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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 #ifndef OPENSSL_NO_EC2M
75 
76 #ifdef OPENSSL_FIPS
77 #include <openssl/fips.h>
78 #endif
79 
80 
EC_GF2m_simple_method(void)81 const EC_METHOD *EC_GF2m_simple_method(void)
82 	{
83 #ifdef OPENSSL_FIPS
84 	return fips_ec_gf2m_simple_method();
85 #else
86 	static const EC_METHOD ret = {
87 		EC_FLAGS_DEFAULT_OCT,
88 		NID_X9_62_characteristic_two_field,
89 		ec_GF2m_simple_group_init,
90 		ec_GF2m_simple_group_finish,
91 		ec_GF2m_simple_group_clear_finish,
92 		ec_GF2m_simple_group_copy,
93 		ec_GF2m_simple_group_set_curve,
94 		ec_GF2m_simple_group_get_curve,
95 		ec_GF2m_simple_group_get_degree,
96 		ec_GF2m_simple_group_check_discriminant,
97 		ec_GF2m_simple_point_init,
98 		ec_GF2m_simple_point_finish,
99 		ec_GF2m_simple_point_clear_finish,
100 		ec_GF2m_simple_point_copy,
101 		ec_GF2m_simple_point_set_to_infinity,
102 		0 /* set_Jprojective_coordinates_GFp */,
103 		0 /* get_Jprojective_coordinates_GFp */,
104 		ec_GF2m_simple_point_set_affine_coordinates,
105 		ec_GF2m_simple_point_get_affine_coordinates,
106 		0,0,0,
107 		ec_GF2m_simple_add,
108 		ec_GF2m_simple_dbl,
109 		ec_GF2m_simple_invert,
110 		ec_GF2m_simple_is_at_infinity,
111 		ec_GF2m_simple_is_on_curve,
112 		ec_GF2m_simple_cmp,
113 		ec_GF2m_simple_make_affine,
114 		ec_GF2m_simple_points_make_affine,
115 
116 		/* the following three method functions are defined in ec2_mult.c */
117 		ec_GF2m_simple_mul,
118 		ec_GF2m_precompute_mult,
119 		ec_GF2m_have_precompute_mult,
120 
121 		ec_GF2m_simple_field_mul,
122 		ec_GF2m_simple_field_sqr,
123 		ec_GF2m_simple_field_div,
124 		0 /* field_encode */,
125 		0 /* field_decode */,
126 		0 /* field_set_to_one */ };
127 
128 	return &ret;
129 #endif
130 	}
131 
132 
133 /* Initialize a GF(2^m)-based EC_GROUP structure.
134  * Note that all other members are handled by EC_GROUP_new.
135  */
ec_GF2m_simple_group_init(EC_GROUP * group)136 int ec_GF2m_simple_group_init(EC_GROUP *group)
137 	{
138 	BN_init(&group->field);
139 	BN_init(&group->a);
140 	BN_init(&group->b);
141 	return 1;
142 	}
143 
144 
145 /* Free a GF(2^m)-based EC_GROUP structure.
146  * Note that all other members are handled by EC_GROUP_free.
147  */
ec_GF2m_simple_group_finish(EC_GROUP * group)148 void ec_GF2m_simple_group_finish(EC_GROUP *group)
149 	{
150 	BN_free(&group->field);
151 	BN_free(&group->a);
152 	BN_free(&group->b);
153 	}
154 
155 
156 /* Clear and free a GF(2^m)-based EC_GROUP structure.
157  * Note that all other members are handled by EC_GROUP_clear_free.
158  */
ec_GF2m_simple_group_clear_finish(EC_GROUP * group)159 void ec_GF2m_simple_group_clear_finish(EC_GROUP *group)
160 	{
161 	BN_clear_free(&group->field);
162 	BN_clear_free(&group->a);
163 	BN_clear_free(&group->b);
164 	group->poly[0] = 0;
165 	group->poly[1] = 0;
166 	group->poly[2] = 0;
167 	group->poly[3] = 0;
168 	group->poly[4] = 0;
169 	group->poly[5] = -1;
170 	}
171 
172 
173 /* Copy a GF(2^m)-based EC_GROUP structure.
174  * Note that all other members are handled by EC_GROUP_copy.
175  */
ec_GF2m_simple_group_copy(EC_GROUP * dest,const EC_GROUP * src)176 int ec_GF2m_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src)
177 	{
178 	int i;
179 	if (!BN_copy(&dest->field, &src->field)) return 0;
180 	if (!BN_copy(&dest->a, &src->a)) return 0;
181 	if (!BN_copy(&dest->b, &src->b)) return 0;
182 	dest->poly[0] = src->poly[0];
183 	dest->poly[1] = src->poly[1];
184 	dest->poly[2] = src->poly[2];
185 	dest->poly[3] = src->poly[3];
186 	dest->poly[4] = src->poly[4];
187 	dest->poly[5] = src->poly[5];
188 	if (bn_wexpand(&dest->a, (int)(dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) return 0;
189 	if (bn_wexpand(&dest->b, (int)(dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) return 0;
190 	for (i = dest->a.top; i < dest->a.dmax; i++) dest->a.d[i] = 0;
191 	for (i = dest->b.top; i < dest->b.dmax; i++) dest->b.d[i] = 0;
192 	return 1;
193 	}
194 
195 
196 /* 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)197 int ec_GF2m_simple_group_set_curve(EC_GROUP *group,
198 	const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
199 	{
200 	int ret = 0, i;
201 
202 	/* group->field */
203 	if (!BN_copy(&group->field, p)) goto err;
204 	i = BN_GF2m_poly2arr(&group->field, group->poly, 6) - 1;
205 	if ((i != 5) && (i != 3))
206 		{
207 		ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_SET_CURVE, EC_R_UNSUPPORTED_FIELD);
208 		goto err;
209 		}
210 
211 	/* group->a */
212 	if (!BN_GF2m_mod_arr(&group->a, a, group->poly)) goto err;
213 	if(bn_wexpand(&group->a, (int)(group->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) goto err;
214 	for (i = group->a.top; i < group->a.dmax; i++) group->a.d[i] = 0;
215 
216 	/* group->b */
217 	if (!BN_GF2m_mod_arr(&group->b, b, group->poly)) goto err;
218 	if(bn_wexpand(&group->b, (int)(group->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) goto err;
219 	for (i = group->b.top; i < group->b.dmax; i++) group->b.d[i] = 0;
220 
221 	ret = 1;
222   err:
223 	return ret;
224 	}
225 
226 
227 /* Get the curve parameters of an EC_GROUP structure.
228  * If p, a, or b are NULL then there values will not be set but the method will return with success.
229  */
ec_GF2m_simple_group_get_curve(const EC_GROUP * group,BIGNUM * p,BIGNUM * a,BIGNUM * b,BN_CTX * ctx)230 int ec_GF2m_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx)
231 	{
232 	int ret = 0;
233 
234 	if (p != NULL)
235 		{
236 		if (!BN_copy(p, &group->field)) return 0;
237 		}
238 
239 	if (a != NULL)
240 		{
241 		if (!BN_copy(a, &group->a)) goto err;
242 		}
243 
244 	if (b != NULL)
245 		{
246 		if (!BN_copy(b, &group->b)) goto err;
247 		}
248 
249 	ret = 1;
250 
251   err:
252 	return ret;
253 	}
254 
255 
256 /* 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)257 int ec_GF2m_simple_group_get_degree(const EC_GROUP *group)
258 	{
259 	return BN_num_bits(&group->field)-1;
260 	}
261 
262 
263 /* Checks the discriminant of the curve.
264  * y^2 + x*y = x^3 + a*x^2 + b is an elliptic curve <=> b != 0 (mod p)
265  */
ec_GF2m_simple_group_check_discriminant(const EC_GROUP * group,BN_CTX * ctx)266 int ec_GF2m_simple_group_check_discriminant(const EC_GROUP *group, BN_CTX *ctx)
267 	{
268 	int ret = 0;
269 	BIGNUM *b;
270 	BN_CTX *new_ctx = NULL;
271 
272 	if (ctx == NULL)
273 		{
274 		ctx = new_ctx = BN_CTX_new();
275 		if (ctx == NULL)
276 			{
277 			ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_CHECK_DISCRIMINANT, ERR_R_MALLOC_FAILURE);
278 			goto err;
279 			}
280 		}
281 	BN_CTX_start(ctx);
282 	b = BN_CTX_get(ctx);
283 	if (b == NULL) goto err;
284 
285 	if (!BN_GF2m_mod_arr(b, &group->b, group->poly)) goto err;
286 
287 	/* check the discriminant:
288 	 * y^2 + x*y = x^3 + a*x^2 + b is an elliptic curve <=> b != 0 (mod p)
289 	 */
290 	if (BN_is_zero(b)) goto err;
291 
292 	ret = 1;
293 
294 err:
295 	if (ctx != NULL)
296 		BN_CTX_end(ctx);
297 	if (new_ctx != NULL)
298 		BN_CTX_free(new_ctx);
299 	return ret;
300 	}
301 
302 
303 /* Initializes an EC_POINT. */
ec_GF2m_simple_point_init(EC_POINT * point)304 int ec_GF2m_simple_point_init(EC_POINT *point)
305 	{
306 	BN_init(&point->X);
307 	BN_init(&point->Y);
308 	BN_init(&point->Z);
309 	return 1;
310 	}
311 
312 
313 /* Frees an EC_POINT. */
ec_GF2m_simple_point_finish(EC_POINT * point)314 void ec_GF2m_simple_point_finish(EC_POINT *point)
315 	{
316 	BN_free(&point->X);
317 	BN_free(&point->Y);
318 	BN_free(&point->Z);
319 	}
320 
321 
322 /* Clears and frees an EC_POINT. */
ec_GF2m_simple_point_clear_finish(EC_POINT * point)323 void ec_GF2m_simple_point_clear_finish(EC_POINT *point)
324 	{
325 	BN_clear_free(&point->X);
326 	BN_clear_free(&point->Y);
327 	BN_clear_free(&point->Z);
328 	point->Z_is_one = 0;
329 	}
330 
331 
332 /* 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)333 int ec_GF2m_simple_point_copy(EC_POINT *dest, const EC_POINT *src)
334 	{
335 	if (!BN_copy(&dest->X, &src->X)) return 0;
336 	if (!BN_copy(&dest->Y, &src->Y)) return 0;
337 	if (!BN_copy(&dest->Z, &src->Z)) return 0;
338 	dest->Z_is_one = src->Z_is_one;
339 
340 	return 1;
341 	}
342 
343 
344 /* Set an EC_POINT to the point at infinity.
345  * A point at infinity is represented by having Z=0.
346  */
ec_GF2m_simple_point_set_to_infinity(const EC_GROUP * group,EC_POINT * point)347 int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *group, EC_POINT *point)
348 	{
349 	point->Z_is_one = 0;
350 	BN_zero(&point->Z);
351 	return 1;
352 	}
353 
354 
355 /* Set the coordinates of an EC_POINT using affine coordinates.
356  * Note that the simple implementation only uses affine coordinates.
357  */
ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP * group,EC_POINT * point,const BIGNUM * x,const BIGNUM * y,BN_CTX * ctx)358 int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *group, EC_POINT *point,
359 	const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx)
360 	{
361 	int ret = 0;
362 	if (x == NULL || y == NULL)
363 		{
364 		ECerr(EC_F_EC_GF2M_SIMPLE_POINT_SET_AFFINE_COORDINATES, ERR_R_PASSED_NULL_PARAMETER);
365 		return 0;
366 		}
367 
368 	if (!BN_copy(&point->X, x)) goto err;
369 	BN_set_negative(&point->X, 0);
370 	if (!BN_copy(&point->Y, y)) goto err;
371 	BN_set_negative(&point->Y, 0);
372 	if (!BN_copy(&point->Z, BN_value_one())) goto err;
373 	BN_set_negative(&point->Z, 0);
374 	point->Z_is_one = 1;
375 	ret = 1;
376 
377   err:
378 	return ret;
379 	}
380 
381 
382 /* Gets the affine coordinates of an EC_POINT.
383  * Note that the simple implementation only uses affine coordinates.
384  */
ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP * group,const EC_POINT * point,BIGNUM * x,BIGNUM * y,BN_CTX * ctx)385 int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point,
386 	BIGNUM *x, BIGNUM *y, BN_CTX *ctx)
387 	{
388 	int ret = 0;
389 
390 	if (EC_POINT_is_at_infinity(group, point))
391 		{
392 		ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES, EC_R_POINT_AT_INFINITY);
393 		return 0;
394 		}
395 
396 	if (BN_cmp(&point->Z, BN_value_one()))
397 		{
398 		ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
399 		return 0;
400 		}
401 	if (x != NULL)
402 		{
403 		if (!BN_copy(x, &point->X)) goto err;
404 		BN_set_negative(x, 0);
405 		}
406 	if (y != NULL)
407 		{
408 		if (!BN_copy(y, &point->Y)) goto err;
409 		BN_set_negative(y, 0);
410 		}
411 	ret = 1;
412 
413  err:
414 	return ret;
415 	}
416 
417 /* Computes a + b and stores the result in r.  r could be a or b, a could be b.
418  * Uses algorithm A.10.2 of IEEE P1363.
419  */
ec_GF2m_simple_add(const EC_GROUP * group,EC_POINT * r,const EC_POINT * a,const EC_POINT * b,BN_CTX * ctx)420 int ec_GF2m_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
421 	{
422 	BN_CTX *new_ctx = NULL;
423 	BIGNUM *x0, *y0, *x1, *y1, *x2, *y2, *s, *t;
424 	int ret = 0;
425 
426 	if (EC_POINT_is_at_infinity(group, a))
427 		{
428 		if (!EC_POINT_copy(r, b)) return 0;
429 		return 1;
430 		}
431 
432 	if (EC_POINT_is_at_infinity(group, b))
433 		{
434 		if (!EC_POINT_copy(r, a)) return 0;
435 		return 1;
436 		}
437 
438 	if (ctx == NULL)
439 		{
440 		ctx = new_ctx = BN_CTX_new();
441 		if (ctx == NULL)
442 			return 0;
443 		}
444 
445 	BN_CTX_start(ctx);
446 	x0 = BN_CTX_get(ctx);
447 	y0 = BN_CTX_get(ctx);
448 	x1 = BN_CTX_get(ctx);
449 	y1 = BN_CTX_get(ctx);
450 	x2 = BN_CTX_get(ctx);
451 	y2 = BN_CTX_get(ctx);
452 	s = BN_CTX_get(ctx);
453 	t = BN_CTX_get(ctx);
454 	if (t == NULL) goto err;
455 
456 	if (a->Z_is_one)
457 		{
458 		if (!BN_copy(x0, &a->X)) goto err;
459 		if (!BN_copy(y0, &a->Y)) goto err;
460 		}
461 	else
462 		{
463 		if (!EC_POINT_get_affine_coordinates_GF2m(group, a, x0, y0, ctx)) goto err;
464 		}
465 	if (b->Z_is_one)
466 		{
467 		if (!BN_copy(x1, &b->X)) goto err;
468 		if (!BN_copy(y1, &b->Y)) goto err;
469 		}
470 	else
471 		{
472 		if (!EC_POINT_get_affine_coordinates_GF2m(group, b, x1, y1, ctx)) goto err;
473 		}
474 
475 
476 	if (BN_GF2m_cmp(x0, x1))
477 		{
478 		if (!BN_GF2m_add(t, x0, x1)) goto err;
479 		if (!BN_GF2m_add(s, y0, y1)) goto err;
480 		if (!group->meth->field_div(group, s, s, t, ctx)) goto err;
481 		if (!group->meth->field_sqr(group, x2, s, ctx)) goto err;
482 		if (!BN_GF2m_add(x2, x2, &group->a)) goto err;
483 		if (!BN_GF2m_add(x2, x2, s)) goto err;
484 		if (!BN_GF2m_add(x2, x2, t)) goto err;
485 		}
486 	else
487 		{
488 		if (BN_GF2m_cmp(y0, y1) || BN_is_zero(x1))
489 			{
490 			if (!EC_POINT_set_to_infinity(group, r)) goto err;
491 			ret = 1;
492 			goto err;
493 			}
494 		if (!group->meth->field_div(group, s, y1, x1, ctx)) goto err;
495 		if (!BN_GF2m_add(s, s, x1)) goto err;
496 
497 		if (!group->meth->field_sqr(group, x2, s, ctx)) goto err;
498 		if (!BN_GF2m_add(x2, x2, s)) goto err;
499 		if (!BN_GF2m_add(x2, x2, &group->a)) goto err;
500 		}
501 
502 	if (!BN_GF2m_add(y2, x1, x2)) goto err;
503 	if (!group->meth->field_mul(group, y2, y2, s, ctx)) goto err;
504 	if (!BN_GF2m_add(y2, y2, x2)) goto err;
505 	if (!BN_GF2m_add(y2, y2, y1)) goto err;
506 
507 	if (!EC_POINT_set_affine_coordinates_GF2m(group, r, x2, y2, ctx)) goto err;
508 
509 	ret = 1;
510 
511  err:
512 	BN_CTX_end(ctx);
513 	if (new_ctx != NULL)
514 		BN_CTX_free(new_ctx);
515 	return ret;
516 	}
517 
518 
519 /* Computes 2 * a and stores the result in r.  r could be a.
520  * Uses algorithm A.10.2 of IEEE P1363.
521  */
ec_GF2m_simple_dbl(const EC_GROUP * group,EC_POINT * r,const EC_POINT * a,BN_CTX * ctx)522 int ec_GF2m_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_CTX *ctx)
523 	{
524 	return ec_GF2m_simple_add(group, r, a, a, ctx);
525 	}
526 
527 
ec_GF2m_simple_invert(const EC_GROUP * group,EC_POINT * point,BN_CTX * ctx)528 int ec_GF2m_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
529 	{
530 	if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(&point->Y))
531 		/* point is its own inverse */
532 		return 1;
533 
534 	if (!EC_POINT_make_affine(group, point, ctx)) return 0;
535 	return BN_GF2m_add(&point->Y, &point->X, &point->Y);
536 	}
537 
538 
539 /* Indicates whether the given point is the point at infinity. */
ec_GF2m_simple_is_at_infinity(const EC_GROUP * group,const EC_POINT * point)540 int ec_GF2m_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point)
541 	{
542 	return BN_is_zero(&point->Z);
543 	}
544 
545 
546 /* Determines whether the given EC_POINT is an actual point on the curve defined
547  * in the EC_GROUP.  A point is valid if it satisfies the Weierstrass equation:
548  *      y^2 + x*y = x^3 + a*x^2 + b.
549  */
ec_GF2m_simple_is_on_curve(const EC_GROUP * group,const EC_POINT * point,BN_CTX * ctx)550 int ec_GF2m_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx)
551 	{
552 	int ret = -1;
553 	BN_CTX *new_ctx = NULL;
554 	BIGNUM *lh, *y2;
555 	int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
556 	int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
557 
558 	if (EC_POINT_is_at_infinity(group, point))
559 		return 1;
560 
561 	field_mul = group->meth->field_mul;
562 	field_sqr = group->meth->field_sqr;
563 
564 	/* only support affine coordinates */
565 	if (!point->Z_is_one) return -1;
566 
567 	if (ctx == NULL)
568 		{
569 		ctx = new_ctx = BN_CTX_new();
570 		if (ctx == NULL)
571 			return -1;
572 		}
573 
574 	BN_CTX_start(ctx);
575 	y2 = BN_CTX_get(ctx);
576 	lh = BN_CTX_get(ctx);
577 	if (lh == NULL) goto err;
578 
579 	/* We have a curve defined by a Weierstrass equation
580 	 *      y^2 + x*y = x^3 + a*x^2 + b.
581 	 *  <=> x^3 + a*x^2 + x*y + b + y^2 = 0
582 	 *  <=> ((x + a) * x + y ) * x + b + y^2 = 0
583 	 */
584 	if (!BN_GF2m_add(lh, &point->X, &group->a)) goto err;
585 	if (!field_mul(group, lh, lh, &point->X, ctx)) goto err;
586 	if (!BN_GF2m_add(lh, lh, &point->Y)) goto err;
587 	if (!field_mul(group, lh, lh, &point->X, ctx)) goto err;
588 	if (!BN_GF2m_add(lh, lh, &group->b)) goto err;
589 	if (!field_sqr(group, y2, &point->Y, ctx)) goto err;
590 	if (!BN_GF2m_add(lh, lh, y2)) goto err;
591 	ret = BN_is_zero(lh);
592  err:
593 	if (ctx) BN_CTX_end(ctx);
594 	if (new_ctx) BN_CTX_free(new_ctx);
595 	return ret;
596 	}
597 
598 
599 /* Indicates whether two points are equal.
600  * Return values:
601  *  -1   error
602  *   0   equal (in affine coordinates)
603  *   1   not equal
604  */
ec_GF2m_simple_cmp(const EC_GROUP * group,const EC_POINT * a,const EC_POINT * b,BN_CTX * ctx)605 int ec_GF2m_simple_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
606 	{
607 	BIGNUM *aX, *aY, *bX, *bY;
608 	BN_CTX *new_ctx = NULL;
609 	int ret = -1;
610 
611 	if (EC_POINT_is_at_infinity(group, a))
612 		{
613 		return EC_POINT_is_at_infinity(group, b) ? 0 : 1;
614 		}
615 
616 	if (EC_POINT_is_at_infinity(group, b))
617 		return 1;
618 
619 	if (a->Z_is_one && b->Z_is_one)
620 		{
621 		return ((BN_cmp(&a->X, &b->X) == 0) && BN_cmp(&a->Y, &b->Y) == 0) ? 0 : 1;
622 		}
623 
624 	if (ctx == NULL)
625 		{
626 		ctx = new_ctx = BN_CTX_new();
627 		if (ctx == NULL)
628 			return -1;
629 		}
630 
631 	BN_CTX_start(ctx);
632 	aX = BN_CTX_get(ctx);
633 	aY = BN_CTX_get(ctx);
634 	bX = BN_CTX_get(ctx);
635 	bY = BN_CTX_get(ctx);
636 	if (bY == NULL) goto err;
637 
638 	if (!EC_POINT_get_affine_coordinates_GF2m(group, a, aX, aY, ctx)) goto err;
639 	if (!EC_POINT_get_affine_coordinates_GF2m(group, b, bX, bY, ctx)) goto err;
640 	ret = ((BN_cmp(aX, bX) == 0) && BN_cmp(aY, bY) == 0) ? 0 : 1;
641 
642   err:
643 	if (ctx) BN_CTX_end(ctx);
644 	if (new_ctx) BN_CTX_free(new_ctx);
645 	return ret;
646 	}
647 
648 
649 /* 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)650 int ec_GF2m_simple_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
651 	{
652 	BN_CTX *new_ctx = NULL;
653 	BIGNUM *x, *y;
654 	int ret = 0;
655 
656 	if (point->Z_is_one || EC_POINT_is_at_infinity(group, point))
657 		return 1;
658 
659 	if (ctx == NULL)
660 		{
661 		ctx = new_ctx = BN_CTX_new();
662 		if (ctx == NULL)
663 			return 0;
664 		}
665 
666 	BN_CTX_start(ctx);
667 	x = BN_CTX_get(ctx);
668 	y = BN_CTX_get(ctx);
669 	if (y == NULL) goto err;
670 
671 	if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err;
672 	if (!BN_copy(&point->X, x)) goto err;
673 	if (!BN_copy(&point->Y, y)) goto err;
674 	if (!BN_one(&point->Z)) goto err;
675 
676 	ret = 1;
677 
678   err:
679 	if (ctx) BN_CTX_end(ctx);
680 	if (new_ctx) BN_CTX_free(new_ctx);
681 	return ret;
682 	}
683 
684 
685 /* 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)686 int ec_GF2m_simple_points_make_affine(const EC_GROUP *group, size_t num, EC_POINT *points[], BN_CTX *ctx)
687 	{
688 	size_t i;
689 
690 	for (i = 0; i < num; i++)
691 		{
692 		if (!group->meth->make_affine(group, points[i], ctx)) return 0;
693 		}
694 
695 	return 1;
696 	}
697 
698 
699 /* 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)700 int ec_GF2m_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
701 	{
702 	return BN_GF2m_mod_mul_arr(r, a, b, group->poly, ctx);
703 	}
704 
705 
706 /* 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)707 int ec_GF2m_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx)
708 	{
709 	return BN_GF2m_mod_sqr_arr(r, a, group->poly, ctx);
710 	}
711 
712 
713 /* 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)714 int ec_GF2m_simple_field_div(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
715 	{
716 	return BN_GF2m_mod_div(r, a, b, &group->field, ctx);
717 	}
718 
719 #endif
720