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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 	static const EC_METHOD ret = {
84 		EC_FLAGS_DEFAULT_OCT,
85 		NID_X9_62_characteristic_two_field,
86 		ec_GF2m_simple_group_init,
87 		ec_GF2m_simple_group_finish,
88 		ec_GF2m_simple_group_clear_finish,
89 		ec_GF2m_simple_group_copy,
90 		ec_GF2m_simple_group_set_curve,
91 		ec_GF2m_simple_group_get_curve,
92 		ec_GF2m_simple_group_get_degree,
93 		ec_GF2m_simple_group_check_discriminant,
94 		ec_GF2m_simple_point_init,
95 		ec_GF2m_simple_point_finish,
96 		ec_GF2m_simple_point_clear_finish,
97 		ec_GF2m_simple_point_copy,
98 		ec_GF2m_simple_point_set_to_infinity,
99 		0 /* set_Jprojective_coordinates_GFp */,
100 		0 /* get_Jprojective_coordinates_GFp */,
101 		ec_GF2m_simple_point_set_affine_coordinates,
102 		ec_GF2m_simple_point_get_affine_coordinates,
103 		0,0,0,
104 		ec_GF2m_simple_add,
105 		ec_GF2m_simple_dbl,
106 		ec_GF2m_simple_invert,
107 		ec_GF2m_simple_is_at_infinity,
108 		ec_GF2m_simple_is_on_curve,
109 		ec_GF2m_simple_cmp,
110 		ec_GF2m_simple_make_affine,
111 		ec_GF2m_simple_points_make_affine,
112 
113 		/* the following three method functions are defined in ec2_mult.c */
114 		ec_GF2m_simple_mul,
115 		ec_GF2m_precompute_mult,
116 		ec_GF2m_have_precompute_mult,
117 
118 		ec_GF2m_simple_field_mul,
119 		ec_GF2m_simple_field_sqr,
120 		ec_GF2m_simple_field_div,
121 		0 /* field_encode */,
122 		0 /* field_decode */,
123 		0 /* field_set_to_one */ };
124 
125 #ifdef OPENSSL_FIPS
126 	if (FIPS_mode())
127 		return fips_ec_gf2m_simple_method();
128 #endif
129 
130 	return &ret;
131 	}
132 
133 
134 /* Initialize a GF(2^m)-based EC_GROUP structure.
135  * Note that all other members are handled by EC_GROUP_new.
136  */
ec_GF2m_simple_group_init(EC_GROUP * group)137 int ec_GF2m_simple_group_init(EC_GROUP *group)
138 	{
139 	BN_init(&group->field);
140 	BN_init(&group->a);
141 	BN_init(&group->b);
142 	return 1;
143 	}
144 
145 
146 /* Free a GF(2^m)-based EC_GROUP structure.
147  * Note that all other members are handled by EC_GROUP_free.
148  */
ec_GF2m_simple_group_finish(EC_GROUP * group)149 void ec_GF2m_simple_group_finish(EC_GROUP *group)
150 	{
151 	BN_free(&group->field);
152 	BN_free(&group->a);
153 	BN_free(&group->b);
154 	}
155 
156 
157 /* Clear and free a GF(2^m)-based EC_GROUP structure.
158  * Note that all other members are handled by EC_GROUP_clear_free.
159  */
ec_GF2m_simple_group_clear_finish(EC_GROUP * group)160 void ec_GF2m_simple_group_clear_finish(EC_GROUP *group)
161 	{
162 	BN_clear_free(&group->field);
163 	BN_clear_free(&group->a);
164 	BN_clear_free(&group->b);
165 	group->poly[0] = 0;
166 	group->poly[1] = 0;
167 	group->poly[2] = 0;
168 	group->poly[3] = 0;
169 	group->poly[4] = 0;
170 	group->poly[5] = -1;
171 	}
172 
173 
174 /* Copy a GF(2^m)-based EC_GROUP structure.
175  * Note that all other members are handled by EC_GROUP_copy.
176  */
ec_GF2m_simple_group_copy(EC_GROUP * dest,const EC_GROUP * src)177 int ec_GF2m_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src)
178 	{
179 	int i;
180 	if (!BN_copy(&dest->field, &src->field)) return 0;
181 	if (!BN_copy(&dest->a, &src->a)) return 0;
182 	if (!BN_copy(&dest->b, &src->b)) return 0;
183 	dest->poly[0] = src->poly[0];
184 	dest->poly[1] = src->poly[1];
185 	dest->poly[2] = src->poly[2];
186 	dest->poly[3] = src->poly[3];
187 	dest->poly[4] = src->poly[4];
188 	dest->poly[5] = src->poly[5];
189 	if (bn_wexpand(&dest->a, (int)(dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) return 0;
190 	if (bn_wexpand(&dest->b, (int)(dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) return 0;
191 	for (i = dest->a.top; i < dest->a.dmax; i++) dest->a.d[i] = 0;
192 	for (i = dest->b.top; i < dest->b.dmax; i++) dest->b.d[i] = 0;
193 	return 1;
194 	}
195 
196 
197 /* 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)198 int ec_GF2m_simple_group_set_curve(EC_GROUP *group,
199 	const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
200 	{
201 	int ret = 0, i;
202 
203 	/* group->field */
204 	if (!BN_copy(&group->field, p)) goto err;
205 	i = BN_GF2m_poly2arr(&group->field, group->poly, 6) - 1;
206 	if ((i != 5) && (i != 3))
207 		{
208 		ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_SET_CURVE, EC_R_UNSUPPORTED_FIELD);
209 		goto err;
210 		}
211 
212 	/* group->a */
213 	if (!BN_GF2m_mod_arr(&group->a, a, group->poly)) goto err;
214 	if(bn_wexpand(&group->a, (int)(group->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) goto err;
215 	for (i = group->a.top; i < group->a.dmax; i++) group->a.d[i] = 0;
216 
217 	/* group->b */
218 	if (!BN_GF2m_mod_arr(&group->b, b, group->poly)) goto err;
219 	if(bn_wexpand(&group->b, (int)(group->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) goto err;
220 	for (i = group->b.top; i < group->b.dmax; i++) group->b.d[i] = 0;
221 
222 	ret = 1;
223   err:
224 	return ret;
225 	}
226 
227 
228 /* Get the curve parameters of an EC_GROUP structure.
229  * If p, a, or b are NULL then there values will not be set but the method will return with success.
230  */
ec_GF2m_simple_group_get_curve(const EC_GROUP * group,BIGNUM * p,BIGNUM * a,BIGNUM * b,BN_CTX * ctx)231 int ec_GF2m_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx)
232 	{
233 	int ret = 0;
234 
235 	if (p != NULL)
236 		{
237 		if (!BN_copy(p, &group->field)) return 0;
238 		}
239 
240 	if (a != NULL)
241 		{
242 		if (!BN_copy(a, &group->a)) goto err;
243 		}
244 
245 	if (b != NULL)
246 		{
247 		if (!BN_copy(b, &group->b)) goto err;
248 		}
249 
250 	ret = 1;
251 
252   err:
253 	return ret;
254 	}
255 
256 
257 /* 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)258 int ec_GF2m_simple_group_get_degree(const EC_GROUP *group)
259 	{
260 	return BN_num_bits(&group->field)-1;
261 	}
262 
263 
264 /* Checks the discriminant of the curve.
265  * y^2 + x*y = x^3 + a*x^2 + b is an elliptic curve <=> b != 0 (mod p)
266  */
ec_GF2m_simple_group_check_discriminant(const EC_GROUP * group,BN_CTX * ctx)267 int ec_GF2m_simple_group_check_discriminant(const EC_GROUP *group, BN_CTX *ctx)
268 	{
269 	int ret = 0;
270 	BIGNUM *b;
271 	BN_CTX *new_ctx = NULL;
272 
273 	if (ctx == NULL)
274 		{
275 		ctx = new_ctx = BN_CTX_new();
276 		if (ctx == NULL)
277 			{
278 			ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_CHECK_DISCRIMINANT, ERR_R_MALLOC_FAILURE);
279 			goto err;
280 			}
281 		}
282 	BN_CTX_start(ctx);
283 	b = BN_CTX_get(ctx);
284 	if (b == NULL) goto err;
285 
286 	if (!BN_GF2m_mod_arr(b, &group->b, group->poly)) goto err;
287 
288 	/* check the discriminant:
289 	 * y^2 + x*y = x^3 + a*x^2 + b is an elliptic curve <=> b != 0 (mod p)
290 	 */
291 	if (BN_is_zero(b)) goto err;
292 
293 	ret = 1;
294 
295 err:
296 	if (ctx != NULL)
297 		BN_CTX_end(ctx);
298 	if (new_ctx != NULL)
299 		BN_CTX_free(new_ctx);
300 	return ret;
301 	}
302 
303 
304 /* Initializes an EC_POINT. */
ec_GF2m_simple_point_init(EC_POINT * point)305 int ec_GF2m_simple_point_init(EC_POINT *point)
306 	{
307 	BN_init(&point->X);
308 	BN_init(&point->Y);
309 	BN_init(&point->Z);
310 	return 1;
311 	}
312 
313 
314 /* Frees an EC_POINT. */
ec_GF2m_simple_point_finish(EC_POINT * point)315 void ec_GF2m_simple_point_finish(EC_POINT *point)
316 	{
317 	BN_free(&point->X);
318 	BN_free(&point->Y);
319 	BN_free(&point->Z);
320 	}
321 
322 
323 /* Clears and frees an EC_POINT. */
ec_GF2m_simple_point_clear_finish(EC_POINT * point)324 void ec_GF2m_simple_point_clear_finish(EC_POINT *point)
325 	{
326 	BN_clear_free(&point->X);
327 	BN_clear_free(&point->Y);
328 	BN_clear_free(&point->Z);
329 	point->Z_is_one = 0;
330 	}
331 
332 
333 /* 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)334 int ec_GF2m_simple_point_copy(EC_POINT *dest, const EC_POINT *src)
335 	{
336 	if (!BN_copy(&dest->X, &src->X)) return 0;
337 	if (!BN_copy(&dest->Y, &src->Y)) return 0;
338 	if (!BN_copy(&dest->Z, &src->Z)) return 0;
339 	dest->Z_is_one = src->Z_is_one;
340 
341 	return 1;
342 	}
343 
344 
345 /* Set an EC_POINT to the point at infinity.
346  * A point at infinity is represented by having Z=0.
347  */
ec_GF2m_simple_point_set_to_infinity(const EC_GROUP * group,EC_POINT * point)348 int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *group, EC_POINT *point)
349 	{
350 	point->Z_is_one = 0;
351 	BN_zero(&point->Z);
352 	return 1;
353 	}
354 
355 
356 /* Set the coordinates of an EC_POINT using affine coordinates.
357  * Note that the simple implementation only uses affine coordinates.
358  */
ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP * group,EC_POINT * point,const BIGNUM * x,const BIGNUM * y,BN_CTX * ctx)359 int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *group, EC_POINT *point,
360 	const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx)
361 	{
362 	int ret = 0;
363 	if (x == NULL || y == NULL)
364 		{
365 		ECerr(EC_F_EC_GF2M_SIMPLE_POINT_SET_AFFINE_COORDINATES, ERR_R_PASSED_NULL_PARAMETER);
366 		return 0;
367 		}
368 
369 	if (!BN_copy(&point->X, x)) goto err;
370 	BN_set_negative(&point->X, 0);
371 	if (!BN_copy(&point->Y, y)) goto err;
372 	BN_set_negative(&point->Y, 0);
373 	if (!BN_copy(&point->Z, BN_value_one())) goto err;
374 	BN_set_negative(&point->Z, 0);
375 	point->Z_is_one = 1;
376 	ret = 1;
377 
378   err:
379 	return ret;
380 	}
381 
382 
383 /* Gets the affine coordinates of an EC_POINT.
384  * Note that the simple implementation only uses affine coordinates.
385  */
ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP * group,const EC_POINT * point,BIGNUM * x,BIGNUM * y,BN_CTX * ctx)386 int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point,
387 	BIGNUM *x, BIGNUM *y, BN_CTX *ctx)
388 	{
389 	int ret = 0;
390 
391 	if (EC_POINT_is_at_infinity(group, point))
392 		{
393 		ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES, EC_R_POINT_AT_INFINITY);
394 		return 0;
395 		}
396 
397 	if (BN_cmp(&point->Z, BN_value_one()))
398 		{
399 		ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
400 		return 0;
401 		}
402 	if (x != NULL)
403 		{
404 		if (!BN_copy(x, &point->X)) goto err;
405 		BN_set_negative(x, 0);
406 		}
407 	if (y != NULL)
408 		{
409 		if (!BN_copy(y, &point->Y)) goto err;
410 		BN_set_negative(y, 0);
411 		}
412 	ret = 1;
413 
414  err:
415 	return ret;
416 	}
417 
418 /* Computes a + b and stores the result in r.  r could be a or b, a could be b.
419  * Uses algorithm A.10.2 of IEEE P1363.
420  */
ec_GF2m_simple_add(const EC_GROUP * group,EC_POINT * r,const EC_POINT * a,const EC_POINT * b,BN_CTX * ctx)421 int ec_GF2m_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
422 	{
423 	BN_CTX *new_ctx = NULL;
424 	BIGNUM *x0, *y0, *x1, *y1, *x2, *y2, *s, *t;
425 	int ret = 0;
426 
427 	if (EC_POINT_is_at_infinity(group, a))
428 		{
429 		if (!EC_POINT_copy(r, b)) return 0;
430 		return 1;
431 		}
432 
433 	if (EC_POINT_is_at_infinity(group, b))
434 		{
435 		if (!EC_POINT_copy(r, a)) return 0;
436 		return 1;
437 		}
438 
439 	if (ctx == NULL)
440 		{
441 		ctx = new_ctx = BN_CTX_new();
442 		if (ctx == NULL)
443 			return 0;
444 		}
445 
446 	BN_CTX_start(ctx);
447 	x0 = BN_CTX_get(ctx);
448 	y0 = BN_CTX_get(ctx);
449 	x1 = BN_CTX_get(ctx);
450 	y1 = BN_CTX_get(ctx);
451 	x2 = BN_CTX_get(ctx);
452 	y2 = BN_CTX_get(ctx);
453 	s = BN_CTX_get(ctx);
454 	t = BN_CTX_get(ctx);
455 	if (t == NULL) goto err;
456 
457 	if (a->Z_is_one)
458 		{
459 		if (!BN_copy(x0, &a->X)) goto err;
460 		if (!BN_copy(y0, &a->Y)) goto err;
461 		}
462 	else
463 		{
464 		if (!EC_POINT_get_affine_coordinates_GF2m(group, a, x0, y0, ctx)) goto err;
465 		}
466 	if (b->Z_is_one)
467 		{
468 		if (!BN_copy(x1, &b->X)) goto err;
469 		if (!BN_copy(y1, &b->Y)) goto err;
470 		}
471 	else
472 		{
473 		if (!EC_POINT_get_affine_coordinates_GF2m(group, b, x1, y1, ctx)) goto err;
474 		}
475 
476 
477 	if (BN_GF2m_cmp(x0, x1))
478 		{
479 		if (!BN_GF2m_add(t, x0, x1)) goto err;
480 		if (!BN_GF2m_add(s, y0, y1)) goto err;
481 		if (!group->meth->field_div(group, s, s, t, ctx)) goto err;
482 		if (!group->meth->field_sqr(group, x2, s, ctx)) goto err;
483 		if (!BN_GF2m_add(x2, x2, &group->a)) goto err;
484 		if (!BN_GF2m_add(x2, x2, s)) goto err;
485 		if (!BN_GF2m_add(x2, x2, t)) goto err;
486 		}
487 	else
488 		{
489 		if (BN_GF2m_cmp(y0, y1) || BN_is_zero(x1))
490 			{
491 			if (!EC_POINT_set_to_infinity(group, r)) goto err;
492 			ret = 1;
493 			goto err;
494 			}
495 		if (!group->meth->field_div(group, s, y1, x1, ctx)) goto err;
496 		if (!BN_GF2m_add(s, s, x1)) goto err;
497 
498 		if (!group->meth->field_sqr(group, x2, s, ctx)) goto err;
499 		if (!BN_GF2m_add(x2, x2, s)) goto err;
500 		if (!BN_GF2m_add(x2, x2, &group->a)) goto err;
501 		}
502 
503 	if (!BN_GF2m_add(y2, x1, x2)) goto err;
504 	if (!group->meth->field_mul(group, y2, y2, s, ctx)) goto err;
505 	if (!BN_GF2m_add(y2, y2, x2)) goto err;
506 	if (!BN_GF2m_add(y2, y2, y1)) goto err;
507 
508 	if (!EC_POINT_set_affine_coordinates_GF2m(group, r, x2, y2, ctx)) goto err;
509 
510 	ret = 1;
511 
512  err:
513 	BN_CTX_end(ctx);
514 	if (new_ctx != NULL)
515 		BN_CTX_free(new_ctx);
516 	return ret;
517 	}
518 
519 
520 /* Computes 2 * a and stores the result in r.  r could be a.
521  * Uses algorithm A.10.2 of IEEE P1363.
522  */
ec_GF2m_simple_dbl(const EC_GROUP * group,EC_POINT * r,const EC_POINT * a,BN_CTX * ctx)523 int ec_GF2m_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_CTX *ctx)
524 	{
525 	return ec_GF2m_simple_add(group, r, a, a, ctx);
526 	}
527 
528 
ec_GF2m_simple_invert(const EC_GROUP * group,EC_POINT * point,BN_CTX * ctx)529 int ec_GF2m_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
530 	{
531 	if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(&point->Y))
532 		/* point is its own inverse */
533 		return 1;
534 
535 	if (!EC_POINT_make_affine(group, point, ctx)) return 0;
536 	return BN_GF2m_add(&point->Y, &point->X, &point->Y);
537 	}
538 
539 
540 /* Indicates whether the given point is the point at infinity. */
ec_GF2m_simple_is_at_infinity(const EC_GROUP * group,const EC_POINT * point)541 int ec_GF2m_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point)
542 	{
543 	return BN_is_zero(&point->Z);
544 	}
545 
546 
547 /* Determines whether the given EC_POINT is an actual point on the curve defined
548  * in the EC_GROUP.  A point is valid if it satisfies the Weierstrass equation:
549  *      y^2 + x*y = x^3 + a*x^2 + b.
550  */
ec_GF2m_simple_is_on_curve(const EC_GROUP * group,const EC_POINT * point,BN_CTX * ctx)551 int ec_GF2m_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx)
552 	{
553 	int ret = -1;
554 	BN_CTX *new_ctx = NULL;
555 	BIGNUM *lh, *y2;
556 	int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
557 	int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
558 
559 	if (EC_POINT_is_at_infinity(group, point))
560 		return 1;
561 
562 	field_mul = group->meth->field_mul;
563 	field_sqr = group->meth->field_sqr;
564 
565 	/* only support affine coordinates */
566 	if (!point->Z_is_one) return -1;
567 
568 	if (ctx == NULL)
569 		{
570 		ctx = new_ctx = BN_CTX_new();
571 		if (ctx == NULL)
572 			return -1;
573 		}
574 
575 	BN_CTX_start(ctx);
576 	y2 = BN_CTX_get(ctx);
577 	lh = BN_CTX_get(ctx);
578 	if (lh == NULL) goto err;
579 
580 	/* We have a curve defined by a Weierstrass equation
581 	 *      y^2 + x*y = x^3 + a*x^2 + b.
582 	 *  <=> x^3 + a*x^2 + x*y + b + y^2 = 0
583 	 *  <=> ((x + a) * x + y ) * x + b + y^2 = 0
584 	 */
585 	if (!BN_GF2m_add(lh, &point->X, &group->a)) goto err;
586 	if (!field_mul(group, lh, lh, &point->X, ctx)) goto err;
587 	if (!BN_GF2m_add(lh, lh, &point->Y)) goto err;
588 	if (!field_mul(group, lh, lh, &point->X, ctx)) goto err;
589 	if (!BN_GF2m_add(lh, lh, &group->b)) goto err;
590 	if (!field_sqr(group, y2, &point->Y, ctx)) goto err;
591 	if (!BN_GF2m_add(lh, lh, y2)) goto err;
592 	ret = BN_is_zero(lh);
593  err:
594 	if (ctx) BN_CTX_end(ctx);
595 	if (new_ctx) BN_CTX_free(new_ctx);
596 	return ret;
597 	}
598 
599 
600 /* Indicates whether two points are equal.
601  * Return values:
602  *  -1   error
603  *   0   equal (in affine coordinates)
604  *   1   not equal
605  */
ec_GF2m_simple_cmp(const EC_GROUP * group,const EC_POINT * a,const EC_POINT * b,BN_CTX * ctx)606 int ec_GF2m_simple_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
607 	{
608 	BIGNUM *aX, *aY, *bX, *bY;
609 	BN_CTX *new_ctx = NULL;
610 	int ret = -1;
611 
612 	if (EC_POINT_is_at_infinity(group, a))
613 		{
614 		return EC_POINT_is_at_infinity(group, b) ? 0 : 1;
615 		}
616 
617 	if (EC_POINT_is_at_infinity(group, b))
618 		return 1;
619 
620 	if (a->Z_is_one && b->Z_is_one)
621 		{
622 		return ((BN_cmp(&a->X, &b->X) == 0) && BN_cmp(&a->Y, &b->Y) == 0) ? 0 : 1;
623 		}
624 
625 	if (ctx == NULL)
626 		{
627 		ctx = new_ctx = BN_CTX_new();
628 		if (ctx == NULL)
629 			return -1;
630 		}
631 
632 	BN_CTX_start(ctx);
633 	aX = BN_CTX_get(ctx);
634 	aY = BN_CTX_get(ctx);
635 	bX = BN_CTX_get(ctx);
636 	bY = BN_CTX_get(ctx);
637 	if (bY == NULL) goto err;
638 
639 	if (!EC_POINT_get_affine_coordinates_GF2m(group, a, aX, aY, ctx)) goto err;
640 	if (!EC_POINT_get_affine_coordinates_GF2m(group, b, bX, bY, ctx)) goto err;
641 	ret = ((BN_cmp(aX, bX) == 0) && BN_cmp(aY, bY) == 0) ? 0 : 1;
642 
643   err:
644 	if (ctx) BN_CTX_end(ctx);
645 	if (new_ctx) BN_CTX_free(new_ctx);
646 	return ret;
647 	}
648 
649 
650 /* 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)651 int ec_GF2m_simple_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
652 	{
653 	BN_CTX *new_ctx = NULL;
654 	BIGNUM *x, *y;
655 	int ret = 0;
656 
657 	if (point->Z_is_one || EC_POINT_is_at_infinity(group, point))
658 		return 1;
659 
660 	if (ctx == NULL)
661 		{
662 		ctx = new_ctx = BN_CTX_new();
663 		if (ctx == NULL)
664 			return 0;
665 		}
666 
667 	BN_CTX_start(ctx);
668 	x = BN_CTX_get(ctx);
669 	y = BN_CTX_get(ctx);
670 	if (y == NULL) goto err;
671 
672 	if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err;
673 	if (!BN_copy(&point->X, x)) goto err;
674 	if (!BN_copy(&point->Y, y)) goto err;
675 	if (!BN_one(&point->Z)) goto err;
676 
677 	ret = 1;
678 
679   err:
680 	if (ctx) BN_CTX_end(ctx);
681 	if (new_ctx) BN_CTX_free(new_ctx);
682 	return ret;
683 	}
684 
685 
686 /* 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)687 int ec_GF2m_simple_points_make_affine(const EC_GROUP *group, size_t num, EC_POINT *points[], BN_CTX *ctx)
688 	{
689 	size_t i;
690 
691 	for (i = 0; i < num; i++)
692 		{
693 		if (!group->meth->make_affine(group, points[i], ctx)) return 0;
694 		}
695 
696 	return 1;
697 	}
698 
699 
700 /* 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)701 int ec_GF2m_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
702 	{
703 	return BN_GF2m_mod_mul_arr(r, a, b, group->poly, ctx);
704 	}
705 
706 
707 /* 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)708 int ec_GF2m_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx)
709 	{
710 	return BN_GF2m_mod_sqr_arr(r, a, group->poly, ctx);
711 	}
712 
713 
714 /* 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)715 int ec_GF2m_simple_field_div(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
716 	{
717 	return BN_GF2m_mod_div(r, a, b, &group->field, ctx);
718 	}
719 
720 #endif
721