1/*
2 * Copyright (c) 2007, 2017, Oracle and/or its affiliates. All rights reserved.
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
7 * License as published by the Free Software Foundation; either
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 *
19 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
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 for binary polynomial field curves.
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
31 * the Initial Developer. All Rights Reserved.
32 *
33 * Contributor(s):
34 *   Sheueling Chang-Shantz <sheueling.chang@sun.com>,
35 *   Stephen Fung <fungstep@hotmail.com>, and
36 *   Douglas Stebila <douglas@stebila.ca>, Sun Microsystems Laboratories.
37 *
38 *  Last Modified Date from the Original Code: May 2017
39 *********************************************************************** */
40
41#include "ec2.h"
42#include "mplogic.h"
43#include "mp_gf2m.h"
44#ifndef _KERNEL
45#include <stdlib.h>
46#endif
47
48/* Compute the x-coordinate x/z for the point 2*(x/z) in Montgomery
49 * projective coordinates. Uses algorithm Mdouble in appendix of Lopez, J.
50 * and Dahab, R.  "Fast multiplication on elliptic curves over GF(2^m)
51 * without precomputation". modified to not require precomputation of
52 * c=b^{2^{m-1}}. */
53static mp_err
54gf2m_Mdouble(mp_int *x, mp_int *z, const ECGroup *group, int kmflag)
55{
56        mp_err res = MP_OKAY;
57        mp_int t1;
58
59        MP_DIGITS(&t1) = 0;
60        MP_CHECKOK(mp_init(&t1, kmflag));
61
62        MP_CHECKOK(group->meth->field_sqr(x, x, group->meth));
63        MP_CHECKOK(group->meth->field_sqr(z, &t1, group->meth));
64        MP_CHECKOK(group->meth->field_mul(x, &t1, z, group->meth));
65        MP_CHECKOK(group->meth->field_sqr(x, x, group->meth));
66        MP_CHECKOK(group->meth->field_sqr(&t1, &t1, group->meth));
67        MP_CHECKOK(group->meth->
68                           field_mul(&group->curveb, &t1, &t1, group->meth));
69        MP_CHECKOK(group->meth->field_add(x, &t1, x, group->meth));
70
71  CLEANUP:
72        mp_clear(&t1);
73        return res;
74}
75
76/* Compute the x-coordinate x1/z1 for the point (x1/z1)+(x2/x2) in
77 * Montgomery projective coordinates. Uses algorithm Madd in appendix of
78 * Lopex, J. and Dahab, R.  "Fast multiplication on elliptic curves over
79 * GF(2^m) without precomputation". */
80static mp_err
81gf2m_Madd(const mp_int *x, mp_int *x1, mp_int *z1, mp_int *x2, mp_int *z2,
82                  const ECGroup *group, int kmflag)
83{
84        mp_err res = MP_OKAY;
85        mp_int t1, t2;
86
87        MP_DIGITS(&t1) = 0;
88        MP_DIGITS(&t2) = 0;
89        MP_CHECKOK(mp_init(&t1, kmflag));
90        MP_CHECKOK(mp_init(&t2, kmflag));
91
92        MP_CHECKOK(mp_copy(x, &t1));
93        MP_CHECKOK(group->meth->field_mul(x1, z2, x1, group->meth));
94        MP_CHECKOK(group->meth->field_mul(z1, x2, z1, group->meth));
95        MP_CHECKOK(group->meth->field_mul(x1, z1, &t2, group->meth));
96        MP_CHECKOK(group->meth->field_add(z1, x1, z1, group->meth));
97        MP_CHECKOK(group->meth->field_sqr(z1, z1, group->meth));
98        MP_CHECKOK(group->meth->field_mul(z1, &t1, x1, group->meth));
99        MP_CHECKOK(group->meth->field_add(x1, &t2, x1, group->meth));
100
101  CLEANUP:
102        mp_clear(&t1);
103        mp_clear(&t2);
104        return res;
105}
106
107/* Compute the x, y affine coordinates from the point (x1, z1) (x2, z2)
108 * using Montgomery point multiplication algorithm Mxy() in appendix of
109 * Lopex, J. and Dahab, R.  "Fast multiplication on elliptic curves over
110 * GF(2^m) without precomputation". Returns: 0 on error 1 if return value
111 * should be the point at infinity 2 otherwise */
112static int
113gf2m_Mxy(const mp_int *x, const mp_int *y, mp_int *x1, mp_int *z1,
114                 mp_int *x2, mp_int *z2, const ECGroup *group)
115{
116        mp_err res = MP_OKAY;
117        int ret = 0;
118        mp_int t3, t4, t5;
119
120        MP_DIGITS(&t3) = 0;
121        MP_DIGITS(&t4) = 0;
122        MP_DIGITS(&t5) = 0;
123        MP_CHECKOK(mp_init(&t3, FLAG(x2)));
124        MP_CHECKOK(mp_init(&t4, FLAG(x2)));
125        MP_CHECKOK(mp_init(&t5, FLAG(x2)));
126
127        if (mp_cmp_z(z1) == 0) {
128                mp_zero(x2);
129                mp_zero(z2);
130                ret = 1;
131                goto CLEANUP;
132        }
133
134        if (mp_cmp_z(z2) == 0) {
135                MP_CHECKOK(mp_copy(x, x2));
136                MP_CHECKOK(group->meth->field_add(x, y, z2, group->meth));
137                ret = 2;
138                goto CLEANUP;
139        }
140
141        MP_CHECKOK(mp_set_int(&t5, 1));
142        if (group->meth->field_enc) {
143                MP_CHECKOK(group->meth->field_enc(&t5, &t5, group->meth));
144        }
145
146        MP_CHECKOK(group->meth->field_mul(z1, z2, &t3, group->meth));
147
148        MP_CHECKOK(group->meth->field_mul(z1, x, z1, group->meth));
149        MP_CHECKOK(group->meth->field_add(z1, x1, z1, group->meth));
150        MP_CHECKOK(group->meth->field_mul(z2, x, z2, group->meth));
151        MP_CHECKOK(group->meth->field_mul(z2, x1, x1, group->meth));
152        MP_CHECKOK(group->meth->field_add(z2, x2, z2, group->meth));
153
154        MP_CHECKOK(group->meth->field_mul(z2, z1, z2, group->meth));
155        MP_CHECKOK(group->meth->field_sqr(x, &t4, group->meth));
156        MP_CHECKOK(group->meth->field_add(&t4, y, &t4, group->meth));
157        MP_CHECKOK(group->meth->field_mul(&t4, &t3, &t4, group->meth));
158        MP_CHECKOK(group->meth->field_add(&t4, z2, &t4, group->meth));
159
160        MP_CHECKOK(group->meth->field_mul(&t3, x, &t3, group->meth));
161        MP_CHECKOK(group->meth->field_div(&t5, &t3, &t3, group->meth));
162        MP_CHECKOK(group->meth->field_mul(&t3, &t4, &t4, group->meth));
163        MP_CHECKOK(group->meth->field_mul(x1, &t3, x2, group->meth));
164        MP_CHECKOK(group->meth->field_add(x2, x, z2, group->meth));
165
166        MP_CHECKOK(group->meth->field_mul(z2, &t4, z2, group->meth));
167        MP_CHECKOK(group->meth->field_add(z2, y, z2, group->meth));
168
169        ret = 2;
170
171  CLEANUP:
172        mp_clear(&t3);
173        mp_clear(&t4);
174        mp_clear(&t5);
175        if (res == MP_OKAY) {
176                return ret;
177        } else {
178                return 0;
179        }
180}
181
182/* Computes R = nP based on algorithm 2P of Lopex, J. and Dahab, R.  "Fast
183 * multiplication on elliptic curves over GF(2^m) without
184 * precomputation". Elliptic curve points P and R can be identical. Uses
185 * Montgomery projective coordinates. The timing parameter is ignored
186 * because this algorithm resists timing attacks by default. */
187mp_err
188ec_GF2m_pt_mul_mont(const mp_int *n, const mp_int *px, const mp_int *py,
189                                        mp_int *rx, mp_int *ry, const ECGroup *group,
190                                        int timing)
191{
192        mp_err res = MP_OKAY;
193        mp_int x1, x2, z1, z2;
194        int i, j;
195        mp_digit top_bit, mask;
196
197        MP_DIGITS(&x1) = 0;
198        MP_DIGITS(&x2) = 0;
199        MP_DIGITS(&z1) = 0;
200        MP_DIGITS(&z2) = 0;
201        MP_CHECKOK(mp_init(&x1, FLAG(n)));
202        MP_CHECKOK(mp_init(&x2, FLAG(n)));
203        MP_CHECKOK(mp_init(&z1, FLAG(n)));
204        MP_CHECKOK(mp_init(&z2, FLAG(n)));
205
206        /* if result should be point at infinity */
207        if ((mp_cmp_z(n) == 0) || (ec_GF2m_pt_is_inf_aff(px, py) == MP_YES)) {
208                MP_CHECKOK(ec_GF2m_pt_set_inf_aff(rx, ry));
209                goto CLEANUP;
210        }
211
212        MP_CHECKOK(mp_copy(px, &x1));   /* x1 = px */
213        MP_CHECKOK(mp_set_int(&z1, 1)); /* z1 = 1 */
214        MP_CHECKOK(group->meth->field_sqr(&x1, &z2, group->meth));      /* z2 =
215                                                                                                                                 * x1^2 =
216                                                                                                                                 * px^2 */
217        MP_CHECKOK(group->meth->field_sqr(&z2, &x2, group->meth));
218        MP_CHECKOK(group->meth->field_add(&x2, &group->curveb, &x2, group->meth));      /* x2
219                                                                                                                                                                 * =
220                                                                                                                                                                 * px^4
221                                                                                                                                                                 * +
222                                                                                                                                                                 * b
223                                                                                                                                                                 */
224
225        /* find top-most bit and go one past it */
226        i = MP_USED(n) - 1;
227        j = MP_DIGIT_BIT - 1;
228        top_bit = 1;
229        top_bit <<= MP_DIGIT_BIT - 1;
230        mask = top_bit;
231        while (!(MP_DIGITS(n)[i] & mask)) {
232                mask >>= 1;
233                j--;
234        }
235        mask >>= 1;
236        j--;
237
238        /* if top most bit was at word break, go to next word */
239        if (!mask) {
240                i--;
241                j = MP_DIGIT_BIT - 1;
242                mask = top_bit;
243        }
244
245        for (; i >= 0; i--) {
246                for (; j >= 0; j--) {
247                        if (MP_DIGITS(n)[i] & mask) {
248                                MP_CHECKOK(gf2m_Madd(px, &x1, &z1, &x2, &z2, group, FLAG(n)));
249                                MP_CHECKOK(gf2m_Mdouble(&x2, &z2, group, FLAG(n)));
250                        } else {
251                                MP_CHECKOK(gf2m_Madd(px, &x2, &z2, &x1, &z1, group, FLAG(n)));
252                                MP_CHECKOK(gf2m_Mdouble(&x1, &z1, group, FLAG(n)));
253                        }
254                        mask >>= 1;
255                }
256                j = MP_DIGIT_BIT - 1;
257                mask = top_bit;
258        }
259
260        /* convert out of "projective" coordinates */
261        i = gf2m_Mxy(px, py, &x1, &z1, &x2, &z2, group);
262        if (i == 0) {
263                res = MP_BADARG;
264                goto CLEANUP;
265        } else if (i == 1) {
266                MP_CHECKOK(ec_GF2m_pt_set_inf_aff(rx, ry));
267        } else {
268                MP_CHECKOK(mp_copy(&x2, rx));
269                MP_CHECKOK(mp_copy(&z2, ry));
270        }
271
272  CLEANUP:
273        mp_clear(&x1);
274        mp_clear(&x2);
275        mp_clear(&z1);
276        mp_clear(&z2);
277        return res;
278}
279