1 /*
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
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  *
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
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
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
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->
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->
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->
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->
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->
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->
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
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 }