx);
646 return ret;
647 }
648
649
650 /* Forces the given EC_POINT to internally use affine coordinates. */
ec_GF2m_simple_make_affine(const EC_GROUP * group,EC_POINT * point,BN_CTX * ctx)651 int ec_GF2m_simple_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
652 {
653 BN_CTX *new_ctx = NULL;
654 BIGNUM *x, *y;
655 int ret = 0;
656
657 if (point->Z_is_one || EC_POINT_is_at_infinity(group, point))
658 return 1;
659
660 if (ctx == NULL)
661 {
662 ctx = new_ctx = BN_CTX_new();
663 if (ctx == NULL)
664 return 0;
665 }
666
667 BN_CTX_start(ctx);
668 x = BN_CTX_get(ctx);
669 y = BN_CTX_get(ctx);
670 if (y == NULL) goto err;
671
672 if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err;
673 if (!BN_copy(&point->X, x)) goto err;
674 if (!BN_copy(&point->Y, y)) goto err;
675 if (!BN_one(&point->Z)) goto err;
676
677 ret = 1;
678
679 err:
680 if (ctx) BN_CTX_end(ctx);
681 if (new_ctx) BN_CTX_free(new_ctx);
682 return ret;
683 }
684
685
686 /* Forces each of the EC_POINTs in the given array to use affine coordinates. */
ec_GF2m_simple_points_make_affine(const EC_GROUP * group,size_t num,EC_POINT * points[],BN_CTX * ctx)687 int ec_GF2m_simple_points_make_affine(const EC_GROUP *group, size_t num, EC_POINT *points[], BN_CTX *ctx)
688 {
689 size_t i;
690
691 for (i = 0; i < num; i++)
692 {
693 if (!group->meth->make_affine(group, points[i], ctx)) return 0;
694 }
695
696 return 1;
697 }
698
699
700 /* Wrapper to simple binary polynomial field multiplication implementation. */
ec_GF2m_simple_field_mul(const EC_GROUP * group,BIGNUM * r,const BIGNUM * a,const BIGNUM * b,BN_CTX * ctx)701 int ec_GF2m_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
702 {
703 return BN_GF2m_mod_mul_arr(r, a, b, group->poly, ctx);
704 }
705
706
707 /* Wrapper to simple binary polynomial field squaring implementation. */
ec_GF2m_simple_field_sqr(const EC_GROUP * group,BIGNUM * r,const BIGNUM * a,BN_CTX * ctx)708 int ec_GF2m_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx)
709 {
710 return BN_GF2m_mod_sqr_arr(r, a, group->poly, ctx);
711 }
712
713
714 /* Wrapper to simple binary polynomial field division implementation. */
ec_GF2m_simple_field_div(const EC_GROUP * group,BIGNUM * r,const BIGNUM * a,const BIGNUM * b,BN_CTX * ctx)715 int ec_GF2m_simple_field_div(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
716 {
717 return BN_GF2m_mod_div(r, a, b, &group->field, ctx);
718 }
719
720 #endif
721