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 #pragma ident "%Z%%M% %I% %E% SMI"
46
47 #include "ecp.h"
48 #include "ecl-priv.h"
49 #include "mplogic.h"
50 #ifndef _KERNEL
51 #include <stdlib.h>
52 #endif
53
54 #define MAX_SCRATCH 6
55
56 /* Computes R = 2P. Elliptic curve points P and R can be identical. Uses
57 * Modified Jacobian coordinates.
58 *
59 * Assumes input is already field-encoded using field_enc, and returns
60 * output that is still field-encoded.
61 *
62 */
63 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)64 ec_GFp_pt_dbl_jm(const mp_int *px, const mp_int *py, const mp_int *pz,
65 const mp_int *paz4, mp_int *rx, mp_int *ry, mp_int *rz,
66 mp_int *raz4, mp_int scratch[], const ECGroup *group)
67 {
68 mp_err res = MP_OKAY;
69 mp_int *t0, *t1, *M, *S;
70
71 t0 = &scratch[0];
72 t1 = &scratch[1];
73 M = &scratch[2];
74 S = &scratch[3];
75
76 #if MAX_SCRATCH < 4
77 #error "Scratch array defined too small "
78 #endif
79
80 /* Check for point at infinity */
81 if (ec_GFp_pt_is_inf_jac(px, py, pz) == MP_YES) {
82 /* Set r = pt at infinity by setting rz = 0 */
83
84 MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, rz));
85 goto CLEANUP;
86 }
87
88 /* M = 3 (px^2) + a*(pz^4) */
89 MP_CHECKOK(group->meth->field_sqr(px, t0, group->meth));
90 MP_CHECKOK(group->meth->field_add(t0, t0, M, group->meth));
91 MP_CHECKOK(group->meth->field_add(t0, M, t0, group->meth));
92 MP_CHECKOK(group->meth->field_add(t0, paz4, M, group->meth));
93
94 /* rz = 2 * py * pz */
95 MP_CHECKOK(group->meth->field_mul(py, pz, S, group->meth));
96 MP_CHECKOK(group->meth->field_add(S, S, rz, group->meth));
97
98 /* t0 = 2y^2 , t1 = 8y^4 */
99 MP_CHECKOK(group->meth->field_sqr(py, t0, group->meth));
100 MP_CHECKOK(group->meth->field_add(t0, t0, t0, group->meth));
101 MP_CHECKOK(group->meth->field_sqr(t0, t1, group->meth));
102 MP_CHECKOK(group->meth->field_add(t1, t1, t1, group->meth));
103
104 /* S = 4 * px * py^2 = 2 * px * t0 */
105 MP_CHECKOK(group->meth->field_mul(px, t0, S, group->meth));
106 MP_CHECKOK(group->meth->field_add(S, S, S, group->meth));
107
108
109 /* rx = M^2 - 2S */
110 MP_CHECKOK(group->meth->field_sqr(M, rx, group->meth));
111 MP_CHECKOK(group->meth->field_sub(rx, S, rx, group->meth));
112 MP_CHECKOK(group->meth->field_sub(rx, S, rx, group->meth));
113
114 /* ry = M * (S - rx) - t1 */
115 MP_CHECKOK(group->meth->field_sub(S, rx, S, group->meth));
116 MP_CHECKOK(group->meth->field_mul(S, M, ry, group->meth));
117 MP_CHECKOK(group->meth->field_sub(ry, t1, ry, group->meth));
118
119 /* ra*z^4 = 2*t1*(apz4) */
120 MP_CHECKOK(group->meth->field_mul(paz4, t1, raz4, group->meth));
121 MP_CHECKOK(group->meth->field_add(raz4, raz4, raz4, group->meth));
122
123
124 CLEANUP:
125 return res;
126 }
127
128 /* Computes R = P + Q where R is (rx, ry, rz), P is (px, py, pz) and Q is
129 * (qx, qy, 1). Elliptic curve points P, Q, and R can all be identical.
130 * Uses mixed Modified_Jacobian-affine coordinates. Assumes input is
131 * already field-encoded using field_enc, and returns output that is still
132 * field-encoded. */
133 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)134 ec_GFp_pt_add_jm_aff(const mp_int *px, const mp_int *py, const mp_int *pz,
135 const mp_int *paz4, const mp_int *qx,
136 const mp_int *qy, mp_int *rx, mp_int *ry, mp_int *rz,
137 mp_int *raz4, mp_int scratch[], const ECGroup *group)
138 {
139 mp_err res = MP_OKAY;
140 mp_int *A, *B, *C, *D, *C2, *C3;
141
142 A = &scratch[0];
143 B = &scratch[1];
144 C = &scratch[2];
145 D = &scratch[3];
146 C2 = &scratch[4];
147 C3 = &scratch[5];
148
149 #if MAX_SCRATCH < 6
150 #error "Scratch array defined too small "
151 #endif
152
153 /* If either P or Q is the point at infinity, then return the other
154 * point */
155 if (ec_GFp_pt_is_inf_jac(px, py, pz) == MP_YES) {
156 MP_CHECKOK(ec_GFp_pt_aff2jac(qx, qy, rx, ry, rz, group));
157 MP_CHECKOK(group->meth->field_sqr(rz, raz4, group->meth));
158 MP_CHECKOK(group->meth->field_sqr(raz4, raz4, group->meth));
159 MP_CHECKOK(group->meth->
160 field_mul(raz4, &group->curvea, raz4, group->meth));
161 goto CLEANUP;
162 }
163 if (ec_GFp_pt_is_inf_aff(qx, qy) == MP_YES) {
164 MP_CHECKOK(mp_copy(px, rx));
165 MP_CHECKOK(mp_copy(py, ry));
166 MP_CHECKOK(mp_copy(pz, rz));
167 MP_CHECKOK(mp_copy(paz4, raz4));
168 goto CLEANUP;
169 }
170
171 /* A = qx * pz^2, B = qy * pz^3 */
172 MP_CHECKOK(group->meth->field_sqr(pz, A, group->meth));
173 MP_CHECKOK(group->meth->field_mul(A, pz, B, group->meth));
174 MP_CHECKOK(group->meth->field_mul(A, qx, A, group->meth));
175 MP_CHECKOK(group->meth->field_mul(B, qy, B, group->meth));
176
177 /* C = A - px, D = B - py */
178 MP_CHECKOK(group->meth->field_sub(A, px, C, group->meth));
179 MP_CHECKOK(group->meth->field_sub(B, py, D, group->meth));
180
181 /* C2 = C^2, C3 = C^3 */
182 MP_CHECKOK(group->meth->field_sqr(C, C2, group->meth));
183 MP_CHECKOK(group->meth->field_mul(C, C2, C3, group->meth));
184
185 /* rz = pz * C */
186 MP_CHECKOK(group->meth->field_mul(pz, C, rz, group->meth));
187
188 /* C = px * C^2 */
189 MP_CHECKOK(group->meth->field_mul(px, C2, C, group->meth));
190 /* A = D^2 */
191 MP_CHECKOK(group->meth->field_sqr(D, A, group->meth));
192
193 /* rx = D^2 - (C^3 + 2 * (px * C^2)) */
194 MP_CHECKOK(group->meth->field_add(C, C, rx, group->meth));
195 MP_CHECKOK(group->meth->field_add(C3, rx, rx, group->meth));
196 MP_CHECKOK(group->meth->field_sub(A, rx, rx, group->meth));
197
198 /* C3 = py * C^3 */
199 MP_CHECKOK(group->meth->field_mul(py, C3, C3, group->meth));
200
201 /* ry = D * (px * C^2 - rx) - py * C^3 */
202 MP_CHECKOK(group->meth->field_sub(C, rx, ry, group->meth));
203 MP_CHECKOK(group->meth->field_mul(D, ry, ry, group->meth));
204 MP_CHECKOK(group->meth->field_sub(ry, C3, ry, group->meth));
205
206 /* raz4 = a * rz^4 */
207 MP_CHECKOK(group->meth->field_sqr(rz, raz4, group->meth));
208 MP_CHECKOK(group->meth->field_sqr(raz4, raz4, group->meth));
209 MP_CHECKOK(group->meth->
210 field_mul(raz4, &group->curvea, raz4, group->meth));
211 CLEANUP:
212 return res;
213 }
214
215 /* Computes R = nP where R is (rx, ry) and P is the base point. Elliptic
216 * curve points P and R can be identical. Uses mixed Modified-Jacobian
217 * co-ordinates for doubling and Chudnovsky Jacobian coordinates for
218 * additions. Assumes input is already field-encoded using field_enc, and
219 * returns output that is still field-encoded. Uses 5-bit window NAF
220 * method (algorithm 11) for scalar-point multiplication from Brown,
221 * Hankerson, Lopez, Menezes. Software Implementation of the NIST Elliptic
222 * Curves Over Prime Fields. */
223 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)224 ec_GFp_pt_mul_jm_wNAF(const mp_int *n, const mp_int *px, const mp_int *py,
225 mp_int *rx, mp_int *ry, const ECGroup *group)
226 {
227 mp_err res = MP_OKAY;
228 mp_int precomp[16][2], rz, tpx, tpy;
229 mp_int raz4;
230 mp_int scratch[MAX_SCRATCH];
231 signed char *naf = NULL;
232 int i, orderBitSize;
233
234 MP_DIGITS(&rz) = 0;
235 MP_DIGITS(&raz4) = 0;
236 MP_DIGITS(&tpx) = 0;
237 MP_DIGITS(&tpy) = 0;
238 for (i = 0; i < 16; i++) {
239 MP_DIGITS(&precomp[i][0]) = 0;
240 MP_DIGITS(&precomp[i][1]) = 0;
241 }
242 for (i = 0; i < MAX_SCRATCH; i++) {
243 MP_DIGITS(&scratch[i]) = 0;
244 }
245
246 ARGCHK(group != NULL, MP_BADARG);
247 ARGCHK((n != NULL) && (px != NULL) && (py != NULL), MP_BADARG);
248
249 /* initialize precomputation table */
250 MP_CHECKOK(mp_init(&tpx, FLAG(n)));
251 MP_CHECKOK(mp_init(&tpy, FLAG(n)));;
252 MP_CHECKOK(mp_init(&rz, FLAG(n)));
253 MP_CHECKOK(mp_init(&raz4, FLAG(n)));
254
255 for (i = 0; i < 16; i++) {
256 MP_CHECKOK(mp_init(&precomp[i][0], FLAG(n)));
257 MP_CHECKOK(mp_init(&precomp[i][1], FLAG(n)));
258 }
259 for (i = 0; i < MAX_SCRATCH; i++) {
260 MP_CHECKOK(mp_init(&scratch[i], FLAG(n)));
261 }
262
263 /* Set out[8] = P */
264 MP_CHECKOK(mp_copy(px, &precomp[8][0]));
265 MP_CHECKOK(mp_copy(py, &precomp[8][1]));
266
267 /* Set (tpx, tpy) = 2P */
268 MP_CHECKOK(group->
269 point_dbl(&precomp[8][0], &precomp[8][1], &tpx, &tpy,
270 group));
271
272 /* Set 3P, 5P, ..., 15P */
273 for (i = 8; i < 15; i++) {
274 MP_CHECKOK(group->
275 point_add(&precomp[i][0], &precomp[i][1], &tpx, &tpy,
276 &precomp[i + 1][0], &precomp[i + 1][1],
277 group));
278 }
279
280 /* Set -15P, -13P, ..., -P */
281 for (i = 0; i < 8; i++) {
282 MP_CHECKOK(mp_copy(&precomp[15 - i][0], &precomp[i][0]));
283 MP_CHECKOK(group->meth->
284 field_neg(&precomp[15 - i][1], &precomp[i][1],
285 group->meth));
286 }
287
288 /* R = inf */
289 MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, &rz));
290
291 orderBitSize = mpl_significant_bits(&group->order);
292
293 /* Allocate memory for NAF */
294 #ifdef _KERNEL
295 naf = (signed char *) kmem_alloc((orderBitSize + 1), FLAG(n));
296 #else
297 naf = (signed char *) malloc(sizeof(signed char) * (orderBitSize + 1));
298 if (naf == NULL) {
299 res = MP_MEM;
300 goto CLEANUP;
301 }
302 #endif
303
304 /* Compute 5NAF */
305 ec_compute_wNAF(naf, orderBitSize, n, 5);
306
307 /* wNAF method */
308 for (i = orderBitSize; i >= 0; i--) {
309 /* R = 2R */
310 ec_GFp_pt_dbl_jm(rx, ry, &rz, &raz4, rx, ry, &rz,
311 &raz4, scratch, group);
312 if (naf[i] != 0) {
313 ec_GFp_pt_add_jm_aff(rx, ry, &rz, &raz4,
314 &precomp[(naf[i] + 15) / 2][0],
315 &precomp[(naf[i] + 15) / 2][1], rx, ry,
316 &rz, &raz4, scratch, group);
317 }
318 }
319
320 /* convert result S to affine coordinates */
321 MP_CHECKOK(ec_GFp_pt_jac2aff(rx, ry, &rz, rx, ry, group));
322
323 CLEANUP:
324 for (i = 0; i < MAX_SCRATCH; i++) {
325 mp_clear(&scratch[i]);
326 }
327 for (i = 0; i < 16; i++) {
328 mp_clear(&precomp[i][0]);
329 mp_clear(&precomp[i][1]);
330 }
331 mp_clear(&tpx);
332 mp_clear(&tpy);
333 mp_clear(&rz);
334 mp_clear(&raz4);
335 #ifdef _KERNEL
336 kmem_free(naf, (orderBitSize + 1));
337 #else
338 free(naf);
339 #endif
340 return res;
341 }
342