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Add additional parameter to dsa_builtin_paramgen to output the generated
[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 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 if (BN_num_bits(x) > BN_num_bits(&group->field))
367 ret = 2;
368 else if (BN_num_bits(y) > BN_num_bits(&group->field))
369 ret = 2;
370 else
371 ret = 1;
372
373 err:
374 return ret;
375 }
376
377
378 /* Gets the affine coordinates of an EC_POINT.
379 * Note that the simple implementation only uses affine coordinates.
380 */
381 int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point,
382 BIGNUM *x, BIGNUM *y, BN_CTX *ctx)
383 {
384 int ret = 0;
385
386 if (EC_POINT_is_at_infinity(group, point))
387 {
388 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES, EC_R_POINT_AT_INFINITY);
389 return 0;
390 }
391
392 if (BN_cmp(&point->Z, BN_value_one()))
393 {
394 ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
395 return 0;
396 }
397 if (x != NULL)
398 {
399 if (!BN_copy(x, &point->X)) goto err;
400 BN_set_negative(x, 0);
401 }
402 if (y != NULL)
403 {
404 if (!BN_copy(y, &point->Y)) goto err;
405 BN_set_negative(y, 0);
406 }
407 ret = 1;
408
409 err:
410 return ret;
411 }
412
413
414 /* Calculates and sets the affine coordinates of an EC_POINT from the given
415 * compressed coordinates. Uses algorithm 2.3.4 of SEC 1.
416 * Note that the simple implementation only uses affine coordinates.
417 *
418 * The method is from the following publication:
419 *
420 * Harper, Menezes, Vanstone:
421 * "Public-Key Cryptosystems with Very Small Key Lengths",
422 * EUROCRYPT '92, Springer-Verlag LNCS 658,
423 * published February 1993
424 *
425 * US Patents 6,141,420 and 6,618,483 (Vanstone, Mullin, Agnew) describe
426 * the same method, but claim no priority date earlier than July 29, 1994
427 * (and additionally fail to cite the EUROCRYPT '92 publication as prior art).
428 */
429 int ec_GF2m_simple_set_compressed_coordinates(const EC_GROUP *group, EC_POINT *point,
430 const BIGNUM *x_, int y_bit, BN_CTX *ctx)
431 {
432 BN_CTX *new_ctx = NULL;
433 BIGNUM *tmp, *x, *y, *z;
434 int ret = 0, z0;
435
436 /* clear error queue */
437 ERR_clear_error();
438
439 if (ctx == NULL)
440 {
441 ctx = new_ctx = BN_CTX_new();
442 if (ctx == NULL)
443 return 0;
444 }
445
446 y_bit = (y_bit != 0) ? 1 : 0;
447
448 BN_CTX_start(ctx);
449 tmp = BN_CTX_get(ctx);
450 x = BN_CTX_get(ctx);
451 y = BN_CTX_get(ctx);
452 z = BN_CTX_get(ctx);
453 if (z == NULL) goto err;
454
455 if (!BN_GF2m_mod_arr(x, x_, group->poly)) goto err;
456 if (BN_is_zero(x))
457 {
458 if (!BN_GF2m_mod_sqrt_arr(y, &group->b, group->poly, ctx)) goto err;
459 }
460 else
461 {
462 if (!group->meth->field_sqr(group, tmp, x, ctx)) goto err;
463 if (!group->meth->field_div(group, tmp, &group->b, tmp, ctx)) goto err;
464 if (!BN_GF2m_add(tmp, &group->a, tmp)) goto err;
465 if (!BN_GF2m_add(tmp, x, tmp)) goto err;
466 if (!BN_GF2m_mod_solve_quad_arr(z, tmp, group->poly, ctx))
467 {
468 unsigned long err = ERR_peek_last_error();
469
470 if (ERR_GET_LIB(err) == ERR_LIB_BN && ERR_GET_REASON(err) == BN_R_NO_SOLUTION)
471 {
472 ERR_clear_error();
473 ECerr(EC_F_EC_GF2M_SIMPLE_SET_COMPRESSED_COORDINATES, EC_R_INVALID_COMPRESSED_POINT);
474 }
475 else
476 ECerr(EC_F_EC_GF2M_SIMPLE_SET_COMPRESSED_COORDINATES, ERR_R_BN_LIB);
477 goto err;
478 }
479 z0 = (BN_is_odd(z)) ? 1 : 0;
480 if (!group->meth->field_mul(group, y, x, z, ctx)) goto err;
481 if (z0 != y_bit)
482 {
483 if (!BN_GF2m_add(y, y, x)) goto err;
484 }
485 }
486
487 if (!EC_POINT_set_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err;
488
489 ret = 1;
490
491 err:
492 BN_CTX_end(ctx);
493 if (new_ctx != NULL)
494 BN_CTX_free(new_ctx);
495 return ret;
496 }
497
498
499 /* Converts an EC_POINT to an octet string.
500 * If buf is NULL, the encoded length will be returned.
501 * If the length len of buf is smaller than required an error will be returned.
502 */
503 size_t ec_GF2m_simple_point2oct(const EC_GROUP *group, const EC_POINT *point, point_conversion_form_t form,
504 unsigned char *buf, size_t len, BN_CTX *ctx)
505 {
506 size_t ret;
507 BN_CTX *new_ctx = NULL;
508 int used_ctx = 0;
509 BIGNUM *x, *y, *yxi;
510 size_t field_len, i, skip;
511
512 if ((form != POINT_CONVERSION_COMPRESSED)
513 && (form != POINT_CONVERSION_UNCOMPRESSED)
514 && (form != POINT_CONVERSION_HYBRID))
515 {
516 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_INVALID_FORM);
517 goto err;
518 }
519
520 if (EC_POINT_is_at_infinity(group, point))
521 {
522 /* encodes to a single 0 octet */
523 if (buf != NULL)
524 {
525 if (len < 1)
526 {
527 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);
528 return 0;
529 }
530 buf[0] = 0;
531 }
532 return 1;
533 }
534
535
536 /* ret := required output buffer length */
537 field_len = (EC_GROUP_get_degree(group) + 7) / 8;
538 ret = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len;
539
540 /* if 'buf' is NULL, just return required length */
541 if (buf != NULL)
542 {
543 if (len < ret)
544 {
545 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);
546 goto err;
547 }
548
549 if (ctx == NULL)
550 {
551 ctx = new_ctx = BN_CTX_new();
552 if (ctx == NULL)
553 return 0;
554 }
555
556 BN_CTX_start(ctx);
557 used_ctx = 1;
558 x = BN_CTX_get(ctx);
559 y = BN_CTX_get(ctx);
560 yxi = BN_CTX_get(ctx);
561 if (yxi == NULL) goto err;
562
563 if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err;
564
565 buf[0] = form;
566 if ((form != POINT_CONVERSION_UNCOMPRESSED) && !BN_is_zero(x))
567 {
568 if (!group->meth->field_div(group, yxi, y, x, ctx)) goto err;
569 if (BN_is_odd(yxi)) buf[0]++;
570 }
571
572 i = 1;
573
574 skip = field_len - BN_num_bytes(x);
575 if (skip > field_len)
576 {
577 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
578 goto err;
579 }
580 while (skip > 0)
581 {
582 buf[i++] = 0;
583 skip--;
584 }
585 skip = BN_bn2bin(x, buf + i);
586 i += skip;
587 if (i != 1 + field_len)
588 {
589 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
590 goto err;
591 }
592
593 if (form == POINT_CONVERSION_UNCOMPRESSED || form == POINT_CONVERSION_HYBRID)
594 {
595 skip = field_len - BN_num_bytes(y);
596 if (skip > field_len)
597 {
598 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
599 goto err;
600 }
601 while (skip > 0)
602 {
603 buf[i++] = 0;
604 skip--;
605 }
606 skip = BN_bn2bin(y, buf + i);
607 i += skip;
608 }
609
610 if (i != ret)
611 {
612 ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
613 goto err;
614 }
615 }
616
617 if (used_ctx)
618 BN_CTX_end(ctx);
619 if (new_ctx != NULL)
620 BN_CTX_free(new_ctx);
621 return ret;
622
623 err:
624 if (used_ctx)
625 BN_CTX_end(ctx);
626 if (new_ctx != NULL)
627 BN_CTX_free(new_ctx);
628 return 0;
629 }
630
631
632 /* Converts an octet string representation to an EC_POINT.
633 * Note that the simple implementation only uses affine coordinates.
634 */
635 int ec_GF2m_simple_oct2point(const EC_GROUP *group, EC_POINT *point,
636 const unsigned char *buf, size_t len, BN_CTX *ctx)
637 {
638 point_conversion_form_t form;
639 int y_bit;
640 BN_CTX *new_ctx = NULL;
641 BIGNUM *x, *y, *yxi;
642 size_t field_len, enc_len;
643 int ret = 0;
644
645 if (len == 0)
646 {
647 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_BUFFER_TOO_SMALL);
648 return 0;
649 }
650 form = buf[0];
651 y_bit = form & 1;
652 form = form & ~1U;
653 if ((form != 0) && (form != POINT_CONVERSION_COMPRESSED)
654 && (form != POINT_CONVERSION_UNCOMPRESSED)
655 && (form != POINT_CONVERSION_HYBRID))
656 {
657 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
658 return 0;
659 }
660 if ((form == 0 || form == POINT_CONVERSION_UNCOMPRESSED) && y_bit)
661 {
662 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
663 return 0;
664 }
665
666 if (form == 0)
667 {
668 if (len != 1)
669 {
670 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
671 return 0;
672 }
673
674 return EC_POINT_set_to_infinity(group, point);
675 }
676
677 field_len = (EC_GROUP_get_degree(group) + 7) / 8;
678 enc_len = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len;
679
680 if (len != enc_len)
681 {
682 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
683 return 0;
684 }
685
686 if (ctx == NULL)
687 {
688 ctx = new_ctx = BN_CTX_new();
689 if (ctx == NULL)
690 return 0;
691 }
692
693 BN_CTX_start(ctx);
694 x = BN_CTX_get(ctx);
695 y = BN_CTX_get(ctx);
696 yxi = BN_CTX_get(ctx);
697 if (yxi == NULL) goto err;
698
699 if (!BN_bin2bn(buf + 1, field_len, x)) goto err;
700 if (BN_ucmp(x, &group->field) >= 0)
701 {
702 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
703 goto err;
704 }
705
706 if (form == POINT_CONVERSION_COMPRESSED)
707 {
708 if (!EC_POINT_set_compressed_coordinates_GF2m(group, point, x, y_bit, ctx)) goto err;
709 }
710 else
711 {
712 if (!BN_bin2bn(buf + 1 + field_len, field_len, y)) goto err;
713 if (BN_ucmp(y, &group->field) >= 0)
714 {
715 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
716 goto err;
717 }
718 if (form == POINT_CONVERSION_HYBRID)
719 {
720 if (!group->meth->field_div(group, yxi, y, x, ctx)) goto err;
721 if (y_bit != BN_is_odd(yxi))
722 {
723 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
724 goto err;
725 }
726 }
727
728 if (!EC_POINT_set_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err;
729 }
730
731 if (!EC_POINT_is_on_curve(group, point, ctx)) /* test required by X9.62 */
732 {
733 ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_POINT_IS_NOT_ON_CURVE);
734 goto err;
735 }
736
737 ret = 1;
738
739 err:
740 BN_CTX_end(ctx);
741 if (new_ctx != NULL)
742 BN_CTX_free(new_ctx);
743 return ret;
744 }
745
746
747 /* Computes a + b and stores the result in r. r could be a or b, a could be b.
748 * Uses algorithm A.10.2 of IEEE P1363.
749 */
750 int ec_GF2m_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
751 {
752 BN_CTX *new_ctx = NULL;
753 BIGNUM *x0, *y0, *x1, *y1, *x2, *y2, *s, *t;
754 int ret = 0;
755
756 if (EC_POINT_is_at_infinity(group, a))
757 {
758 if (!EC_POINT_copy(r, b)) return 0;
759 return 1;
760 }
761
762 if (EC_POINT_is_at_infinity(group, b))
763 {
764 if (!EC_POINT_copy(r, a)) return 0;
765 return 1;
766 }
767
768 if (ctx == NULL)
769 {
770 ctx = new_ctx = BN_CTX_new();
771 if (ctx == NULL)
772 return 0;
773 }
774
775 BN_CTX_start(ctx);
776 x0 = BN_CTX_get(ctx);
777 y0 = BN_CTX_get(ctx);
778 x1 = BN_CTX_get(ctx);
779 y1 = BN_CTX_get(ctx);
780 x2 = BN_CTX_get(ctx);
781 y2 = BN_CTX_get(ctx);
782 s = BN_CTX_get(ctx);
783 t = BN_CTX_get(ctx);
784 if (t == NULL) goto err;
785
786 if (a->Z_is_one)
787 {
788 if (!BN_copy(x0, &a->X)) goto err;
789 if (!BN_copy(y0, &a->Y)) goto err;
790 }
791 else
792 {
793 if (!EC_POINT_get_affine_coordinates_GF2m(group, a, x0, y0, ctx)) goto err;
794 }
795 if (b->Z_is_one)
796 {
797 if (!BN_copy(x1, &b->X)) goto err;
798 if (!BN_copy(y1, &b->Y)) goto err;
799 }
800 else
801 {
802 if (!EC_POINT_get_affine_coordinates_GF2m(group, b, x1, y1, ctx)) goto err;
803 }
804
805
806 if (BN_GF2m_cmp(x0, x1))
807 {
808 if (!BN_GF2m_add(t, x0, x1)) goto err;
809 if (!BN_GF2m_add(s, y0, y1)) goto err;
810 if (!group->meth->field_div(group, s, s, t, ctx)) goto err;
811 if (!group->meth->field_sqr(group, x2, s, ctx)) goto err;
812 if (!BN_GF2m_add(x2, x2, &group->a)) goto err;
813 if (!BN_GF2m_add(x2, x2, s)) goto err;
814 if (!BN_GF2m_add(x2, x2, t)) goto err;
815 }
816 else
817 {
818 if (BN_GF2m_cmp(y0, y1) || BN_is_zero(x1))
819 {
820 if (!EC_POINT_set_to_infinity(group, r)) goto err;
821 ret = 1;
822 goto err;
823 }
824 if (!group->meth->field_div(group, s, y1, x1, ctx)) goto err;
825 if (!BN_GF2m_add(s, s, x1)) goto err;
826
827 if (!group->meth->field_sqr(group, x2, s, ctx)) goto err;
828 if (!BN_GF2m_add(x2, x2, s)) goto err;
829 if (!BN_GF2m_add(x2, x2, &group->a)) goto err;
830 }
831
832 if (!BN_GF2m_add(y2, x1, x2)) goto err;
833 if (!group->meth->field_mul(group, y2, y2, s, ctx)) goto err;
834 if (!BN_GF2m_add(y2, y2, x2)) goto err;
835 if (!BN_GF2m_add(y2, y2, y1)) goto err;
836
837 if (!EC_POINT_set_affine_coordinates_GF2m(group, r, x2, y2, ctx)) goto err;
838
839 ret = 1;
840
841 err:
842 BN_CTX_end(ctx);
843 if (new_ctx != NULL)
844 BN_CTX_free(new_ctx);
845 return ret;
846 }
847
848
849 /* Computes 2 * a and stores the result in r. r could be a.
850 * Uses algorithm A.10.2 of IEEE P1363.
851 */
852 int ec_GF2m_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_CTX *ctx)
853 {
854 return ec_GF2m_simple_add(group, r, a, a, ctx);
855 }
856
857
858 int ec_GF2m_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
859 {
860 if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(&point->Y))
861 /* point is its own inverse */
862 return 1;
863
864 if (!EC_POINT_make_affine(group, point, ctx)) return 0;
865 return BN_GF2m_add(&point->Y, &point->X, &point->Y);
866 }
867
868
869 /* Indicates whether the given point is the point at infinity. */
870 int ec_GF2m_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point)
871 {
872 return BN_is_zero(&point->Z);
873 }
874
875
876 /* Determines whether the given EC_POINT is an actual point on the curve defined
877 * in the EC_GROUP. A point is valid if it satisfies the Weierstrass equation:
878 * y^2 + x*y = x^3 + a*x^2 + b.
879 */
880 int ec_GF2m_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx)
881 {
882 int ret = -1;
883 BN_CTX *new_ctx = NULL;
884 BIGNUM *lh, *y2;
885 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
886 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
887
888 if (EC_POINT_is_at_infinity(group, point))
889 return 1;
890
891 field_mul = group->meth->field_mul;
892 field_sqr = group->meth->field_sqr;
893
894 /* only support affine coordinates */
895 if (!point->Z_is_one) goto err;
896
897 if (ctx == NULL)
898 {
899 ctx = new_ctx = BN_CTX_new();
900 if (ctx == NULL)
901 return -1;
902 }
903
904 BN_CTX_start(ctx);
905 y2 = BN_CTX_get(ctx);
906 lh = BN_CTX_get(ctx);
907 if (lh == NULL) goto err;
908
909 /* We have a curve defined by a Weierstrass equation
910 * y^2 + x*y = x^3 + a*x^2 + b.
911 * <=> x^3 + a*x^2 + x*y + b + y^2 = 0
912 * <=> ((x + a) * x + y ) * x + b + y^2 = 0
913 */
914 if (!BN_GF2m_add(lh, &point->X, &group->a)) goto err;
915 if (!field_mul(group, lh, lh, &point->X, ctx)) goto err;
916 if (!BN_GF2m_add(lh, lh, &point->Y)) goto err;
917 if (!field_mul(group, lh, lh, &point->X, ctx)) goto err;
918 if (!BN_GF2m_add(lh, lh, &group->b)) goto err;
919 if (!field_sqr(group, y2, &point->Y, ctx)) goto err;
920 if (!BN_GF2m_add(lh, lh, y2)) goto err;
921 ret = BN_is_zero(lh);
922 err:
923 if (ctx) BN_CTX_end(ctx);
924 if (new_ctx) BN_CTX_free(new_ctx);
925 return ret;
926 }
927
928
929 /* Indicates whether two points are equal.
930 * Return values:
931 * -1 error
932 * 0 equal (in affine coordinates)
933 * 1 not equal
934 */
935 int ec_GF2m_simple_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
936 {
937 BIGNUM *aX, *aY, *bX, *bY;
938 BN_CTX *new_ctx = NULL;
939 int ret = -1;
940
941 if (EC_POINT_is_at_infinity(group, a))
942 {
943 return EC_POINT_is_at_infinity(group, b) ? 0 : 1;
944 }
945
946 if (EC_POINT_is_at_infinity(group, b))
947 return 1;
948
949 if (a->Z_is_one && b->Z_is_one)
950 {
951 return ((BN_cmp(&a->X, &b->X) == 0) && BN_cmp(&a->Y, &b->Y) == 0) ? 0 : 1;
952 }
953
954 if (ctx == NULL)
955 {
956 ctx = new_ctx = BN_CTX_new();
957 if (ctx == NULL)
958 return -1;
959 }
960
961 BN_CTX_start(ctx);
962 aX = BN_CTX_get(ctx);
963 aY = BN_CTX_get(ctx);
964 bX = BN_CTX_get(ctx);
965 bY = BN_CTX_get(ctx);
966 if (bY == NULL) goto err;
967
968 if (!EC_POINT_get_affine_coordinates_GF2m(group, a, aX, aY, ctx)) goto err;
969 if (!EC_POINT_get_affine_coordinates_GF2m(group, b, bX, bY, ctx)) goto err;
970 ret = ((BN_cmp(aX, bX) == 0) && BN_cmp(aY, bY) == 0) ? 0 : 1;
971
972 err:
973 if (ctx) BN_CTX_end(ctx);
974 if (new_ctx) BN_CTX_free(new_ctx);
975 return ret;
976 }
977
978 int ec_GF2m_simple_range(const EC_GROUP *group, const EC_POINT *a)
979 {
980 if (BN_num_bits(&a->X) > BN_num_bits(&group->field))
981 return 0;
982 if (BN_num_bits(&a->Y) > BN_num_bits(&group->field))
983 return 0;
984 return 1;
985 }
986
987
988 /* Forces the given EC_POINT to internally use affine coordinates. */
989 int ec_GF2m_simple_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
990 {
991 BN_CTX *new_ctx = NULL;
992 BIGNUM *x, *y;
993 int ret = 0;
994
995 if (point->Z_is_one || EC_POINT_is_at_infinity(group, point))
996 return 1;
997
998 if (ctx == NULL)
999 {
1000 ctx = new_ctx = BN_CTX_new();
1001 if (ctx == NULL)
1002 return 0;
1003 }
1004
1005 BN_CTX_start(ctx);
1006 x = BN_CTX_get(ctx);
1007 y = BN_CTX_get(ctx);
1008 if (y == NULL) goto err;
1009
1010 if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err;
1011 if (!BN_copy(&point->X, x)) goto err;
1012 if (!BN_copy(&point->Y, y)) goto err;
1013 if (!BN_one(&point->Z)) goto err;
1014
1015 ret = 1;
1016
1017 err:
1018 if (ctx) BN_CTX_end(ctx);
1019 if (new_ctx) BN_CTX_free(new_ctx);
1020 return ret;
1021 }
1022
1023
1024 /* Forces each of the EC_POINTs in the given array to use affine coordinates. */
1025 int ec_GF2m_simple_points_make_affine(const EC_GROUP *group, size_t num, EC_POINT *points[], BN_CTX *ctx)
1026 {
1027 size_t i;
1028
1029 for (i = 0; i < num; i++)
1030 {
1031 if (!group->meth->make_affine(group, points[i], ctx)) return 0;
1032 }
1033
1034 return 1;
1035 }
1036
1037
1038 /* Wrapper to simple binary polynomial field multiplication implementation. */
1039 int ec_GF2m_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
1040 {
1041 return BN_GF2m_mod_mul_arr(r, a, b, group->poly, ctx);
1042 }
1043
1044
1045 /* Wrapper to simple binary polynomial field squaring implementation. */
1046 int ec_GF2m_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx)
1047 {
1048 return BN_GF2m_mod_sqr_arr(r, a, group->poly, ctx);
1049 }
1050
1051
1052 /* Wrapper to simple binary polynomial field division implementation. */
1053 int ec_GF2m_simple_field_div(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
1054 {
1055 return BN_GF2m_mod_div(r, a, b, &group->field, ctx);
1056 }
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