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