1 /* This Source Code Form is subject to the terms of the Mozilla Public
2  * License, v. 2.0. If a copy of the MPL was not distributed with this
3  * file, You can obtain one at http://mozilla.org/MPL/2.0/. */
4 
5 #include "mpi.h"
6 #include "mplogic.h"
7 #include "ecl.h"
8 #include "ecl-priv.h"
9 #include <stdlib.h>
10 
11 /* Elliptic curve scalar-point multiplication. Computes R(x, y) = k * P(x,
12  * y).  If x, y = NULL, then P is assumed to be the generator (base point)
13  * of the group of points on the elliptic curve. Input and output values
14  * are assumed to be NOT field-encoded. */
15 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)16 ECPoint_mul(const ECGroup *group, const mp_int *k, const mp_int *px,
17             const mp_int *py, mp_int *rx, mp_int *ry)
18 {
19     mp_err res = MP_OKAY;
20     mp_int kt;
21 
22     ARGCHK((k != NULL) && (group != NULL), MP_BADARG);
23     MP_DIGITS(&kt) = 0;
24 
25     /* want scalar to be less than or equal to group order */
26     if (mp_cmp(k, &group->order) > 0) {
27         MP_CHECKOK(mp_init(&kt));
28         MP_CHECKOK(mp_mod(k, &group->order, &kt));
29     } else {
30         MP_SIGN(&kt) = MP_ZPOS;
31         MP_USED(&kt) = MP_USED(k);
32         MP_ALLOC(&kt) = MP_ALLOC(k);
33         MP_DIGITS(&kt) = MP_DIGITS(k);
34     }
35 
36     if ((px == NULL) || (py == NULL)) {
37         if (group->base_point_mul) {
38             MP_CHECKOK(group->base_point_mul(&kt, rx, ry, group));
39         } else {
40             MP_CHECKOK(group->point_mul(&kt, &group->genx, &group->geny, rx, ry,
41                                         group));
42         }
43     } else {
44         if (group->meth->field_enc) {
45             MP_CHECKOK(group->meth->field_enc(px, rx, group->meth));
46             MP_CHECKOK(group->meth->field_enc(py, ry, group->meth));
47             MP_CHECKOK(group->point_mul(&kt, rx, ry, rx, ry, group));
48         } else {
49             MP_CHECKOK(group->point_mul(&kt, px, py, rx, ry, group));
50         }
51     }
52     if (group->meth->field_dec) {
53         MP_CHECKOK(group->meth->field_dec(rx, rx, group->meth));
54         MP_CHECKOK(group->meth->field_dec(ry, ry, group->meth));
55     }
56 
57 CLEANUP:
58     if (MP_DIGITS(&kt) != MP_DIGITS(k)) {
59         mp_clear(&kt);
60     }
61     return res;
62 }
63 
64 /* Elliptic curve scalar-point multiplication. Computes R(x, y) = k1 * G +
65  * k2 * P(x, y), where G is the generator (base point) of the group of
66  * points on the elliptic curve. Allows k1 = NULL or { k2, P } = NULL.
67  * Input and output values are assumed to be NOT field-encoded. */
68 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)69 ec_pts_mul_basic(const mp_int *k1, const mp_int *k2, const mp_int *px,
70                  const mp_int *py, mp_int *rx, mp_int *ry,
71                  const ECGroup *group)
72 {
73     mp_err res = MP_OKAY;
74     mp_int sx, sy;
75 
76     ARGCHK(group != NULL, MP_BADARG);
77     ARGCHK(!((k1 == NULL) && ((k2 == NULL) || (px == NULL) || (py == NULL))), MP_BADARG);
78 
79     /* if some arguments are not defined used ECPoint_mul */
80     if (k1 == NULL) {
81         return ECPoint_mul(group, k2, px, py, rx, ry);
82     } else if ((k2 == NULL) || (px == NULL) || (py == NULL)) {
83         return ECPoint_mul(group, k1, NULL, NULL, rx, ry);
84     }
85 
86     MP_DIGITS(&sx) = 0;
87     MP_DIGITS(&sy) = 0;
88     MP_CHECKOK(mp_init(&sx));
89     MP_CHECKOK(mp_init(&sy));
90 
91     MP_CHECKOK(ECPoint_mul(group, k1, NULL, NULL, &sx, &sy));
92     MP_CHECKOK(ECPoint_mul(group, k2, px, py, rx, ry));
93 
94     if (group->meth->field_enc) {
95         MP_CHECKOK(group->meth->field_enc(&sx, &sx, group->meth));
96         MP_CHECKOK(group->meth->field_enc(&sy, &sy, group->meth));
97         MP_CHECKOK(group->meth->field_enc(rx, rx, group->meth));
98         MP_CHECKOK(group->meth->field_enc(ry, ry, group->meth));
99     }
100 
101     MP_CHECKOK(group->point_add(&sx, &sy, rx, ry, rx, ry, group));
102 
103     if (group->meth->field_dec) {
104         MP_CHECKOK(group->meth->field_dec(rx, rx, group->meth));
105         MP_CHECKOK(group->meth->field_dec(ry, ry, group->meth));
106     }
107 
108 CLEANUP:
109     mp_clear(&sx);
110     mp_clear(&sy);
111     return res;
112 }
113 
114 /* Elliptic curve scalar-point multiplication. Computes R(x, y) = k1 * G +
115  * k2 * P(x, y), where G is the generator (base point) of the group of
116  * points on the elliptic curve. Allows k1 = NULL or { k2, P } = NULL.
117  * Input and output values are assumed to be NOT field-encoded. Uses
118  * algorithm 15 (simultaneous multiple point multiplication) from Brown,
119  * Hankerson, Lopez, Menezes. Software Implementation of the NIST
120  * Elliptic Curves over Prime Fields. */
121 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)122 ec_pts_mul_simul_w2(const mp_int *k1, const mp_int *k2, const mp_int *px,
123                     const mp_int *py, mp_int *rx, mp_int *ry,
124                     const ECGroup *group)
125 {
126     mp_err res = MP_OKAY;
127     mp_int precomp[4][4][2];
128     const mp_int *a, *b;
129     unsigned int i, j;
130     int ai, bi, d;
131 
132     ARGCHK(group != NULL, MP_BADARG);
133     ARGCHK(!((k1 == NULL) && ((k2 == NULL) || (px == NULL) || (py == NULL))), MP_BADARG);
134 
135     /* if some arguments are not defined used ECPoint_mul */
136     if (k1 == NULL) {
137         return ECPoint_mul(group, k2, px, py, rx, ry);
138     } else if ((k2 == NULL) || (px == NULL) || (py == NULL)) {
139         return ECPoint_mul(group, k1, NULL, NULL, rx, ry);
140     }
141 
142     /* initialize precomputation table */
143     for (i = 0; i < 4; i++) {
144         for (j = 0; j < 4; j++) {
145             MP_DIGITS(&precomp[i][j][0]) = 0;
146             MP_DIGITS(&precomp[i][j][1]) = 0;
147         }
148     }
149     for (i = 0; i < 4; i++) {
150         for (j = 0; j < 4; j++) {
151             MP_CHECKOK(mp_init_size(&precomp[i][j][0],
152                                     ECL_MAX_FIELD_SIZE_DIGITS));
153             MP_CHECKOK(mp_init_size(&precomp[i][j][1],
154                                     ECL_MAX_FIELD_SIZE_DIGITS));
155         }
156     }
157 
158     /* fill precomputation table */
159     /* assign {k1, k2} = {a, b} such that len(a) >= len(b) */
160     if (mpl_significant_bits(k1) < mpl_significant_bits(k2)) {
161         a = k2;
162         b = k1;
163         if (group->meth->field_enc) {
164             MP_CHECKOK(group->meth->field_enc(px, &precomp[1][0][0], group->meth));
165             MP_CHECKOK(group->meth->field_enc(py, &precomp[1][0][1], group->meth));
166         } else {
167             MP_CHECKOK(mp_copy(px, &precomp[1][0][0]));
168             MP_CHECKOK(mp_copy(py, &precomp[1][0][1]));
169         }
170         MP_CHECKOK(mp_copy(&group->genx, &precomp[0][1][0]));
171         MP_CHECKOK(mp_copy(&group->geny, &precomp[0][1][1]));
172     } else {
173         a = k1;
174         b = k2;
175         MP_CHECKOK(mp_copy(&group->genx, &precomp[1][0][0]));
176         MP_CHECKOK(mp_copy(&group->geny, &precomp[1][0][1]));
177         if (group->meth->field_enc) {
178             MP_CHECKOK(group->meth->field_enc(px, &precomp[0][1][0], group->meth));
179             MP_CHECKOK(group->meth->field_enc(py, &precomp[0][1][1], group->meth));
180         } else {
181             MP_CHECKOK(mp_copy(px, &precomp[0][1][0]));
182             MP_CHECKOK(mp_copy(py, &precomp[0][1][1]));
183         }
184     }
185     /* precompute [*][0][*] */
186     mp_zero(&precomp[0][0][0]);
187     mp_zero(&precomp[0][0][1]);
188     MP_CHECKOK(group->point_dbl(&precomp[1][0][0], &precomp[1][0][1],
189                                 &precomp[2][0][0], &precomp[2][0][1], group));
190     MP_CHECKOK(group->point_add(&precomp[1][0][0], &precomp[1][0][1],
191                                 &precomp[2][0][0], &precomp[2][0][1],
192                                 &precomp[3][0][0], &precomp[3][0][1], group));
193     /* precompute [*][1][*] */
194     for (i = 1; i < 4; i++) {
195         MP_CHECKOK(group->point_add(&precomp[0][1][0], &precomp[0][1][1],
196                                     &precomp[i][0][0], &precomp[i][0][1],
197                                     &precomp[i][1][0], &precomp[i][1][1], group));
198     }
199     /* precompute [*][2][*] */
200     MP_CHECKOK(group->point_dbl(&precomp[0][1][0], &precomp[0][1][1],
201                                 &precomp[0][2][0], &precomp[0][2][1], group));
202     for (i = 1; i < 4; i++) {
203         MP_CHECKOK(group->point_add(&precomp[0][2][0], &precomp[0][2][1],
204                                     &precomp[i][0][0], &precomp[i][0][1],
205                                     &precomp[i][2][0], &precomp[i][2][1], group));
206     }
207     /* precompute [*][3][*] */
208     MP_CHECKOK(group->point_add(&precomp[0][1][0], &precomp[0][1][1],
209                                 &precomp[0][2][0], &precomp[0][2][1],
210                                 &precomp[0][3][0], &precomp[0][3][1], group));
211     for (i = 1; i < 4; i++) {
212         MP_CHECKOK(group->point_add(&precomp[0][3][0], &precomp[0][3][1],
213                                     &precomp[i][0][0], &precomp[i][0][1],
214                                     &precomp[i][3][0], &precomp[i][3][1], group));
215     }
216 
217     d = (mpl_significant_bits(a) + 1) / 2;
218 
219     /* R = inf */
220     mp_zero(rx);
221     mp_zero(ry);
222 
223     for (i = d; i-- > 0;) {
224         ai = MP_GET_BIT(a, 2 * i + 1);
225         ai <<= 1;
226         ai |= MP_GET_BIT(a, 2 * i);
227         bi = MP_GET_BIT(b, 2 * i + 1);
228         bi <<= 1;
229         bi |= MP_GET_BIT(b, 2 * i);
230         /* R = 2^2 * R */
231         MP_CHECKOK(group->point_dbl(rx, ry, rx, ry, group));
232         MP_CHECKOK(group->point_dbl(rx, ry, rx, ry, group));
233         /* R = R + (ai * A + bi * B) */
234         MP_CHECKOK(group->point_add(rx, ry, &precomp[ai][bi][0],
235                                     &precomp[ai][bi][1], rx, ry, group));
236     }
237 
238     if (group->meth->field_dec) {
239         MP_CHECKOK(group->meth->field_dec(rx, rx, group->meth));
240         MP_CHECKOK(group->meth->field_dec(ry, ry, group->meth));
241     }
242 
243 CLEANUP:
244     for (i = 0; i < 4; i++) {
245         for (j = 0; j < 4; j++) {
246             mp_clear(&precomp[i][j][0]);
247             mp_clear(&precomp[i][j][1]);
248         }
249     }
250     return res;
251 }
252 
253 /* Elliptic curve scalar-point multiplication. Computes R(x, y) = k1 * G +
254  * k2 * P(x, y), where G is the generator (base point) of the group of
255  * points on the elliptic curve. Allows k1 = NULL or { k2, P } = NULL.
256  * Input and output values are assumed to be NOT field-encoded. */
257 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)258 ECPoints_mul(const ECGroup *group, const mp_int *k1, const mp_int *k2,
259              const mp_int *px, const mp_int *py, mp_int *rx, mp_int *ry)
260 {
261     mp_err res = MP_OKAY;
262     mp_int k1t, k2t;
263     const mp_int *k1p, *k2p;
264 
265     MP_DIGITS(&k1t) = 0;
266     MP_DIGITS(&k2t) = 0;
267 
268     ARGCHK(group != NULL, MP_BADARG);
269 
270     /* want scalar to be less than or equal to group order */
271     if (k1 != NULL) {
272         if (mp_cmp(k1, &group->order) >= 0) {
273             MP_CHECKOK(mp_init(&k1t));
274             MP_CHECKOK(mp_mod(k1, &group->order, &k1t));
275             k1p = &k1t;
276         } else {
277             k1p = k1;
278         }
279     } else {
280         k1p = k1;
281     }
282     if (k2 != NULL) {
283         if (mp_cmp(k2, &group->order) >= 0) {
284             MP_CHECKOK(mp_init(&k2t));
285             MP_CHECKOK(mp_mod(k2, &group->order, &k2t));
286             k2p = &k2t;
287         } else {
288             k2p = k2;
289         }
290     } else {
291         k2p = k2;
292     }
293 
294     /* if points_mul is defined, then use it */
295     if (group->points_mul) {
296         res = group->points_mul(k1p, k2p, px, py, rx, ry, group);
297     } else {
298         res = ec_pts_mul_simul_w2(k1p, k2p, px, py, rx, ry, group);
299     }
300 
301 CLEANUP:
302     mp_clear(&k1t);
303     mp_clear(&k2t);
304     return res;
305 }
306