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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 * In addition, Sun covenants to all licensees who provide a reciprocal
13 * covenant with respect to their own patents if any, not to sue under
14 * current and future patent claims necessarily infringed by the making,
15 * using, practicing, selling, offering for sale and/or otherwise
16 * disposing of the ECC Code as delivered hereunder (or portions thereof),
17 * provided that such covenant shall not apply:
18 * 1) for code that a licensee deletes from the ECC Code;
19 * 2) separates from the ECC Code; or
20 * 3) for infringements caused by:
21 * i) the modification of the ECC Code or
22 * ii) the combination of the ECC Code with other software or
23 * devices where such combination causes the infringement.
24 *
25 * The software is originally written by Sheueling Chang Shantz and
26 * Douglas Stebila of Sun Microsystems Laboratories.
27 *
28 */
29 /* ====================================================================
30 * Copyright (c) 1998-2002 The OpenSSL Project. All rights reserved.
31 *
32 * Redistribution and use in source and binary forms, with or without
33 * modification, are permitted provided that the following conditions
34 * are met:
35 *
36 * 1. Redistributions of source code must retain the above copyright
37 * notice, this list of conditions and the following disclaimer.
38 *
39 * 2. Redistributions in binary form must reproduce the above copyright
40 * notice, this list of conditions and the following disclaimer in
41 * the documentation and/or other materials provided with the
42 * distribution.
43 *
44 * 3. All advertising materials mentioning features or use of this
45 * software must display the following acknowledgment:
46 * "This product includes software developed by the OpenSSL Project
47 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
48 *
49 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
50 * endorse or promote products derived from this software without
51 * prior written permission. For written permission, please contact
52 * openssl-core@openssl.org.
53 *
54 * 5. Products derived from this software may not be called "OpenSSL"
55 * nor may "OpenSSL" appear in their names without prior written
56 * permission of the OpenSSL Project.
57 *
58 * 6. Redistributions of any form whatsoever must retain the following
59 * acknowledgment:
60 * "This product includes software developed by the OpenSSL Project
61 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
62 *
63 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
64 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
65 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
66 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
67 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
68 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
69 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
70 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
71 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
72 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
73 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
74 * OF THE POSSIBILITY OF SUCH DAMAGE.
75 * ====================================================================
76 *
77 * This product includes cryptographic software written by Eric Young
78 * (eay@cryptsoft.com). This product includes software written by Tim
79 * Hudson (tjh@cryptsoft.com).
80 *
81 */
82
83 #include <openssl/err.h>
84
85 #include "ec_lcl.h"
86
87
88 const EC_METHOD *EC_GF2m_simple_method(void)
89 {
90 static const EC_METHOD ret = {
91 NID_X9_62_characteristic_two_field,
92 ec_GF2m_simple_group_init,
93 ec_GF2m_simple_group_finish,
94 ec_GF2m_simple_group_clear_finish,
95 ec_GF2m_simple_group_copy,
96 ec_GF2m_simple_group_set_curve,
97 ec_GF2m_simple_group_get_curve,
98 ec_GF2m_simple_group_get_degree,
99 ec_GF2m_simple_group_check_discriminant,
100 ec_GF2m_simple_point_init,
101 ec_GF2m_simple_point_finish,
102 ec_GF2m_simple_point_clear_finish,
103 ec_GF2m_simple_point_copy,
104 ec_GF2m_simple_point_set_to_infinity,
105 0 /* set_Jprojective_coordinates_GFp */,
106 0 /* get_Jprojective_coordinates_GFp */,
107 ec_GF2m_simple_point_set_affine_coordinates,
108 ec_GF2m_simple_point_get_affine_coordinates,
109 ec_GF2m_simple_set_compressed_coordinates,
110 ec_GF2m_simple_point2oct,
111 ec_GF2m_simple_oct2point,
112 ec_GF2m_simple_add,
113 ec_GF2m_simple_dbl,
114 ec_GF2m_simple_invert,
115 ec_GF2m_mont_mul,
116 ec_GF2m_mont_precompute_mult,
117 ec_GF2m_simple_is_at_infinity,
118 ec_GF2m_simple_is_on_curve,
119 ec_GF2m_simple_cmp,
120 ec_GF2m_simple_make_affine,
121 ec_GF2m_simple_points_make_affine,
122 ec_GF2m_simple_field_mul,
123 ec_GF2m_simple_field_sqr,
124 ec_GF2m_simple_field_div,
125 0 /* field_encode */,
126 0 /* field_decode */,
127 0 /* field_set_to_one */ };
128
129 return &ret;
130 }
131
132
133 /* Initialize a GF(2^m)-based EC_GROUP structure.
134 * Note that all other members are handled by EC_GROUP_new.
135 */
136 int ec_GF2m_simple_group_init(EC_GROUP *group)
137 {
138 BN_init(&group->field);
139 BN_init(&group->a);
140 BN_init(&group->b);
141 return 1;
142 }
143
144
145 /* Free a GF(2^m)-based EC_GROUP structure.
146 * Note that all other members are handled by EC_GROUP_free.
147 */
148 void ec_GF2m_simple_group_finish(EC_GROUP *group)
149 {
150 BN_free(&group->field);
151 BN_free(&group->a);
152 BN_free(&group->b);
153 }
154
155
156 /* Clear and free a GF(2^m)-based EC_GROUP structure.
157 * Note that all other members are handled by EC_GROUP_clear_free.
158 */
159 void ec_GF2m_simple_group_clear_finish(EC_GROUP *group)
160 {
161 BN_clear_free(&group->field);
162 BN_clear_free(&group->a);
163 BN_clear_free(&group->b);
164 group->poly[0] = 0;
165 group->poly[1] = 0;
166 group->poly[2] = 0;
167 group->poly[3] = 0;
168 group->poly[4] = 0;
169 }
170
171
172 /* Copy a GF(2^m)-based EC_GROUP structure.
173 * Note that all other members are handled by EC_GROUP_copy.
174 */
175 int ec_GF2m_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src)
176 {
177 int i;
178 if (!BN_copy(&dest->field, &src->field)) return 0;
179 if (!BN_copy(&dest->a, &src->a)) return 0;
180 if (!BN_copy(&dest->b, &src->b)) return 0;
181 dest->poly[0] = src->poly[0];
182 dest->poly[1] = src->poly[1];
183 dest->poly[2] = src->poly[2];
184 dest->poly[3] = src->poly[3];
185 dest->poly[4] = src->poly[4];
186 bn_wexpand(&dest->a, (dest->poly[0] + BN_BITS2 - 1) / BN_BITS2);
187 bn_wexpand(&dest->b, (dest->poly[0] + BN_BITS2 - 1) / BN_BITS2);
188 for (i = dest->a.top; i < dest->a.dmax; i++) dest->a.d[i] = 0;
189 for (i = dest->b.top; i < dest->b.dmax; i++) dest->b.d[i] = 0;
190 return 1;
191 }
192
193
194 /* Set the curve parameters of an EC_GROUP structure. */
195 int ec_GF2m_simple_group_set_curve(EC_GROUP *group,
196 const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
197 {
198 int ret = 0, i;
199
200 /* group->field */
201 if (!BN_copy(&group->field, p)) goto err;
202 i = BN_GF2m_poly2arr(&group->field, group->poly, 5);
203 if ((i != 5) && (i != 3))
204 {
205 ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_SET_CURVE, EC_R_UNSUPPORTED_FIELD);
206 goto err;
207 }
208
209 /* group->a */
210 if (!BN_GF2m_mod_arr(&group->a, a, group->poly)) goto err;
211 bn_wexpand(&group->a, (group->poly[0] + BN_BITS2 - 1) / BN_BITS2);
212 for (i = group->a.top; i < group->a.dmax; i++) group->a.d[i] = 0;
213
214 /* group->b */
215 if (!BN_GF2m_mod_arr(&group->b, b, group->poly)) goto err;
216 bn_wexpand(&group->b, (group->poly[0] + BN_BITS2 - 1) / BN_BITS2);
217 for (i = group->b.top; i < group->b.dmax; i++) group->b.d[i] = 0;
218
219 ret = 1;
220 err:
221 return ret;
222 }
223
224
225 /* Get the curve parameters of an EC_GROUP structure.
226 * If p, a, or b are NULL then there values will not be set but the method will return with success.
227 */
228 int ec_GF2m_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx)
229 {
230 int ret = 0;
231
232 if (p != NULL)
233 {
234 if (!BN_copy(p, &group->field)) return 0;
235 }
236
237 if (a != NULL)
238 {
239 if (!BN_copy(a, &group->a)) goto err;
240 }
241
242 if (b != NULL)
243 {
244 if (!BN_copy(b, &group->b)) goto err;
245 }
246
247 ret = 1;
248
249 err:
250 return ret;
251 }
252
253
254 /* Gets the degree of the field. For a curve over GF(2^m) this is the value m. */
255 int ec_GF2m_simple_group_get_degree(const EC_GROUP *group)
256 {
257 return BN_num_bits(&group->field)-1;
258 }
259
260
261 /* Checks the discriminant of the curve.
262 * y^2 + x*y = x^3 + a*x^2 + b is an elliptic curve <=> b != 0 (mod p)
263 */
264 int ec_GF2m_simple_group_check_discriminant(const EC_GROUP *group, BN_CTX *ctx)
265 {
266 int ret = 0;
267 BIGNUM *b;
268 BN_CTX *new_ctx = NULL;
269
270 if (ctx == NULL)
271 {
272 ctx = new_ctx = BN_CTX_new();
273 if (ctx == NULL)
274 {
275 ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_CHECK_DISCRIMINANT, ERR_R_MALLOC_FAILURE);
276 goto err;
277 }
278 }
279 BN_CTX_start(ctx);
280 b = BN_CTX_get(ctx);
281 if (b == NULL) goto err;
282
283 if (!BN_GF2m_mod_arr(b, &group->b, group->poly)) goto err;
284
285 /* check the discriminant:
286 * y^2 + x*y = x^3 + a*x^2 + b is an elliptic curve <=> b != 0 (mod p)
287 */
288 if (BN_is_zero(b)) goto err;
289
290 ret = 1;
291
292 err:
293 BN_CTX_end(ctx);
294 if (new_ctx != NULL)
295 BN_CTX_free(new_ctx);
296 return ret;
297 }
298
299
300 /* Initializes an EC_POINT. */
301 int ec_GF2m_simple_point_init(EC_POINT *point)
302 {
303 BN_init(&point->X);
304 BN_init(&point->Y);
305 BN_init(&point->Z);
306 return 1;
307 }
308
309
310 /* Frees an EC_POINT. */
311 void ec_GF2m_simple_point_finish(EC_POINT *point)
312 {
313 BN_free(&point->X);
314 BN_free(&point->Y);
315 BN_free(&point->Z);
316 }
317
318
319 /* Clears and frees an EC_POINT. */
320 void ec_GF2m_simple_point_clear_finish(EC_POINT *point)
321 {
322 BN_clear_free(&point->X);
323 BN_clear_free(&point->Y);
324 BN_clear_free(&point->Z);
325 point->Z_is_one = 0;
326 }
327
328
329 /* Copy the contents of one EC_POINT into another. Assumes dest is initialized. */
330 int ec_GF2m_simple_point_copy(EC_POINT *dest, const EC_POINT *src)
331 {
332 if (!BN_copy(&dest->X, &src->X)) return 0;
333 if (!BN_copy(&dest->Y, &src->Y)) return 0;
334 if (!BN_copy(&dest->Z, &src->Z)) return 0;
335 dest->Z_is_one = src->Z_is_one;
336
337 return 1;
338 }
339
340
341 /* Set an EC_POINT to the point at infinity.
342 * A point at infinity is represented by having Z=0.
343 */
344 int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *group, EC_POINT *point)
345 {
346 point->Z_is_one = 0;
347 return (BN_zero(&point->Z));
348 }
349
350
351 /* Set the coordinates of an EC_POINT using affine coordinates.
352 * Note that the simple implementation only uses affine coordinates.
353 */
354 int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *group, EC_POINT *point,
355 const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx)
356 {
357 int ret = 0;
358 if (x == NULL || y == NULL)
359 {
360 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_SET_AFFINE_COORDINATES, ERR_R_PASSED_NULL_PARAMETER);
361 return 0;
362 }
363
364 if (!BN_copy(&point->X, x)) goto err;
365 point->X.neg = 0;
366 if (!BN_copy(&point->Y, y)) goto err;
367 point->Y.neg = 0;
368 if (!BN_copy(&point->Z, BN_value_one())) goto err;
369 point->Z.neg = 0;
370 point->Z_is_one = 1;
371 ret = 1;
372
373 err:
374 return ret;
375 }
376
377
378 /* Gets the affine coordinates of an EC_POINT.
379 * Note that the simple implementation only uses affine coordinates.
380 */
381 int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point,
382 BIGNUM *x, BIGNUM *y, BN_CTX *ctx)
383 {
384 int ret = 0;
385
386 if (EC_POINT_is_at_infinity(group, point))
387 {
388 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES, EC_R_POINT_AT_INFINITY);
389 return 0;
390 }
391
392 if (BN_cmp(&point->Z, BN_value_one()))
393 {
394 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
395 return 0;
396 }
397 if (x != NULL)
398 {
399 if (!BN_copy(x, &point->X)) goto err;
400 x->neg = 0;
401 }
402 if (y != NULL)
403 {
404 if (!BN_copy(y, &point->Y)) goto err;
405 y->neg = 0;
406 }
407 ret = 1;
408
409 err:
410 return ret;
411 }
412
413
414 /* Include patented algorithms. */
415 #include "ec2_smpt.c"
416
417
418 /* Converts an EC_POINT to an octet string.
419 * If buf is NULL, the encoded length will be returned.
420 * If the length len of buf is smaller than required an error will be returned.
421 *
422 * The point compression section of this function is patented by Certicom Corp.
423 * under US Patent 6,141,420. Point compression is disabled by default and can
424 * be enabled by defining the preprocessor macro OPENSSL_EC_BIN_PT_COMP at
425 * Configure-time.
426 */
427 size_t ec_GF2m_simple_point2oct(const EC_GROUP *group, const EC_POINT *point, point_conversion_form_t form,
428 unsigned char *buf, size_t len, BN_CTX *ctx)
429 {
430 size_t ret;
431 BN_CTX *new_ctx = NULL;
432 int used_ctx = 0;
433 BIGNUM *x, *y, *yxi;
434 size_t field_len, i, skip;
435
436 #ifndef OPENSSL_EC_BIN_PT_COMP
437 if ((form == POINT_CONVERSION_COMPRESSED) || (form == POINT_CONVERSION_HYBRID))
438 {
439 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_DISABLED);
440 goto err;
441 }
442 #endif
443
444 if ((form != POINT_CONVERSION_COMPRESSED)
445 && (form != POINT_CONVERSION_UNCOMPRESSED)
446 && (form != POINT_CONVERSION_HYBRID))
447 {
448 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_INVALID_FORM);
449 goto err;
450 }
451
452 if (EC_POINT_is_at_infinity(group, point))
453 {
454 /* encodes to a single 0 octet */
455 if (buf != NULL)
456 {
457 if (len < 1)
458 {
459 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);
460 return 0;
461 }
462 buf[0] = 0;
463 }
464 return 1;
465 }
466
467
468 /* ret := required output buffer length */
469 field_len = (EC_GROUP_get_degree(group) + 7) / 8;
470 ret = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len;
471
472 /* if 'buf' is NULL, just return required length */
473 if (buf != NULL)
474 {
475 if (len < ret)
476 {
477 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);
478 goto err;
479 }
480
481 if (ctx == NULL)
482 {
483 ctx = new_ctx = BN_CTX_new();
484 if (ctx == NULL)
485 return 0;
486 }
487
488 BN_CTX_start(ctx);
489 used_ctx = 1;
490 x = BN_CTX_get(ctx);
491 y = BN_CTX_get(ctx);
492 yxi = BN_CTX_get(ctx);
493 if (yxi == NULL) goto err;
494
495 if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err;
496
497 buf[0] = form;
498 #ifdef OPENSSL_EC_BIN_PT_COMP
499 if ((form != POINT_CONVERSION_UNCOMPRESSED) && !BN_is_zero(x))
500 {
501 if (!group->meth->field_div(group, yxi, y, x, ctx)) goto err;
502 if (BN_is_odd(yxi)) buf[0]++;
503 }
504 #endif
505
506 i = 1;
507
508 skip = field_len - BN_num_bytes(x);
509 if (skip > field_len)
510 {
511 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
512 goto err;
513 }
514 while (skip > 0)
515 {
516 buf[i++] = 0;
517 skip--;
518 }
519 skip = BN_bn2bin(x, buf + i);
520 i += skip;
521 if (i != 1 + field_len)
522 {
523 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
524 goto err;
525 }
526
527 if (form == POINT_CONVERSION_UNCOMPRESSED || form == POINT_CONVERSION_HYBRID)
528 {
529 skip = field_len - BN_num_bytes(y);
530 if (skip > field_len)
531 {
532 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
533 goto err;
534 }
535 while (skip > 0)
536 {
537 buf[i++] = 0;
538 skip--;
539 }
540 skip = BN_bn2bin(y, buf + i);
541 i += skip;
542 }
543
544 if (i != ret)
545 {
546 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
547 goto err;
548 }
549 }
550
551 if (used_ctx)
552 BN_CTX_end(ctx);
553 if (new_ctx != NULL)
554 BN_CTX_free(new_ctx);
555 return ret;
556
557 err:
558 if (used_ctx)
559 BN_CTX_end(ctx);
560 if (new_ctx != NULL)
561 BN_CTX_free(new_ctx);
562 return 0;
563 }
564
565
566 /* Converts an octet string representation to an EC_POINT.
567 * Note that the simple implementation only uses affine coordinates.
568 */
569 int ec_GF2m_simple_oct2point(const EC_GROUP *group, EC_POINT *point,
570 const unsigned char *buf, size_t len, BN_CTX *ctx)
571 {
572 point_conversion_form_t form;
573 int y_bit;
574 BN_CTX *new_ctx = NULL;
575 BIGNUM *x, *y, *yxi;
576 size_t field_len, enc_len;
577 int ret = 0;
578
579 if (len == 0)
580 {
581 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_BUFFER_TOO_SMALL);
582 return 0;
583 }
584 form = buf[0];
585 y_bit = form & 1;
586 form = form & ~1;
587 if ((form != 0) && (form != POINT_CONVERSION_COMPRESSED)
588 && (form != POINT_CONVERSION_UNCOMPRESSED)
589 && (form != POINT_CONVERSION_HYBRID))
590 {
591 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
592 return 0;
593 }
594 if ((form == 0 || form == POINT_CONVERSION_UNCOMPRESSED) && y_bit)
595 {
596 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
597 return 0;
598 }
599
600 if (form == 0)
601 {
602 if (len != 1)
603 {
604 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
605 return 0;
606 }
607
608 return EC_POINT_set_to_infinity(group, point);
609 }
610
611 field_len = (EC_GROUP_get_degree(group) + 7) / 8;
612 enc_len = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len;
613
614 if (len != enc_len)
615 {
616 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
617 return 0;
618 }
619
620 if (ctx == NULL)
621 {
622 ctx = new_ctx = BN_CTX_new();
623 if (ctx == NULL)
624 return 0;
625 }
626
627 BN_CTX_start(ctx);
628 x = BN_CTX_get(ctx);
629 y = BN_CTX_get(ctx);
630 yxi = BN_CTX_get(ctx);
631 if (yxi == NULL) goto err;
632
633 if (!BN_bin2bn(buf + 1, field_len, x)) goto err;
634 if (BN_ucmp(x, &group->field) >= 0)
635 {
636 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
637 goto err;
638 }
639
640 if (form == POINT_CONVERSION_COMPRESSED)
641 {
642 if (!EC_POINT_set_compressed_coordinates_GF2m(group, point, x, y_bit, ctx)) goto err;
643 }
644 else
645 {
646 if (!BN_bin2bn(buf + 1 + field_len, field_len, y)) goto err;
647 if (BN_ucmp(y, &group->field) >= 0)
648 {
649 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
650 goto err;
651 }
652 if (form == POINT_CONVERSION_HYBRID)
653 {
654 if (!group->meth->field_div(group, yxi, y, x, ctx)) goto err;
655 if (y_bit != BN_is_odd(yxi))
656 {
657 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
658 goto err;
659 }
660 }
661
662 if (!EC_POINT_set_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err;
663 }
664
665 if (!EC_POINT_is_on_curve(group, point, ctx)) /* test required by X9.62 */
666 {
667 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_POINT_IS_NOT_ON_CURVE);
668 goto err;
669 }
670
671 ret = 1;
672
673 err:
674 BN_CTX_end(ctx);
675 if (new_ctx != NULL)
676 BN_CTX_free(new_ctx);
677 return ret;
678 }
679
680
681 /* Computes a + b and stores the result in r. r could be a or b, a could be b.
682 * Uses algorithm A.10.2 of IEEE P1363.
683 */
684 int ec_GF2m_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
685 {
686 BN_CTX *new_ctx = NULL;
687 BIGNUM *x0, *y0, *x1, *y1, *x2, *y2, *s, *t;
688 int ret = 0;
689
690 if (EC_POINT_is_at_infinity(group, a))
691 {
692 if (!EC_POINT_copy(r, b)) return 0;
693 return 1;
694 }
695
696 if (EC_POINT_is_at_infinity(group, b))
697 {
698 if (!EC_POINT_copy(r, a)) return 0;
699 return 1;
700 }
701
702 if (ctx == NULL)
703 {
704 ctx = new_ctx = BN_CTX_new();
705 if (ctx == NULL)
706 return 0;
707 }
708
709 BN_CTX_start(ctx);
710 x0 = BN_CTX_get(ctx);
711 y0 = BN_CTX_get(ctx);
712 x1 = BN_CTX_get(ctx);
713 y1 = BN_CTX_get(ctx);
714 x2 = BN_CTX_get(ctx);
715 y2 = BN_CTX_get(ctx);
716 s = BN_CTX_get(ctx);
717 t = BN_CTX_get(ctx);
718 if (t == NULL) goto err;
719
720 if (a->Z_is_one)
721 {
722 if (!BN_copy(x0, &a->X)) goto err;
723 if (!BN_copy(y0, &a->Y)) goto err;
724 }
725 else
726 {
727 if (!EC_POINT_get_affine_coordinates_GF2m(group, a, x0, y0, ctx)) goto err;
728 }
729 if (b->Z_is_one)
730 {
731 if (!BN_copy(x1, &b->X)) goto err;
732 if (!BN_copy(y1, &b->Y)) goto err;
733 }
734 else
735 {
736 if (!EC_POINT_get_affine_coordinates_GF2m(group, b, x1, y1, ctx)) goto err;
737 }
738
739
740 if (BN_GF2m_cmp(x0, x1))
741 {
742 if (!BN_GF2m_add(t, x0, x1)) goto err;
743 if (!BN_GF2m_add(s, y0, y1)) goto err;
744 if (!group->meth->field_div(group, s, s, t, ctx)) goto err;
745 if (!group->meth->field_sqr(group, x2, s, ctx)) goto err;
746 if (!BN_GF2m_add(x2, x2, &group->a)) goto err;
747 if (!BN_GF2m_add(x2, x2, s)) goto err;
748 if (!BN_GF2m_add(x2, x2, t)) goto err;
749 }
750 else
751 {
752 if (BN_GF2m_cmp(y0, y1) || BN_is_zero(x1))
753 {
754 if (!EC_POINT_set_to_infinity(group, r)) goto err;
755 ret = 1;
756 goto err;
757 }
758 if (!group->meth->field_div(group, s, y1, x1, ctx)) goto err;
759 if (!BN_GF2m_add(s, s, x1)) goto err;
760
761 if (!group->meth->field_sqr(group, x2, s, ctx)) goto err;
762 if (!BN_GF2m_add(x2, x2, s)) goto err;
763 if (!BN_GF2m_add(x2, x2, &group->a)) goto err;
764 }
765
766 if (!BN_GF2m_add(y2, x1, x2)) goto err;
767 if (!group->meth->field_mul(group, y2, y2, s, ctx)) goto err;
768 if (!BN_GF2m_add(y2, y2, x2)) goto err;
769 if (!BN_GF2m_add(y2, y2, y1)) goto err;
770
771 if (!EC_POINT_set_affine_coordinates_GF2m(group, r, x2, y2, ctx)) goto err;
772
773 ret = 1;
774
775 err:
776 BN_CTX_end(ctx);
777 if (new_ctx != NULL)
778 BN_CTX_free(new_ctx);
779 return ret;
780 }
781
782
783 /* Computes 2 * a and stores the result in r. r could be a.
784 * Uses algorithm A.10.2 of IEEE P1363.
785 */
786 int ec_GF2m_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_CTX *ctx)
787 {
788 return ec_GF2m_simple_add(group, r, a, a, ctx);
789 }
790
791
792 int ec_GF2m_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
793 {
794 if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(&point->Y))
795 /* point is its own inverse */
796 return 1;
797
798 if (!EC_POINT_make_affine(group, point, ctx)) return 0;
799 return BN_GF2m_add(&point->Y, &point->X, &point->Y);
800 }
801
802
803 /* Indicates whether the given point is the point at infinity. */
804 int ec_GF2m_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point)
805 {
806 return BN_is_zero(&point->Z);
807 }
808
809
810 /* Determines whether the given EC_POINT is an actual point on the curve defined
811 * in the EC_GROUP. A point is valid if it satisfies the Weierstrass equation:
812 * y^2 + x*y = x^3 + a*x^2 + b.
813 */
814 int ec_GF2m_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx)
815 {
816 BN_CTX *new_ctx = NULL;
817 BIGNUM *rh, *lh, *tmp1;
818 int ret = -1;
819
820 if (EC_POINT_is_at_infinity(group, point))
821 return 1;
822
823 /* only support affine coordinates */
824 if (!point->Z_is_one) goto err;
825
826 if (ctx == NULL)
827 {
828 ctx = new_ctx = BN_CTX_new();
829 if (ctx == NULL)
830 return -1;
831 }
832
833 BN_CTX_start(ctx);
834 rh = BN_CTX_get(ctx);
835 lh = BN_CTX_get(ctx);
836 tmp1 = BN_CTX_get(ctx);
837 if (tmp1 == NULL) goto err;
838
839 /* We have a curve defined by a Weierstrass equation
840 * y^2 + x*y = x^3 + a*x^2 + b.
841 * To test this, we add up the right-hand side in 'rh'
842 * and the left-hand side in 'lh'.
843 */
844
845 /* rh := X^3 */
846 if (!group->meth->field_sqr(group, tmp1, &point->X, ctx)) goto err;
847 if (!group->meth->field_mul(group, rh, tmp1, &point->X, ctx)) goto err;
848
849 /* rh := rh + a*X^2 */
850 if (!group->meth->field_mul(group, tmp1, tmp1, &group->a, ctx)) goto err;
851 if (!BN_GF2m_add(rh, rh, tmp1)) goto err;
852
853 /* rh := rh + b */
854 if (!BN_GF2m_add(rh, rh, &group->b)) goto err;
855
856 /* lh := Y^2 */
857 if (!group->meth->field_sqr(group, lh, &point->Y, ctx)) goto err;
858
859 /* lh := lh + x*y */
860 if (!group->meth->field_mul(group, tmp1, &point->X, &point->Y, ctx)) goto err;
861 if (!BN_GF2m_add(lh, lh, tmp1)) goto err;
862
863 ret = (0 == BN_GF2m_cmp(lh, rh));
864
865 err:
866 if (ctx) BN_CTX_end(ctx);
867 if (new_ctx) BN_CTX_free(new_ctx);
868 return ret;
869 }
870
871
872 /* Indicates whether two points are equal.
873 * Return values:
874 * -1 error
875 * 0 equal (in affine coordinates)
876 * 1 not equal
877 */
878 int ec_GF2m_simple_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
879 {
880 BIGNUM *aX, *aY, *bX, *bY;
881 BN_CTX *new_ctx = NULL;
882 int ret = -1;
883
884 if (EC_POINT_is_at_infinity(group, a))
885 {
886 return EC_POINT_is_at_infinity(group, b) ? 0 : 1;
887 }
888
889 if (a->Z_is_one && b->Z_is_one)
890 {
891 return ((BN_cmp(&a->X, &b->X) == 0) && BN_cmp(&a->Y, &b->Y) == 0) ? 0 : 1;
892 }
893
894 if (ctx == NULL)
895 {
896 ctx = new_ctx = BN_CTX_new();
897 if (ctx == NULL)
898 return -1;
899 }
900
901 BN_CTX_start(ctx);
902 aX = BN_CTX_get(ctx);
903 aY = BN_CTX_get(ctx);
904 bX = BN_CTX_get(ctx);
905 bY = BN_CTX_get(ctx);
906 if (bY == NULL) goto err;
907
908 if (!EC_POINT_get_affine_coordinates_GF2m(group, a, aX, aY, ctx)) goto err;
909 if (!EC_POINT_get_affine_coordinates_GF2m(group, b, bX, bY, ctx)) goto err;
910 ret = ((BN_cmp(aX, bX) == 0) && BN_cmp(aY, bY) == 0) ? 0 : 1;
911
912 err:
913 if (ctx) BN_CTX_end(ctx);
914 if (new_ctx) BN_CTX_free(new_ctx);
915 return ret;
916 }
917
918
919 /* Forces the given EC_POINT to internally use affine coordinates. */
920 int ec_GF2m_simple_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
921 {
922 BN_CTX *new_ctx = NULL;
923 BIGNUM *x, *y;
924 int ret = 0;
925
926 if (point->Z_is_one || EC_POINT_is_at_infinity(group, point))
927 return 1;
928
929 if (ctx == NULL)
930 {
931 ctx = new_ctx = BN_CTX_new();
932 if (ctx == NULL)
933 return 0;
934 }
935
936 BN_CTX_start(ctx);
937 x = BN_CTX_get(ctx);
938 y = BN_CTX_get(ctx);
939 if (y == NULL) goto err;
940
941 if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err;
942 if (!BN_copy(&point->X, x)) goto err;
943 if (!BN_copy(&point->Y, y)) goto err;
944 if (!BN_one(&point->Z)) goto err;
945
946 ret = 1;
947
948 err:
949 if (ctx) BN_CTX_end(ctx);
950 if (new_ctx) BN_CTX_free(new_ctx);
951 return ret;
952 }
953
954
955 /* Forces each of the EC_POINTs in the given array to use affine coordinates. */
956 int ec_GF2m_simple_points_make_affine(const EC_GROUP *group, size_t num, EC_POINT *points[], BN_CTX *ctx)
957 {
958 size_t i;
959
960 for (i = 0; i < num; i++)
961 {
962 if (!group->meth->make_affine(group, points[i], ctx)) return 0;
963 }
964
965 return 1;
966 }
967
968
969 /* Wrapper to simple binary polynomial field multiplication implementation. */
970 int ec_GF2m_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
971 {
972 return BN_GF2m_mod_mul_arr(r, a, b, group->poly, ctx);
973 }
974
975
976 /* Wrapper to simple binary polynomial field squaring implementation. */
977 int ec_GF2m_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx)
978 {
979 return BN_GF2m_mod_sqr_arr(r, a, group->poly, ctx);
980 }
981
982
983 /* Wrapper to simple binary polynomial field division implementation. */
984 int ec_GF2m_simple_field_div(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
985 {
986 return BN_GF2m_mod_div(r, a, b, &group->field, ctx);
987 }
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