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