1 /*
2 * Copyright (c) 2007, 2011, Oracle and/or its affiliates. All rights reserved.
3 * Use is subject to license terms.
4 *
5 * This library is free software; you can redistribute it and/or
6 * modify it under the terms of the GNU Lesser General Public
7 * License as published by the Free Software Foundation; either
8 * version 2.1 of the License, or (at your option) any later version.
9 *
10 * This library is distributed in the hope that it will be useful,
11 * but WITHOUT ANY WARRANTY; without even the implied warranty of
12 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
13 * Lesser General Public License for more details.
14 *
15 * You should have received a copy of the GNU Lesser General Public License
16 * along with this library; if not, write to the Free Software Foundation,
17 * Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
18 *
19 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
20 * or visit www.oracle.com if you need additional information or have any
21 * questions.
22 */
23
24 /* *********************************************************************
25 *
26 * The Original Code is the elliptic curve math library.
27 *
28 * The Initial Developer of the Original Code is
29 * Sun Microsystems, Inc.
30 * Portions created by the Initial Developer are Copyright (C) 2003
31 * the Initial Developer. All Rights Reserved.
32 *
33 * Contributor(s):
34 * Douglas Stebila <douglas@stebila.ca>, Sun Microsystems Laboratories
35 *
36 *********************************************************************** */
37
38 #include "mpi.h"
39 #include "mplogic.h"
40 #include "ecl.h"
41 #include "ecl-priv.h"
42 #ifndef _KERNEL
43 #include <stdlib.h>
44 #endif
45
46 /* Elliptic curve scalar-point multiplication. Computes R(x, y) = k * P(x,
47 * y). If x, y = NULL, then P is assumed to be the generator (base point)
48 * of the group of points on the elliptic curve. Input and output values
49 * are assumed to be NOT field-encoded. */
50 mp_err
51 ECPoint_mul(const ECGroup *group, const mp_int *k, const mp_int *px,
52 const mp_int *py, mp_int *rx, mp_int *ry)
53 {
54 mp_err res = MP_OKAY;
55 mp_int kt;
56
57 ARGCHK((k != NULL) && (group != NULL), MP_BADARG);
58 MP_DIGITS(&kt) = 0;
59
60 /* want scalar to be less than or equal to group order */
61 if (mp_cmp(k, &group->order) > 0) {
62 MP_CHECKOK(mp_init(&kt, FLAG(k)));
63 MP_CHECKOK(mp_mod(k, &group->order, &kt));
64 } else {
65 MP_SIGN(&kt) = MP_ZPOS;
66 MP_USED(&kt) = MP_USED(k);
67 MP_ALLOC(&kt) = MP_ALLOC(k);
68 MP_DIGITS(&kt) = MP_DIGITS(k);
69 }
70
71 if ((px == NULL) || (py == NULL)) {
72 if (group->base_point_mul) {
73 MP_CHECKOK(group->base_point_mul(&kt, rx, ry, group));
74 } else {
75 kt.flag = (mp_sign)0;
76 MP_CHECKOK(group->
77 point_mul(&kt, &group->genx, &group->geny, rx, ry,
78 group));
79 }
80 } else {
81 if (group->meth->field_enc) {
82 MP_CHECKOK(group->meth->field_enc(px, rx, group->meth));
83 MP_CHECKOK(group->meth->field_enc(py, ry, group->meth));
84 MP_CHECKOK(group->point_mul(&kt, rx, ry, rx, ry, group));
85 } else {
86 kt.flag = (mp_sign)0;
87 MP_CHECKOK(group->point_mul(&kt, px, py, rx, ry, group));
88 }
89 }
90 if (group->meth->field_dec) {
91 MP_CHECKOK(group->meth->field_dec(rx, rx, group->meth));
92 MP_CHECKOK(group->meth->field_dec(ry, ry, group->meth));
93 }
94
95 CLEANUP:
96 if (MP_DIGITS(&kt) != MP_DIGITS(k)) {
97 mp_clear(&kt);
98 }
99 return res;
100 }
101
102 /* Elliptic curve scalar-point multiplication. Computes R(x, y) = k1 * G +
103 * k2 * P(x, y), where G is the generator (base point) of the group of
104 * points on the elliptic curve. Allows k1 = NULL or { k2, P } = NULL.
105 * Input and output values are assumed to be NOT field-encoded. */
106 mp_err
107 ec_pts_mul_basic(const mp_int *k1, const mp_int *k2, const mp_int *px,
108 const mp_int *py, mp_int *rx, mp_int *ry,
109 const ECGroup *group)
110 {
111 mp_err res = MP_OKAY;
112 mp_int sx, sy;
113
114 ARGCHK(group != NULL, MP_BADARG);
115 ARGCHK(!((k1 == NULL)
116 && ((k2 == NULL) || (px == NULL)
117 || (py == NULL))), MP_BADARG);
118
119 /* if some arguments are not defined used ECPoint_mul */
120 if (k1 == NULL) {
121 return ECPoint_mul(group, k2, px, py, rx, ry);
122 } else if ((k2 == NULL) || (px == NULL) || (py == NULL)) {
123 return ECPoint_mul(group, k1, NULL, NULL, rx, ry);
124 }
125
126 MP_DIGITS(&sx) = 0;
127 MP_DIGITS(&sy) = 0;
128 MP_CHECKOK(mp_init(&sx, FLAG(k1)));
129 MP_CHECKOK(mp_init(&sy, FLAG(k1)));
130
131 MP_CHECKOK(ECPoint_mul(group, k1, NULL, NULL, &sx, &sy));
132 MP_CHECKOK(ECPoint_mul(group, k2, px, py, rx, ry));
133
134 if (group->meth->field_enc) {
135 MP_CHECKOK(group->meth->field_enc(&sx, &sx, group->meth));
136 MP_CHECKOK(group->meth->field_enc(&sy, &sy, group->meth));
137 MP_CHECKOK(group->meth->field_enc(rx, rx, group->meth));
138 MP_CHECKOK(group->meth->field_enc(ry, ry, group->meth));
139 }
140
141 MP_CHECKOK(group->point_add(&sx, &sy, rx, ry, rx, ry, group));
142
143 if (group->meth->field_dec) {
144 MP_CHECKOK(group->meth->field_dec(rx, rx, group->meth));
145 MP_CHECKOK(group->meth->field_dec(ry, ry, group->meth));
146 }
147
148 CLEANUP:
149 mp_clear(&sx);
150 mp_clear(&sy);
151 return res;
152 }
153
154 /* Elliptic curve scalar-point multiplication. Computes R(x, y) = k1 * G +
155 * k2 * P(x, y), where G is the generator (base point) of the group of
156 * points on the elliptic curve. Allows k1 = NULL or { k2, P } = NULL.
157 * Input and output values are assumed to be NOT field-encoded. Uses
158 * algorithm 15 (simultaneous multiple point multiplication) from Brown,
159 * Hankerson, Lopez, Menezes. Software Implementation of the NIST
160 * Elliptic Curves over Prime Fields. */
161 mp_err
162 ec_pts_mul_simul_w2(const mp_int *k1, const mp_int *k2, const mp_int *px,
163 const mp_int *py, mp_int *rx, mp_int *ry,
164 const ECGroup *group)
165 {
166 mp_err res = MP_OKAY;
167 mp_int precomp[4][4][2];
168 const mp_int *a, *b;
169 int i, j;
170 int ai, bi, d;
171
172 ARGCHK(group != NULL, MP_BADARG);
173 ARGCHK(!((k1 == NULL)
174 && ((k2 == NULL) || (px == NULL)
175 || (py == NULL))), MP_BADARG);
176
177 /* if some arguments are not defined used ECPoint_mul */
178 if (k1 == NULL) {
179 return ECPoint_mul(group, k2, px, py, rx, ry);
180 } else if ((k2 == NULL) || (px == NULL) || (py == NULL)) {
181 return ECPoint_mul(group, k1, NULL, NULL, rx, ry);
182 }
183
184 /* initialize precomputation table */
185 for (i = 0; i < 4; i++) {
186 for (j = 0; j < 4; j++) {
187 MP_DIGITS(&precomp[i][j][0]) = 0;
188 MP_DIGITS(&precomp[i][j][1]) = 0;
189 }
190 }
191 for (i = 0; i < 4; i++) {
192 for (j = 0; j < 4; j++) {
193 MP_CHECKOK( mp_init_size(&precomp[i][j][0],
194 ECL_MAX_FIELD_SIZE_DIGITS, FLAG(k1)) );
195 MP_CHECKOK( mp_init_size(&precomp[i][j][1],
196 ECL_MAX_FIELD_SIZE_DIGITS, FLAG(k1)) );
197 }
198 }
199
200 /* fill precomputation table */
201 /* assign {k1, k2} = {a, b} such that len(a) >= len(b) */
202 if (mpl_significant_bits(k1) < mpl_significant_bits(k2)) {
203 a = k2;
204 b = k1;
205 if (group->meth->field_enc) {
206 MP_CHECKOK(group->meth->
207 field_enc(px, &precomp[1][0][0], group->meth));
208 MP_CHECKOK(group->meth->
209 field_enc(py, &precomp[1][0][1], group->meth));
210 } else {
211 MP_CHECKOK(mp_copy(px, &precomp[1][0][0]));
212 MP_CHECKOK(mp_copy(py, &precomp[1][0][1]));
213 }
214 MP_CHECKOK(mp_copy(&group->genx, &precomp[0][1][0]));
215 MP_CHECKOK(mp_copy(&group->geny, &precomp[0][1][1]));
216 } else {
217 a = k1;
218 b = k2;
219 MP_CHECKOK(mp_copy(&group->genx, &precomp[1][0][0]));
220 MP_CHECKOK(mp_copy(&group->geny, &precomp[1][0][1]));
221 if (group->meth->field_enc) {
222 MP_CHECKOK(group->meth->
223 field_enc(px, &precomp[0][1][0], group->meth));
224 MP_CHECKOK(group->meth->
225 field_enc(py, &precomp[0][1][1], group->meth));
226 } else {
227 MP_CHECKOK(mp_copy(px, &precomp[0][1][0]));
228 MP_CHECKOK(mp_copy(py, &precomp[0][1][1]));
229 }
230 }
231 /* precompute [*][0][*] */
232 mp_zero(&precomp[0][0][0]);
233 mp_zero(&precomp[0][0][1]);
234 MP_CHECKOK(group->
235 point_dbl(&precomp[1][0][0], &precomp[1][0][1],
236 &precomp[2][0][0], &precomp[2][0][1], group));
237 MP_CHECKOK(group->
238 point_add(&precomp[1][0][0], &precomp[1][0][1],
239 &precomp[2][0][0], &precomp[2][0][1],
240 &precomp[3][0][0], &precomp[3][0][1], group));
241 /* precompute [*][1][*] */
242 for (i = 1; i < 4; i++) {
243 MP_CHECKOK(group->
244 point_add(&precomp[0][1][0], &precomp[0][1][1],
245 &precomp[i][0][0], &precomp[i][0][1],
246 &precomp[i][1][0], &precomp[i][1][1], group));
247 }
248 /* precompute [*][2][*] */
249 MP_CHECKOK(group->
250 point_dbl(&precomp[0][1][0], &precomp[0][1][1],
251 &precomp[0][2][0], &precomp[0][2][1], group));
252 for (i = 1; i < 4; i++) {
253 MP_CHECKOK(group->
254 point_add(&precomp[0][2][0], &precomp[0][2][1],
255 &precomp[i][0][0], &precomp[i][0][1],
256 &precomp[i][2][0], &precomp[i][2][1], group));
257 }
258 /* precompute [*][3][*] */
259 MP_CHECKOK(group->
260 point_add(&precomp[0][1][0], &precomp[0][1][1],
261 &precomp[0][2][0], &precomp[0][2][1],
262 &precomp[0][3][0], &precomp[0][3][1], group));
263 for (i = 1; i < 4; i++) {
264 MP_CHECKOK(group->
265 point_add(&precomp[0][3][0], &precomp[0][3][1],
266 &precomp[i][0][0], &precomp[i][0][1],
267 &precomp[i][3][0], &precomp[i][3][1], group));
268 }
269
270 d = (mpl_significant_bits(a) + 1) / 2;
271
272 /* R = inf */
273 mp_zero(rx);
274 mp_zero(ry);
275
276 for (i = d - 1; i >= 0; i--) {
277 ai = MP_GET_BIT(a, 2 * i + 1);
278 ai <<= 1;
279 ai |= MP_GET_BIT(a, 2 * i);
280 bi = MP_GET_BIT(b, 2 * i + 1);
281 bi <<= 1;
282 bi |= MP_GET_BIT(b, 2 * i);
283 /* R = 2^2 * R */
284 MP_CHECKOK(group->point_dbl(rx, ry, rx, ry, group));
285 MP_CHECKOK(group->point_dbl(rx, ry, rx, ry, group));
286 /* R = R + (ai * A + bi * B) */
287 MP_CHECKOK(group->
288 point_add(rx, ry, &precomp[ai][bi][0],
289 &precomp[ai][bi][1], rx, ry, group));
290 }
291
292 if (group->meth->field_dec) {
293 MP_CHECKOK(group->meth->field_dec(rx, rx, group->meth));
294 MP_CHECKOK(group->meth->field_dec(ry, ry, group->meth));
295 }
296
297 CLEANUP:
298 for (i = 0; i < 4; i++) {
299 for (j = 0; j < 4; j++) {
300 mp_clear(&precomp[i][j][0]);
301 mp_clear(&precomp[i][j][1]);
302 }
303 }
304 return res;
305 }
306
307 /* Elliptic curve scalar-point multiplication. Computes R(x, y) = k1 * G +
308 * k2 * P(x, y), where G is the generator (base point) of the group of
309 * points on the elliptic curve. Allows k1 = NULL or { k2, P } = NULL.
310 * Input and output values are assumed to be NOT field-encoded. */
311 mp_err
312 ECPoints_mul(const ECGroup *group, const mp_int *k1, const mp_int *k2,
313 const mp_int *px, const mp_int *py, mp_int *rx, mp_int *ry)
314 {
315 mp_err res = MP_OKAY;
316 mp_int k1t, k2t;
317 const mp_int *k1p, *k2p;
318
319 MP_DIGITS(&k1t) = 0;
320 MP_DIGITS(&k2t) = 0;
321
322 ARGCHK(group != NULL, MP_BADARG);
323
324 /* want scalar to be less than or equal to group order */
325 if (k1 != NULL) {
326 if (mp_cmp(k1, &group->order) >= 0) {
327 MP_CHECKOK(mp_init(&k1t, FLAG(k1)));
328 MP_CHECKOK(mp_mod(k1, &group->order, &k1t));
329 k1p = &k1t;
330 } else {
331 k1p = k1;
332 }
333 } else {
334 k1p = k1;
335 }
336 if (k2 != NULL) {
337 if (mp_cmp(k2, &group->order) >= 0) {
338 MP_CHECKOK(mp_init(&k2t, FLAG(k2)));
339 MP_CHECKOK(mp_mod(k2, &group->order, &k2t));
340 k2p = &k2t;
341 } else {
342 k2p = k2;
343 }
344 } else {
345 k2p = k2;
346 }
347
348 /* if points_mul is defined, then use it */
349 if (group->points_mul) {
350 res = group->points_mul(k1p, k2p, px, py, rx, ry, group);
351 } else {
352 res = ec_pts_mul_simul_w2(k1p, k2p, px, py, rx, ry, group);
353 }
354
355 CLEANUP:
356 mp_clear(&k1t);
357 mp_clear(&k2t);
358 return res;
359 }