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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 
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 	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  */
ec_GF2m_simple_group_copy(EC_GROUP * dest,const EC_GROUP * src)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. */
ec_GF2m_simple_group_set_curve(EC_GROUP * group,const BIGNUM * p,const BIGNUM * a,const BIGNUM * b,BN_CTX * ctx)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  */
ec_GF2m_simple_group_get_curve(const EC_GROUP * group,BIGNUM * p,BIGNUM * a,BIGNUM * b,BN_CTX * ctx)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. */
ec_GF2m_simple_group_get_degree(const EC_GROUP * group)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  */
ec_GF2m_simple_group_check_discriminant(const EC_GROUP * group,BN_CTX * ctx)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. */
ec_GF2m_simple_point_init(EC_POINT * 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. */
ec_GF2m_simple_point_finish(EC_POINT * 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. */
ec_GF2m_simple_point_clear_finish(EC_POINT * 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. */
ec_GF2m_simple_point_copy(EC_POINT * dest,const EC_POINT * src)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  */
ec_GF2m_simple_point_set_to_infinity(const EC_GROUP * group,EC_POINT * point)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  */
ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP * group,EC_POINT * point,const BIGNUM * x,const BIGNUM * y,BN_CTX * ctx)349 int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *group, EC_POINT *point,
350 	const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx)
351 	{
352 	int ret = 0;
353 	if (x == NULL || y == NULL)
354 		{
355 		ECerr(EC_F_EC_GF2M_SIMPLE_POINT_SET_AFFINE_COORDINATES, ERR_R_PASSED_NULL_PARAMETER);
356 		return 0;
357 		}
358 
359 	if (!BN_copy(&point->X, x)) goto err;
360 	BN_set_negative(&point->X, 0);
361 	if (!BN_copy(&point->Y, y)) goto err;
362 	BN_set_negative(&point->Y, 0);
363 	if (!BN_copy(&point->Z, BN_value_one())) goto err;
364 	BN_set_negative(&point->Z, 0);
365 	point->Z_is_one = 1;
366 	ret = 1;
367 
368   err:
369 	return ret;
370 	}
371 
372 
373 /* Gets the affine coordinates of an EC_POINT.
374  * Note that the simple implementation only uses affine coordinates.
375  */
ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP * group,const EC_POINT * point,BIGNUM * x,BIGNUM * y,BN_CTX * ctx)376 int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point,
377 	BIGNUM *x, BIGNUM *y, BN_CTX *ctx)
378 	{
379 	int ret = 0;
380 
381 	if (EC_POINT_is_at_infinity(group, point))
382 		{
383 		ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES, EC_R_POINT_AT_INFINITY);
384 		return 0;
385 		}
386 
387 	if (BN_cmp(&point->Z, BN_value_one()))
388 		{
389 		ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
390 		return 0;
391 		}
392 	if (x != NULL)
393 		{
394 		if (!BN_copy(x, &point->X)) goto err;
395 		BN_set_negative(x, 0);
396 		}
397 	if (y != NULL)
398 		{
399 		if (!BN_copy(y, &point->Y)) goto err;
400 		BN_set_negative(y, 0);
401 		}
402 	ret = 1;
403 
404  err:
405 	return ret;
406 	}
407 
408 
409 /* Calculates and sets the affine coordinates of an EC_POINT from the given
410  * compressed coordinates.  Uses algorithm 2.3.4 of SEC 1.
411  * Note that the simple implementation only uses affine coordinates.
412  *
413  * The method is from the following publication:
414  *
415  *     Harper, Menezes, Vanstone:
416  *     "Public-Key Cryptosystems with Very Small Key Lengths",
417  *     EUROCRYPT '92, Springer-Verlag LNCS 658,
418  *     published February 1993
419  *
420  * US Patents 6,141,420 and 6,618,483 (Vanstone, Mullin, Agnew) describe
421  * the same method, but claim no priority date earlier than July 29, 1994
422  * (and additionally fail to cite the EUROCRYPT '92 publication as prior art).
423  */
ec_GF2m_simple_set_compressed_coordinates(const EC_GROUP * group,EC_POINT * point,const BIGNUM * x_,int y_bit,BN_CTX * ctx)424 int ec_GF2m_simple_set_compressed_coordinates(const EC_GROUP *group, EC_POINT *point,
425 	const BIGNUM *x_, int y_bit, BN_CTX *ctx)
426 	{
427 	BN_CTX *new_ctx = NULL;
428 	BIGNUM *tmp, *x, *y, *z;
429 	int ret = 0, z0;
430 
431 	/* clear error queue */
432 	ERR_clear_error();
433 
434 	if (ctx == NULL)
435 		{
436 		ctx = new_ctx = BN_CTX_new();
437 		if (ctx == NULL)
438 			return 0;
439 		}
440 
441 	y_bit = (y_bit != 0) ? 1 : 0;
442 
443 	BN_CTX_start(ctx);
444 	tmp = BN_CTX_get(ctx);
445 	x = BN_CTX_get(ctx);
446 	y = BN_CTX_get(ctx);
447 	z = BN_CTX_get(ctx);
448 	if (z == NULL) goto err;
449 
450 	if (!BN_GF2m_mod_arr(x, x_, group->poly)) goto err;
451 	if (BN_is_zero(x))
452 		{
453 		if (!BN_GF2m_mod_sqrt_arr(y, &group->b, group->poly, ctx)) goto err;
454 		}
455 	else
456 		{
457 		if (!group->meth->field_sqr(group, tmp, x, ctx)) goto err;
458 		if (!group->meth->field_div(group, tmp, &group->b, tmp, ctx)) goto err;
459 		if (!BN_GF2m_add(tmp, &group->a, tmp)) goto err;
460 		if (!BN_GF2m_add(tmp, x, tmp)) goto err;
461 		if (!BN_GF2m_mod_solve_quad_arr(z, tmp, group->poly, ctx))
462 			{
463 			unsigned long err = ERR_peek_last_error();
464 
465 			if (ERR_GET_LIB(err) == ERR_LIB_BN && ERR_GET_REASON(err) == BN_R_NO_SOLUTION)
466 				{
467 				ERR_clear_error();
468 				ECerr(EC_F_EC_GF2M_SIMPLE_SET_COMPRESSED_COORDINATES, EC_R_INVALID_COMPRESSED_POINT);
469 				}
470 			else
471 				ECerr(EC_F_EC_GF2M_SIMPLE_SET_COMPRESSED_COORDINATES, ERR_R_BN_LIB);
472 			goto err;
473 			}
474 		z0 = (BN_is_odd(z)) ? 1 : 0;
475 		if (!group->meth->field_mul(group, y, x, z, ctx)) goto err;
476 		if (z0 != y_bit)
477 			{
478 			if (!BN_GF2m_add(y, y, x)) goto err;
479 			}
480 		}
481 
482 	if (!EC_POINT_set_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err;
483 
484 	ret = 1;
485 
486  err:
487 	BN_CTX_end(ctx);
488 	if (new_ctx != NULL)
489 		BN_CTX_free(new_ctx);
490 	return ret;
491 	}
492 
493 
494 /* Converts an EC_POINT to an octet string.
495  * If buf is NULL, the encoded length will be returned.
496  * If the length len of buf is smaller than required an error will be returned.
497  */
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)498 size_t ec_GF2m_simple_point2oct(const EC_GROUP *group, const EC_POINT *point, point_conversion_form_t form,
499 	unsigned char *buf, size_t len, BN_CTX *ctx)
500 	{
501 	size_t ret;
502 	BN_CTX *new_ctx = NULL;
503 	int used_ctx = 0;
504 	BIGNUM *x, *y, *yxi;
505 	size_t field_len, i, skip;
506 
507 	if ((form != POINT_CONVERSION_COMPRESSED)
508 		&& (form != POINT_CONVERSION_UNCOMPRESSED)
509 		&& (form != POINT_CONVERSION_HYBRID))
510 		{
511 		ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_INVALID_FORM);
512 		goto err;
513 		}
514 
515 	if (EC_POINT_is_at_infinity(group, point))
516 		{
517 		/* encodes to a single 0 octet */
518 		if (buf != NULL)
519 			{
520 			if (len < 1)
521 				{
522 				ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);
523 				return 0;
524 				}
525 			buf[0] = 0;
526 			}
527 		return 1;
528 		}
529 
530 
531 	/* ret := required output buffer length */
532 	field_len = (EC_GROUP_get_degree(group) + 7) / 8;
533 	ret = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len;
534 
535 	/* if 'buf' is NULL, just return required length */
536 	if (buf != NULL)
537 		{
538 		if (len < ret)
539 			{
540 			ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);
541 			goto err;
542 			}
543 
544 		if (ctx == NULL)
545 			{
546 			ctx = new_ctx = BN_CTX_new();
547 			if (ctx == NULL)
548 				return 0;
549 			}
550 
551 		BN_CTX_start(ctx);
552 		used_ctx = 1;
553 		x = BN_CTX_get(ctx);
554 		y = BN_CTX_get(ctx);
555 		yxi = BN_CTX_get(ctx);
556 		if (yxi == NULL) goto err;
557 
558 		if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err;
559 
560 		buf[0] = form;
561 		if ((form != POINT_CONVERSION_UNCOMPRESSED) && !BN_is_zero(x))
562 			{
563 			if (!group->meth->field_div(group, yxi, y, x, ctx)) goto err;
564 			if (BN_is_odd(yxi)) buf[0]++;
565 			}
566 
567 		i = 1;
568 
569 		skip = field_len - BN_num_bytes(x);
570 		if (skip > field_len)
571 			{
572 			ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
573 			goto err;
574 			}
575 		while (skip > 0)
576 			{
577 			buf[i++] = 0;
578 			skip--;
579 			}
580 		skip = BN_bn2bin(x, buf + i);
581 		i += skip;
582 		if (i != 1 + field_len)
583 			{
584 			ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
585 			goto err;
586 			}
587 
588 		if (form == POINT_CONVERSION_UNCOMPRESSED || form == POINT_CONVERSION_HYBRID)
589 			{
590 			skip = field_len - BN_num_bytes(y);
591 			if (skip > field_len)
592 				{
593 				ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
594 				goto err;
595 				}
596 			while (skip > 0)
597 				{
598 				buf[i++] = 0;
599 				skip--;
600 				}
601 			skip = BN_bn2bin(y, buf + i);
602 			i += skip;
603 			}
604 
605 		if (i != ret)
606 			{
607 			ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
608 			goto err;
609 			}
610 		}
611 
612 	if (used_ctx)
613 		BN_CTX_end(ctx);
614 	if (new_ctx != NULL)
615 		BN_CTX_free(new_ctx);
616 	return ret;
617 
618  err:
619 	if (used_ctx)
620 		BN_CTX_end(ctx);
621 	if (new_ctx != NULL)
622 		BN_CTX_free(new_ctx);
623 	return 0;
624 	}
625 
626 
627 /* Converts an octet string representation to an EC_POINT.
628  * Note that the simple implementation only uses affine coordinates.
629  */
ec_GF2m_simple_oct2point(const EC_GROUP * group,EC_POINT * point,const unsigned char * buf,size_t len,BN_CTX * ctx)630 int ec_GF2m_simple_oct2point(const EC_GROUP *group, EC_POINT *point,
631 	const unsigned char *buf, size_t len, BN_CTX *ctx)
632 	{
633 	point_conversion_form_t form;
634 	int y_bit;
635 	BN_CTX *new_ctx = NULL;
636 	BIGNUM *x, *y, *yxi;
637 	size_t field_len, enc_len;
638 	int ret = 0;
639 
640 	if (len == 0)
641 		{
642 		ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_BUFFER_TOO_SMALL);
643 		return 0;
644 		}
645 	form = buf[0];
646 	y_bit = form & 1;
647 	form = form & ~1U;
648 	if ((form != 0)	&& (form != POINT_CONVERSION_COMPRESSED)
649 		&& (form != POINT_CONVERSION_UNCOMPRESSED)
650 		&& (form != POINT_CONVERSION_HYBRID))
651 		{
652 		ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
653 		return 0;
654 		}
655 	if ((form == 0 || form == POINT_CONVERSION_UNCOMPRESSED) && y_bit)
656 		{
657 		ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
658 		return 0;
659 		}
660 
661 	if (form == 0)
662 		{
663 		if (len != 1)
664 			{
665 			ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
666 			return 0;
667 			}
668 
669 		return EC_POINT_set_to_infinity(group, point);
670 		}
671 
672 	field_len = (EC_GROUP_get_degree(group) + 7) / 8;
673 	enc_len = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len;
674 
675 	if (len != enc_len)
676 		{
677 		ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
678 		return 0;
679 		}
680 
681 	if (ctx == NULL)
682 		{
683 		ctx = new_ctx = BN_CTX_new();
684 		if (ctx == NULL)
685 			return 0;
686 		}
687 
688 	BN_CTX_start(ctx);
689 	x = BN_CTX_get(ctx);
690 	y = BN_CTX_get(ctx);
691 	yxi = BN_CTX_get(ctx);
692 	if (yxi == NULL) goto err;
693 
694 	if (!BN_bin2bn(buf + 1, field_len, x)) goto err;
695 	if (BN_ucmp(x, &group->field) >= 0)
696 		{
697 		ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
698 		goto err;
699 		}
700 
701 	if (form == POINT_CONVERSION_COMPRESSED)
702 		{
703 		if (!EC_POINT_set_compressed_coordinates_GF2m(group, point, x, y_bit, ctx)) goto err;
704 		}
705 	else
706 		{
707 		if (!BN_bin2bn(buf + 1 + field_len, field_len, y)) goto err;
708 		if (BN_ucmp(y, &group->field) >= 0)
709 			{
710 			ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
711 			goto err;
712 			}
713 		if (form == POINT_CONVERSION_HYBRID)
714 			{
715 			if (!group->meth->field_div(group, yxi, y, x, ctx)) goto err;
716 			if (y_bit != BN_is_odd(yxi))
717 				{
718 				ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
719 				goto err;
720 				}
721 			}
722 
723 		if (!EC_POINT_set_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err;
724 		}
725 
726 	if (!EC_POINT_is_on_curve(group, point, ctx)) /* test required by X9.62 */
727 		{
728 		ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_POINT_IS_NOT_ON_CURVE);
729 		goto err;
730 		}
731 
732 	ret = 1;
733 
734  err:
735 	BN_CTX_end(ctx);
736 	if (new_ctx != NULL)
737 		BN_CTX_free(new_ctx);
738 	return ret;
739 	}
740 
741 
742 /* Computes a + b and stores the result in r.  r could be a or b, a could be b.
743  * Uses algorithm A.10.2 of IEEE P1363.
744  */
ec_GF2m_simple_add(const EC_GROUP * group,EC_POINT * r,const EC_POINT * a,const EC_POINT * b,BN_CTX * ctx)745 int ec_GF2m_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
746 	{
747 	BN_CTX *new_ctx = NULL;
748 	BIGNUM *x0, *y0, *x1, *y1, *x2, *y2, *s, *t;
749 	int ret = 0;
750 
751 	if (EC_POINT_is_at_infinity(group, a))
752 		{
753 		if (!EC_POINT_copy(r, b)) return 0;
754 		return 1;
755 		}
756 
757 	if (EC_POINT_is_at_infinity(group, b))
758 		{
759 		if (!EC_POINT_copy(r, a)) return 0;
760 		return 1;
761 		}
762 
763 	if (ctx == NULL)
764 		{
765 		ctx = new_ctx = BN_CTX_new();
766 		if (ctx == NULL)
767 			return 0;
768 		}
769 
770 	BN_CTX_start(ctx);
771 	x0 = BN_CTX_get(ctx);
772 	y0 = BN_CTX_get(ctx);
773 	x1 = BN_CTX_get(ctx);
774 	y1 = BN_CTX_get(ctx);
775 	x2 = BN_CTX_get(ctx);
776 	y2 = BN_CTX_get(ctx);
777 	s = BN_CTX_get(ctx);
778 	t = BN_CTX_get(ctx);
779 	if (t == NULL) goto err;
780 
781 	if (a->Z_is_one)
782 		{
783 		if (!BN_copy(x0, &a->X)) goto err;
784 		if (!BN_copy(y0, &a->Y)) goto err;
785 		}
786 	else
787 		{
788 		if (!EC_POINT_get_affine_coordinates_GF2m(group, a, x0, y0, ctx)) goto err;
789 		}
790 	if (b->Z_is_one)
791 		{
792 		if (!BN_copy(x1, &b->X)) goto err;
793 		if (!BN_copy(y1, &b->Y)) goto err;
794 		}
795 	else
796 		{
797 		if (!EC_POINT_get_affine_coordinates_GF2m(group, b, x1, y1, ctx)) goto err;
798 		}
799 
800 
801 	if (BN_GF2m_cmp(x0, x1))
802 		{
803 		if (!BN_GF2m_add(t, x0, x1)) goto err;
804 		if (!BN_GF2m_add(s, y0, y1)) goto err;
805 		if (!group->meth->field_div(group, s, s, t, ctx)) goto err;
806 		if (!group->meth->field_sqr(group, x2, s, ctx)) goto err;
807 		if (!BN_GF2m_add(x2, x2, &group->a)) goto err;
808 		if (!BN_GF2m_add(x2, x2, s)) goto err;
809 		if (!BN_GF2m_add(x2, x2, t)) goto err;
810 		}
811 	else
812 		{
813 		if (BN_GF2m_cmp(y0, y1) || BN_is_zero(x1))
814 			{
815 			if (!EC_POINT_set_to_infinity(group, r)) goto err;
816 			ret = 1;
817 			goto err;
818 			}
819 		if (!group->meth->field_div(group, s, y1, x1, ctx)) goto err;
820 		if (!BN_GF2m_add(s, s, x1)) goto err;
821 
822 		if (!group->meth->field_sqr(group, x2, s, ctx)) goto err;
823 		if (!BN_GF2m_add(x2, x2, s)) goto err;
824 		if (!BN_GF2m_add(x2, x2, &group->a)) goto err;
825 		}
826 
827 	if (!BN_GF2m_add(y2, x1, x2)) goto err;
828 	if (!group->meth->field_mul(group, y2, y2, s, ctx)) goto err;
829 	if (!BN_GF2m_add(y2, y2, x2)) goto err;
830 	if (!BN_GF2m_add(y2, y2, y1)) goto err;
831 
832 	if (!EC_POINT_set_affine_coordinates_GF2m(group, r, x2, y2, ctx)) goto err;
833 
834 	ret = 1;
835 
836  err:
837 	BN_CTX_end(ctx);
838 	if (new_ctx != NULL)
839 		BN_CTX_free(new_ctx);
840 	return ret;
841 	}
842 
843 
844 /* Computes 2 * a and stores the result in r.  r could be a.
845  * Uses algorithm A.10.2 of IEEE P1363.
846  */
ec_GF2m_simple_dbl(const EC_GROUP * group,EC_POINT * r,const EC_POINT * a,BN_CTX * ctx)847 int ec_GF2m_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_CTX *ctx)
848 	{
849 	return ec_GF2m_simple_add(group, r, a, a, ctx);
850 	}
851 
852 
ec_GF2m_simple_invert(const EC_GROUP * group,EC_POINT * point,BN_CTX * ctx)853 int ec_GF2m_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
854 	{
855 	if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(&point->Y))
856 		/* point is its own inverse */
857 		return 1;
858 
859 	if (!EC_POINT_make_affine(group, point, ctx)) return 0;
860 	return BN_GF2m_add(&point->Y, &point->X, &point->Y);
861 	}
862 
863 
864 /* Indicates whether the given point is the point at infinity. */
ec_GF2m_simple_is_at_infinity(const EC_GROUP * group,const EC_POINT * point)865 int ec_GF2m_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point)
866 	{
867 	return BN_is_zero(&point->Z);
868 	}
869 
870 
871 /* Determines whether the given EC_POINT is an actual point on the curve defined
872  * in the EC_GROUP.  A point is valid if it satisfies the Weierstrass equation:
873  *      y^2 + x*y = x^3 + a*x^2 + b.
874  */
ec_GF2m_simple_is_on_curve(const EC_GROUP * group,const EC_POINT * point,BN_CTX * ctx)875 int ec_GF2m_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx)
876 	{
877 	int ret = -1;
878 	BN_CTX *new_ctx = NULL;
879 	BIGNUM *lh, *y2;
880 	int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
881 	int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
882 
883 	if (EC_POINT_is_at_infinity(group, point))
884 		return 1;
885 
886 	field_mul = group->meth->field_mul;
887 	field_sqr = group->meth->field_sqr;
888 
889 	/* only support affine coordinates */
890 	if (!point->Z_is_one) goto err;
891 
892 	if (ctx == NULL)
893 		{
894 		ctx = new_ctx = BN_CTX_new();
895 		if (ctx == NULL)
896 			return -1;
897 		}
898 
899 	BN_CTX_start(ctx);
900 	y2 = BN_CTX_get(ctx);
901 	lh = BN_CTX_get(ctx);
902 	if (lh == NULL) goto err;
903 
904 	/* We have a curve defined by a Weierstrass equation
905 	 *      y^2 + x*y = x^3 + a*x^2 + b.
906 	 *  <=> x^3 + a*x^2 + x*y + b + y^2 = 0
907 	 *  <=> ((x + a) * x + y ) * x + b + y^2 = 0
908 	 */
909 	if (!BN_GF2m_add(lh, &point->X, &group->a)) goto err;
910 	if (!field_mul(group, lh, lh, &point->X, ctx)) goto err;
911 	if (!BN_GF2m_add(lh, lh, &point->Y)) goto err;
912 	if (!field_mul(group, lh, lh, &point->X, ctx)) goto err;
913 	if (!BN_GF2m_add(lh, lh, &group->b)) goto err;
914 	if (!field_sqr(group, y2, &point->Y, ctx)) goto err;
915 	if (!BN_GF2m_add(lh, lh, y2)) goto err;
916 	ret = BN_is_zero(lh);
917  err:
918 	if (ctx) BN_CTX_end(ctx);
919 	if (new_ctx) BN_CTX_free(new_ctx);
920 	return ret;
921 	}
922 
923 
924 /* Indicates whether two points are equal.
925  * Return values:
926  *  -1   error
927  *   0   equal (in affine coordinates)
928  *   1   not equal
929  */
ec_GF2m_simple_cmp(const EC_GROUP * group,const EC_POINT * a,const EC_POINT * b,BN_CTX * ctx)930 int ec_GF2m_simple_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
931 	{
932 	BIGNUM *aX, *aY, *bX, *bY;
933 	BN_CTX *new_ctx = NULL;
934 	int ret = -1;
935 
936 	if (EC_POINT_is_at_infinity(group, a))
937 		{
938 		return EC_POINT_is_at_infinity(group, b) ? 0 : 1;
939 		}
940 
941 	if (a->Z_is_one && b->Z_is_one)
942 		{
943 		return ((BN_cmp(&a->X, &b->X) == 0) && BN_cmp(&a->Y, &b->Y) == 0) ? 0 : 1;
944 		}
945 
946 	if (ctx == NULL)
947 		{
948 		ctx = new_ctx = BN_CTX_new();
949 		if (ctx == NULL)
950 			return -1;
951 		}
952 
953 	BN_CTX_start(ctx);
954 	aX = BN_CTX_get(ctx);
955 	aY = BN_CTX_get(ctx);
956 	bX = BN_CTX_get(ctx);
957 	bY = BN_CTX_get(ctx);
958 	if (bY == NULL) goto err;
959 
960 	if (!EC_POINT_get_affine_coordinates_GF2m(group, a, aX, aY, ctx)) goto err;
961 	if (!EC_POINT_get_affine_coordinates_GF2m(group, b, bX, bY, ctx)) goto err;
962 	ret = ((BN_cmp(aX, bX) == 0) && BN_cmp(aY, bY) == 0) ? 0 : 1;
963 
964   err:
965 	if (ctx) BN_CTX_end(ctx);
966 	if (new_ctx) BN_CTX_free(new_ctx);
967 	return ret;
968 	}
969 
970 
971 /* Forces the given EC_POINT to internally use affine coordinates. */
ec_GF2m_simple_make_affine(const EC_GROUP * group,EC_POINT * point,BN_CTX * ctx)972 int ec_GF2m_simple_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
973 	{
974 	BN_CTX *new_ctx = NULL;
975 	BIGNUM *x, *y;
976 	int ret = 0;
977 
978 	if (point->Z_is_one || EC_POINT_is_at_infinity(group, point))
979 		return 1;
980 
981 	if (ctx == NULL)
982 		{
983 		ctx = new_ctx = BN_CTX_new();
984 		if (ctx == NULL)
985 			return 0;
986 		}
987 
988 	BN_CTX_start(ctx);
989 	x = BN_CTX_get(ctx);
990 	y = BN_CTX_get(ctx);
991 	if (y == NULL) goto err;
992 
993 	if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err;
994 	if (!BN_copy(&point->X, x)) goto err;
995 	if (!BN_copy(&point->Y, y)) goto err;
996 	if (!BN_one(&point->Z)) goto err;
997 
998 	ret = 1;
999 
1000   err:
1001 	if (ctx) BN_CTX_end(ctx);
1002 	if (new_ctx) BN_CTX_free(new_ctx);
1003 	return ret;
1004 	}
1005 
1006 
1007 /* Forces each of the EC_POINTs in the given array to use affine coordinates. */
ec_GF2m_simple_points_make_affine(const EC_GROUP * group,size_t num,EC_POINT * points[],BN_CTX * ctx)1008 int ec_GF2m_simple_points_make_affine(const EC_GROUP *group, size_t num, EC_POINT *points[], BN_CTX *ctx)
1009 	{
1010 	size_t i;
1011 
1012 	for (i = 0; i < num; i++)
1013 		{
1014 		if (!group->meth->make_affine(group, points[i], ctx)) return 0;
1015 		}
1016 
1017 	return 1;
1018 	}
1019 
1020 
1021 /* Wrapper to simple binary polynomial field multiplication implementation. */
ec_GF2m_simple_field_mul(const EC_GROUP * group,BIGNUM * r,const BIGNUM * a,const BIGNUM * b,BN_CTX * ctx)1022 int ec_GF2m_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
1023 	{
1024 	return BN_GF2m_mod_mul_arr(r, a, b, group->poly, ctx);
1025 	}
1026 
1027 
1028 /* Wrapper to simple binary polynomial field squaring implementation. */
ec_GF2m_simple_field_sqr(const EC_GROUP * group,BIGNUM * r,const BIGNUM * a,BN_CTX * ctx)1029 int ec_GF2m_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx)
1030 	{
1031 	return BN_GF2m_mod_sqr_arr(r, a, group->poly, ctx);
1032 	}
1033 
1034 
1035 /* Wrapper to simple binary polynomial field division implementation. */
ec_GF2m_simple_field_div(const EC_GROUP * group,BIGNUM * r,const BIGNUM * a,const BIGNUM * b,BN_CTX * ctx)1036 int ec_GF2m_simple_field_div(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
1037 	{
1038 	return BN_GF2m_mod_div(r, a, b, &group->field, ctx);
1039 	}
1040