1 /* crypto/ec/ec2_smpl.c */
2 /* ====================================================================
3 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
4 *
5 * The Elliptic Curve Public-Key Crypto Library (ECC Code) included
6 * herein is developed by SUN MICROSYSTEMS, INC., and is contributed
7 * to the OpenSSL project.
8 *
9 * The ECC Code is licensed pursuant to the OpenSSL open source
10 * license provided below.
11 *
12 * The software is originally written by Sheueling Chang Shantz and
13 * Douglas Stebila of Sun Microsystems Laboratories.
14 *
15 */
16 /* ====================================================================
17 * Copyright (c) 1998-2003 The OpenSSL Project. All rights reserved.
18 *
19 * Redistribution and use in source and binary forms, with or without
20 * modification, are permitted provided that the following conditions
21 * are met:
22 *
23 * 1. Redistributions of source code must retain the above copyright
24 * notice, this list of conditions and the following disclaimer.
25 *
26 * 2. Redistributions in binary form must reproduce the above copyright
27 * notice, this list of conditions and the following disclaimer in
28 * the documentation and/or other materials provided with the
29 * distribution.
30 *
31 * 3. All advertising materials mentioning features or use of this
32 * software must display the following acknowledgment:
33 * "This product includes software developed by the OpenSSL Project
34 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
35 *
36 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
37 * endorse or promote products derived from this software without
38 * prior written permission. For written permission, please contact
39 * openssl-core@openssl.org.
40 *
41 * 5. Products derived from this software may not be called "OpenSSL"
42 * nor may "OpenSSL" appear in their names without prior written
43 * permission of the OpenSSL Project.
44 *
45 * 6. Redistributions of any form whatsoever must retain the following
46 * acknowledgment:
47 * "This product includes software developed by the OpenSSL Project
48 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
49 *
50 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
51 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
52 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
53 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
54 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
55 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
56 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
57 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
58 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
59 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
60 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
61 * OF THE POSSIBILITY OF SUCH DAMAGE.
62 * ====================================================================
63 *
64 * This product includes cryptographic software written by Eric Young
65 * (eay@cryptsoft.com). This product includes software written by Tim
66 * Hudson (tjh@cryptsoft.com).
67 *
68 */
69
70 #include <openssl/err.h>
71
72 #include "ec_lcl.h"
73
74
EC_GF2m_simple_method(void)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 */
ec_GF2m_simple_group_init(EC_GROUP * group)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 */
ec_GF2m_simple_group_finish(EC_GROUP * group)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 */
ec_GF2m_simple_group_clear_finish(EC_GROUP * group)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 */
ec_GF2m_simple_group_copy(EC_GROUP * dest,const EC_GROUP * src)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. */
ec_GF2m_simple_group_set_curve(EC_GROUP * group,const BIGNUM * p,const BIGNUM * a,const BIGNUM * b,BN_CTX * ctx)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 */
ec_GF2m_simple_group_get_curve(const EC_GROUP * group,BIGNUM * p,BIGNUM * a,BIGNUM * b,BN_CTX * ctx)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. */
ec_GF2m_simple_group_get_degree(const EC_GROUP * group)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 */
ec_GF2m_simple_group_check_discriminant(const EC_GROUP * group,BN_CTX * ctx)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. */
ec_GF2m_simple_point_init(EC_POINT * 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. */
ec_GF2m_simple_point_finish(EC_POINT * 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. */
ec_GF2m_simple_point_clear_finish(EC_POINT * 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. */
ec_GF2m_simple_point_copy(EC_POINT * dest,const EC_POINT * src)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 */
ec_GF2m_simple_point_set_to_infinity(const EC_GROUP * group,EC_POINT * point)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 */
ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP * group,EC_POINT * point,const BIGNUM * x,const BIGNUM * y,BN_CTX * ctx)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 */
ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP * group,const EC_POINT * point,BIGNUM * x,BIGNUM * y,BN_CTX * ctx)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 /* Include patented algorithms. */
407 #include "ec2_smpt.c"
408
409
410 /* Converts an EC_POINT to an octet string.
411 * If buf is NULL, the encoded length will be returned.
412 * If the length len of buf is smaller than required an error will be returned.
413 *
414 * The point compression section of this function is patented by Certicom Corp.
415 * under US Patent 6,141,420. Point compression is disabled by default and can
416 * be enabled by defining the preprocessor macro OPENSSL_EC_BIN_PT_COMP at
417 * Configure-time.
418 */
ec_GF2m_simple_point2oct(const EC_GROUP * group,const EC_POINT * point,point_conversion_form_t form,unsigned char * buf,size_t len,BN_CTX * ctx)419 size_t ec_GF2m_simple_point2oct(const EC_GROUP *group, const EC_POINT *point, point_conversion_form_t form,
420 unsigned char *buf, size_t len, BN_CTX *ctx)
421 {
422 size_t ret;
423 BN_CTX *new_ctx = NULL;
424 int used_ctx = 0;
425 BIGNUM *x, *y, *yxi;
426 size_t field_len, i, skip;
427
428 #ifndef OPENSSL_EC_BIN_PT_COMP
429 if ((form == POINT_CONVERSION_COMPRESSED) || (form == POINT_CONVERSION_HYBRID))
430 {
431 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_DISABLED);
432 goto err;
433 }
434 #endif
435
436 if ((form != POINT_CONVERSION_COMPRESSED)
437 && (form != POINT_CONVERSION_UNCOMPRESSED)
438 && (form != POINT_CONVERSION_HYBRID))
439 {
440 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_INVALID_FORM);
441 goto err;
442 }
443
444 if (EC_POINT_is_at_infinity(group, point))
445 {
446 /* encodes to a single 0 octet */
447 if (buf != NULL)
448 {
449 if (len < 1)
450 {
451 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);
452 return 0;
453 }
454 buf[0] = 0;
455 }
456 return 1;
457 }
458
459
460 /* ret := required output buffer length */
461 field_len = (EC_GROUP_get_degree(group) + 7) / 8;
462 ret = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len;
463
464 /* if 'buf' is NULL, just return required length */
465 if (buf != NULL)
466 {
467 if (len < ret)
468 {
469 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);
470 goto err;
471 }
472
473 if (ctx == NULL)
474 {
475 ctx = new_ctx = BN_CTX_new();
476 if (ctx == NULL)
477 return 0;
478 }
479
480 BN_CTX_start(ctx);
481 used_ctx = 1;
482 x = BN_CTX_get(ctx);
483 y = BN_CTX_get(ctx);
484 yxi = BN_CTX_get(ctx);
485 if (yxi == NULL) goto err;
486
487 if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err;
488
489 buf[0] = form;
490 #ifdef OPENSSL_EC_BIN_PT_COMP
491 if ((form != POINT_CONVERSION_UNCOMPRESSED) && !BN_is_zero(x))
492 {
493 if (!group->meth->field_div(group, yxi, y, x, ctx)) goto err;
494 if (BN_is_odd(yxi)) buf[0]++;
495 }
496 #endif
497
498 i = 1;
499
500 skip = field_len - BN_num_bytes(x);
501 if (skip > field_len)
502 {
503 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
504 goto err;
505 }
506 while (skip > 0)
507 {
508 buf[i++] = 0;
509 skip--;
510 }
511 skip = BN_bn2bin(x, buf + i);
512 i += skip;
513 if (i != 1 + field_len)
514 {
515 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
516 goto err;
517 }
518
519 if (form == POINT_CONVERSION_UNCOMPRESSED || form == POINT_CONVERSION_HYBRID)
520 {
521 skip = field_len - BN_num_bytes(y);
522 if (skip > field_len)
523 {
524 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
525 goto err;
526 }
527 while (skip > 0)
528 {
529 buf[i++] = 0;
530 skip--;
531 }
532 skip = BN_bn2bin(y, buf + i);
533 i += skip;
534 }
535
536 if (i != ret)
537 {
538 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
539 goto err;
540 }
541 }
542
543 if (used_ctx)
544 BN_CTX_end(ctx);
545 if (new_ctx != NULL)
546 BN_CTX_free(new_ctx);
547 return ret;
548
549 err:
550 if (used_ctx)
551 BN_CTX_end(ctx);
552 if (new_ctx != NULL)
553 BN_CTX_free(new_ctx);
554 return 0;
555 }
556
557
558 /* Converts an octet string representation to an EC_POINT.
559 * Note that the simple implementation only uses affine coordinates.
560 */
ec_GF2m_simple_oct2point(const EC_GROUP * group,EC_POINT * point,const unsigned char * buf,size_t len,BN_CTX * ctx)561 int ec_GF2m_simple_oct2point(const EC_GROUP *group, EC_POINT *point,
562 const unsigned char *buf, size_t len, BN_CTX *ctx)
563 {
564 point_conversion_form_t form;
565 int y_bit;
566 BN_CTX *new_ctx = NULL;
567 BIGNUM *x, *y, *yxi;
568 size_t field_len, enc_len;
569 int ret = 0;
570
571 if (len == 0)
572 {
573 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_BUFFER_TOO_SMALL);
574 return 0;
575 }
576 form = buf[0];
577 y_bit = form & 1;
578 form = form & ~1U;
579 if ((form != 0) && (form != POINT_CONVERSION_COMPRESSED)
580 && (form != POINT_CONVERSION_UNCOMPRESSED)
581 && (form != POINT_CONVERSION_HYBRID))
582 {
583 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
584 return 0;
585 }
586 if ((form == 0 || form == POINT_CONVERSION_UNCOMPRESSED) && y_bit)
587 {
588 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
589 return 0;
590 }
591
592 if (form == 0)
593 {
594 if (len != 1)
595 {
596 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
597 return 0;
598 }
599
600 return EC_POINT_set_to_infinity(group, point);
601 }
602
603 field_len = (EC_GROUP_get_degree(group) + 7) / 8;
604 enc_len = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len;
605
606 if (len != enc_len)
607 {
608 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
609 return 0;
610 }
611
612 if (ctx == NULL)
613 {
614 ctx = new_ctx = BN_CTX_new();
615 if (ctx == NULL)
616 return 0;
617 }
618
619 BN_CTX_start(ctx);
620 x = BN_CTX_get(ctx);
621 y = BN_CTX_get(ctx);
622 yxi = BN_CTX_get(ctx);
623 if (yxi == NULL) goto err;
624
625 if (!BN_bin2bn(buf + 1, field_len, x)) goto err;
626 if (BN_ucmp(x, &group->field) >= 0)
627 {
628 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
629 goto err;
630 }
631
632 if (form == POINT_CONVERSION_COMPRESSED)
633 {
634 if (!EC_POINT_set_compressed_coordinates_GF2m(group, point, x, y_bit, ctx)) goto err;
635 }
636 else
637 {
638 if (!BN_bin2bn(buf + 1 + field_len, field_len, y)) goto err;
639 if (BN_ucmp(y, &group->field) >= 0)
640 {
641 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
642 goto err;
643 }
644 if (form == POINT_CONVERSION_HYBRID)
645 {
646 if (!group->meth->field_div(group, yxi, y, x, ctx)) goto err;
647 if (y_bit != BN_is_odd(yxi))
648 {
649 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
650 goto err;
651 }
652 }
653
654 if (!EC_POINT_set_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err;
655 }
656
657 if (!EC_POINT_is_on_curve(group, point, ctx)) /* test required by X9.62 */
658 {
659 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_POINT_IS_NOT_ON_CURVE);
660 goto err;
661 }
662
663 ret = 1;
664
665 err:
666 BN_CTX_end(ctx);
667 if (new_ctx != NULL)
668 BN_CTX_free(new_ctx);
669 return ret;
670 }
671
672
673 /* Computes a + b and stores the result in r. r could be a or b, a could be b.
674 * Uses algorithm A.10.2 of IEEE P1363.
675 */
ec_GF2m_simple_add(const EC_GROUP * group,EC_POINT * r,const EC_POINT * a,const EC_POINT * b,BN_CTX * ctx)676 int ec_GF2m_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
677 {
678 BN_CTX *new_ctx = NULL;
679 BIGNUM *x0, *y0, *x1, *y1, *x2, *y2, *s, *t;
680 int ret = 0;
681
682 if (EC_POINT_is_at_infinity(group, a))
683 {
684 if (!EC_POINT_copy(r, b)) return 0;
685 return 1;
686 }
687
688 if (EC_POINT_is_at_infinity(group, b))
689 {
690 if (!EC_POINT_copy(r, a)) return 0;
691 return 1;
692 }
693
694 if (ctx == NULL)
695 {
696 ctx = new_ctx = BN_CTX_new();
697 if (ctx == NULL)
698 return 0;
699 }
700
701 BN_CTX_start(ctx);
702 x0 = BN_CTX_get(ctx);
703 y0 = BN_CTX_get(ctx);
704 x1 = BN_CTX_get(ctx);
705 y1 = BN_CTX_get(ctx);
706 x2 = BN_CTX_get(ctx);
707 y2 = BN_CTX_get(ctx);
708 s = BN_CTX_get(ctx);
709 t = BN_CTX_get(ctx);
710 if (t == NULL) goto err;
711
712 if (a->Z_is_one)
713 {
714 if (!BN_copy(x0, &a->X)) goto err;
715 if (!BN_copy(y0, &a->Y)) goto err;
716 }
717 else
718 {
719 if (!EC_POINT_get_affine_coordinates_GF2m(group, a, x0, y0, ctx)) goto err;
720 }
721 if (b->Z_is_one)
722 {
723 if (!BN_copy(x1, &b->X)) goto err;
724 if (!BN_copy(y1, &b->Y)) goto err;
725 }
726 else
727 {
728 if (!EC_POINT_get_affine_coordinates_GF2m(group, b, x1, y1, ctx)) goto err;
729 }
730
731
732 if (BN_GF2m_cmp(x0, x1))
733 {
734 if (!BN_GF2m_add(t, x0, x1)) goto err;
735 if (!BN_GF2m_add(s, y0, y1)) goto err;
736 if (!group->meth->field_div(group, s, s, t, ctx)) goto err;
737 if (!group->meth->field_sqr(group, x2, s, ctx)) goto err;
738 if (!BN_GF2m_add(x2, x2, &group->a)) goto err;
739 if (!BN_GF2m_add(x2, x2, s)) goto err;
740 if (!BN_GF2m_add(x2, x2, t)) goto err;
741 }
742 else
743 {
744 if (BN_GF2m_cmp(y0, y1) || BN_is_zero(x1))
745 {
746 if (!EC_POINT_set_to_infinity(group, r)) goto err;
747 ret = 1;
748 goto err;
749 }
750 if (!group->meth->field_div(group, s, y1, x1, ctx)) goto err;
751 if (!BN_GF2m_add(s, s, x1)) goto err;
752
753 if (!group->meth->field_sqr(group, x2, s, ctx)) goto err;
754 if (!BN_GF2m_add(x2, x2, s)) goto err;
755 if (!BN_GF2m_add(x2, x2, &group->a)) goto err;
756 }
757
758 if (!BN_GF2m_add(y2, x1, x2)) goto err;
759 if (!group->meth->field_mul(group, y2, y2, s, ctx)) goto err;
760 if (!BN_GF2m_add(y2, y2, x2)) goto err;
761 if (!BN_GF2m_add(y2, y2, y1)) goto err;
762
763 if (!EC_POINT_set_affine_coordinates_GF2m(group, r, x2, y2, ctx)) goto err;
764
765 ret = 1;
766
767 err:
768 BN_CTX_end(ctx);
769 if (new_ctx != NULL)
770 BN_CTX_free(new_ctx);
771 return ret;
772 }
773
774
775 /* Computes 2 * a and stores the result in r. r could be a.
776 * Uses algorithm A.10.2 of IEEE P1363.
777 */
ec_GF2m_simple_dbl(const EC_GROUP * group,EC_POINT * r,const EC_POINT * a,BN_CTX * ctx)778 int ec_GF2m_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_CTX *ctx)
779 {
780 return ec_GF2m_simple_add(group, r, a, a, ctx);
781 }
782
783
ec_GF2m_simple_invert(const EC_GROUP * group,EC_POINT * point,BN_CTX * ctx)784 int ec_GF2m_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
785 {
786 if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(&point->Y))
787 /* point is its own inverse */
788 return 1;
789
790 if (!EC_POINT_make_affine(group, point, ctx)) return 0;
791 return BN_GF2m_add(&point->Y, &point->X, &point->Y);
792 }
793
794
795 /* Indicates whether the given point is the point at infinity. */
ec_GF2m_simple_is_at_infinity(const EC_GROUP * group,const EC_POINT * point)796 int ec_GF2m_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point)
797 {
798 return BN_is_zero(&point->Z);
799 }
800
801
802 /* Determines whether the given EC_POINT is an actual point on the curve defined
803 * in the EC_GROUP. A point is valid if it satisfies the Weierstrass equation:
804 * y^2 + x*y = x^3 + a*x^2 + b.
805 */
ec_GF2m_simple_is_on_curve(const EC_GROUP * group,const EC_POINT * point,BN_CTX * ctx)806 int ec_GF2m_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx)
807 {
808 int ret = -1;
809 BN_CTX *new_ctx = NULL;
810 BIGNUM *lh, *y2;
811 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
812 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
813
814 if (EC_POINT_is_at_infinity(group, point))
815 return 1;
816
817 field_mul = group->meth->field_mul;
818 field_sqr = group->meth->field_sqr;
819
820 /* only support affine coordinates */
821 if (!point->Z_is_one) goto err;
822
823 if (ctx == NULL)
824 {
825 ctx = new_ctx = BN_CTX_new();
826 if (ctx == NULL)
827 return -1;
828 }
829
830 BN_CTX_start(ctx);
831 y2 = BN_CTX_get(ctx);
832 lh = BN_CTX_get(ctx);
833 if (lh == NULL) goto err;
834
835 /* We have a curve defined by a Weierstrass equation
836 * y^2 + x*y = x^3 + a*x^2 + b.
837 * <=> x^3 + a*x^2 + x*y + b + y^2 = 0
838 * <=> ((x + a) * x + y ) * x + b + y^2 = 0
839 */
840 if (!BN_GF2m_add(lh, &point->X, &group->a)) goto err;
841 if (!field_mul(group, lh, lh, &point->X, ctx)) goto err;
842 if (!BN_GF2m_add(lh, lh, &point->Y)) goto err;
843 if (!field_mul(group, lh, lh, &point->X, ctx)) goto err;
844 if (!BN_GF2m_add(lh, lh, &group->b)) goto err;
845 if (!field_sqr(group, y2, &point->Y, ctx)) goto err;
846 if (!BN_GF2m_add(lh, lh, y2)) goto err;
847 ret = BN_is_zero(lh);
848 err:
849 if (ctx) BN_CTX_end(ctx);
850 if (new_ctx) BN_CTX_free(new_ctx);
851 return ret;
852 }
853
854
855 /* Indicates whether two points are equal.
856 * Return values:
857 * -1 error
858 * 0 equal (in affine coordinates)
859 * 1 not equal
860 */
ec_GF2m_simple_cmp(const EC_GROUP * group,const EC_POINT * a,const EC_POINT * b,BN_CTX * ctx)861 int ec_GF2m_simple_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
862 {
863 BIGNUM *aX, *aY, *bX, *bY;
864 BN_CTX *new_ctx = NULL;
865 int ret = -1;
866
867 if (EC_POINT_is_at_infinity(group, a))
868 {
869 return EC_POINT_is_at_infinity(group, b) ? 0 : 1;
870 }
871
872 if (a->Z_is_one && b->Z_is_one)
873 {
874 return ((BN_cmp(&a->X, &b->X) == 0) && BN_cmp(&a->Y, &b->Y) == 0) ? 0 : 1;
875 }
876
877 if (ctx == NULL)
878 {
879 ctx = new_ctx = BN_CTX_new();
880 if (ctx == NULL)
881 return -1;
882 }
883
884 BN_CTX_start(ctx);
885 aX = BN_CTX_get(ctx);
886 aY = BN_CTX_get(ctx);
887 bX = BN_CTX_get(ctx);
888 bY = BN_CTX_get(ctx);
889 if (bY == NULL) goto err;
890
891 if (!EC_POINT_get_affine_coordinates_GF2m(group, a, aX, aY, ctx)) goto err;
892 if (!EC_POINT_get_affine_coordinates_GF2m(group, b, bX, bY, ctx)) goto err;
893 ret = ((BN_cmp(aX, bX) == 0) && BN_cmp(aY, bY) == 0) ? 0 : 1;
894
895 err:
896 if (ctx) BN_CTX_end(ctx);
897 if (new_ctx) BN_CTX_free(new_ctx);
898 return ret;
899 }
900
901
902 /* Forces the given EC_POINT to internally use affine coordinates. */
ec_GF2m_simple_make_affine(const EC_GROUP * group,EC_POINT * point,BN_CTX * ctx)903 int ec_GF2m_simple_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
904 {
905 BN_CTX *new_ctx = NULL;
906 BIGNUM *x, *y;
907 int ret = 0;
908
909 if (point->Z_is_one || EC_POINT_is_at_infinity(group, point))
910 return 1;
911
912 if (ctx == NULL)
913 {
914 ctx = new_ctx = BN_CTX_new();
915 if (ctx == NULL)
916 return 0;
917 }
918
919 BN_CTX_start(ctx);
920 x = BN_CTX_get(ctx);
921 y = BN_CTX_get(ctx);
922 if (y == NULL) goto err;
923
924 if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err;
925 if (!BN_copy(&point->X, x)) goto err;
926 if (!BN_copy(&point->Y, y)) goto err;
927 if (!BN_one(&point->Z)) goto err;
928
929 ret = 1;
930
931 err:
932 if (ctx) BN_CTX_end(ctx);
933 if (new_ctx) BN_CTX_free(new_ctx);
934 return ret;
935 }
936
937
938 /* Forces each of the EC_POINTs in the given array to use affine coordinates. */
ec_GF2m_simple_points_make_affine(const EC_GROUP * group,size_t num,EC_POINT * points[],BN_CTX * ctx)939 int ec_GF2m_simple_points_make_affine(const EC_GROUP *group, size_t num, EC_POINT *points[], BN_CTX *ctx)
940 {
941 size_t i;
942
943 for (i = 0; i < num; i++)
944 {
945 if (!group->meth->make_affine(group, points[i], ctx)) return 0;
946 }
947
948 return 1;
949 }
950
951
952 /* Wrapper to simple binary polynomial field multiplication implementation. */
ec_GF2m_simple_field_mul(const EC_GROUP * group,BIGNUM * r,const BIGNUM * a,const BIGNUM * b,BN_CTX * ctx)953 int ec_GF2m_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
954 {
955 return BN_GF2m_mod_mul_arr(r, a, b, group->poly, ctx);
956 }
957
958
959 /* Wrapper to simple binary polynomial field squaring implementation. */
ec_GF2m_simple_field_sqr(const EC_GROUP * group,BIGNUM * r,const BIGNUM * a,BN_CTX * ctx)960 int ec_GF2m_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx)
961 {
962 return BN_GF2m_mod_sqr_arr(r, a, group->poly, ctx);
963 }
964
965
966 /* Wrapper to simple binary polynomial field division implementation. */
ec_GF2m_simple_field_div(const EC_GROUP * group,BIGNUM * r,const BIGNUM * a,const BIGNUM * b,BN_CTX * ctx)967 int ec_GF2m_simple_field_div(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
968 {
969 return BN_GF2m_mod_div(r, a, b, &group->field, ctx);
970 }
971