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
75const 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 */
127int 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 */
139void 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 */
150void 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 */
167int 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. */
188int 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 */
221int 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. */
248int 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 */
257int 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
285err:
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. */
295int 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. */
305void 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. */
314void 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. */
324int 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 */
338int 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 */
349int 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 */
376int 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 */
424int 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 */
498size_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 */
630int 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 */
745int 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 */
847int 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
853int 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. */
865int 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 */
875int 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 */
930int 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 (EC_POINT_is_at_infinity(group, b))
942		return 1;
943
944	if (a->Z_is_one && b->Z_is_one)
945		{
946		return ((BN_cmp(&a->X, &b->X) == 0) && BN_cmp(&a->Y, &b->Y) == 0) ? 0 : 1;
947		}
948
949	if (ctx == NULL)
950		{
951		ctx = new_ctx = BN_CTX_new();
952		if (ctx == NULL)
953			return -1;
954		}
955
956	BN_CTX_start(ctx);
957	aX = BN_CTX_get(ctx);
958	aY = BN_CTX_get(ctx);
959	bX = BN_CTX_get(ctx);
960	bY = BN_CTX_get(ctx);
961	if (bY == NULL) goto err;
962
963	if (!EC_POINT_get_affine_coordinates_GF2m(group, a, aX, aY, ctx)) goto err;
964	if (!EC_POINT_get_affine_coordinates_GF2m(group, b, bX, bY, ctx)) goto err;
965	ret = ((BN_cmp(aX, bX) == 0) && BN_cmp(aY, bY) == 0) ? 0 : 1;
966
967  err:
968	if (ctx) BN_CTX_end(ctx);
969	if (new_ctx) BN_CTX_free(new_ctx);
970	return ret;
971	}
972
973
974/* Forces the given EC_POINT to internally use affine coordinates. */
975int ec_GF2m_simple_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
976	{
977	BN_CTX *new_ctx = NULL;
978	BIGNUM *x, *y;
979	int ret = 0;
980
981	if (point->Z_is_one || EC_POINT_is_at_infinity(group, point))
982		return 1;
983
984	if (ctx == NULL)
985		{
986		ctx = new_ctx = BN_CTX_new();
987		if (ctx == NULL)
988			return 0;
989		}
990
991	BN_CTX_start(ctx);
992	x = BN_CTX_get(ctx);
993	y = BN_CTX_get(ctx);
994	if (y == NULL) goto err;
995
996	if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err;
997	if (!BN_copy(&point->X, x)) goto err;
998	if (!BN_copy(&point->Y, y)) goto err;
999	if (!BN_one(&point->Z)) goto err;
1000
1001	ret = 1;
1002
1003  err:
1004	if (ctx) BN_CTX_end(ctx);
1005	if (new_ctx) BN_CTX_free(new_ctx);
1006	return ret;
1007	}
1008
1009
1010/* Forces each of the EC_POINTs in the given array to use affine coordinates. */
1011int ec_GF2m_simple_points_make_affine(const EC_GROUP *group, size_t num, EC_POINT *points[], BN_CTX *ctx)
1012	{
1013	size_t i;
1014
1015	for (i = 0; i < num; i++)
1016		{
1017		if (!group->meth->make_affine(group, points[i], ctx)) return 0;
1018		}
1019
1020	return 1;
1021	}
1022
1023
1024/* Wrapper to simple binary polynomial field multiplication implementation. */
1025int ec_GF2m_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
1026	{
1027	return BN_GF2m_mod_mul_arr(r, a, b, group->poly, ctx);
1028	}
1029
1030
1031/* Wrapper to simple binary polynomial field squaring implementation. */
1032int ec_GF2m_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx)
1033	{
1034	return BN_GF2m_mod_sqr_arr(r, a, group->poly, ctx);
1035	}
1036
1037
1038/* Wrapper to simple binary polynomial field division implementation. */
1039int ec_GF2m_simple_field_div(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
1040	{
1041	return BN_GF2m_mod_div(r, a, b, &group->field, ctx);
1042	}
1043