1 /*
2 * ***** BEGIN LICENSE BLOCK *****
3 * Version: MPL 1.1/GPL 2.0/LGPL 2.1
4 *
5 * The contents of this file are subject to the Mozilla Public License Version
6 * 1.1 (the "License"); you may not use this file except in compliance with
7 * the License. You may obtain a copy of the License at
8 * http://www.mozilla.org/MPL/
9 *
10 * Software distributed under the License is distributed on an "AS IS" basis,
11 * WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License
12 * for the specific language governing rights and limitations under the
13 * License.
14 *
15 * The Original Code is the elliptic curve math library for prime field curves.
16 *
17 * The Initial Developer of the Original Code is
18 * Sun Microsystems, Inc.
19 * Portions created by the Initial Developer are Copyright (C) 2003
20 * the Initial Developer. All Rights Reserved.
21 *
22 * Contributor(s):
23 * Stephen Fung <fungstep@hotmail.com>, Sun Microsystems Laboratories
24 *
25 * Alternatively, the contents of this file may be used under the terms of
26 * either the GNU General Public License Version 2 or later (the "GPL"), or
27 * the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
28 * in which case the provisions of the GPL or the LGPL are applicable instead
29 * of those above. If you wish to allow use of your version of this file only
30 * under the terms of either the GPL or the LGPL, and not to allow others to
31 * use your version of this file under the terms of the MPL, indicate your
32 * decision by deleting the provisions above and replace them with the notice
33 * and other provisions required by the GPL or the LGPL. If you do not delete
34 * the provisions above, a recipient may use your version of this file under
35 * the terms of any one of the MPL, the GPL or the LGPL.
36 *
37 * ***** END LICENSE BLOCK ***** */
38 /*
39 * Copyright 2007 Sun Microsystems, Inc. All rights reserved.
40 * Use is subject to license terms.
41 *
42 * Sun elects to use this software under the MPL license.
43 */
44
45 #include "ecp.h"
46 #include "ecl-priv.h"
47 #include "mplogic.h"
48 #ifndef _KERNEL
49 #include <stdlib.h>
50 #endif
51
52 #define MAX_SCRATCH 6
53
54 /* Computes R = 2P. Elliptic curve points P and R can be identical. Uses
55 * Modified Jacobian coordinates.
56 *
57 * Assumes input is already field-encoded using field_enc, and returns
58 * output that is still field-encoded.
59 *
60 */
61 mp_err
ec_GFp_pt_dbl_jm(const mp_int * px,const mp_int * py,const mp_int * pz,const mp_int * paz4,mp_int * rx,mp_int * ry,mp_int * rz,mp_int * raz4,mp_int scratch[],const ECGroup * group)62 ec_GFp_pt_dbl_jm(const mp_int *px, const mp_int *py, const mp_int *pz,
63 const mp_int *paz4, mp_int *rx, mp_int *ry, mp_int *rz,
64 mp_int *raz4, mp_int scratch[], const ECGroup *group)
65 {
66 mp_err res = MP_OKAY;
67 mp_int *t0, *t1, *M, *S;
68
69 t0 = &scratch[0];
70 t1 = &scratch[1];
71 M = &scratch[2];
72 S = &scratch[3];
73
74 #if MAX_SCRATCH < 4
75 #error "Scratch array defined too small "
76 #endif
77
78 /* Check for point at infinity */
79 if (ec_GFp_pt_is_inf_jac(px, py, pz) == MP_YES) {
80 /* Set r = pt at infinity by setting rz = 0 */
81
82 MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, rz));
83 goto CLEANUP;
84 }
85
86 /* M = 3 (px^2) + a*(pz^4) */
87 MP_CHECKOK(group->meth->field_sqr(px, t0, group->meth));
88 MP_CHECKOK(group->meth->field_add(t0, t0, M, group->meth));
89 MP_CHECKOK(group->meth->field_add(t0, M, t0, group->meth));
90 MP_CHECKOK(group->meth->field_add(t0, paz4, M, group->meth));
91
92 /* rz = 2 * py * pz */
93 MP_CHECKOK(group->meth->field_mul(py, pz, S, group->meth));
94 MP_CHECKOK(group->meth->field_add(S, S, rz, group->meth));
95
96 /* t0 = 2y^2 , t1 = 8y^4 */
97 MP_CHECKOK(group->meth->field_sqr(py, t0, group->meth));
98 MP_CHECKOK(group->meth->field_add(t0, t0, t0, group->meth));
99 MP_CHECKOK(group->meth->field_sqr(t0, t1, group->meth));
100 MP_CHECKOK(group->meth->field_add(t1, t1, t1, group->meth));
101
102 /* S = 4 * px * py^2 = 2 * px * t0 */
103 MP_CHECKOK(group->meth->field_mul(px, t0, S, group->meth));
104 MP_CHECKOK(group->meth->field_add(S, S, S, group->meth));
105
106
107 /* rx = M^2 - 2S */
108 MP_CHECKOK(group->meth->field_sqr(M, rx, group->meth));
109 MP_CHECKOK(group->meth->field_sub(rx, S, rx, group->meth));
110 MP_CHECKOK(group->meth->field_sub(rx, S, rx, group->meth));
111
112 /* ry = M * (S - rx) - t1 */
113 MP_CHECKOK(group->meth->field_sub(S, rx, S, group->meth));
114 MP_CHECKOK(group->meth->field_mul(S, M, ry, group->meth));
115 MP_CHECKOK(group->meth->field_sub(ry, t1, ry, group->meth));
116
117 /* ra*z^4 = 2*t1*(apz4) */
118 MP_CHECKOK(group->meth->field_mul(paz4, t1, raz4, group->meth));
119 MP_CHECKOK(group->meth->field_add(raz4, raz4, raz4, group->meth));
120
121
122 CLEANUP:
123 return res;
124 }
125
126 /* Computes R = P + Q where R is (rx, ry, rz), P is (px, py, pz) and Q is
127 * (qx, qy, 1). Elliptic curve points P, Q, and R can all be identical.
128 * Uses mixed Modified_Jacobian-affine coordinates. Assumes input is
129 * already field-encoded using field_enc, and returns output that is still
130 * field-encoded. */
131 mp_err
ec_GFp_pt_add_jm_aff(const mp_int * px,const mp_int * py,const mp_int * pz,const mp_int * paz4,const mp_int * qx,const mp_int * qy,mp_int * rx,mp_int * ry,mp_int * rz,mp_int * raz4,mp_int scratch[],const ECGroup * group)132 ec_GFp_pt_add_jm_aff(const mp_int *px, const mp_int *py, const mp_int *pz,
133 const mp_int *paz4, const mp_int *qx,
134 const mp_int *qy, mp_int *rx, mp_int *ry, mp_int *rz,
135 mp_int *raz4, mp_int scratch[], const ECGroup *group)
136 {
137 mp_err res = MP_OKAY;
138 mp_int *A, *B, *C, *D, *C2, *C3;
139
140 A = &scratch[0];
141 B = &scratch[1];
142 C = &scratch[2];
143 D = &scratch[3];
144 C2 = &scratch[4];
145 C3 = &scratch[5];
146
147 #if MAX_SCRATCH < 6
148 #error "Scratch array defined too small "
149 #endif
150
151 /* If either P or Q is the point at infinity, then return the other
152 * point */
153 if (ec_GFp_pt_is_inf_jac(px, py, pz) == MP_YES) {
154 MP_CHECKOK(ec_GFp_pt_aff2jac(qx, qy, rx, ry, rz, group));
155 MP_CHECKOK(group->meth->field_sqr(rz, raz4, group->meth));
156 MP_CHECKOK(group->meth->field_sqr(raz4, raz4, group->meth));
157 MP_CHECKOK(group->meth->
158 field_mul(raz4, &group->curvea, raz4, group->meth));
159 goto CLEANUP;
160 }
161 if (ec_GFp_pt_is_inf_aff(qx, qy) == MP_YES) {
162 MP_CHECKOK(mp_copy(px, rx));
163 MP_CHECKOK(mp_copy(py, ry));
164 MP_CHECKOK(mp_copy(pz, rz));
165 MP_CHECKOK(mp_copy(paz4, raz4));
166 goto CLEANUP;
167 }
168
169 /* A = qx * pz^2, B = qy * pz^3 */
170 MP_CHECKOK(group->meth->field_sqr(pz, A, group->meth));
171 MP_CHECKOK(group->meth->field_mul(A, pz, B, group->meth));
172 MP_CHECKOK(group->meth->field_mul(A, qx, A, group->meth));
173 MP_CHECKOK(group->meth->field_mul(B, qy, B, group->meth));
174
175 /* C = A - px, D = B - py */
176 MP_CHECKOK(group->meth->field_sub(A, px, C, group->meth));
177 MP_CHECKOK(group->meth->field_sub(B, py, D, group->meth));
178
179 /* C2 = C^2, C3 = C^3 */
180 MP_CHECKOK(group->meth->field_sqr(C, C2, group->meth));
181 MP_CHECKOK(group->meth->field_mul(C, C2, C3, group->meth));
182
183 /* rz = pz * C */
184 MP_CHECKOK(group->meth->field_mul(pz, C, rz, group->meth));
185
186 /* C = px * C^2 */
187 MP_CHECKOK(group->meth->field_mul(px, C2, C, group->meth));
188 /* A = D^2 */
189 MP_CHECKOK(group->meth->field_sqr(D, A, group->meth));
190
191 /* rx = D^2 - (C^3 + 2 * (px * C^2)) */
192 MP_CHECKOK(group->meth->field_add(C, C, rx, group->meth));
193 MP_CHECKOK(group->meth->field_add(C3, rx, rx, group->meth));
194 MP_CHECKOK(group->meth->field_sub(A, rx, rx, group->meth));
195
196 /* C3 = py * C^3 */
197 MP_CHECKOK(group->meth->field_mul(py, C3, C3, group->meth));
198
199 /* ry = D * (px * C^2 - rx) - py * C^3 */
200 MP_CHECKOK(group->meth->field_sub(C, rx, ry, group->meth));
201 MP_CHECKOK(group->meth->field_mul(D, ry, ry, group->meth));
202 MP_CHECKOK(group->meth->field_sub(ry, C3, ry, group->meth));
203
204 /* raz4 = a * rz^4 */
205 MP_CHECKOK(group->meth->field_sqr(rz, raz4, group->meth));
206 MP_CHECKOK(group->meth->field_sqr(raz4, raz4, group->meth));
207 MP_CHECKOK(group->meth->
208 field_mul(raz4, &group->curvea, raz4, group->meth));
209 CLEANUP:
210 return res;
211 }
212
213 /* Computes R = nP where R is (rx, ry) and P is the base point. Elliptic
214 * curve points P and R can be identical. Uses mixed Modified-Jacobian
215 * co-ordinates for doubling and Chudnovsky Jacobian coordinates for
216 * additions. Assumes input is already field-encoded using field_enc, and
217 * returns output that is still field-encoded. Uses 5-bit window NAF
218 * method (algorithm 11) for scalar-point multiplication from Brown,
219 * Hankerson, Lopez, Menezes. Software Implementation of the NIST Elliptic
220 * Curves Over Prime Fields. */
221 mp_err
ec_GFp_pt_mul_jm_wNAF(const mp_int * n,const mp_int * px,const mp_int * py,mp_int * rx,mp_int * ry,const ECGroup * group)222 ec_GFp_pt_mul_jm_wNAF(const mp_int *n, const mp_int *px, const mp_int *py,
223 mp_int *rx, mp_int *ry, const ECGroup *group)
224 {
225 mp_err res = MP_OKAY;
226 mp_int precomp[16][2], rz, tpx, tpy;
227 mp_int raz4;
228 mp_int scratch[MAX_SCRATCH];
229 signed char *naf = NULL;
230 int i, orderBitSize;
231
232 MP_DIGITS(&rz) = 0;
233 MP_DIGITS(&raz4) = 0;
234 MP_DIGITS(&tpx) = 0;
235 MP_DIGITS(&tpy) = 0;
236 for (i = 0; i < 16; i++) {
237 MP_DIGITS(&precomp[i][0]) = 0;
238 MP_DIGITS(&precomp[i][1]) = 0;
239 }
240 for (i = 0; i < MAX_SCRATCH; i++) {
241 MP_DIGITS(&scratch[i]) = 0;
242 }
243
244 ARGCHK(group != NULL, MP_BADARG);
245 ARGCHK((n != NULL) && (px != NULL) && (py != NULL), MP_BADARG);
246
247 /* initialize precomputation table */
248 MP_CHECKOK(mp_init(&tpx, FLAG(n)));
249 MP_CHECKOK(mp_init(&tpy, FLAG(n)));;
250 MP_CHECKOK(mp_init(&rz, FLAG(n)));
251 MP_CHECKOK(mp_init(&raz4, FLAG(n)));
252
253 for (i = 0; i < 16; i++) {
254 MP_CHECKOK(mp_init(&precomp[i][0], FLAG(n)));
255 MP_CHECKOK(mp_init(&precomp[i][1], FLAG(n)));
256 }
257 for (i = 0; i < MAX_SCRATCH; i++) {
258 MP_CHECKOK(mp_init(&scratch[i], FLAG(n)));
259 }
260
261 /* Set out[8] = P */
262 MP_CHECKOK(mp_copy(px, &precomp[8][0]));
263 MP_CHECKOK(mp_copy(py, &precomp[8][1]));
264
265 /* Set (tpx, tpy) = 2P */
266 MP_CHECKOK(group->
267 point_dbl(&precomp[8][0], &precomp[8][1], &tpx, &tpy,
268 group));
269
270 /* Set 3P, 5P, ..., 15P */
271 for (i = 8; i < 15; i++) {
272 MP_CHECKOK(group->
273 point_add(&precomp[i][0], &precomp[i][1], &tpx, &tpy,
274 &precomp[i + 1][0], &precomp[i + 1][1],
275 group));
276 }
277
278 /* Set -15P, -13P, ..., -P */
279 for (i = 0; i < 8; i++) {
280 MP_CHECKOK(mp_copy(&precomp[15 - i][0], &precomp[i][0]));
281 MP_CHECKOK(group->meth->
282 field_neg(&precomp[15 - i][1], &precomp[i][1],
283 group->meth));
284 }
285
286 /* R = inf */
287 MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, &rz));
288
289 orderBitSize = mpl_significant_bits(&group->order);
290
291 /* Allocate memory for NAF */
292 #ifdef _KERNEL
293 naf = (signed char *) kmem_alloc((orderBitSize + 1), FLAG(n));
294 #else
295 naf = (signed char *) malloc(sizeof(signed char) * (orderBitSize + 1));
296 if (naf == NULL) {
297 res = MP_MEM;
298 goto CLEANUP;
299 }
300 #endif
301
302 /* Compute 5NAF */
303 ec_compute_wNAF(naf, orderBitSize, n, 5);
304
305 /* wNAF method */
306 for (i = orderBitSize; i >= 0; i--) {
307 /* R = 2R */
308 ec_GFp_pt_dbl_jm(rx, ry, &rz, &raz4, rx, ry, &rz,
309 &raz4, scratch, group);
310 if (naf[i] != 0) {
311 ec_GFp_pt_add_jm_aff(rx, ry, &rz, &raz4,
312 &precomp[(naf[i] + 15) / 2][0],
313 &precomp[(naf[i] + 15) / 2][1], rx, ry,
314 &rz, &raz4, scratch, group);
315 }
316 }
317
318 /* convert result S to affine coordinates */
319 MP_CHECKOK(ec_GFp_pt_jac2aff(rx, ry, &rz, rx, ry, group));
320
321 CLEANUP:
322 for (i = 0; i < MAX_SCRATCH; i++) {
323 mp_clear(&scratch[i]);
324 }
325 for (i = 0; i < 16; i++) {
326 mp_clear(&precomp[i][0]);
327 mp_clear(&precomp[i][1]);
328 }
329 mp_clear(&tpx);
330 mp_clear(&tpy);
331 mp_clear(&rz);
332 mp_clear(&raz4);
333 #ifdef _KERNEL
334 kmem_free(naf, (orderBitSize + 1));
335 #else
336 free(naf);
337 #endif
338 return res;
339 }
340