aboutsummaryrefslogtreecommitdiff
path: root/openssl/crypto/ec/ec2_mult.c
blob: ff368fd7d7b3d277db18ab1884aa59201d80692a (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
/* crypto/ec/ec2_mult.c */
/* ====================================================================
 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
 *
 * The Elliptic Curve Public-Key Crypto Library (ECC Code) included
 * herein is developed by SUN MICROSYSTEMS, INC., and is contributed
 * to the OpenSSL project.
 *
 * The ECC Code is licensed pursuant to the OpenSSL open source
 * license provided below.
 *
 * The software is originally written by Sheueling Chang Shantz and
 * Douglas Stebila of Sun Microsystems Laboratories.
 *
 */
/* ====================================================================
 * Copyright (c) 1998-2003 The OpenSSL Project.  All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 *
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer. 
 *
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in
 *    the documentation and/or other materials provided with the
 *    distribution.
 *
 * 3. All advertising materials mentioning features or use of this
 *    software must display the following acknowledgment:
 *    "This product includes software developed by the OpenSSL Project
 *    for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
 *
 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
 *    endorse or promote products derived from this software without
 *    prior written permission. For written permission, please contact
 *    openssl-core@openssl.org.
 *
 * 5. Products derived from this software may not be called "OpenSSL"
 *    nor may "OpenSSL" appear in their names without prior written
 *    permission of the OpenSSL Project.
 *
 * 6. Redistributions of any form whatsoever must retain the following
 *    acknowledgment:
 *    "This product includes software developed by the OpenSSL Project
 *    for use in the OpenSSL Toolkit (http://www.openssl.org/)"
 *
 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
 * PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE OpenSSL PROJECT OR
 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
 * OF THE POSSIBILITY OF SUCH DAMAGE.
 * ====================================================================
 *
 * This product includes cryptographic software written by Eric Young
 * (eay@cryptsoft.com).  This product includes software written by Tim
 * Hudson (tjh@cryptsoft.com).
 *
 */

#include <openssl/err.h>

#include "ec_lcl.h"


/* Compute the x-coordinate x/z for the point 2*(x/z) in Montgomery projective 
 * coordinates.
 * Uses algorithm Mdouble in appendix of 
 *     Lopez, J. and Dahab, R.  "Fast multiplication on elliptic curves over 
 *     GF(2^m) without precomputation".
 * modified to not require precomputation of c=b^{2^{m-1}}.
 */
static int gf2m_Mdouble(const EC_GROUP *group, BIGNUM *x, BIGNUM *z, BN_CTX *ctx)
	{
	BIGNUM *t1;
	int ret = 0;
	
	/* Since Mdouble is static we can guarantee that ctx != NULL. */
	BN_CTX_start(ctx);
	t1 = BN_CTX_get(ctx);
	if (t1 == NULL) goto err;

	if (!group->meth->field_sqr(group, x, x, ctx)) goto err;
	if (!group->meth->field_sqr(group, t1, z, ctx)) goto err;
	if (!group->meth->field_mul(group, z, x, t1, ctx)) goto err;
	if (!group->meth->field_sqr(group, x, x, ctx)) goto err;
	if (!group->meth->field_sqr(group, t1, t1, ctx)) goto err;
	if (!group->meth->field_mul(group, t1, &group->b, t1, ctx)) goto err;
	if (!BN_GF2m_add(x, x, t1)) goto err;

	ret = 1;

 err:
	BN_CTX_end(ctx);
	return ret;
	}

/* Compute the x-coordinate x1/z1 for the point (x1/z1)+(x2/x2) in Montgomery 
 * projective coordinates.
 * Uses algorithm Madd in appendix of 
 *     Lopex, J. and Dahab, R.  "Fast multiplication on elliptic curves over 
 *     GF(2^m) without precomputation".
 */
static int gf2m_Madd(const EC_GROUP *group, const BIGNUM *x, BIGNUM *x1, BIGNUM *z1, 
	const BIGNUM *x2, const BIGNUM *z2, BN_CTX *ctx)
	{
	BIGNUM *t1, *t2;
	int ret = 0;
	
	/* Since Madd is static we can guarantee that ctx != NULL. */
	BN_CTX_start(ctx);
	t1 = BN_CTX_get(ctx);
	t2 = BN_CTX_get(ctx);
	if (t2 == NULL) goto err;

	if (!BN_copy(t1, x)) goto err;
	if (!group->meth->field_mul(group, x1, x1, z2, ctx)) goto err;
	if (!group->meth->field_mul(group, z1, z1, x2, ctx)) goto err;
	if (!group->meth->field_mul(group, t2, x1, z1, ctx)) goto err;
	if (!BN_GF2m_add(z1, z1, x1)) goto err;
	if (!group->meth->field_sqr(group, z1, z1, ctx)) goto err;
	if (!group->meth->field_mul(group, x1, z1, t1, ctx)) goto err;
	if (!BN_GF2m_add(x1, x1, t2)) goto err;

	ret = 1;

 err:
	BN_CTX_end(ctx);
	return ret;
	}

/* Compute the x, y affine coordinates from the point (x1, z1) (x2, z2) 
 * using Montgomery point multiplication algorithm Mxy() in appendix of 
 *     Lopex, J. and Dahab, R.  "Fast multiplication on elliptic curves over 
 *     GF(2^m) without precomputation".
 * Returns:
 *     0 on error
 *     1 if return value should be the point at infinity
 *     2 otherwise
 */
static int gf2m_Mxy(const EC_GROUP *group, const BIGNUM *x, const BIGNUM *y, BIGNUM *x1, 
	BIGNUM *z1, BIGNUM *x2, BIGNUM *z2, BN_CTX *ctx)
	{
	BIGNUM *t3, *t4, *t5;
	int ret = 0;
	
	if (BN_is_zero(z1))
		{
		BN_zero(x2);
		BN_zero(z2);
		return 1;
		}
	
	if (BN_is_zero(z2))
		{
		if (!BN_copy(x2, x)) return 0;
		if (!BN_GF2m_add(z2, x, y)) return 0;
		return 2;
		}
		
	/* Since Mxy is static we can guarantee that ctx != NULL. */
	BN_CTX_start(ctx);
	t3 = BN_CTX_get(ctx);
	t4 = BN_CTX_get(ctx);
	t5 = BN_CTX_get(ctx);
	if (t5 == NULL) goto err;

	if (!BN_one(t5)) goto err;

	if (!group->meth->field_mul(group, t3, z1, z2, ctx)) goto err;

	if (!group->meth->field_mul(group, z1, z1, x, ctx)) goto err;
	if (!BN_GF2m_add(z1, z1, x1)) goto err;
	if (!group->meth->field_mul(group, z2, z2, x, ctx)) goto err;
	if (!group->meth->field_mul(group, x1, z2, x1, ctx)) goto err;
	if (!BN_GF2m_add(z2, z2, x2)) goto err;

	if (!group->meth->field_mul(group, z2, z2, z1, ctx)) goto err;
	if (!group->meth->field_sqr(group, t4, x, ctx)) goto err;
	if (!BN_GF2m_add(t4, t4, y)) goto err;
	if (!group->meth->field_mul(group, t4, t4, t3, ctx)) goto err;
	if (!BN_GF2m_add(t4, t4, z2)) goto err;

	if (!group->meth->field_mul(group, t3, t3, x, ctx)) goto err;
	if (!group->meth->field_div(group, t3, t5, t3, ctx)) goto err;
	if (!group->meth->field_mul(group, t4, t3, t4, ctx)) goto err;
	if (!group->meth->field_mul(group, x2, x1, t3, ctx)) goto err;
	if (!BN_GF2m_add(z2, x2, x)) goto err;

	if (!group->meth->field_mul(group, z2, z2, t4, ctx)) goto err;
	if (!BN_GF2m_add(z2, z2, y)) goto err;

	ret = 2;

 err:
	BN_CTX_end(ctx);
	return ret;
	}

/* Computes scalar*point and stores the result in r.
 * point can not equal r.
 * Uses algorithm 2P of
 *     Lopex, J. and Dahab, R.  "Fast multiplication on elliptic curves over 
 *     GF(2^m) without precomputation".
 */
static int ec_GF2m_montgomery_point_multiply(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
	const EC_POINT *point, BN_CTX *ctx)
	{
	BIGNUM *x1, *x2, *z1, *z2;
	int ret = 0, i, j;
	BN_ULONG mask;

	if (r == point)
		{
		ECerr(EC_F_EC_GF2M_MONTGOMERY_POINT_MULTIPLY, EC_R_INVALID_ARGUMENT);
		return 0;
		}
	
	/* if result should be point at infinity */
	if ((scalar == NULL) || BN_is_zero(scalar) || (point == NULL) || 
		EC_POINT_is_at_infinity(group, point))
		{
		return EC_POINT_set_to_infinity(group, r);
		}

	/* only support affine coordinates */
	if (!point->Z_is_one) return 0;

	/* Since point_multiply is static we can guarantee that ctx != NULL. */
	BN_CTX_start(ctx);
	x1 = BN_CTX_get(ctx);
	z1 = BN_CTX_get(ctx);
	if (z1 == NULL) goto err;

	x2 = &r->X;
	z2 = &r->Y;

	if (!BN_GF2m_mod_arr(x1, &point->X, group->poly)) goto err; /* x1 = x */
	if (!BN_one(z1)) goto err; /* z1 = 1 */
	if (!group->meth->field_sqr(group, z2, x1, ctx)) goto err; /* z2 = x1^2 = x^2 */
	if (!group->meth->field_sqr(group, x2, z2, ctx)) goto err;
	if (!BN_GF2m_add(x2, x2, &group->b)) goto err; /* x2 = x^4 + b */

	/* find top most bit and go one past it */
	i = scalar->top - 1; j = BN_BITS2 - 1;
	mask = BN_TBIT;
	while (!(scalar->d[i] & mask)) { mask >>= 1; j--; }
	mask >>= 1; j--;
	/* if top most bit was at word break, go to next word */
	if (!mask) 
		{
		i--; j = BN_BITS2 - 1;
		mask = BN_TBIT;
		}

	for (; i >= 0; i--)
		{
		for (; j >= 0; j--)
			{
			if (scalar->d[i] & mask)
				{
				if (!gf2m_Madd(group, &point->X, x1, z1, x2, z2, ctx)) goto err;
				if (!gf2m_Mdouble(group, x2, z2, ctx)) goto err;
				}
			else
				{
				if (!gf2m_Madd(group, &point->X, x2, z2, x1, z1, ctx)) goto err;
				if (!gf2m_Mdouble(group, x1, z1, ctx)) goto err;
				}
			mask >>= 1;
			}
		j = BN_BITS2 - 1;
		mask = BN_TBIT;
		}

	/* convert out of "projective" coordinates */
	i = gf2m_Mxy(group, &point->X, &point->Y, x1, z1, x2, z2, ctx);
	if (i == 0) goto err;
	else if (i == 1) 
		{
		if (!EC_POINT_set_to_infinity(group, r)) goto err;
		}
	else
		{
		if (!BN_one(&r->Z)) goto err;
		r->Z_is_one = 1;
		}

	/* GF(2^m) field elements should always have BIGNUM::neg = 0 */
	BN_set_negative(&r->X, 0);
	BN_set_negative(&r->Y, 0);

	ret = 1;

 err:
	BN_CTX_end(ctx);
	return ret;
	}


/* Computes the sum
 *     scalar*group->generator + scalars[0]*points[0] + ... + scalars[num-1]*points[num-1]
 * gracefully ignoring NULL scalar values.
 */
int ec_GF2m_simple_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
	size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx)
	{
	BN_CTX *new_ctx = NULL;
	int ret = 0;
	size_t i;
	EC_POINT *p=NULL;

	if (ctx == NULL)
		{
		ctx = new_ctx = BN_CTX_new();
		if (ctx == NULL)
			return 0;
		}

	/* This implementation is more efficient than the wNAF implementation for 2
	 * or fewer points.  Use the ec_wNAF_mul implementation for 3 or more points,
	 * or if we can perform a fast multiplication based on precomputation.
	 */
	if ((scalar && (num > 1)) || (num > 2) || (num == 0 && EC_GROUP_have_precompute_mult(group)))
		{
		ret = ec_wNAF_mul(group, r, scalar, num, points, scalars, ctx);
		goto err;
		}

	if ((p = EC_POINT_new(group)) == NULL) goto err;

	if (!EC_POINT_set_to_infinity(group, r)) goto err;

	if (scalar)
		{
		if (!ec_GF2m_montgomery_point_multiply(group, p, scalar, group->generator, ctx)) goto err;
		if (BN_is_negative(scalar)) 
			if (!group->meth->invert(group, p, ctx)) goto err;
		if (!group->meth->add(group, r, r, p, ctx)) goto err;
		}

	for (i = 0; i < num; i++)
		{
		if (!ec_GF2m_montgomery_point_multiply(group, p, scalars[i], points[i], ctx)) goto err;
		if (BN_is_negative(scalars[i]))
			if (!group->meth->invert(group, p, ctx)) goto err;
		if (!group->meth->add(group, r, r, p, ctx)) goto err;
		}

	ret = 1;

  err:
	if (p) EC_POINT_free(p);
	if (new_ctx != NULL)
		BN_CTX_free(new_ctx);
	return ret;
	}


/* Precomputation for point multiplication: fall back to wNAF methods
 * because ec_GF2m_simple_mul() uses ec_wNAF_mul() if appropriate */

int ec_GF2m_precompute_mult(EC_GROUP *group, BN_CTX *ctx)
	{
	return ec_wNAF_precompute_mult(group, ctx);
 	}

int ec_GF2m_have_precompute_mult(const EC_GROUP *group)
	{
	return ec_wNAF_have_precompute_mult(group);
 	}