1/*
2 * ***** BEGIN LICENSE BLOCK *****
3 * Version: MPL 1.1/GPL 2.0/LGPL 2.1
4 *
5 * The contents of this file are subject to the Mozilla Public License Version
6 * 1.1 (the "License"); you may not use this file except in compliance with
7 * the License. You may obtain a copy of the License at
8 * http://www.mozilla.org/MPL/
9 *
10 * Software distributed under the License is distributed on an "AS IS" basis,
11 * WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License
12 * for the specific language governing rights and limitations under the
13 * License.
14 *
15 * The Original Code is the elliptic curve math library.
16 *
17 * The Initial Developer of the Original Code is
18 * Sun Microsystems, Inc.
19 * Portions created by the Initial Developer are Copyright (C) 2003
20 * the Initial Developer. All Rights Reserved.
21 *
22 * Contributor(s):
23 *   Douglas Stebila <douglas@stebila.ca>, Sun Microsystems Laboratories
24 *
25 * Alternatively, the contents of this file may be used under the terms of
26 * either the GNU General Public License Version 2 or later (the "GPL"), or
27 * the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
28 * in which case the provisions of the GPL or the LGPL are applicable instead
29 * of those above. If you wish to allow use of your version of this file only
30 * under the terms of either the GPL or the LGPL, and not to allow others to
31 * use your version of this file under the terms of the MPL, indicate your
32 * decision by deleting the provisions above and replace them with the notice
33 * and other provisions required by the GPL or the LGPL. If you do not delete
34 * the provisions above, a recipient may use your version of this file under
35 * the terms of any one of the MPL, the GPL or the LGPL.
36 *
37 * ***** END LICENSE BLOCK ***** */
38/*
39 * Copyright 2007 Sun Microsystems, Inc.  All rights reserved.
40 * Use is subject to license terms.
41 *
42 * Sun elects to use this software under the MPL license.
43 */
44
45#pragma ident	"%Z%%M%	%I%	%E% SMI"
46
47#include "mpi.h"
48#include "mplogic.h"
49#include "ecl.h"
50#include "ecl-priv.h"
51#ifndef _KERNEL
52#include <stdlib.h>
53#endif
54
55/* Elliptic curve scalar-point multiplication. Computes R(x, y) = k * P(x,
56 * y).  If x, y = NULL, then P is assumed to be the generator (base point)
57 * of the group of points on the elliptic curve. Input and output values
58 * are assumed to be NOT field-encoded. */
59mp_err
60ECPoint_mul(const ECGroup *group, const mp_int *k, const mp_int *px,
61			const mp_int *py, mp_int *rx, mp_int *ry)
62{
63	mp_err res = MP_OKAY;
64	mp_int kt;
65
66	ARGCHK((k != NULL) && (group != NULL), MP_BADARG);
67	MP_DIGITS(&kt) = 0;
68
69	/* want scalar to be less than or equal to group order */
70	if (mp_cmp(k, &group->order) > 0) {
71		MP_CHECKOK(mp_init(&kt, FLAG(k)));
72		MP_CHECKOK(mp_mod(k, &group->order, &kt));
73	} else {
74		MP_SIGN(&kt) = MP_ZPOS;
75		MP_USED(&kt) = MP_USED(k);
76		MP_ALLOC(&kt) = MP_ALLOC(k);
77		MP_DIGITS(&kt) = MP_DIGITS(k);
78	}
79
80	if ((px == NULL) || (py == NULL)) {
81		if (group->base_point_mul) {
82			MP_CHECKOK(group->base_point_mul(&kt, rx, ry, group));
83		} else {
84			MP_CHECKOK(group->
85					   point_mul(&kt, &group->genx, &group->geny, rx, ry,
86								 group));
87		}
88	} else {
89		if (group->meth->field_enc) {
90			MP_CHECKOK(group->meth->field_enc(px, rx, group->meth));
91			MP_CHECKOK(group->meth->field_enc(py, ry, group->meth));
92			MP_CHECKOK(group->point_mul(&kt, rx, ry, rx, ry, group));
93		} else {
94			MP_CHECKOK(group->point_mul(&kt, px, py, rx, ry, group));
95		}
96	}
97	if (group->meth->field_dec) {
98		MP_CHECKOK(group->meth->field_dec(rx, rx, group->meth));
99		MP_CHECKOK(group->meth->field_dec(ry, ry, group->meth));
100	}
101
102  CLEANUP:
103	if (MP_DIGITS(&kt) != MP_DIGITS(k)) {
104		mp_clear(&kt);
105	}
106	return res;
107}
108
109/* Elliptic curve scalar-point multiplication. Computes R(x, y) = k1 * G +
110 * k2 * P(x, y), where G is the generator (base point) of the group of
111 * points on the elliptic curve. Allows k1 = NULL or { k2, P } = NULL.
112 * Input and output values are assumed to be NOT field-encoded. */
113mp_err
114ec_pts_mul_basic(const mp_int *k1, const mp_int *k2, const mp_int *px,
115				 const mp_int *py, mp_int *rx, mp_int *ry,
116				 const ECGroup *group)
117{
118	mp_err res = MP_OKAY;
119	mp_int sx, sy;
120
121	ARGCHK(group != NULL, MP_BADARG);
122	ARGCHK(!((k1 == NULL)
123			 && ((k2 == NULL) || (px == NULL)
124				 || (py == NULL))), MP_BADARG);
125
126	/* if some arguments are not defined used ECPoint_mul */
127	if (k1 == NULL) {
128		return ECPoint_mul(group, k2, px, py, rx, ry);
129	} else if ((k2 == NULL) || (px == NULL) || (py == NULL)) {
130		return ECPoint_mul(group, k1, NULL, NULL, rx, ry);
131	}
132
133	MP_DIGITS(&sx) = 0;
134	MP_DIGITS(&sy) = 0;
135	MP_CHECKOK(mp_init(&sx, FLAG(k1)));
136	MP_CHECKOK(mp_init(&sy, FLAG(k1)));
137
138	MP_CHECKOK(ECPoint_mul(group, k1, NULL, NULL, &sx, &sy));
139	MP_CHECKOK(ECPoint_mul(group, k2, px, py, rx, ry));
140
141	if (group->meth->field_enc) {
142		MP_CHECKOK(group->meth->field_enc(&sx, &sx, group->meth));
143		MP_CHECKOK(group->meth->field_enc(&sy, &sy, group->meth));
144		MP_CHECKOK(group->meth->field_enc(rx, rx, group->meth));
145		MP_CHECKOK(group->meth->field_enc(ry, ry, group->meth));
146	}
147
148	MP_CHECKOK(group->point_add(&sx, &sy, rx, ry, rx, ry, group));
149
150	if (group->meth->field_dec) {
151		MP_CHECKOK(group->meth->field_dec(rx, rx, group->meth));
152		MP_CHECKOK(group->meth->field_dec(ry, ry, group->meth));
153	}
154
155  CLEANUP:
156	mp_clear(&sx);
157	mp_clear(&sy);
158	return res;
159}
160
161/* Elliptic curve scalar-point multiplication. Computes R(x, y) = k1 * G +
162 * k2 * P(x, y), where G is the generator (base point) of the group of
163 * points on the elliptic curve. Allows k1 = NULL or { k2, P } = NULL.
164 * Input and output values are assumed to be NOT field-encoded. Uses
165 * algorithm 15 (simultaneous multiple point multiplication) from Brown,
166 * Hankerson, Lopez, Menezes. Software Implementation of the NIST
167 * Elliptic Curves over Prime Fields. */
168mp_err
169ec_pts_mul_simul_w2(const mp_int *k1, const mp_int *k2, const mp_int *px,
170					const mp_int *py, mp_int *rx, mp_int *ry,
171					const ECGroup *group)
172{
173	mp_err res = MP_OKAY;
174	mp_int precomp[4][4][2];
175	const mp_int *a, *b;
176	int i, j;
177	int ai, bi, d;
178
179	ARGCHK(group != NULL, MP_BADARG);
180	ARGCHK(!((k1 == NULL)
181			 && ((k2 == NULL) || (px == NULL)
182				 || (py == NULL))), MP_BADARG);
183
184	/* if some arguments are not defined used ECPoint_mul */
185	if (k1 == NULL) {
186		return ECPoint_mul(group, k2, px, py, rx, ry);
187	} else if ((k2 == NULL) || (px == NULL) || (py == NULL)) {
188		return ECPoint_mul(group, k1, NULL, NULL, rx, ry);
189	}
190
191	/* initialize precomputation table */
192	for (i = 0; i < 4; i++) {
193		for (j = 0; j < 4; j++) {
194			MP_DIGITS(&precomp[i][j][0]) = 0;
195			MP_DIGITS(&precomp[i][j][1]) = 0;
196		}
197	}
198	for (i = 0; i < 4; i++) {
199		for (j = 0; j < 4; j++) {
200			 MP_CHECKOK( mp_init_size(&precomp[i][j][0],
201					 ECL_MAX_FIELD_SIZE_DIGITS, FLAG(k1)) );
202			 MP_CHECKOK( mp_init_size(&precomp[i][j][1],
203					 ECL_MAX_FIELD_SIZE_DIGITS, FLAG(k1)) );
204		}
205	}
206
207	/* fill precomputation table */
208	/* assign {k1, k2} = {a, b} such that len(a) >= len(b) */
209	if (mpl_significant_bits(k1) < mpl_significant_bits(k2)) {
210		a = k2;
211		b = k1;
212		if (group->meth->field_enc) {
213			MP_CHECKOK(group->meth->
214					   field_enc(px, &precomp[1][0][0], group->meth));
215			MP_CHECKOK(group->meth->
216					   field_enc(py, &precomp[1][0][1], group->meth));
217		} else {
218			MP_CHECKOK(mp_copy(px, &precomp[1][0][0]));
219			MP_CHECKOK(mp_copy(py, &precomp[1][0][1]));
220		}
221		MP_CHECKOK(mp_copy(&group->genx, &precomp[0][1][0]));
222		MP_CHECKOK(mp_copy(&group->geny, &precomp[0][1][1]));
223	} else {
224		a = k1;
225		b = k2;
226		MP_CHECKOK(mp_copy(&group->genx, &precomp[1][0][0]));
227		MP_CHECKOK(mp_copy(&group->geny, &precomp[1][0][1]));
228		if (group->meth->field_enc) {
229			MP_CHECKOK(group->meth->
230					   field_enc(px, &precomp[0][1][0], group->meth));
231			MP_CHECKOK(group->meth->
232					   field_enc(py, &precomp[0][1][1], group->meth));
233		} else {
234			MP_CHECKOK(mp_copy(px, &precomp[0][1][0]));
235			MP_CHECKOK(mp_copy(py, &precomp[0][1][1]));
236		}
237	}
238	/* precompute [*][0][*] */
239	mp_zero(&precomp[0][0][0]);
240	mp_zero(&precomp[0][0][1]);
241	MP_CHECKOK(group->
242			   point_dbl(&precomp[1][0][0], &precomp[1][0][1],
243						 &precomp[2][0][0], &precomp[2][0][1], group));
244	MP_CHECKOK(group->
245			   point_add(&precomp[1][0][0], &precomp[1][0][1],
246						 &precomp[2][0][0], &precomp[2][0][1],
247						 &precomp[3][0][0], &precomp[3][0][1], group));
248	/* precompute [*][1][*] */
249	for (i = 1; i < 4; i++) {
250		MP_CHECKOK(group->
251				   point_add(&precomp[0][1][0], &precomp[0][1][1],
252							 &precomp[i][0][0], &precomp[i][0][1],
253							 &precomp[i][1][0], &precomp[i][1][1], group));
254	}
255	/* precompute [*][2][*] */
256	MP_CHECKOK(group->
257			   point_dbl(&precomp[0][1][0], &precomp[0][1][1],
258						 &precomp[0][2][0], &precomp[0][2][1], group));
259	for (i = 1; i < 4; i++) {
260		MP_CHECKOK(group->
261				   point_add(&precomp[0][2][0], &precomp[0][2][1],
262							 &precomp[i][0][0], &precomp[i][0][1],
263							 &precomp[i][2][0], &precomp[i][2][1], group));
264	}
265	/* precompute [*][3][*] */
266	MP_CHECKOK(group->
267			   point_add(&precomp[0][1][0], &precomp[0][1][1],
268						 &precomp[0][2][0], &precomp[0][2][1],
269						 &precomp[0][3][0], &precomp[0][3][1], group));
270	for (i = 1; i < 4; i++) {
271		MP_CHECKOK(group->
272				   point_add(&precomp[0][3][0], &precomp[0][3][1],
273							 &precomp[i][0][0], &precomp[i][0][1],
274							 &precomp[i][3][0], &precomp[i][3][1], group));
275	}
276
277	d = (mpl_significant_bits(a) + 1) / 2;
278
279	/* R = inf */
280	mp_zero(rx);
281	mp_zero(ry);
282
283	for (i = d - 1; i >= 0; i--) {
284		ai = MP_GET_BIT(a, 2 * i + 1);
285		ai <<= 1;
286		ai |= MP_GET_BIT(a, 2 * i);
287		bi = MP_GET_BIT(b, 2 * i + 1);
288		bi <<= 1;
289		bi |= MP_GET_BIT(b, 2 * i);
290		/* R = 2^2 * R */
291		MP_CHECKOK(group->point_dbl(rx, ry, rx, ry, group));
292		MP_CHECKOK(group->point_dbl(rx, ry, rx, ry, group));
293		/* R = R + (ai * A + bi * B) */
294		MP_CHECKOK(group->
295				   point_add(rx, ry, &precomp[ai][bi][0],
296							 &precomp[ai][bi][1], rx, ry, group));
297	}
298
299	if (group->meth->field_dec) {
300		MP_CHECKOK(group->meth->field_dec(rx, rx, group->meth));
301		MP_CHECKOK(group->meth->field_dec(ry, ry, group->meth));
302	}
303
304  CLEANUP:
305	for (i = 0; i < 4; i++) {
306		for (j = 0; j < 4; j++) {
307			mp_clear(&precomp[i][j][0]);
308			mp_clear(&precomp[i][j][1]);
309		}
310	}
311	return res;
312}
313
314/* Elliptic curve scalar-point multiplication. Computes R(x, y) = k1 * G +
315 * k2 * P(x, y), where G is the generator (base point) of the group of
316 * points on the elliptic curve. Allows k1 = NULL or { k2, P } = NULL.
317 * Input and output values are assumed to be NOT field-encoded. */
318mp_err
319ECPoints_mul(const ECGroup *group, const mp_int *k1, const mp_int *k2,
320			 const mp_int *px, const mp_int *py, mp_int *rx, mp_int *ry)
321{
322	mp_err res = MP_OKAY;
323	mp_int k1t, k2t;
324	const mp_int *k1p, *k2p;
325
326	MP_DIGITS(&k1t) = 0;
327	MP_DIGITS(&k2t) = 0;
328
329	ARGCHK(group != NULL, MP_BADARG);
330
331	/* want scalar to be less than or equal to group order */
332	if (k1 != NULL) {
333		if (mp_cmp(k1, &group->order) >= 0) {
334			MP_CHECKOK(mp_init(&k1t, FLAG(k1)));
335			MP_CHECKOK(mp_mod(k1, &group->order, &k1t));
336			k1p = &k1t;
337		} else {
338			k1p = k1;
339		}
340	} else {
341		k1p = k1;
342	}
343	if (k2 != NULL) {
344		if (mp_cmp(k2, &group->order) >= 0) {
345			MP_CHECKOK(mp_init(&k2t, FLAG(k2)));
346			MP_CHECKOK(mp_mod(k2, &group->order, &k2t));
347			k2p = &k2t;
348		} else {
349			k2p = k2;
350		}
351	} else {
352		k2p = k2;
353	}
354
355	/* if points_mul is defined, then use it */
356	if (group->points_mul) {
357		res = group->points_mul(k1p, k2p, px, py, rx, ry, group);
358	} else {
359		res = ec_pts_mul_simul_w2(k1p, k2p, px, py, rx, ry, group);
360	}
361
362  CLEANUP:
363	mp_clear(&k1t);
364	mp_clear(&k2t);
365	return res;
366}
367