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[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) 1998-2005 The OpenSSL Project. All rights reserved.
18 *
19 * Redistribution and use in source and binary forms, with or without
20 * modification, are permitted provided that the following conditions
21 * are met:
22 *
23 * 1. Redistributions of source code must retain the above copyright
24 * notice, this list of conditions and the following disclaimer.
25 *
26 * 2. Redistributions in binary form must reproduce the above copyright
27 * notice, this list of conditions and the following disclaimer in
28 * the documentation and/or other materials provided with the
29 * distribution.
30 *
31 * 3. All advertising materials mentioning features or use of this
32 * software must display the following acknowledgment:
33 * "This product includes software developed by the OpenSSL Project
34 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
35 *
36 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
37 * endorse or promote products derived from this software without
38 * prior written permission. For written permission, please contact
39 * openssl-core@openssl.org.
40 *
41 * 5. Products derived from this software may not be called "OpenSSL"
42 * nor may "OpenSSL" appear in their names without prior written
43 * permission of the OpenSSL Project.
44 *
45 * 6. Redistributions of any form whatsoever must retain the following
46 * acknowledgment:
47 * "This product includes software developed by the OpenSSL Project
48 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
49 *
50 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
51 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
52 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
53 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
54 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
55 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
56 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
57 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
58 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
59 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
60 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
61 * OF THE POSSIBILITY OF SUCH DAMAGE.
62 * ====================================================================
63 *
64 * This product includes cryptographic software written by Eric Young
65 * (eay@cryptsoft.com). This product includes software written by Tim
66 * Hudson (tjh@cryptsoft.com).
67 *
68 */
69
70 #include <openssl/err.h>
71
72 #include "ec_lcl.h"
73
74
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 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. */
186 int 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 */
219 int 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. */
246 int 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 */
255 int 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
283 err:
284 BN_CTX_end(ctx);
285 if (new_ctx != NULL)
286 BN_CTX_free(new_ctx);
287 return ret;
288 }
289
290
291 /* Initializes an EC_POINT. */
292 int ec_GF2m_simple_point_init(EC_POINT *point)
293 {
294 BN_init(&point->X);
295 BN_init(&point->Y);
296 BN_init(&point->Z);
297 return 1;
298 }
299
300
301 /* Frees an EC_POINT. */
302 void ec_GF2m_simple_point_finish(EC_POINT *point)
303 {
304 BN_free(&point->X);
305 BN_free(&point->Y);
306 BN_free(&point->Z);
307 }
308
309
310 /* Clears and frees an EC_POINT. */
311 void ec_GF2m_simple_point_clear_finish(EC_POINT *point)
312 {
313 BN_clear_free(&point->X);
314 BN_clear_free(&point->Y);
315 BN_clear_free(&point->Z);
316 point->Z_is_one = 0;
317 }
318
319
320 /* Copy the contents of one EC_POINT into another. Assumes dest is initialized. */
321 int ec_GF2m_simple_point_copy(EC_POINT *dest, const EC_POINT *src)
322 {
323 if (!BN_copy(&dest->X, &src->X)) return 0;
324 if (!BN_copy(&dest->Y, &src->Y)) return 0;
325 if (!BN_copy(&dest->Z, &src->Z)) return 0;
326 dest->Z_is_one = src->Z_is_one;
327
328 return 1;
329 }
330
331
332 /* Set an EC_POINT to the point at infinity.
333 * A point at infinity is represented by having Z=0.
334 */
335 int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *group, EC_POINT *point)
336 {
337 point->Z_is_one = 0;
338 BN_zero(&point->Z);
339 return 1;
340 }
341
342
343 /* Set the coordinates of an EC_POINT using affine coordinates.
344 * Note that the simple implementation only uses affine coordinates.
345 */
346 int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *group, EC_POINT *point,
347 const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx)
348 {
349 int ret = 0;
350 if (x == NULL || y == NULL)
351 {
352 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_SET_AFFINE_COORDINATES, ERR_R_PASSED_NULL_PARAMETER);
353 return 0;
354 }
355
356 if (!BN_copy(&point->X, x)) goto err;
357 BN_set_negative(&point->X, 0);
358 if (!BN_copy(&point->Y, y)) goto err;
359 BN_set_negative(&point->Y, 0);
360 if (!BN_copy(&point->Z, BN_value_one())) goto err;
361 BN_set_negative(&point->Z, 0);
362 point->Z_is_one = 1;
363 ret = 1;
364
365 err:
366 return ret;
367 }
368
369
370 /* Gets the affine coordinates of an EC_POINT.
371 * Note that the simple implementation only uses affine coordinates.
372 */
373 int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point,
374 BIGNUM *x, BIGNUM *y, BN_CTX *ctx)
375 {
376 int ret = 0;
377
378 if (EC_POINT_is_at_infinity(group, point))
379 {
380 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES, EC_R_POINT_AT_INFINITY);
381 return 0;
382 }
383
384 if (BN_cmp(&point->Z, BN_value_one()))
385 {
386 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
387 return 0;
388 }
389 if (x != NULL)
390 {
391 if (!BN_copy(x, &point->X)) goto err;
392 BN_set_negative(x, 0);
393 }
394 if (y != NULL)
395 {
396 if (!BN_copy(y, &point->Y)) goto err;
397 BN_set_negative(y, 0);
398 }
399 ret = 1;
400
401 err:
402 return ret;
403 }
404
405
406 /* Calculates and sets the affine coordinates of an EC_POINT from the given
407 * compressed coordinates. Uses algorithm 2.3.4 of SEC 1.
408 * Note that the simple implementation only uses affine coordinates.
409 *
410 * The method is from the following publication:
411 *
412 * Harper, Menezes, Vanstone:
413 * "Public-Key Cryptosystems with Very Small Key Lengths",
414 * EUROCRYPT '92, Springer-Verlag LNCS 658,
415 * published February 1993
416 *
417 * US Patents 6,141,420 and 6,618,483 (Vanstone, Mullin, Agnew) describe
418 * the same method, but claim no priority date earlier than July 29, 1994
419 * (and additionally fail to cite the EUROCRYPT '92 publication as prior art).
420 */
421 int ec_GF2m_simple_set_compressed_coordinates(const EC_GROUP *group, EC_POINT *point,
422 const BIGNUM *x_, int y_bit, BN_CTX *ctx)
423 {
424 BN_CTX *new_ctx = NULL;
425 BIGNUM *tmp, *x, *y, *z;
426 int ret = 0, z0;
427
428 /* clear error queue */
429 ERR_clear_error();
430
431 if (ctx == NULL)
432 {
433 ctx = new_ctx = BN_CTX_new();
434 if (ctx == NULL)
435 return 0;
436 }
437
438 y_bit = (y_bit != 0) ? 1 : 0;
439
440 BN_CTX_start(ctx);
441 tmp = BN_CTX_get(ctx);
442 x = BN_CTX_get(ctx);
443 y = BN_CTX_get(ctx);
444 z = BN_CTX_get(ctx);
445 if (z == NULL) goto err;
446
447 if (!BN_GF2m_mod_arr(x, x_, group->poly)) goto err;
448 if (BN_is_zero(x))
449 {
450 if (!BN_GF2m_mod_sqrt_arr(y, &group->b, group->poly, ctx)) goto err;
451 }
452 else
453 {
454 if (!group->meth->field_sqr(group, tmp, x, ctx)) goto err;
455 if (!group->meth->field_div(group, tmp, &group->b, tmp, ctx)) goto err;
456 if (!BN_GF2m_add(tmp, &group->a, tmp)) goto err;
457 if (!BN_GF2m_add(tmp, x, tmp)) goto err;
458 if (!BN_GF2m_mod_solve_quad_arr(z, tmp, group->poly, ctx))
459 {
460 unsigned long err = ERR_peek_last_error();
461
462 if (ERR_GET_LIB(err) == ERR_LIB_BN && ERR_GET_REASON(err) == BN_R_NO_SOLUTION)
463 {
464 ERR_clear_error();
465 ECerr(EC_F_EC_GF2M_SIMPLE_SET_COMPRESSED_COORDINATES, EC_R_INVALID_COMPRESSED_POINT);
466 }
467 else
468 ECerr(EC_F_EC_GF2M_SIMPLE_SET_COMPRESSED_COORDINATES, ERR_R_BN_LIB);
469 goto err;
470 }
471 z0 = (BN_is_odd(z)) ? 1 : 0;
472 if (!group->meth->field_mul(group, y, x, z, ctx)) goto err;
473 if (z0 != y_bit)
474 {
475 if (!BN_GF2m_add(y, y, x)) goto err;
476 }
477 }
478
479 if (!EC_POINT_set_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err;
480
481 ret = 1;
482
483 err:
484 BN_CTX_end(ctx);
485 if (new_ctx != NULL)
486 BN_CTX_free(new_ctx);
487 return ret;
488 }
489
490
491 /* Converts an EC_POINT to an octet string.
492 * If buf is NULL, the encoded length will be returned.
493 * If the length len of buf is smaller than required an error will be returned.
494 */
495 size_t ec_GF2m_simple_point2oct(const EC_GROUP *group, const EC_POINT *point, point_conversion_form_t form,
496 unsigned char *buf, size_t len, BN_CTX *ctx)
497 {
498 size_t ret;
499 BN_CTX *new_ctx = NULL;
500 int used_ctx = 0;
501 BIGNUM *x, *y, *yxi;
502 size_t field_len, i, skip;
503
504 if ((form != POINT_CONVERSION_COMPRESSED)
505 && (form != POINT_CONVERSION_UNCOMPRESSED)
506 && (form != POINT_CONVERSION_HYBRID))
507 {
508 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_INVALID_FORM);
509 goto err;
510 }
511
512 if (EC_POINT_is_at_infinity(group, point))
513 {
514 /* encodes to a single 0 octet */
515 if (buf != NULL)
516 {
517 if (len < 1)
518 {
519 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);
520 return 0;
521 }
522 buf[0] = 0;
523 }
524 return 1;
525 }
526
527
528 /* ret := required output buffer length */
529 field_len = (EC_GROUP_get_degree(group) + 7) / 8;
530 ret = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len;
531
532 /* if 'buf' is NULL, just return required length */
533 if (buf != NULL)
534 {
535 if (len < ret)
536 {
537 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);
538 goto err;
539 }
540
541 if (ctx == NULL)
542 {
543 ctx = new_ctx = BN_CTX_new();
544 if (ctx == NULL)
545 return 0;
546 }
547
548 BN_CTX_start(ctx);
549 used_ctx = 1;
550 x = BN_CTX_get(ctx);
551 y = BN_CTX_get(ctx);
552 yxi = BN_CTX_get(ctx);
553 if (yxi == NULL) goto err;
554
555 if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err;
556
557 buf[0] = form;
558 if ((form != POINT_CONVERSION_UNCOMPRESSED) && !BN_is_zero(x))
559 {
560 if (!group->meth->field_div(group, yxi, y, x, ctx)) goto err;
561 if (BN_is_odd(yxi)) buf[0]++;
562 }
563
564 i = 1;
565
566 skip = field_len - BN_num_bytes(x);
567 if (skip > field_len)
568 {
569 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
570 goto err;
571 }
572 while (skip > 0)
573 {
574 buf[i++] = 0;
575 skip--;
576 }
577 skip = BN_bn2bin(x, buf + i);
578 i += skip;
579 if (i != 1 + field_len)
580 {
581 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
582 goto err;
583 }
584
585 if (form == POINT_CONVERSION_UNCOMPRESSED || form == POINT_CONVERSION_HYBRID)
586 {
587 skip = field_len - BN_num_bytes(y);
588 if (skip > field_len)
589 {
590 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
591 goto err;
592 }
593 while (skip > 0)
594 {
595 buf[i++] = 0;
596 skip--;
597 }
598 skip = BN_bn2bin(y, buf + i);
599 i += skip;
600 }
601
602 if (i != ret)
603 {
604 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
605 goto err;
606 }
607 }
608
609 if (used_ctx)
610 BN_CTX_end(ctx);
611 if (new_ctx != NULL)
612 BN_CTX_free(new_ctx);
613 return ret;
614
615 err:
616 if (used_ctx)
617 BN_CTX_end(ctx);
618 if (new_ctx != NULL)
619 BN_CTX_free(new_ctx);
620 return 0;
621 }
622
623
624 /* Converts an octet string representation to an EC_POINT.
625 * Note that the simple implementation only uses affine coordinates.
626 */
627 int ec_GF2m_simple_oct2point(const EC_GROUP *group, EC_POINT *point,
628 const unsigned char *buf, size_t len, BN_CTX *ctx)
629 {
630 point_conversion_form_t form;
631 int y_bit;
632 BN_CTX *new_ctx = NULL;
633 BIGNUM *x, *y, *yxi;
634 size_t field_len, enc_len;
635 int ret = 0;
636
637 if (len == 0)
638 {
639 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_BUFFER_TOO_SMALL);
640 return 0;
641 }
642 form = buf[0];
643 y_bit = form & 1;
644 form = form & ~1U;
645 if ((form != 0) && (form != POINT_CONVERSION_COMPRESSED)
646 && (form != POINT_CONVERSION_UNCOMPRESSED)
647 && (form != POINT_CONVERSION_HYBRID))
648 {
649 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
650 return 0;
651 }
652 if ((form == 0 || form == POINT_CONVERSION_UNCOMPRESSED) && y_bit)
653 {
654 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
655 return 0;
656 }
657
658 if (form == 0)
659 {
660 if (len != 1)
661 {
662 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
663 return 0;
664 }
665
666 return EC_POINT_set_to_infinity(group, point);
667 }
668
669 field_len = (EC_GROUP_get_degree(group) + 7) / 8;
670 enc_len = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len;
671
672 if (len != enc_len)
673 {
674 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
675 return 0;
676 }
677
678 if (ctx == NULL)
679 {
680 ctx = new_ctx = BN_CTX_new();
681 if (ctx == NULL)
682 return 0;
683 }
684
685 BN_CTX_start(ctx);
686 x = BN_CTX_get(ctx);
687 y = BN_CTX_get(ctx);
688 yxi = BN_CTX_get(ctx);
689 if (yxi == NULL) goto err;
690
691 if (!BN_bin2bn(buf + 1, field_len, x)) goto err;
692 if (BN_ucmp(x, &group->field) >= 0)
693 {
694 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
695 goto err;
696 }
697
698 if (form == POINT_CONVERSION_COMPRESSED)
699 {
700 if (!EC_POINT_set_compressed_coordinates_GF2m(group, point, x, y_bit, ctx)) goto err;
701 }
702 else
703 {
704 if (!BN_bin2bn(buf + 1 + field_len, field_len, y)) goto err;
705 if (BN_ucmp(y, &group->field) >= 0)
706 {
707 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
708 goto err;
709 }
710 if (form == POINT_CONVERSION_HYBRID)
711 {
712 if (!group->meth->field_div(group, yxi, y, x, ctx)) goto err;
713 if (y_bit != BN_is_odd(yxi))
714 {
715 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
716 goto err;
717 }
718 }
719
720 if (!EC_POINT_set_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err;
721 }
722
723 if (!EC_POINT_is_on_curve(group, point, ctx)) /* test required by X9.62 */
724 {
725 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_POINT_IS_NOT_ON_CURVE);
726 goto err;
727 }
728
729 ret = 1;
730
731 err:
732 BN_CTX_end(ctx);
733 if (new_ctx != NULL)
734 BN_CTX_free(new_ctx);
735 return ret;
736 }
737
738
739 /* Computes a + b and stores the result in r. r could be a or b, a could be b.
740 * Uses algorithm A.10.2 of IEEE P1363.
741 */
742 int ec_GF2m_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
743 {
744 BN_CTX *new_ctx = NULL;
745 BIGNUM *x0, *y0, *x1, *y1, *x2, *y2, *s, *t;
746 int ret = 0;
747
748 if (EC_POINT_is_at_infinity(group, a))
749 {
750 if (!EC_POINT_copy(r, b)) return 0;
751 return 1;
752 }
753
754 if (EC_POINT_is_at_infinity(group, b))
755 {
756 if (!EC_POINT_copy(r, a)) return 0;
757 return 1;
758 }
759
760 if (ctx == NULL)
761 {
762 ctx = new_ctx = BN_CTX_new();
763 if (ctx == NULL)
764 return 0;
765 }
766
767 BN_CTX_start(ctx);
768 x0 = BN_CTX_get(ctx);
769 y0 = BN_CTX_get(ctx);
770 x1 = BN_CTX_get(ctx);
771 y1 = BN_CTX_get(ctx);
772 x2 = BN_CTX_get(ctx);
773 y2 = BN_CTX_get(ctx);
774 s = BN_CTX_get(ctx);
775 t = BN_CTX_get(ctx);
776 if (t == NULL) goto err;
777
778 if (a->Z_is_one)
779 {
780 if (!BN_copy(x0, &a->X)) goto err;
781 if (!BN_copy(y0, &a->Y)) goto err;
782 }
783 else
784 {
785 if (!EC_POINT_get_affine_coordinates_GF2m(group, a, x0, y0, ctx)) goto err;
786 }
787 if (b->Z_is_one)
788 {
789 if (!BN_copy(x1, &b->X)) goto err;
790 if (!BN_copy(y1, &b->Y)) goto err;
791 }
792 else
793 {
794 if (!EC_POINT_get_affine_coordinates_GF2m(group, b, x1, y1, ctx)) goto err;
795 }
796
797
798 if (BN_GF2m_cmp(x0, x1))
799 {
800 if (!BN_GF2m_add(t, x0, x1)) goto err;
801 if (!BN_GF2m_add(s, y0, y1)) goto err;
802 if (!group->meth->field_div(group, s, s, t, ctx)) goto err;
803 if (!group->meth->field_sqr(group, x2, s, ctx)) goto err;
804 if (!BN_GF2m_add(x2, x2, &group->a)) goto err;
805 if (!BN_GF2m_add(x2, x2, s)) goto err;
806 if (!BN_GF2m_add(x2, x2, t)) goto err;
807 }
808 else
809 {
810 if (BN_GF2m_cmp(y0, y1) || BN_is_zero(x1))
811 {
812 if (!EC_POINT_set_to_infinity(group, r)) goto err;
813 ret = 1;
814 goto err;
815 }
816 if (!group->meth->field_div(group, s, y1, x1, ctx)) goto err;
817 if (!BN_GF2m_add(s, s, x1)) goto err;
818
819 if (!group->meth->field_sqr(group, x2, s, ctx)) goto err;
820 if (!BN_GF2m_add(x2, x2, s)) goto err;
821 if (!BN_GF2m_add(x2, x2, &group->a)) goto err;
822 }
823
824 if (!BN_GF2m_add(y2, x1, x2)) goto err;
825 if (!group->meth->field_mul(group, y2, y2, s, ctx)) goto err;
826 if (!BN_GF2m_add(y2, y2, x2)) goto err;
827 if (!BN_GF2m_add(y2, y2, y1)) goto err;
828
829 if (!EC_POINT_set_affine_coordinates_GF2m(group, r, x2, y2, ctx)) goto err;
830
831 ret = 1;
832
833 err:
834 BN_CTX_end(ctx);
835 if (new_ctx != NULL)
836 BN_CTX_free(new_ctx);
837 return ret;
838 }
839
840
841 /* Computes 2 * a and stores the result in r. r could be a.
842 * Uses algorithm A.10.2 of IEEE P1363.
843 */
844 int ec_GF2m_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_CTX *ctx)
845 {
846 return ec_GF2m_simple_add(group, r, a, a, ctx);
847 }
848
849
850 int ec_GF2m_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
851 {
852 if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(&point->Y))
853 /* point is its own inverse */
854 return 1;
855
856 if (!EC_POINT_make_affine(group, point, ctx)) return 0;
857 return BN_GF2m_add(&point->Y, &point->X, &point->Y);
858 }
859
860
861 /* Indicates whether the given point is the point at infinity. */
862 int ec_GF2m_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point)
863 {
864 return BN_is_zero(&point->Z);
865 }
866
867
868 /* Determines whether the given EC_POINT is an actual point on the curve defined
869 * in the EC_GROUP. A point is valid if it satisfies the Weierstrass equation:
870 * y^2 + x*y = x^3 + a*x^2 + b.
871 */
872 int ec_GF2m_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx)
873 {
874 int ret = -1;
875 BN_CTX *new_ctx = NULL;
876 BIGNUM *lh, *y2;
877 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
878 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
879
880 if (EC_POINT_is_at_infinity(group, point))
881 return 1;
882
883 field_mul = group->meth->field_mul;
884 field_sqr = group->meth->field_sqr;
885
886 /* only support affine coordinates */
887 if (!point->Z_is_one) goto err;
888
889 if (ctx == NULL)
890 {
891 ctx = new_ctx = BN_CTX_new();
892 if (ctx == NULL)
893 return -1;
894 }
895
896 BN_CTX_start(ctx);
897 y2 = BN_CTX_get(ctx);
898 lh = BN_CTX_get(ctx);
899 if (lh == NULL) goto err;
900
901 /* We have a curve defined by a Weierstrass equation
902 * y^2 + x*y = x^3 + a*x^2 + b.
903 * <=> x^3 + a*x^2 + x*y + b + y^2 = 0
904 * <=> ((x + a) * x + y ) * x + b + y^2 = 0
905 */
906 if (!BN_GF2m_add(lh, &point->X, &group->a)) goto err;
907 if (!field_mul(group, lh, lh, &point->X, ctx)) goto err;
908 if (!BN_GF2m_add(lh, lh, &point->Y)) goto err;
909 if (!field_mul(group, lh, lh, &point->X, ctx)) goto err;
910 if (!BN_GF2m_add(lh, lh, &group->b)) goto err;
911 if (!field_sqr(group, y2, &point->Y, ctx)) goto err;
912 if (!BN_GF2m_add(lh, lh, y2)) goto err;
913 ret = BN_is_zero(lh);
914 err:
915 if (ctx) BN_CTX_end(ctx);
916 if (new_ctx) BN_CTX_free(new_ctx);
917 return ret;
918 }
919
920
921 /* Indicates whether two points are equal.
922 * Return values:
923 * -1 error
924 * 0 equal (in affine coordinates)
925 * 1 not equal
926 */
927 int ec_GF2m_simple_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
928 {
929 BIGNUM *aX, *aY, *bX, *bY;
930 BN_CTX *new_ctx = NULL;
931 int ret = -1;
932
933 if (EC_POINT_is_at_infinity(group, a))
934 {
935 return EC_POINT_is_at_infinity(group, b) ? 0 : 1;
936 }
937
938 if (a->Z_is_one && b->Z_is_one)
939 {
940 return ((BN_cmp(&a->X, &b->X) == 0) && BN_cmp(&a->Y, &b->Y) == 0) ? 0 : 1;
941 }
942
943 if (ctx == NULL)
944 {
945 ctx = new_ctx = BN_CTX_new();
946 if (ctx == NULL)
947 return -1;
948 }
949
950 BN_CTX_start(ctx);
951 aX = BN_CTX_get(ctx);
952 aY = BN_CTX_get(ctx);
953 bX = BN_CTX_get(ctx);
954 bY = BN_CTX_get(ctx);
955 if (bY == NULL) goto err;
956
957 if (!EC_POINT_get_affine_coordinates_GF2m(group, a, aX, aY, ctx)) goto err;
958 if (!EC_POINT_get_affine_coordinates_GF2m(group, b, bX, bY, ctx)) goto err;
959 ret = ((BN_cmp(aX, bX) == 0) && BN_cmp(aY, bY) == 0) ? 0 : 1;
960
961 err:
962 if (ctx) BN_CTX_end(ctx);
963 if (new_ctx) BN_CTX_free(new_ctx);
964 return ret;
965 }
966
967
968 /* Forces the given EC_POINT to internally use affine coordinates. */
969 int ec_GF2m_simple_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
970 {
971 BN_CTX *new_ctx = NULL;
972 BIGNUM *x, *y;
973 int ret = 0;
974
975 if (point->Z_is_one || EC_POINT_is_at_infinity(group, point))
976 return 1;
977
978 if (ctx == NULL)
979 {
980 ctx = new_ctx = BN_CTX_new();
981 if (ctx == NULL)
982 return 0;
983 }
984
985 BN_CTX_start(ctx);
986 x = BN_CTX_get(ctx);
987 y = BN_CTX_get(ctx);
988 if (y == NULL) goto err;
989
990 if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err;
991 if (!BN_copy(&point->X, x)) goto err;
992 if (!BN_copy(&point->Y, y)) goto err;
993 if (!BN_one(&point->Z)) goto err;
994
995 ret = 1;
996
997 err:
998 if (ctx) BN_CTX_end(ctx);
999 if (new_ctx) BN_CTX_free(new_ctx);
1000 return ret;
1001 }
1002
1003
1004 /* Forces each of the EC_POINTs in the given array to use affine coordinates. */
1005 int ec_GF2m_simple_points_make_affine(const EC_GROUP *group, size_t num, EC_POINT *points[], BN_CTX *ctx)
1006 {
1007 size_t i;
1008
1009 for (i = 0; i < num; i++)
1010 {
1011 if (!group->meth->make_affine(group, points[i], ctx)) return 0;
1012 }
1013
1014 return 1;
1015 }
1016
1017
1018 /* Wrapper to simple binary polynomial field multiplication implementation. */
1019 int ec_GF2m_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
1020 {
1021 return BN_GF2m_mod_mul_arr(r, a, b, group->poly, ctx);
1022 }
1023
1024
1025 /* Wrapper to simple binary polynomial field squaring implementation. */
1026 int ec_GF2m_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx)
1027 {
1028 return BN_GF2m_mod_sqr_arr(r, a, group->poly, ctx);
1029 }
1030
1031
1032 /* Wrapper to simple binary polynomial field division implementation. */
1033 int ec_GF2m_simple_field_div(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
1034 {
1035 return BN_GF2m_mod_div(r, a, b, &group->field, ctx);
1036 }
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