]> git.ipfire.org Git - thirdparty/openssl.git/blob - crypto/ec/ec2_smpl.c
projects / thirdparty / openssl.git / blob
? search:


52cb94fb551b9d09455951ef562e5e9a8fa5d75b
[thirdparty/openssl.git] / crypto / ec / ec2_smpl.c
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) 1998-2003 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,
83 ec_GF2m_simple_group_set_curve,
84 ec_GF2m_simple_group_get_curve,
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,
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,
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_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,
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
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;
160 }
161
162
163 /* Copy a GF(2^m)-based EC_GROUP structure.
164 * Note that all other members are handled by EC_GROUP_copy.
165 */
166 int ec_GF2m_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src)
167 {
168 int i;
169 if (!BN_copy(&dest->field, &src->field)) return 0;
170 if (!BN_copy(&dest->a, &src->a)) return 0;
171 if (!BN_copy(&dest->b, &src->b)) return 0;
172 dest->poly[0] = src->poly[0];
173 dest->poly[1] = src->poly[1];
174 dest->poly[2] = src->poly[2];
175 dest->poly[3] = src->poly[3];
176 dest->poly[4] = src->poly[4];
177 if(bn_wexpand(&dest->a, (int)(dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL)
178 return 0;
179 if(bn_wexpand(&dest->b, (int)(dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL)
180 return 0;
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. */
188 int ec_GF2m_simple_group_set_curve(EC_GROUP *group,
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;
195 i = BN_GF2m_poly2arr(&group->field, group->poly, 5);
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 }
201
202 /* group->a */
203 if (!BN_GF2m_mod_arr(&group->a, a, group->poly)) goto err;
204 if(bn_wexpand(&group->a, (int)(group->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) goto err;
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;
209 if(bn_wexpand(&group->b, (int)(group->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) goto err;
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 */
221 int ec_GF2m_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx)
222 {
223 int ret = 0;
224
225 if (p != NULL)
226 {
227 if (!BN_copy(p, &group->field)) return 0;
228 }
229
230 if (a != NULL)
231 {
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;
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:
286 if (ctx != NULL)
287 BN_CTX_end(ctx);
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;
341 BN_zero(&point->Z);
342 return 1;
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 */
349 int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *group, EC_POINT *point,
350 const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx)
351 {
352 int ret = 0;
353 if (x == NULL || y == NULL)
354 {
355 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_SET_AFFINE_COORDINATES, ERR_R_PASSED_NULL_PARAMETER);
356 return 0;
357 }
358
359 if (!BN_copy(&point->X, x)) goto err;
360 BN_set_negative(&point->X, 0);
361 if (!BN_copy(&point->Y, y)) goto err;
362 BN_set_negative(&point->Y, 0);
363 if (!BN_copy(&point->Z, BN_value_one())) goto err;
364 BN_set_negative(&point->Z, 0);
365 point->Z_is_one = 1;
366 ret = 1;
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 */
376 int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point,
377 BIGNUM *x, BIGNUM *y, BN_CTX *ctx)
378 {
379 int ret = 0;
380
381 if (EC_POINT_is_at_infinity(group, point))
382 {
383 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES, EC_R_POINT_AT_INFINITY);
384 return 0;
385 }
386
387 if (BN_cmp(&point->Z, BN_value_one()))
388 {
389 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
390 return 0;
391 }
392 if (x != NULL)
393 {
394 if (!BN_copy(x, &point->X)) goto err;
395 BN_set_negative(x, 0);
396 }
397 if (y != NULL)
398 {
399 if (!BN_copy(y, &point->Y)) goto err;
400 BN_set_negative(y, 0);
401 }
402 ret = 1;
403
404 err:
405 return ret;
406 }
407
408
409 /* Include patented algorithms. */
410 #include "ec2_smpt.c"
411
412
413 /* Converts an EC_POINT to an octet string.
414 * If buf is NULL, the encoded length will be returned.
415 * If the length len of buf is smaller than required an error will be returned.
416 *
417 * The point compression section of this function is patented by Certicom Corp.
418 * under US Patent 6,141,420. Point compression is disabled by default and can
419 * be enabled by defining the preprocessor macro OPENSSL_EC_BIN_PT_COMP at
420 * Configure-time.
421 */
422 size_t ec_GF2m_simple_point2oct(const EC_GROUP *group, const EC_POINT *point, point_conversion_form_t form,
423 unsigned char *buf, size_t len, BN_CTX *ctx)
424 {
425 size_t ret;
426 BN_CTX *new_ctx = NULL;
427 int used_ctx = 0;
428 BIGNUM *x, *y, *yxi;
429 size_t field_len, i, skip;
430
431 #ifndef OPENSSL_EC_BIN_PT_COMP
432 if ((form == POINT_CONVERSION_COMPRESSED) || (form == POINT_CONVERSION_HYBRID))
433 {
434 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_DISABLED);
435 goto err;
436 }
437 #endif
438
439 if ((form != POINT_CONVERSION_COMPRESSED)
440 && (form != POINT_CONVERSION_UNCOMPRESSED)
441 && (form != POINT_CONVERSION_HYBRID))
442 {
443 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_INVALID_FORM);
444 goto err;
445 }
446
447 if (EC_POINT_is_at_infinity(group, point))
448 {
449 /* encodes to a single 0 octet */
450 if (buf != NULL)
451 {
452 if (len < 1)
453 {
454 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);
455 return 0;
456 }
457 buf[0] = 0;
458 }
459 return 1;
460 }
461
462
463 /* ret := required output buffer length */
464 field_len = (EC_GROUP_get_degree(group) + 7) / 8;
465 ret = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len;
466
467 /* if 'buf' is NULL, just return required length */
468 if (buf != NULL)
469 {
470 if (len < ret)
471 {
472 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);
473 goto err;
474 }
475
476 if (ctx == NULL)
477 {
478 ctx = new_ctx = BN_CTX_new();
479 if (ctx == NULL)
480 return 0;
481 }
482
483 BN_CTX_start(ctx);
484 used_ctx = 1;
485 x = BN_CTX_get(ctx);
486 y = BN_CTX_get(ctx);
487 yxi = BN_CTX_get(ctx);
488 if (yxi == NULL) goto err;
489
490 if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err;
491
492 buf[0] = form;
493 #ifdef OPENSSL_EC_BIN_PT_COMP
494 if ((form != POINT_CONVERSION_UNCOMPRESSED) && !BN_is_zero(x))
495 {
496 if (!group->meth->field_div(group, yxi, y, x, ctx)) goto err;
497 if (BN_is_odd(yxi)) buf[0]++;
498 }
499 #endif
500
501 i = 1;
502
503 skip = field_len - BN_num_bytes(x);
504 if (skip > field_len)
505 {
506 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
507 goto err;
508 }
509 while (skip > 0)
510 {
511 buf[i++] = 0;
512 skip--;
513 }
514 skip = BN_bn2bin(x, buf + i);
515 i += skip;
516 if (i != 1 + field_len)
517 {
518 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
519 goto err;
520 }
521
522 if (form == POINT_CONVERSION_UNCOMPRESSED || form == POINT_CONVERSION_HYBRID)
523 {
524 skip = field_len - BN_num_bytes(y);
525 if (skip > field_len)
526 {
527 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
528 goto err;
529 }
530 while (skip > 0)
531 {
532 buf[i++] = 0;
533 skip--;
534 }
535 skip = BN_bn2bin(y, buf + i);
536 i += skip;
537 }
538
539 if (i != ret)
540 {
541 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
542 goto err;
543 }
544 }
545
546 if (used_ctx)
547 BN_CTX_end(ctx);
548 if (new_ctx != NULL)
549 BN_CTX_free(new_ctx);
550 return ret;
551
552 err:
553 if (used_ctx)
554 BN_CTX_end(ctx);
555 if (new_ctx != NULL)
556 BN_CTX_free(new_ctx);
557 return 0;
558 }
559
560
561 /* Converts an octet string representation to an EC_POINT.
562 * Note that the simple implementation only uses affine coordinates.
563 */
564 int ec_GF2m_simple_oct2point(const EC_GROUP *group, EC_POINT *point,
565 const unsigned char *buf, size_t len, BN_CTX *ctx)
566 {
567 point_conversion_form_t form;
568 int y_bit;
569 BN_CTX *new_ctx = NULL;
570 BIGNUM *x, *y, *yxi;
571 size_t field_len, enc_len;
572 int ret = 0;
573
574 if (len == 0)
575 {
576 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_BUFFER_TOO_SMALL);
577 return 0;
578 }
579 form = buf[0];
580 y_bit = form & 1;
581 form = form & ~1U;
582 if ((form != 0) && (form != POINT_CONVERSION_COMPRESSED)
583 && (form != POINT_CONVERSION_UNCOMPRESSED)
584 && (form != POINT_CONVERSION_HYBRID))
585 {
586 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
587 return 0;
588 }
589 if ((form == 0 || form == POINT_CONVERSION_UNCOMPRESSED) && y_bit)
590 {
591 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
592 return 0;
593 }
594
595 if (form == 0)
596 {
597 if (len != 1)
598 {
599 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
600 return 0;
601 }
602
603 return EC_POINT_set_to_infinity(group, point);
604 }
605
606 field_len = (EC_GROUP_get_degree(group) + 7) / 8;
607 enc_len = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len;
608
609 if (len != enc_len)
610 {
611 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
612 return 0;
613 }
614
615 if (ctx == NULL)
616 {
617 ctx = new_ctx = BN_CTX_new();
618 if (ctx == NULL)
619 return 0;
620 }
621
622 BN_CTX_start(ctx);
623 x = BN_CTX_get(ctx);
624 y = BN_CTX_get(ctx);
625 yxi = BN_CTX_get(ctx);
626 if (yxi == NULL) goto err;
627
628 if (!BN_bin2bn(buf + 1, field_len, x)) goto err;
629 if (BN_ucmp(x, &group->field) >= 0)
630 {
631 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
632 goto err;
633 }
634
635 if (form == POINT_CONVERSION_COMPRESSED)
636 {
637 if (!EC_POINT_set_compressed_coordinates_GF2m(group, point, x, y_bit, ctx)) goto err;
638 }
639 else
640 {
641 if (!BN_bin2bn(buf + 1 + field_len, field_len, y)) goto err;
642 if (BN_ucmp(y, &group->field) >= 0)
643 {
644 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
645 goto err;
646 }
647 if (form == POINT_CONVERSION_HYBRID)
648 {
649 if (!group->meth->field_div(group, yxi, y, x, ctx)) goto err;
650 if (y_bit != BN_is_odd(yxi))
651 {
652 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
653 goto err;
654 }
655 }
656
657 if (!EC_POINT_set_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err;
658 }
659
660 if (!EC_POINT_is_on_curve(group, point, ctx)) /* test required by X9.62 */
661 {
662 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_POINT_IS_NOT_ON_CURVE);
663 goto err;
664 }
665
666 ret = 1;
667
668 err:
669 BN_CTX_end(ctx);
670 if (new_ctx != NULL)
671 BN_CTX_free(new_ctx);
672 return ret;
673 }
674
675
676 /* Computes a + b and stores the result in r. r could be a or b, a could be b.
677 * Uses algorithm A.10.2 of IEEE P1363.
678 */
679 int ec_GF2m_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
680 {
681 BN_CTX *new_ctx = NULL;
682 BIGNUM *x0, *y0, *x1, *y1, *x2, *y2, *s, *t;
683 int ret = 0;
684
685 if (EC_POINT_is_at_infinity(group, a))
686 {
687 if (!EC_POINT_copy(r, b)) return 0;
688 return 1;
689 }
690
691 if (EC_POINT_is_at_infinity(group, b))
692 {
693 if (!EC_POINT_copy(r, a)) return 0;
694 return 1;
695 }
696
697 if (ctx == NULL)
698 {
699 ctx = new_ctx = BN_CTX_new();
700 if (ctx == NULL)
701 return 0;
702 }
703
704 BN_CTX_start(ctx);
705 x0 = BN_CTX_get(ctx);
706 y0 = BN_CTX_get(ctx);
707 x1 = BN_CTX_get(ctx);
708 y1 = BN_CTX_get(ctx);
709 x2 = BN_CTX_get(ctx);
710 y2 = BN_CTX_get(ctx);
711 s = BN_CTX_get(ctx);
712 t = BN_CTX_get(ctx);
713 if (t == NULL) goto err;
714
715 if (a->Z_is_one)
716 {
717 if (!BN_copy(x0, &a->X)) goto err;
718 if (!BN_copy(y0, &a->Y)) goto err;
719 }
720 else
721 {
722 if (!EC_POINT_get_affine_coordinates_GF2m(group, a, x0, y0, ctx)) goto err;
723 }
724 if (b->Z_is_one)
725 {
726 if (!BN_copy(x1, &b->X)) goto err;
727 if (!BN_copy(y1, &b->Y)) goto err;
728 }
729 else
730 {
731 if (!EC_POINT_get_affine_coordinates_GF2m(group, b, x1, y1, ctx)) goto err;
732 }
733
734
735 if (BN_GF2m_cmp(x0, x1))
736 {
737 if (!BN_GF2m_add(t, x0, x1)) goto err;
738 if (!BN_GF2m_add(s, y0, y1)) goto err;
739 if (!group->meth->field_div(group, s, s, t, ctx)) goto err;
740 if (!group->meth->field_sqr(group, x2, s, ctx)) goto err;
741 if (!BN_GF2m_add(x2, x2, &group->a)) goto err;
742 if (!BN_GF2m_add(x2, x2, s)) goto err;
743 if (!BN_GF2m_add(x2, x2, t)) goto err;
744 }
745 else
746 {
747 if (BN_GF2m_cmp(y0, y1) || BN_is_zero(x1))
748 {
749 if (!EC_POINT_set_to_infinity(group, r)) goto err;
750 ret = 1;
751 goto err;
752 }
753 if (!group->meth->field_div(group, s, y1, x1, ctx)) goto err;
754 if (!BN_GF2m_add(s, s, x1)) goto err;
755
756 if (!group->meth->field_sqr(group, x2, s, ctx)) goto err;
757 if (!BN_GF2m_add(x2, x2, s)) goto err;
758 if (!BN_GF2m_add(x2, x2, &group->a)) goto err;
759 }
760
761 if (!BN_GF2m_add(y2, x1, x2)) goto err;
762 if (!group->meth->field_mul(group, y2, y2, s, ctx)) goto err;
763 if (!BN_GF2m_add(y2, y2, x2)) goto err;
764 if (!BN_GF2m_add(y2, y2, y1)) goto err;
765
766 if (!EC_POINT_set_affine_coordinates_GF2m(group, r, x2, y2, ctx)) goto err;
767
768 ret = 1;
769
770 err:
771 BN_CTX_end(ctx);
772 if (new_ctx != NULL)
773 BN_CTX_free(new_ctx);
774 return ret;
775 }
776
777
778 /* Computes 2 * a and stores the result in r. r could be a.
779 * Uses algorithm A.10.2 of IEEE P1363.
780 */
781 int ec_GF2m_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_CTX *ctx)
782 {
783 return ec_GF2m_simple_add(group, r, a, a, ctx);
784 }
785
786
787 int ec_GF2m_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
788 {
789 if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(&point->Y))
790 /* point is its own inverse */
791 return 1;
792
793 if (!EC_POINT_make_affine(group, point, ctx)) return 0;
794 return BN_GF2m_add(&point->Y, &point->X, &point->Y);
795 }
796
797
798 /* Indicates whether the given point is the point at infinity. */
799 int ec_GF2m_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point)
800 {
801 return BN_is_zero(&point->Z);
802 }
803
804
805 /*-
806 * Determines whether the given EC_POINT is an actual point on the curve defined
807 * in the EC_GROUP. A point is valid if it satisfies the Weierstrass equation:
808 * y^2 + x*y = x^3 + a*x^2 + b.
809 */
810 int ec_GF2m_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx)
811 {
812 int ret = -1;
813 BN_CTX *new_ctx = NULL;
814 BIGNUM *lh, *y2;
815 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
816 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
817
818 if (EC_POINT_is_at_infinity(group, point))
819 return 1;
820
821 field_mul = group->meth->field_mul;
822 field_sqr = group->meth->field_sqr;
823
824 /* only support affine coordinates */
825 if (!point->Z_is_one) return -1;
826
827 if (ctx == NULL)
828 {
829 ctx = new_ctx = BN_CTX_new();
830 if (ctx == NULL)
831 return -1;
832 }
833
834 BN_CTX_start(ctx);
835 y2 = BN_CTX_get(ctx);
836 lh = BN_CTX_get(ctx);
837 if (lh == NULL) goto err;
838
839 /*-
840 * We have a curve defined by a Weierstrass equation
841 * y^2 + x*y = x^3 + a*x^2 + b.
842 * <=> x^3 + a*x^2 + x*y + b + y^2 = 0
843 * <=> ((x + a) * x + y ) * x + b + y^2 = 0
844 */
845 if (!BN_GF2m_add(lh, &point->X, &group->a)) goto err;
846 if (!field_mul(group, lh, lh, &point->X, ctx)) goto err;
847 if (!BN_GF2m_add(lh, lh, &point->Y)) goto err;
848 if (!field_mul(group, lh, lh, &point->X, ctx)) goto err;
849 if (!BN_GF2m_add(lh, lh, &group->b)) goto err;
850 if (!field_sqr(group, y2, &point->Y, ctx)) goto err;
851 if (!BN_GF2m_add(lh, lh, y2)) goto err;
852 ret = BN_is_zero(lh);
853 err:
854 if (ctx) BN_CTX_end(ctx);
855 if (new_ctx) BN_CTX_free(new_ctx);
856 return ret;
857 }
858
859
860 /*-
861 * Indicates whether two points are equal.
862 * Return values:
863 * -1 error
864 * 0 equal (in affine coordinates)
865 * 1 not equal
866 */
867 int ec_GF2m_simple_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
868 {
869 BIGNUM *aX, *aY, *bX, *bY;
870 BN_CTX *new_ctx = NULL;
871 int ret = -1;
872
873 if (EC_POINT_is_at_infinity(group, a))
874 {
875 return EC_POINT_is_at_infinity(group, b) ? 0 : 1;
876 }
877
878 if (EC_POINT_is_at_infinity(group, b))
879 return 1;
880
881 if (a->Z_is_one && b->Z_is_one)
882 {
883 return ((BN_cmp(&a->X, &b->X) == 0) && BN_cmp(&a->Y, &b->Y) == 0) ? 0 : 1;
884 }
885
886 if (ctx == NULL)
887 {
888 ctx = new_ctx = BN_CTX_new();
889 if (ctx == NULL)
890 return -1;
891 }
892
893 BN_CTX_start(ctx);
894 aX = BN_CTX_get(ctx);
895 aY = BN_CTX_get(ctx);
896 bX = BN_CTX_get(ctx);
897 bY = BN_CTX_get(ctx);
898 if (bY == NULL) goto err;
899
900 if (!EC_POINT_get_affine_coordinates_GF2m(group, a, aX, aY, ctx)) goto err;
901 if (!EC_POINT_get_affine_coordinates_GF2m(group, b, bX, bY, ctx)) goto err;
902 ret = ((BN_cmp(aX, bX) == 0) && BN_cmp(aY, bY) == 0) ? 0 : 1;
903
904 err:
905 if (ctx) BN_CTX_end(ctx);
906 if (new_ctx) BN_CTX_free(new_ctx);
907 return ret;
908 }
909
910
911 /* Forces the given EC_POINT to internally use affine coordinates. */
912 int ec_GF2m_simple_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
913 {
914 BN_CTX *new_ctx = NULL;
915 BIGNUM *x, *y;
916 int ret = 0;
917
918 if (point->Z_is_one || EC_POINT_is_at_infinity(group, point))
919 return 1;
920
921 if (ctx == NULL)
922 {
923 ctx = new_ctx = BN_CTX_new();
924 if (ctx == NULL)
925 return 0;
926 }
927
928 BN_CTX_start(ctx);
929 x = BN_CTX_get(ctx);
930 y = BN_CTX_get(ctx);
931 if (y == NULL) goto err;
932
933 if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err;
934 if (!BN_copy(&point->X, x)) goto err;
935 if (!BN_copy(&point->Y, y)) goto err;
936 if (!BN_one(&point->Z)) goto err;
937
938 ret = 1;
939
940 err:
941 if (ctx) BN_CTX_end(ctx);
942 if (new_ctx) BN_CTX_free(new_ctx);
943 return ret;
944 }
945
946
947 /* Forces each of the EC_POINTs in the given array to use affine coordinates. */
948 int ec_GF2m_simple_points_make_affine(const EC_GROUP *group, size_t num, EC_POINT *points[], BN_CTX *ctx)
949 {
950 size_t i;
951
952 for (i = 0; i < num; i++)
953 {
954 if (!group->meth->make_affine(group, points[i], ctx)) return 0;
955 }
956
957 return 1;
958 }
959
960
961 /* Wrapper to simple binary polynomial field multiplication implementation. */
962 int ec_GF2m_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
963 {
964 return BN_GF2m_mod_mul_arr(r, a, b, group->poly, ctx);
965 }
966
967
968 /* Wrapper to simple binary polynomial field squaring implementation. */
969 int ec_GF2m_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx)
970 {
971 return BN_GF2m_mod_sqr_arr(r, a, group->poly, ctx);
972 }
973
974
975 /* Wrapper to simple binary polynomial field division implementation. */
976 int ec_GF2m_simple_field_div(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
977 {
978 return BN_GF2m_mod_div(r, a, b, &group->field, ctx);
979 }
A mirror of the official openssl repository