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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) 1998-2005 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 group->poly[5] = -1;
161 }
162
163
164 /* Copy a GF(2^m)-based EC_GROUP structure.
165 * Note that all other members are handled by EC_GROUP_copy.
166 */
167 int ec_GF2m_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src)
168 {
169 int i;
170 if (!BN_copy(&dest->field, &src->field)) return 0;
171 if (!BN_copy(&dest->a, &src->a)) return 0;
172 if (!BN_copy(&dest->b, &src->b)) return 0;
173 dest->poly[0] = src->poly[0];
174 dest->poly[1] = src->poly[1];
175 dest->poly[2] = src->poly[2];
176 dest->poly[3] = src->poly[3];
177 dest->poly[4] = src->poly[4];
178 dest->poly[5] = src->poly[5];
179 if (bn_wexpand(&dest->a, (int)(dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) return 0;
180 if (bn_wexpand(&dest->b, (int)(dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) return 0;
181 for (i = dest->a.top; i < dest->a.dmax; i++) dest->a.d[i] = 0;
182 for (i = dest->b.top; i < dest->b.dmax; i++) dest->b.d[i] = 0;
183 return 1;
184 }
185
186
187 /* Set the curve parameters of an EC_GROUP structure. */
188 int ec_GF2m_simple_group_set_curve(EC_GROUP *group,
189 const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
190 {
191 int ret = 0, i;
192
193 /* group->field */
194 if (!BN_copy(&group->field, p)) goto err;
195 i = BN_GF2m_poly2arr(&group->field, group->poly, 6) - 1;
196 if ((i != 5) && (i != 3))
197 {
198 ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_SET_CURVE, EC_R_UNSUPPORTED_FIELD);
199 goto err;
200 }
201
202 /* group->a */
203 if (!BN_GF2m_mod_arr(&group->a, a, group->poly)) goto err;
204 if(bn_wexpand(&group->a, (int)(group->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) goto err;
205 for (i = group->a.top; i < group->a.dmax; i++) group->a.d[i] = 0;
206
207 /* group->b */
208 if (!BN_GF2m_mod_arr(&group->b, b, group->poly)) goto err;
209 if(bn_wexpand(&group->b, (int)(group->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) goto err;
210 for (i = group->b.top; i < group->b.dmax; i++) group->b.d[i] = 0;
211
212 ret = 1;
213 err:
214 return ret;
215 }
216
217
218 /* Get the curve parameters of an EC_GROUP structure.
219 * If p, a, or b are NULL then there values will not be set but the method will return with success.
220 */
221 int ec_GF2m_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx)
222 {
223 int ret = 0;
224
225 if (p != NULL)
226 {
227 if (!BN_copy(p, &group->field)) return 0;
228 }
229
230 if (a != NULL)
231 {
232 if (!BN_copy(a, &group->a)) goto err;
233 }
234
235 if (b != NULL)
236 {
237 if (!BN_copy(b, &group->b)) goto err;
238 }
239
240 ret = 1;
241
242 err:
243 return ret;
244 }
245
246
247 /* Gets the degree of the field. For a curve over GF(2^m) this is the value m. */
248 int ec_GF2m_simple_group_get_degree(const EC_GROUP *group)
249 {
250 return BN_num_bits(&group->field)-1;
251 }
252
253
254 /* Checks the discriminant of the curve.
255 * y^2 + x*y = x^3 + a*x^2 + b is an elliptic curve <=> b != 0 (mod p)
256 */
257 int ec_GF2m_simple_group_check_discriminant(const EC_GROUP *group, BN_CTX *ctx)
258 {
259 int ret = 0;
260 BIGNUM *b;
261 BN_CTX *new_ctx = NULL;
262
263 if (ctx == NULL)
264 {
265 ctx = new_ctx = BN_CTX_new();
266 if (ctx == NULL)
267 {
268 ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_CHECK_DISCRIMINANT, ERR_R_MALLOC_FAILURE);
269 goto err;
270 }
271 }
272 BN_CTX_start(ctx);
273 b = BN_CTX_get(ctx);
274 if (b == NULL) goto err;
275
276 if (!BN_GF2m_mod_arr(b, &group->b, group->poly)) goto err;
277
278 /* check the discriminant:
279 * y^2 + x*y = x^3 + a*x^2 + b is an elliptic curve <=> b != 0 (mod p)
280 */
281 if (BN_is_zero(b)) goto err;
282
283 ret = 1;
284
285 err:
286 if (ctx != NULL)
287 BN_CTX_end(ctx);
288 if (new_ctx != NULL)
289 BN_CTX_free(new_ctx);
290 return ret;
291 }
292
293
294 /* Initializes an EC_POINT. */
295 int ec_GF2m_simple_point_init(EC_POINT *point)
296 {
297 BN_init(&point->X);
298 BN_init(&point->Y);
299 BN_init(&point->Z);
300 return 1;
301 }
302
303
304 /* Frees an EC_POINT. */
305 void ec_GF2m_simple_point_finish(EC_POINT *point)
306 {
307 BN_free(&point->X);
308 BN_free(&point->Y);
309 BN_free(&point->Z);
310 }
311
312
313 /* Clears and frees an EC_POINT. */
314 void ec_GF2m_simple_point_clear_finish(EC_POINT *point)
315 {
316 BN_clear_free(&point->X);
317 BN_clear_free(&point->Y);
318 BN_clear_free(&point->Z);
319 point->Z_is_one = 0;
320 }
321
322
323 /* Copy the contents of one EC_POINT into another. Assumes dest is initialized. */
324 int ec_GF2m_simple_point_copy(EC_POINT *dest, const EC_POINT *src)
325 {
326 if (!BN_copy(&dest->X, &src->X)) return 0;
327 if (!BN_copy(&dest->Y, &src->Y)) return 0;
328 if (!BN_copy(&dest->Z, &src->Z)) return 0;
329 dest->Z_is_one = src->Z_is_one;
330
331 return 1;
332 }
333
334
335 /* Set an EC_POINT to the point at infinity.
336 * A point at infinity is represented by having Z=0.
337 */
338 int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *group, EC_POINT *point)
339 {
340 point->Z_is_one = 0;
341 BN_zero(&point->Z);
342 return 1;
343 }
344
345
346 /* Set the coordinates of an EC_POINT using affine coordinates.
347 * Note that the simple implementation only uses affine coordinates.
348 */
349 int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *group, EC_POINT *point,
350 const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx)
351 {
352 int ret = 0;
353 if (x == NULL || y == NULL)
354 {
355 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_SET_AFFINE_COORDINATES, ERR_R_PASSED_NULL_PARAMETER);
356 return 0;
357 }
358
359 if (!BN_copy(&point->X, x)) goto err;
360 BN_set_negative(&point->X, 0);
361 if (!BN_copy(&point->Y, y)) goto err;
362 BN_set_negative(&point->Y, 0);
363 if (!BN_copy(&point->Z, BN_value_one())) goto err;
364 BN_set_negative(&point->Z, 0);
365 point->Z_is_one = 1;
366 ret = 1;
367
368 err:
369 return ret;
370 }
371
372
373 /* Gets the affine coordinates of an EC_POINT.
374 * Note that the simple implementation only uses affine coordinates.
375 */
376 int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point,
377 BIGNUM *x, BIGNUM *y, BN_CTX *ctx)
378 {
379 int ret = 0;
380
381 if (EC_POINT_is_at_infinity(group, point))
382 {
383 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES, EC_R_POINT_AT_INFINITY);
384 return 0;
385 }
386
387 if (BN_cmp(&point->Z, BN_value_one()))
388 {
389 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
390 return 0;
391 }
392 if (x != NULL)
393 {
394 if (!BN_copy(x, &point->X)) goto err;
395 BN_set_negative(x, 0);
396 }
397 if (y != NULL)
398 {
399 if (!BN_copy(y, &point->Y)) goto err;
400 BN_set_negative(y, 0);
401 }
402 ret = 1;
403
404 err:
405 return ret;
406 }
407
408
409 /* Calculates and sets the affine coordinates of an EC_POINT from the given
410 * compressed coordinates. Uses algorithm 2.3.4 of SEC 1.
411 * Note that the simple implementation only uses affine coordinates.
412 *
413 * The method is from the following publication:
414 *
415 * Harper, Menezes, Vanstone:
416 * "Public-Key Cryptosystems with Very Small Key Lengths",
417 * EUROCRYPT '92, Springer-Verlag LNCS 658,
418 * published February 1993
419 *
420 * US Patents 6,141,420 and 6,618,483 (Vanstone, Mullin, Agnew) describe
421 * the same method, but claim no priority date earlier than July 29, 1994
422 * (and additionally fail to cite the EUROCRYPT '92 publication as prior art).
423 */
424 int ec_GF2m_simple_set_compressed_coordinates(const EC_GROUP *group, EC_POINT *point,
425 const BIGNUM *x_, int y_bit, BN_CTX *ctx)
426 {
427 BN_CTX *new_ctx = NULL;
428 BIGNUM *tmp, *x, *y, *z;
429 int ret = 0, z0;
430
431 /* clear error queue */
432 ERR_clear_error();
433
434 if (ctx == NULL)
435 {
436 ctx = new_ctx = BN_CTX_new();
437 if (ctx == NULL)
438 return 0;
439 }
440
441 y_bit = (y_bit != 0) ? 1 : 0;
442
443 BN_CTX_start(ctx);
444 tmp = BN_CTX_get(ctx);
445 x = BN_CTX_get(ctx);
446 y = BN_CTX_get(ctx);
447 z = BN_CTX_get(ctx);
448 if (z == NULL) goto err;
449
450 if (!BN_GF2m_mod_arr(x, x_, group->poly)) goto err;
451 if (BN_is_zero(x))
452 {
453 if (!BN_GF2m_mod_sqrt_arr(y, &group->b, group->poly, ctx)) goto err;
454 }
455 else
456 {
457 if (!group->meth->field_sqr(group, tmp, x, ctx)) goto err;
458 if (!group->meth->field_div(group, tmp, &group->b, tmp, ctx)) goto err;
459 if (!BN_GF2m_add(tmp, &group->a, tmp)) goto err;
460 if (!BN_GF2m_add(tmp, x, tmp)) goto err;
461 if (!BN_GF2m_mod_solve_quad_arr(z, tmp, group->poly, ctx))
462 {
463 unsigned long err = ERR_peek_last_error();
464
465 if (ERR_GET_LIB(err) == ERR_LIB_BN && ERR_GET_REASON(err) == BN_R_NO_SOLUTION)
466 {
467 ERR_clear_error();
468 ECerr(EC_F_EC_GF2M_SIMPLE_SET_COMPRESSED_COORDINATES, EC_R_INVALID_COMPRESSED_POINT);
469 }
470 else
471 ECerr(EC_F_EC_GF2M_SIMPLE_SET_COMPRESSED_COORDINATES, ERR_R_BN_LIB);
472 goto err;
473 }
474 z0 = (BN_is_odd(z)) ? 1 : 0;
475 if (!group->meth->field_mul(group, y, x, z, ctx)) goto err;
476 if (z0 != y_bit)
477 {
478 if (!BN_GF2m_add(y, y, x)) goto err;
479 }
480 }
481
482 if (!EC_POINT_set_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err;
483
484 ret = 1;
485
486 err:
487 BN_CTX_end(ctx);
488 if (new_ctx != NULL)
489 BN_CTX_free(new_ctx);
490 return ret;
491 }
492
493
494 /* Converts an EC_POINT to an octet string.
495 * If buf is NULL, the encoded length will be returned.
496 * If the length len of buf is smaller than required an error will be returned.
497 */
498 size_t ec_GF2m_simple_point2oct(const EC_GROUP *group, const EC_POINT *point, point_conversion_form_t form,
499 unsigned char *buf, size_t len, BN_CTX *ctx)
500 {
501 size_t ret;
502 BN_CTX *new_ctx = NULL;
503 int used_ctx = 0;
504 BIGNUM *x, *y, *yxi;
505 size_t field_len, i, skip;
506
507 if ((form != POINT_CONVERSION_COMPRESSED)
508 && (form != POINT_CONVERSION_UNCOMPRESSED)
509 && (form != POINT_CONVERSION_HYBRID))
510 {
511 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_INVALID_FORM);
512 goto err;
513 }
514
515 if (EC_POINT_is_at_infinity(group, point))
516 {
517 /* encodes to a single 0 octet */
518 if (buf != NULL)
519 {
520 if (len < 1)
521 {
522 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);
523 return 0;
524 }
525 buf[0] = 0;
526 }
527 return 1;
528 }
529
530
531 /* ret := required output buffer length */
532 field_len = (EC_GROUP_get_degree(group) + 7) / 8;
533 ret = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len;
534
535 /* if 'buf' is NULL, just return required length */
536 if (buf != NULL)
537 {
538 if (len < ret)
539 {
540 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);
541 goto err;
542 }
543
544 if (ctx == NULL)
545 {
546 ctx = new_ctx = BN_CTX_new();
547 if (ctx == NULL)
548 return 0;
549 }
550
551 BN_CTX_start(ctx);
552 used_ctx = 1;
553 x = BN_CTX_get(ctx);
554 y = BN_CTX_get(ctx);
555 yxi = BN_CTX_get(ctx);
556 if (yxi == NULL) goto err;
557
558 if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err;
559
560 buf[0] = form;
561 if ((form != POINT_CONVERSION_UNCOMPRESSED) && !BN_is_zero(x))
562 {
563 if (!group->meth->field_div(group, yxi, y, x, ctx)) goto err;
564 if (BN_is_odd(yxi)) buf[0]++;
565 }
566
567 i = 1;
568
569 skip = field_len - BN_num_bytes(x);
570 if (skip > field_len)
571 {
572 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
573 goto err;
574 }
575 while (skip > 0)
576 {
577 buf[i++] = 0;
578 skip--;
579 }
580 skip = BN_bn2bin(x, buf + i);
581 i += skip;
582 if (i != 1 + field_len)
583 {
584 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
585 goto err;
586 }
587
588 if (form == POINT_CONVERSION_UNCOMPRESSED || form == POINT_CONVERSION_HYBRID)
589 {
590 skip = field_len - BN_num_bytes(y);
591 if (skip > field_len)
592 {
593 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
594 goto err;
595 }
596 while (skip > 0)
597 {
598 buf[i++] = 0;
599 skip--;
600 }
601 skip = BN_bn2bin(y, buf + i);
602 i += skip;
603 }
604
605 if (i != ret)
606 {
607 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
608 goto err;
609 }
610 }
611
612 if (used_ctx)
613 BN_CTX_end(ctx);
614 if (new_ctx != NULL)
615 BN_CTX_free(new_ctx);
616 return ret;
617
618 err:
619 if (used_ctx)
620 BN_CTX_end(ctx);
621 if (new_ctx != NULL)
622 BN_CTX_free(new_ctx);
623 return 0;
624 }
625
626
627 /* Converts an octet string representation to an EC_POINT.
628 * Note that the simple implementation only uses affine coordinates.
629 */
630 int ec_GF2m_simple_oct2point(const EC_GROUP *group, EC_POINT *point,
631 const unsigned char *buf, size_t len, BN_CTX *ctx)
632 {
633 point_conversion_form_t form;
634 int y_bit;
635 BN_CTX *new_ctx = NULL;
636 BIGNUM *x, *y, *yxi;
637 size_t field_len, enc_len;
638 int ret = 0;
639
640 if (len == 0)
641 {
642 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_BUFFER_TOO_SMALL);
643 return 0;
644 }
645 form = buf[0];
646 y_bit = form & 1;
647 form = form & ~1U;
648 if ((form != 0) && (form != POINT_CONVERSION_COMPRESSED)
649 && (form != POINT_CONVERSION_UNCOMPRESSED)
650 && (form != POINT_CONVERSION_HYBRID))
651 {
652 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
653 return 0;
654 }
655 if ((form == 0 || form == POINT_CONVERSION_UNCOMPRESSED) && y_bit)
656 {
657 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
658 return 0;
659 }
660
661 if (form == 0)
662 {
663 if (len != 1)
664 {
665 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
666 return 0;
667 }
668
669 return EC_POINT_set_to_infinity(group, point);
670 }
671
672 field_len = (EC_GROUP_get_degree(group) + 7) / 8;
673 enc_len = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len;
674
675 if (len != enc_len)
676 {
677 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
678 return 0;
679 }
680
681 if (ctx == NULL)
682 {
683 ctx = new_ctx = BN_CTX_new();
684 if (ctx == NULL)
685 return 0;
686 }
687
688 BN_CTX_start(ctx);
689 x = BN_CTX_get(ctx);
690 y = BN_CTX_get(ctx);
691 yxi = BN_CTX_get(ctx);
692 if (yxi == NULL) goto err;
693
694 if (!BN_bin2bn(buf + 1, field_len, x)) goto err;
695 if (BN_ucmp(x, &group->field) >= 0)
696 {
697 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
698 goto err;
699 }
700
701 if (form == POINT_CONVERSION_COMPRESSED)
702 {
703 if (!EC_POINT_set_compressed_coordinates_GF2m(group, point, x, y_bit, ctx)) goto err;
704 }
705 else
706 {
707 if (!BN_bin2bn(buf + 1 + field_len, field_len, y)) goto err;
708 if (BN_ucmp(y, &group->field) >= 0)
709 {
710 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
711 goto err;
712 }
713 if (form == POINT_CONVERSION_HYBRID)
714 {
715 if (!group->meth->field_div(group, yxi, y, x, ctx)) goto err;
716 if (y_bit != BN_is_odd(yxi))
717 {
718 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
719 goto err;
720 }
721 }
722
723 if (!EC_POINT_set_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err;
724 }
725
726 if (!EC_POINT_is_on_curve(group, point, ctx)) /* test required by X9.62 */
727 {
728 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_POINT_IS_NOT_ON_CURVE);
729 goto err;
730 }
731
732 ret = 1;
733
734 err:
735 BN_CTX_end(ctx);
736 if (new_ctx != NULL)
737 BN_CTX_free(new_ctx);
738 return ret;
739 }
740
741
742 /* Computes a + b and stores the result in r. r could be a or b, a could be b.
743 * Uses algorithm A.10.2 of IEEE P1363.
744 */
745 int ec_GF2m_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
746 {
747 BN_CTX *new_ctx = NULL;
748 BIGNUM *x0, *y0, *x1, *y1, *x2, *y2, *s, *t;
749 int ret = 0;
750
751 if (EC_POINT_is_at_infinity(group, a))
752 {
753 if (!EC_POINT_copy(r, b)) return 0;
754 return 1;
755 }
756
757 if (EC_POINT_is_at_infinity(group, b))
758 {
759 if (!EC_POINT_copy(r, a)) return 0;
760 return 1;
761 }
762
763 if (ctx == NULL)
764 {
765 ctx = new_ctx = BN_CTX_new();
766 if (ctx == NULL)
767 return 0;
768 }
769
770 BN_CTX_start(ctx);
771 x0 = BN_CTX_get(ctx);
772 y0 = BN_CTX_get(ctx);
773 x1 = BN_CTX_get(ctx);
774 y1 = BN_CTX_get(ctx);
775 x2 = BN_CTX_get(ctx);
776 y2 = BN_CTX_get(ctx);
777 s = BN_CTX_get(ctx);
778 t = BN_CTX_get(ctx);
779 if (t == NULL) goto err;
780
781 if (a->Z_is_one)
782 {
783 if (!BN_copy(x0, &a->X)) goto err;
784 if (!BN_copy(y0, &a->Y)) goto err;
785 }
786 else
787 {
788 if (!EC_POINT_get_affine_coordinates_GF2m(group, a, x0, y0, ctx)) goto err;
789 }
790 if (b->Z_is_one)
791 {
792 if (!BN_copy(x1, &b->X)) goto err;
793 if (!BN_copy(y1, &b->Y)) goto err;
794 }
795 else
796 {
797 if (!EC_POINT_get_affine_coordinates_GF2m(group, b, x1, y1, ctx)) goto err;
798 }
799
800
801 if (BN_GF2m_cmp(x0, x1))
802 {
803 if (!BN_GF2m_add(t, x0, x1)) goto err;
804 if (!BN_GF2m_add(s, y0, y1)) goto err;
805 if (!group->meth->field_div(group, s, s, t, ctx)) goto err;
806 if (!group->meth->field_sqr(group, x2, s, ctx)) goto err;
807 if (!BN_GF2m_add(x2, x2, &group->a)) goto err;
808 if (!BN_GF2m_add(x2, x2, s)) goto err;
809 if (!BN_GF2m_add(x2, x2, t)) goto err;
810 }
811 else
812 {
813 if (BN_GF2m_cmp(y0, y1) || BN_is_zero(x1))
814 {
815 if (!EC_POINT_set_to_infinity(group, r)) goto err;
816 ret = 1;
817 goto err;
818 }
819 if (!group->meth->field_div(group, s, y1, x1, ctx)) goto err;
820 if (!BN_GF2m_add(s, s, x1)) goto err;
821
822 if (!group->meth->field_sqr(group, x2, s, ctx)) goto err;
823 if (!BN_GF2m_add(x2, x2, s)) goto err;
824 if (!BN_GF2m_add(x2, x2, &group->a)) goto err;
825 }
826
827 if (!BN_GF2m_add(y2, x1, x2)) goto err;
828 if (!group->meth->field_mul(group, y2, y2, s, ctx)) goto err;
829 if (!BN_GF2m_add(y2, y2, x2)) goto err;
830 if (!BN_GF2m_add(y2, y2, y1)) goto err;
831
832 if (!EC_POINT_set_affine_coordinates_GF2m(group, r, x2, y2, ctx)) goto err;
833
834 ret = 1;
835
836 err:
837 BN_CTX_end(ctx);
838 if (new_ctx != NULL)
839 BN_CTX_free(new_ctx);
840 return ret;
841 }
842
843
844 /* Computes 2 * a and stores the result in r. r could be a.
845 * Uses algorithm A.10.2 of IEEE P1363.
846 */
847 int ec_GF2m_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_CTX *ctx)
848 {
849 return ec_GF2m_simple_add(group, r, a, a, ctx);
850 }
851
852
853 int ec_GF2m_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
854 {
855 if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(&point->Y))
856 /* point is its own inverse */
857 return 1;
858
859 if (!EC_POINT_make_affine(group, point, ctx)) return 0;
860 return BN_GF2m_add(&point->Y, &point->X, &point->Y);
861 }
862
863
864 /* Indicates whether the given point is the point at infinity. */
865 int ec_GF2m_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point)
866 {
867 return BN_is_zero(&point->Z);
868 }
869
870
871 /* Determines whether the given EC_POINT is an actual point on the curve defined
872 * in the EC_GROUP. A point is valid if it satisfies the Weierstrass equation:
873 * y^2 + x*y = x^3 + a*x^2 + b.
874 */
875 int ec_GF2m_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx)
876 {
877 int ret = -1;
878 BN_CTX *new_ctx = NULL;
879 BIGNUM *lh, *y2;
880 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
881 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
882
883 if (EC_POINT_is_at_infinity(group, point))
884 return 1;
885
886 field_mul = group->meth->field_mul;
887 field_sqr = group->meth->field_sqr;
888
889 /* only support affine coordinates */
890 if (!point->Z_is_one) goto err;
891
892 if (ctx == NULL)
893 {
894 ctx = new_ctx = BN_CTX_new();
895 if (ctx == NULL)
896 return -1;
897 }
898
899 BN_CTX_start(ctx);
900 y2 = BN_CTX_get(ctx);
901 lh = BN_CTX_get(ctx);
902 if (lh == NULL) goto err;
903
904 /* We have a curve defined by a Weierstrass equation
905 * y^2 + x*y = x^3 + a*x^2 + b.
906 * <=> x^3 + a*x^2 + x*y + b + y^2 = 0
907 * <=> ((x + a) * x + y ) * x + b + y^2 = 0
908 */
909 if (!BN_GF2m_add(lh, &point->X, &group->a)) goto err;
910 if (!field_mul(group, lh, lh, &point->X, ctx)) goto err;
911 if (!BN_GF2m_add(lh, lh, &point->Y)) goto err;
912 if (!field_mul(group, lh, lh, &point->X, ctx)) goto err;
913 if (!BN_GF2m_add(lh, lh, &group->b)) goto err;
914 if (!field_sqr(group, y2, &point->Y, ctx)) goto err;
915 if (!BN_GF2m_add(lh, lh, y2)) goto err;
916 ret = BN_is_zero(lh);
917 err:
918 if (ctx) BN_CTX_end(ctx);
919 if (new_ctx) BN_CTX_free(new_ctx);
920 return ret;
921 }
922
923
924 /* Indicates whether two points are equal.
925 * Return values:
926 * -1 error
927 * 0 equal (in affine coordinates)
928 * 1 not equal
929 */
930 int ec_GF2m_simple_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
931 {
932 BIGNUM *aX, *aY, *bX, *bY;
933 BN_CTX *new_ctx = NULL;
934 int ret = -1;
935
936 if (EC_POINT_is_at_infinity(group, a))
937 {
938 return EC_POINT_is_at_infinity(group, b) ? 0 : 1;
939 }
940
941 if (a->Z_is_one && b->Z_is_one)
942 {
943 return ((BN_cmp(&a->X, &b->X) == 0) && BN_cmp(&a->Y, &b->Y) == 0) ? 0 : 1;
944 }
945
946 if (ctx == NULL)
947 {
948 ctx = new_ctx = BN_CTX_new();
949 if (ctx == NULL)
950 return -1;
951 }
952
953 BN_CTX_start(ctx);
954 aX = BN_CTX_get(ctx);
955 aY = BN_CTX_get(ctx);
956 bX = BN_CTX_get(ctx);
957 bY = BN_CTX_get(ctx);
958 if (bY == NULL) goto err;
959
960 if (!EC_POINT_get_affine_coordinates_GF2m(group, a, aX, aY, ctx)) goto err;
961 if (!EC_POINT_get_affine_coordinates_GF2m(group, b, bX, bY, ctx)) goto err;
962 ret = ((BN_cmp(aX, bX) == 0) && BN_cmp(aY, bY) == 0) ? 0 : 1;
963
964 err:
965 if (ctx) BN_CTX_end(ctx);
966 if (new_ctx) BN_CTX_free(new_ctx);
967 return ret;
968 }
969
970
971 /* Forces the given EC_POINT to internally use affine coordinates. */
972 int ec_GF2m_simple_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
973 {
974 BN_CTX *new_ctx = NULL;
975 BIGNUM *x, *y;
976 int ret = 0;
977
978 if (point->Z_is_one || EC_POINT_is_at_infinity(group, point))
979 return 1;
980
981 if (ctx == NULL)
982 {
983 ctx = new_ctx = BN_CTX_new();
984 if (ctx == NULL)
985 return 0;
986 }
987
988 BN_CTX_start(ctx);
989 x = BN_CTX_get(ctx);
990 y = BN_CTX_get(ctx);
991 if (y == NULL) goto err;
992
993 if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err;
994 if (!BN_copy(&point->X, x)) goto err;
995 if (!BN_copy(&point->Y, y)) goto err;
996 if (!BN_one(&point->Z)) goto err;
997
998 ret = 1;
999
1000 err:
1001 if (ctx) BN_CTX_end(ctx);
1002 if (new_ctx) BN_CTX_free(new_ctx);
1003 return ret;
1004 }
1005
1006
1007 /* Forces each of the EC_POINTs in the given array to use affine coordinates. */
1008 int ec_GF2m_simple_points_make_affine(const EC_GROUP *group, size_t num, EC_POINT *points[], BN_CTX *ctx)
1009 {
1010 size_t i;
1011
1012 for (i = 0; i < num; i++)
1013 {
1014 if (!group->meth->make_affine(group, points[i], ctx)) return 0;
1015 }
1016
1017 return 1;
1018 }
1019
1020
1021 /* Wrapper to simple binary polynomial field multiplication implementation. */
1022 int ec_GF2m_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
1023 {
1024 return BN_GF2m_mod_mul_arr(r, a, b, group->poly, ctx);
1025 }
1026
1027
1028 /* Wrapper to simple binary polynomial field squaring implementation. */
1029 int ec_GF2m_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx)
1030 {
1031 return BN_GF2m_mod_sqr_arr(r, a, group->poly, ctx);
1032 }
1033
1034
1035 /* Wrapper to simple binary polynomial field division implementation. */
1036 int ec_GF2m_simple_field_div(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
1037 {
1038 return BN_GF2m_mod_div(r, a, b, &group->field, ctx);
1039 }
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