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. */
59 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)60 ECPoint_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. */
113 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)114 ec_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. */
168 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)169 ec_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. */
318 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)319 ECPoints_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