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 #include "mpi.h"
46 #include "mplogic.h"
47 #include "ecl.h"
48 #include "ecl-priv.h"
49 #ifndef _KERNEL
50 #include <stdlib.h>
51 #endif
52
53 /* Elliptic curve scalar-point multiplication. Computes R(x, y) = k * P(x,
54 * y). If x, y = NULL, then P is assumed to be the generator (base point)
55 * of the group of points on the elliptic curve. Input and output values
56 * are assumed to be NOT field-encoded. */
57 mp_err
ECPoint_mul(const ECGroup * group,const mp_int * k,const mp_int * px,const mp_int * py,mp_int * rx,mp_int * ry)58 ECPoint_mul(const ECGroup *group, const mp_int *k, const mp_int *px,
59 const mp_int *py, mp_int *rx, mp_int *ry)
60 {
61 mp_err res = MP_OKAY;
62 mp_int kt;
63
64 ARGCHK((k != NULL) && (group != NULL), MP_BADARG);
65 MP_DIGITS(&kt) = 0;
66
67 /* want scalar to be less than or equal to group order */
68 if (mp_cmp(k, &group->order) > 0) {
69 MP_CHECKOK(mp_init(&kt, FLAG(k)));
70 MP_CHECKOK(mp_mod(k, &group->order, &kt));
71 } else {
72 MP_SIGN(&kt) = MP_ZPOS;
73 MP_USED(&kt) = MP_USED(k);
74 MP_ALLOC(&kt) = MP_ALLOC(k);
75 MP_DIGITS(&kt) = MP_DIGITS(k);
76 }
77
78 if ((px == NULL) || (py == NULL)) {
79 if (group->base_point_mul) {
80 MP_CHECKOK(group->base_point_mul(&kt, rx, ry, group));
81 } else {
82 MP_CHECKOK(group->
83 point_mul(&kt, &group->genx, &group->geny, rx, ry,
84 group));
85 }
86 } else {
87 if (group->meth->field_enc) {
88 MP_CHECKOK(group->meth->field_enc(px, rx, group->meth));
89 MP_CHECKOK(group->meth->field_enc(py, ry, group->meth));
90 MP_CHECKOK(group->point_mul(&kt, rx, ry, rx, ry, group));
91 } else {
92 MP_CHECKOK(group->point_mul(&kt, px, py, rx, ry, group));
93 }
94 }
95 if (group->meth->field_dec) {
96 MP_CHECKOK(group->meth->field_dec(rx, rx, group->meth));
97 MP_CHECKOK(group->meth->field_dec(ry, ry, group->meth));
98 }
99
100 CLEANUP:
101 if (MP_DIGITS(&kt) != MP_DIGITS(k)) {
102 mp_clear(&kt);
103 }
104 return res;
105 }
106
107 /* Elliptic curve scalar-point multiplication. Computes R(x, y) = k1 * G +
108 * k2 * P(x, y), where G is the generator (base point) of the group of
109 * points on the elliptic curve. Allows k1 = NULL or { k2, P } = NULL.
110 * Input and output values are assumed to be NOT field-encoded. */
111 mp_err
ec_pts_mul_basic(const mp_int * k1,const mp_int * k2,const mp_int * px,const mp_int * py,mp_int * rx,mp_int * ry,const ECGroup * group)112 ec_pts_mul_basic(const mp_int *k1, const mp_int *k2, const mp_int *px,
113 const mp_int *py, mp_int *rx, mp_int *ry,
114 const ECGroup *group)
115 {
116 mp_err res = MP_OKAY;
117 mp_int sx, sy;
118
119 ARGCHK(group != NULL, MP_BADARG);
120 ARGCHK(!((k1 == NULL)
121 && ((k2 == NULL) || (px == NULL)
122 || (py == NULL))), MP_BADARG);
123
124 /* if some arguments are not defined used ECPoint_mul */
125 if (k1 == NULL) {
126 return ECPoint_mul(group, k2, px, py, rx, ry);
127 } else if ((k2 == NULL) || (px == NULL) || (py == NULL)) {
128 return ECPoint_mul(group, k1, NULL, NULL, rx, ry);
129 }
130
131 MP_DIGITS(&sx) = 0;
132 MP_DIGITS(&sy) = 0;
133 MP_CHECKOK(mp_init(&sx, FLAG(k1)));
134 MP_CHECKOK(mp_init(&sy, FLAG(k1)));
135
136 MP_CHECKOK(ECPoint_mul(group, k1, NULL, NULL, &sx, &sy));
137 MP_CHECKOK(ECPoint_mul(group, k2, px, py, rx, ry));
138
139 if (group->meth->field_enc) {
140 MP_CHECKOK(group->meth->field_enc(&sx, &sx, group->meth));
141 MP_CHECKOK(group->meth->field_enc(&sy, &sy, group->meth));
142 MP_CHECKOK(group->meth->field_enc(rx, rx, group->meth));
143 MP_CHECKOK(group->meth->field_enc(ry, ry, group->meth));
144 }
145
146 MP_CHECKOK(group->point_add(&sx, &sy, rx, ry, rx, ry, group));
147
148 if (group->meth->field_dec) {
149 MP_CHECKOK(group->meth->field_dec(rx, rx, group->meth));
150 MP_CHECKOK(group->meth->field_dec(ry, ry, group->meth));
151 }
152
153 CLEANUP:
154 mp_clear(&sx);
155 mp_clear(&sy);
156 return res;
157 }
158
159 /* Elliptic curve scalar-point multiplication. Computes R(x, y) = k1 * G +
160 * k2 * P(x, y), where G is the generator (base point) of the group of
161 * points on the elliptic curve. Allows k1 = NULL or { k2, P } = NULL.
162 * Input and output values are assumed to be NOT field-encoded. Uses
163 * algorithm 15 (simultaneous multiple point multiplication) from Brown,
164 * Hankerson, Lopez, Menezes. Software Implementation of the NIST
165 * Elliptic Curves over Prime Fields. */
166 mp_err
ec_pts_mul_simul_w2(const mp_int * k1,const mp_int * k2,const mp_int * px,const mp_int * py,mp_int * rx,mp_int * ry,const ECGroup * group)167 ec_pts_mul_simul_w2(const mp_int *k1, const mp_int *k2, const mp_int *px,
168 const mp_int *py, mp_int *rx, mp_int *ry,
169 const ECGroup *group)
170 {
171 mp_err res = MP_OKAY;
172 mp_int precomp[4][4][2];
173 const mp_int *a, *b;
174 int i, j;
175 int ai, bi, d;
176
177 ARGCHK(group != NULL, MP_BADARG);
178 ARGCHK(!((k1 == NULL)
179 && ((k2 == NULL) || (px == NULL)
180 || (py == NULL))), MP_BADARG);
181
182 /* if some arguments are not defined used ECPoint_mul */
183 if (k1 == NULL) {
184 return ECPoint_mul(group, k2, px, py, rx, ry);
185 } else if ((k2 == NULL) || (px == NULL) || (py == NULL)) {
186 return ECPoint_mul(group, k1, NULL, NULL, rx, ry);
187 }
188
189 /* initialize precomputation table */
190 for (i = 0; i < 4; i++) {
191 for (j = 0; j < 4; j++) {
192 MP_DIGITS(&precomp[i][j][0]) = 0;
193 MP_DIGITS(&precomp[i][j][1]) = 0;
194 }
195 }
196 for (i = 0; i < 4; i++) {
197 for (j = 0; j < 4; j++) {
198 MP_CHECKOK( mp_init_size(&precomp[i][j][0],
199 ECL_MAX_FIELD_SIZE_DIGITS, FLAG(k1)) );
200 MP_CHECKOK( mp_init_size(&precomp[i][j][1],
201 ECL_MAX_FIELD_SIZE_DIGITS, FLAG(k1)) );
202 }
203 }
204
205 /* fill precomputation table */
206 /* assign {k1, k2} = {a, b} such that len(a) >= len(b) */
207 if (mpl_significant_bits(k1) < mpl_significant_bits(k2)) {
208 a = k2;
209 b = k1;
210 if (group->meth->field_enc) {
211 MP_CHECKOK(group->meth->
212 field_enc(px, &precomp[1][0][0], group->meth));
213 MP_CHECKOK(group->meth->
214 field_enc(py, &precomp[1][0][1], group->meth));
215 } else {
216 MP_CHECKOK(mp_copy(px, &precomp[1][0][0]));
217 MP_CHECKOK(mp_copy(py, &precomp[1][0][1]));
218 }
219 MP_CHECKOK(mp_copy(&group->genx, &precomp[0][1][0]));
220 MP_CHECKOK(mp_copy(&group->geny, &precomp[0][1][1]));
221 } else {
222 a = k1;
223 b = k2;
224 MP_CHECKOK(mp_copy(&group->genx, &precomp[1][0][0]));
225 MP_CHECKOK(mp_copy(&group->geny, &precomp[1][0][1]));
226 if (group->meth->field_enc) {
227 MP_CHECKOK(group->meth->
228 field_enc(px, &precomp[0][1][0], group->meth));
229 MP_CHECKOK(group->meth->
230 field_enc(py, &precomp[0][1][1], group->meth));
231 } else {
232 MP_CHECKOK(mp_copy(px, &precomp[0][1][0]));
233 MP_CHECKOK(mp_copy(py, &precomp[0][1][1]));
234 }
235 }
236 /* precompute [*][0][*] */
237 mp_zero(&precomp[0][0][0]);
238 mp_zero(&precomp[0][0][1]);
239 MP_CHECKOK(group->
240 point_dbl(&precomp[1][0][0], &precomp[1][0][1],
241 &precomp[2][0][0], &precomp[2][0][1], group));
242 MP_CHECKOK(group->
243 point_add(&precomp[1][0][0], &precomp[1][0][1],
244 &precomp[2][0][0], &precomp[2][0][1],
245 &precomp[3][0][0], &precomp[3][0][1], group));
246 /* precompute [*][1][*] */
247 for (i = 1; i < 4; i++) {
248 MP_CHECKOK(group->
249 point_add(&precomp[0][1][0], &precomp[0][1][1],
250 &precomp[i][0][0], &precomp[i][0][1],
251 &precomp[i][1][0], &precomp[i][1][1], group));
252 }
253 /* precompute [*][2][*] */
254 MP_CHECKOK(group->
255 point_dbl(&precomp[0][1][0], &precomp[0][1][1],
256 &precomp[0][2][0], &precomp[0][2][1], group));
257 for (i = 1; i < 4; i++) {
258 MP_CHECKOK(group->
259 point_add(&precomp[0][2][0], &precomp[0][2][1],
260 &precomp[i][0][0], &precomp[i][0][1],
261 &precomp[i][2][0], &precomp[i][2][1], group));
262 }
263 /* precompute [*][3][*] */
264 MP_CHECKOK(group->
265 point_add(&precomp[0][1][0], &precomp[0][1][1],
266 &precomp[0][2][0], &precomp[0][2][1],
267 &precomp[0][3][0], &precomp[0][3][1], group));
268 for (i = 1; i < 4; i++) {
269 MP_CHECKOK(group->
270 point_add(&precomp[0][3][0], &precomp[0][3][1],
271 &precomp[i][0][0], &precomp[i][0][1],
272 &precomp[i][3][0], &precomp[i][3][1], group));
273 }
274
275 d = (mpl_significant_bits(a) + 1) / 2;
276
277 /* R = inf */
278 mp_zero(rx);
279 mp_zero(ry);
280
281 for (i = d - 1; i >= 0; i--) {
282 ai = MP_GET_BIT(a, 2 * i + 1);
283 ai <<= 1;
284 ai |= MP_GET_BIT(a, 2 * i);
285 bi = MP_GET_BIT(b, 2 * i + 1);
286 bi <<= 1;
287 bi |= MP_GET_BIT(b, 2 * i);
288 /* R = 2^2 * R */
289 MP_CHECKOK(group->point_dbl(rx, ry, rx, ry, group));
290 MP_CHECKOK(group->point_dbl(rx, ry, rx, ry, group));
291 /* R = R + (ai * A + bi * B) */
292 MP_CHECKOK(group->
293 point_add(rx, ry, &precomp[ai][bi][0],
294 &precomp[ai][bi][1], rx, ry, group));
295 }
296
297 if (group->meth->field_dec) {
298 MP_CHECKOK(group->meth->field_dec(rx, rx, group->meth));
299 MP_CHECKOK(group->meth->field_dec(ry, ry, group->meth));
300 }
301
302 CLEANUP:
303 for (i = 0; i < 4; i++) {
304 for (j = 0; j < 4; j++) {
305 mp_clear(&precomp[i][j][0]);
306 mp_clear(&precomp[i][j][1]);
307 }
308 }
309 return res;
310 }
311
312 /* Elliptic curve scalar-point multiplication. Computes R(x, y) = k1 * G +
313 * k2 * P(x, y), where G is the generator (base point) of the group of
314 * points on the elliptic curve. Allows k1 = NULL or { k2, P } = NULL.
315 * Input and output values are assumed to be NOT field-encoded. */
316 mp_err
ECPoints_mul(const ECGroup * group,const mp_int * k1,const mp_int * k2,const mp_int * px,const mp_int * py,mp_int * rx,mp_int * ry)317 ECPoints_mul(const ECGroup *group, const mp_int *k1, const mp_int *k2,
318 const mp_int *px, const mp_int *py, mp_int *rx, mp_int *ry)
319 {
320 mp_err res = MP_OKAY;
321 mp_int k1t, k2t;
322 const mp_int *k1p, *k2p;
323
324 MP_DIGITS(&k1t) = 0;
325 MP_DIGITS(&k2t) = 0;
326
327 ARGCHK(group != NULL, MP_BADARG);
328
329 /* want scalar to be less than or equal to group order */
330 if (k1 != NULL) {
331 if (mp_cmp(k1, &group->order) >= 0) {
332 MP_CHECKOK(mp_init(&k1t, FLAG(k1)));
333 MP_CHECKOK(mp_mod(k1, &group->order, &k1t));
334 k1p = &k1t;
335 } else {
336 k1p = k1;
337 }
338 } else {
339 k1p = k1;
340 }
341 if (k2 != NULL) {
342 if (mp_cmp(k2, &group->order) >= 0) {
343 MP_CHECKOK(mp_init(&k2t, FLAG(k2)));
344 MP_CHECKOK(mp_mod(k2, &group->order, &k2t));
345 k2p = &k2t;
346 } else {
347 k2p = k2;
348 }
349 } else {
350 k2p = k2;
351 }
352
353 /* if points_mul is defined, then use it */
354 if (group->points_mul) {
355 res = group->points_mul(k1p, k2p, px, py, rx, ry, group);
356 } else {
357 res = ec_pts_mul_simul_w2(k1p, k2p, px, py, rx, ry, group);
358 }
359
360 CLEANUP:
361 mp_clear(&k1t);
362 mp_clear(&k2t);
363 return res;
364 }
365