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diff --git a/src/lib/libcrypto/ec/ec2_smpl.c b/src/lib/libcrypto/ec/ec2_smpl.c
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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
75const 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 */
127int 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 */
139void 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 */
150void 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 */
166int 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 bn_wexpand(&dest->a, (int)(dest->poly[0] + BN_BITS2 - 1) / BN_BITS2);
178 bn_wexpand(&dest->b, (int)(dest->poly[0] + BN_BITS2 - 1) / BN_BITS2);
179 for (i = dest->a.top; i < dest->a.dmax; i++) dest->a.d[i] = 0;
180 for (i = dest->b.top; i < dest->b.dmax; i++) dest->b.d[i] = 0;
181 return 1;
182 }
183
184
185/* Set the curve parameters of an EC_GROUP structure. */
186int ec_GF2m_simple_group_set_curve(EC_GROUP *group,
187 const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
188 {
189 int ret = 0, i;
190
191 /* group->field */
192 if (!BN_copy(&group->field, p)) goto err;
193 i = BN_GF2m_poly2arr(&group->field, group->poly, 5);
194 if ((i != 5) && (i != 3))
195 {
196 ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_SET_CURVE, EC_R_UNSUPPORTED_FIELD);
197 goto err;
198 }
199
200 /* group->a */
201 if (!BN_GF2m_mod_arr(&group->a, a, group->poly)) goto err;
202 bn_wexpand(&group->a, (int)(group->poly[0] + BN_BITS2 - 1) / BN_BITS2);
203 for (i = group->a.top; i < group->a.dmax; i++) group->a.d[i] = 0;
204
205 /* group->b */
206 if (!BN_GF2m_mod_arr(&group->b, b, group->poly)) goto err;
207 bn_wexpand(&group->b, (int)(group->poly[0] + BN_BITS2 - 1) / BN_BITS2);
208 for (i = group->b.top; i < group->b.dmax; i++) group->b.d[i] = 0;
209
210 ret = 1;
211 err:
212 return ret;
213 }
214
215
216/* Get the curve parameters of an EC_GROUP structure.
217 * If p, a, or b are NULL then there values will not be set but the method will return with success.
218 */
219int ec_GF2m_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx)
220 {
221 int ret = 0;
222
223 if (p != NULL)
224 {
225 if (!BN_copy(p, &group->field)) return 0;
226 }
227
228 if (a != NULL)
229 {
230 if (!BN_copy(a, &group->a)) goto err;
231 }
232
233 if (b != NULL)
234 {
235 if (!BN_copy(b, &group->b)) goto err;
236 }
237
238 ret = 1;
239
240 err:
241 return ret;
242 }
243
244
245/* Gets the degree of the field. For a curve over GF(2^m) this is the value m. */
246int ec_GF2m_simple_group_get_degree(const EC_GROUP *group)
247 {
248 return BN_num_bits(&group->field)-1;
249 }
250
251
252/* Checks the discriminant of the curve.
253 * y^2 + x*y = x^3 + a*x^2 + b is an elliptic curve <=> b != 0 (mod p)
254 */
255int ec_GF2m_simple_group_check_discriminant(const EC_GROUP *group, BN_CTX *ctx)
256 {
257 int ret = 0;
258 BIGNUM *b;
259 BN_CTX *new_ctx = NULL;
260
261 if (ctx == NULL)
262 {
263 ctx = new_ctx = BN_CTX_new();
264 if (ctx == NULL)
265 {
266 ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_CHECK_DISCRIMINANT, ERR_R_MALLOC_FAILURE);
267 goto err;
268 }
269 }
270 BN_CTX_start(ctx);
271 b = BN_CTX_get(ctx);
272 if (b == NULL) goto err;
273
274 if (!BN_GF2m_mod_arr(b, &group->b, group->poly)) goto err;
275
276 /* check the discriminant:
277 * y^2 + x*y = x^3 + a*x^2 + b is an elliptic curve <=> b != 0 (mod p)
278 */
279 if (BN_is_zero(b)) goto err;
280
281 ret = 1;
282
283err:
284 if (ctx != NULL)
285 BN_CTX_end(ctx);
286 if (new_ctx != NULL)
287 BN_CTX_free(new_ctx);
288 return ret;
289 }
290
291
292/* Initializes an EC_POINT. */
293int ec_GF2m_simple_point_init(EC_POINT *point)
294 {
295 BN_init(&point->X);
296 BN_init(&point->Y);
297 BN_init(&point->Z);
298 return 1;
299 }
300
301
302/* Frees an EC_POINT. */
303void ec_GF2m_simple_point_finish(EC_POINT *point)
304 {
305 BN_free(&point->X);
306 BN_free(&point->Y);
307 BN_free(&point->Z);
308 }
309
310
311/* Clears and frees an EC_POINT. */
312void ec_GF2m_simple_point_clear_finish(EC_POINT *point)
313 {
314 BN_clear_free(&point->X);
315 BN_clear_free(&point->Y);
316 BN_clear_free(&point->Z);
317 point->Z_is_one = 0;
318 }
319
320
321/* Copy the contents of one EC_POINT into another. Assumes dest is initialized. */
322int ec_GF2m_simple_point_copy(EC_POINT *dest, const EC_POINT *src)
323 {
324 if (!BN_copy(&dest->X, &src->X)) return 0;
325 if (!BN_copy(&dest->Y, &src->Y)) return 0;
326 if (!BN_copy(&dest->Z, &src->Z)) return 0;
327 dest->Z_is_one = src->Z_is_one;
328
329 return 1;
330 }
331
332
333/* Set an EC_POINT to the point at infinity.
334 * A point at infinity is represented by having Z=0.
335 */
336int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *group, EC_POINT *point)
337 {
338 point->Z_is_one = 0;
339 BN_zero(&point->Z);
340 return 1;
341 }
342
343
344/* Set the coordinates of an EC_POINT using affine coordinates.
345 * Note that the simple implementation only uses affine coordinates.
346 */
347int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *group, EC_POINT *point,
348 const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx)
349 {
350 int ret = 0;
351 if (x == NULL || y == NULL)
352 {
353 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_SET_AFFINE_COORDINATES, ERR_R_PASSED_NULL_PARAMETER);
354 return 0;
355 }
356
357 if (!BN_copy(&point->X, x)) goto err;
358 BN_set_negative(&point->X, 0);
359 if (!BN_copy(&point->Y, y)) goto err;
360 BN_set_negative(&point->Y, 0);
361 if (!BN_copy(&point->Z, BN_value_one())) goto err;
362 BN_set_negative(&point->Z, 0);
363 point->Z_is_one = 1;
364 ret = 1;
365
366 err:
367 return ret;
368 }
369
370
371/* Gets the affine coordinates of an EC_POINT.
372 * Note that the simple implementation only uses affine coordinates.
373 */
374int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point,
375 BIGNUM *x, BIGNUM *y, BN_CTX *ctx)
376 {
377 int ret = 0;
378
379 if (EC_POINT_is_at_infinity(group, point))
380 {
381 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES, EC_R_POINT_AT_INFINITY);
382 return 0;
383 }
384
385 if (BN_cmp(&point->Z, BN_value_one()))
386 {
387 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
388 return 0;
389 }
390 if (x != NULL)
391 {
392 if (!BN_copy(x, &point->X)) goto err;
393 BN_set_negative(x, 0);
394 }
395 if (y != NULL)
396 {
397 if (!BN_copy(y, &point->Y)) goto err;
398 BN_set_negative(y, 0);
399 }
400 ret = 1;
401
402 err:
403 return ret;
404 }
405
406
407/* Include patented algorithms. */
408#include "ec2_smpt.c"
409
410
411/* Converts an EC_POINT to an octet string.
412 * If buf is NULL, the encoded length will be returned.
413 * If the length len of buf is smaller than required an error will be returned.
414 *
415 * The point compression section of this function is patented by Certicom Corp.
416 * under US Patent 6,141,420. Point compression is disabled by default and can
417 * be enabled by defining the preprocessor macro OPENSSL_EC_BIN_PT_COMP at
418 * Configure-time.
419 */
420size_t ec_GF2m_simple_point2oct(const EC_GROUP *group, const EC_POINT *point, point_conversion_form_t form,
421 unsigned char *buf, size_t len, BN_CTX *ctx)
422 {
423 size_t ret;
424 BN_CTX *new_ctx = NULL;
425 int used_ctx = 0;
426 BIGNUM *x, *y, *yxi;
427 size_t field_len, i, skip;
428
429#ifndef OPENSSL_EC_BIN_PT_COMP
430 if ((form == POINT_CONVERSION_COMPRESSED) || (form == POINT_CONVERSION_HYBRID))
431 {
432 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_DISABLED);
433 goto err;
434 }
435#endif
436
437 if ((form != POINT_CONVERSION_COMPRESSED)
438 && (form != POINT_CONVERSION_UNCOMPRESSED)
439 && (form != POINT_CONVERSION_HYBRID))
440 {
441 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_INVALID_FORM);
442 goto err;
443 }
444
445 if (EC_POINT_is_at_infinity(group, point))
446 {
447 /* encodes to a single 0 octet */
448 if (buf != NULL)
449 {
450 if (len < 1)
451 {
452 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);
453 return 0;
454 }
455 buf[0] = 0;
456 }
457 return 1;
458 }
459
460
461 /* ret := required output buffer length */
462 field_len = (EC_GROUP_get_degree(group) + 7) / 8;
463 ret = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len;
464
465 /* if 'buf' is NULL, just return required length */
466 if (buf != NULL)
467 {
468 if (len < ret)
469 {
470 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);
471 goto err;
472 }
473
474 if (ctx == NULL)
475 {
476 ctx = new_ctx = BN_CTX_new();
477 if (ctx == NULL)
478 return 0;
479 }
480
481 BN_CTX_start(ctx);
482 used_ctx = 1;
483 x = BN_CTX_get(ctx);
484 y = BN_CTX_get(ctx);
485 yxi = BN_CTX_get(ctx);
486 if (yxi == NULL) goto err;
487
488 if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err;
489
490 buf[0] = form;
491#ifdef OPENSSL_EC_BIN_PT_COMP
492 if ((form != POINT_CONVERSION_UNCOMPRESSED) && !BN_is_zero(x))
493 {
494 if (!group->meth->field_div(group, yxi, y, x, ctx)) goto err;
495 if (BN_is_odd(yxi)) buf[0]++;
496 }
497#endif
498
499 i = 1;
500
501 skip = field_len - BN_num_bytes(x);
502 if (skip > field_len)
503 {
504 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
505 goto err;
506 }
507 while (skip > 0)
508 {
509 buf[i++] = 0;
510 skip--;
511 }
512 skip = BN_bn2bin(x, buf + i);
513 i += skip;
514 if (i != 1 + field_len)
515 {
516 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
517 goto err;
518 }
519
520 if (form == POINT_CONVERSION_UNCOMPRESSED || form == POINT_CONVERSION_HYBRID)
521 {
522 skip = field_len - BN_num_bytes(y);
523 if (skip > field_len)
524 {
525 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
526 goto err;
527 }
528 while (skip > 0)
529 {
530 buf[i++] = 0;
531 skip--;
532 }
533 skip = BN_bn2bin(y, buf + i);
534 i += skip;
535 }
536
537 if (i != ret)
538 {
539 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
540 goto err;
541 }
542 }
543
544 if (used_ctx)
545 BN_CTX_end(ctx);
546 if (new_ctx != NULL)
547 BN_CTX_free(new_ctx);
548 return ret;
549
550 err:
551 if (used_ctx)
552 BN_CTX_end(ctx);
553 if (new_ctx != NULL)
554 BN_CTX_free(new_ctx);
555 return 0;
556 }
557
558
559/* Converts an octet string representation to an EC_POINT.
560 * Note that the simple implementation only uses affine coordinates.
561 */
562int ec_GF2m_simple_oct2point(const EC_GROUP *group, EC_POINT *point,
563 const unsigned char *buf, size_t len, BN_CTX *ctx)
564 {
565 point_conversion_form_t form;
566 int y_bit;
567 BN_CTX *new_ctx = NULL;
568 BIGNUM *x, *y, *yxi;
569 size_t field_len, enc_len;
570 int ret = 0;
571
572 if (len == 0)
573 {
574 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_BUFFER_TOO_SMALL);
575 return 0;
576 }
577 form = buf[0];
578 y_bit = form & 1;
579 form = form & ~1U;
580 if ((form != 0) && (form != POINT_CONVERSION_COMPRESSED)
581 && (form != POINT_CONVERSION_UNCOMPRESSED)
582 && (form != POINT_CONVERSION_HYBRID))
583 {
584 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
585 return 0;
586 }
587 if ((form == 0 || form == POINT_CONVERSION_UNCOMPRESSED) && y_bit)
588 {
589 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
590 return 0;
591 }
592
593 if (form == 0)
594 {
595 if (len != 1)
596 {
597 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
598 return 0;
599 }
600
601 return EC_POINT_set_to_infinity(group, point);
602 }
603
604 field_len = (EC_GROUP_get_degree(group) + 7) / 8;
605 enc_len = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len;
606
607 if (len != enc_len)
608 {
609 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
610 return 0;
611 }
612
613 if (ctx == NULL)
614 {
615 ctx = new_ctx = BN_CTX_new();
616 if (ctx == NULL)
617 return 0;
618 }
619
620 BN_CTX_start(ctx);
621 x = BN_CTX_get(ctx);
622 y = BN_CTX_get(ctx);
623 yxi = BN_CTX_get(ctx);
624 if (yxi == NULL) goto err;
625
626 if (!BN_bin2bn(buf + 1, field_len, x)) goto err;
627 if (BN_ucmp(x, &group->field) >= 0)
628 {
629 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
630 goto err;
631 }
632
633 if (form == POINT_CONVERSION_COMPRESSED)
634 {
635 if (!EC_POINT_set_compressed_coordinates_GF2m(group, point, x, y_bit, ctx)) goto err;
636 }
637 else
638 {
639 if (!BN_bin2bn(buf + 1 + field_len, field_len, y)) goto err;
640 if (BN_ucmp(y, &group->field) >= 0)
641 {
642 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
643 goto err;
644 }
645 if (form == POINT_CONVERSION_HYBRID)
646 {
647 if (!group->meth->field_div(group, yxi, y, x, ctx)) goto err;
648 if (y_bit != BN_is_odd(yxi))
649 {
650 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
651 goto err;
652 }
653 }
654
655 if (!EC_POINT_set_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err;
656 }
657
658 if (!EC_POINT_is_on_curve(group, point, ctx)) /* test required by X9.62 */
659 {
660 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_POINT_IS_NOT_ON_CURVE);
661 goto err;
662 }
663
664 ret = 1;
665
666 err:
667 BN_CTX_end(ctx);
668 if (new_ctx != NULL)
669 BN_CTX_free(new_ctx);
670 return ret;
671 }
672
673
674/* Computes a + b and stores the result in r. r could be a or b, a could be b.
675 * Uses algorithm A.10.2 of IEEE P1363.
676 */
677int ec_GF2m_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
678 {
679 BN_CTX *new_ctx = NULL;
680 BIGNUM *x0, *y0, *x1, *y1, *x2, *y2, *s, *t;
681 int ret = 0;
682
683 if (EC_POINT_is_at_infinity(group, a))
684 {
685 if (!EC_POINT_copy(r, b)) return 0;
686 return 1;
687 }
688
689 if (EC_POINT_is_at_infinity(group, b))
690 {
691 if (!EC_POINT_copy(r, a)) return 0;
692 return 1;
693 }
694
695 if (ctx == NULL)
696 {
697 ctx = new_ctx = BN_CTX_new();
698 if (ctx == NULL)
699 return 0;
700 }
701
702 BN_CTX_start(ctx);
703 x0 = BN_CTX_get(ctx);
704 y0 = BN_CTX_get(ctx);
705 x1 = BN_CTX_get(ctx);
706 y1 = BN_CTX_get(ctx);
707 x2 = BN_CTX_get(ctx);
708 y2 = BN_CTX_get(ctx);
709 s = BN_CTX_get(ctx);
710 t = BN_CTX_get(ctx);
711 if (t == NULL) goto err;
712
713 if (a->Z_is_one)
714 {
715 if (!BN_copy(x0, &a->X)) goto err;
716 if (!BN_copy(y0, &a->Y)) goto err;
717 }
718 else
719 {
720 if (!EC_POINT_get_affine_coordinates_GF2m(group, a, x0, y0, ctx)) goto err;
721 }
722 if (b->Z_is_one)
723 {
724 if (!BN_copy(x1, &b->X)) goto err;
725 if (!BN_copy(y1, &b->Y)) goto err;
726 }
727 else
728 {
729 if (!EC_POINT_get_affine_coordinates_GF2m(group, b, x1, y1, ctx)) goto err;
730 }
731
732
733 if (BN_GF2m_cmp(x0, x1))
734 {
735 if (!BN_GF2m_add(t, x0, x1)) goto err;
736 if (!BN_GF2m_add(s, y0, y1)) goto err;
737 if (!group->meth->field_div(group, s, s, t, ctx)) goto err;
738 if (!group->meth->field_sqr(group, x2, s, ctx)) goto err;
739 if (!BN_GF2m_add(x2, x2, &group->a)) goto err;
740 if (!BN_GF2m_add(x2, x2, s)) goto err;
741 if (!BN_GF2m_add(x2, x2, t)) goto err;
742 }
743 else
744 {
745 if (BN_GF2m_cmp(y0, y1) || BN_is_zero(x1))
746 {
747 if (!EC_POINT_set_to_infinity(group, r)) goto err;
748 ret = 1;
749 goto err;
750 }
751 if (!group->meth->field_div(group, s, y1, x1, ctx)) goto err;
752 if (!BN_GF2m_add(s, s, x1)) goto err;
753
754 if (!group->meth->field_sqr(group, x2, s, ctx)) goto err;
755 if (!BN_GF2m_add(x2, x2, s)) goto err;
756 if (!BN_GF2m_add(x2, x2, &group->a)) goto err;
757 }
758
759 if (!BN_GF2m_add(y2, x1, x2)) goto err;
760 if (!group->meth->field_mul(group, y2, y2, s, ctx)) goto err;
761 if (!BN_GF2m_add(y2, y2, x2)) goto err;
762 if (!BN_GF2m_add(y2, y2, y1)) goto err;
763
764 if (!EC_POINT_set_affine_coordinates_GF2m(group, r, x2, y2, ctx)) goto err;
765
766 ret = 1;
767
768 err:
769 BN_CTX_end(ctx);
770 if (new_ctx != NULL)
771 BN_CTX_free(new_ctx);
772 return ret;
773 }
774
775
776/* Computes 2 * a and stores the result in r. r could be a.
777 * Uses algorithm A.10.2 of IEEE P1363.
778 */
779int ec_GF2m_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_CTX *ctx)
780 {
781 return ec_GF2m_simple_add(group, r, a, a, ctx);
782 }
783
784
785int ec_GF2m_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
786 {
787 if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(&point->Y))
788 /* point is its own inverse */
789 return 1;
790
791 if (!EC_POINT_make_affine(group, point, ctx)) return 0;
792 return BN_GF2m_add(&point->Y, &point->X, &point->Y);
793 }
794
795
796/* Indicates whether the given point is the point at infinity. */
797int ec_GF2m_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point)
798 {
799 return BN_is_zero(&point->Z);
800 }
801
802
803/* Determines whether the given EC_POINT is an actual point on the curve defined
804 * in the EC_GROUP. A point is valid if it satisfies the Weierstrass equation:
805 * y^2 + x*y = x^3 + a*x^2 + b.
806 */
807int ec_GF2m_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx)
808 {
809 int ret = -1;
810 BN_CTX *new_ctx = NULL;
811 BIGNUM *lh, *y2;
812 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
813 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
814
815 if (EC_POINT_is_at_infinity(group, point))
816 return 1;
817
818 field_mul = group->meth->field_mul;
819 field_sqr = group->meth->field_sqr;
820
821 /* only support affine coordinates */
822 if (!point->Z_is_one) goto err;
823
824 if (ctx == NULL)
825 {
826 ctx = new_ctx = BN_CTX_new();
827 if (ctx == NULL)
828 return -1;
829 }
830
831 BN_CTX_start(ctx);
832 y2 = BN_CTX_get(ctx);
833 lh = BN_CTX_get(ctx);
834 if (lh == NULL) goto err;
835
836 /* We have a curve defined by a Weierstrass equation
837 * y^2 + x*y = x^3 + a*x^2 + b.
838 * <=> x^3 + a*x^2 + x*y + b + y^2 = 0
839 * <=> ((x + a) * x + y ) * x + b + y^2 = 0
840 */
841 if (!BN_GF2m_add(lh, &point->X, &group->a)) goto err;
842 if (!field_mul(group, lh, lh, &point->X, ctx)) goto err;
843 if (!BN_GF2m_add(lh, lh, &point->Y)) goto err;
844 if (!field_mul(group, lh, lh, &point->X, ctx)) goto err;
845 if (!BN_GF2m_add(lh, lh, &group->b)) goto err;
846 if (!field_sqr(group, y2, &point->Y, ctx)) goto err;
847 if (!BN_GF2m_add(lh, lh, y2)) goto err;
848 ret = BN_is_zero(lh);
849 err:
850 if (ctx) BN_CTX_end(ctx);
851 if (new_ctx) BN_CTX_free(new_ctx);
852 return ret;
853 }
854
855
856/* Indicates whether two points are equal.
857 * Return values:
858 * -1 error
859 * 0 equal (in affine coordinates)
860 * 1 not equal
861 */
862int ec_GF2m_simple_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
863 {
864 BIGNUM *aX, *aY, *bX, *bY;
865 BN_CTX *new_ctx = NULL;
866 int ret = -1;
867
868 if (EC_POINT_is_at_infinity(group, a))
869 {
870 return EC_POINT_is_at_infinity(group, b) ? 0 : 1;
871 }
872
873 if (a->Z_is_one && b->Z_is_one)
874 {
875 return ((BN_cmp(&a->X, &b->X) == 0) && BN_cmp(&a->Y, &b->Y) == 0) ? 0 : 1;
876 }
877
878 if (ctx == NULL)
879 {
880 ctx = new_ctx = BN_CTX_new();
881 if (ctx == NULL)
882 return -1;
883 }
884
885 BN_CTX_start(ctx);
886 aX = BN_CTX_get(ctx);
887 aY = BN_CTX_get(ctx);
888 bX = BN_CTX_get(ctx);
889 bY = BN_CTX_get(ctx);
890 if (bY == NULL) goto err;
891
892 if (!EC_POINT_get_affine_coordinates_GF2m(group, a, aX, aY, ctx)) goto err;
893 if (!EC_POINT_get_affine_coordinates_GF2m(group, b, bX, bY, ctx)) goto err;
894 ret = ((BN_cmp(aX, bX) == 0) && BN_cmp(aY, bY) == 0) ? 0 : 1;
895
896 err:
897 if (ctx) BN_CTX_end(ctx);
898 if (new_ctx) BN_CTX_free(new_ctx);
899 return ret;
900 }
901
902
903/* Forces the given EC_POINT to internally use affine coordinates. */
904int ec_GF2m_simple_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
905 {
906 BN_CTX *new_ctx = NULL;
907 BIGNUM *x, *y;
908 int ret = 0;
909
910 if (point->Z_is_one || EC_POINT_is_at_infinity(group, point))
911 return 1;
912
913 if (ctx == NULL)
914 {
915 ctx = new_ctx = BN_CTX_new();
916 if (ctx == NULL)
917 return 0;
918 }
919
920 BN_CTX_start(ctx);
921 x = BN_CTX_get(ctx);
922 y = BN_CTX_get(ctx);
923 if (y == NULL) goto err;
924
925 if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err;
926 if (!BN_copy(&point->X, x)) goto err;
927 if (!BN_copy(&point->Y, y)) goto err;
928 if (!BN_one(&point->Z)) goto err;
929
930 ret = 1;
931
932 err:
933 if (ctx) BN_CTX_end(ctx);
934 if (new_ctx) BN_CTX_free(new_ctx);
935 return ret;
936 }
937
938
939/* Forces each of the EC_POINTs in the given array to use affine coordinates. */
940int ec_GF2m_simple_points_make_affine(const EC_GROUP *group, size_t num, EC_POINT *points[], BN_CTX *ctx)
941 {
942 size_t i;
943
944 for (i = 0; i < num; i++)
945 {
946 if (!group->meth->make_affine(group, points[i], ctx)) return 0;
947 }
948
949 return 1;
950 }
951
952
953/* Wrapper to simple binary polynomial field multiplication implementation. */
954int ec_GF2m_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
955 {
956 return BN_GF2m_mod_mul_arr(r, a, b, group->poly, ctx);
957 }
958
959
960/* Wrapper to simple binary polynomial field squaring implementation. */
961int ec_GF2m_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx)
962 {
963 return BN_GF2m_mod_sqr_arr(r, a, group->poly, ctx);
964 }
965
966
967/* Wrapper to simple binary polynomial field division implementation. */
968int ec_GF2m_simple_field_div(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
969 {
970 return BN_GF2m_mod_div(r, a, b, &group->field, ctx);
971 }
generated by cgit v1.2.3-55-g6feb (git 2.39.1) at 2025-04-04 23:49:58 +0000