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