1/*
2 * Copyright (c) 2007, 2011, 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 *********************************************************************** */
39
40#include "ec2.h"
41#include "mp_gf2m.h"
42#include "mp_gf2m-priv.h"
43#include "mpi.h"
44#include "mpi-priv.h"
45#ifndef _KERNEL
46#include <stdlib.h>
47#endif
48
49/* Fast reduction for polynomials over a 233-bit curve. Assumes reduction
50 * polynomial with terms {233, 74, 0}. */
51mp_err
52ec_GF2m_233_mod(const mp_int *a, mp_int *r, const GFMethod *meth)
53{
54        mp_err res = MP_OKAY;
55        mp_digit *u, z;
56
57        if (a != r) {
58                MP_CHECKOK(mp_copy(a, r));
59        }
60#ifdef ECL_SIXTY_FOUR_BIT
61        if (MP_USED(r) < 8) {
62                MP_CHECKOK(s_mp_pad(r, 8));
63        }
64        u = MP_DIGITS(r);
65        MP_USED(r) = 8;
66
67        /* u[7] only has 18 significant bits */
68        z = u[7];
69        u[4] ^= (z << 33) ^ (z >> 41);
70        u[3] ^= (z << 23);
71        z = u[6];
72        u[4] ^= (z >> 31);
73        u[3] ^= (z << 33) ^ (z >> 41);
74        u[2] ^= (z << 23);
75        z = u[5];
76        u[3] ^= (z >> 31);
77        u[2] ^= (z << 33) ^ (z >> 41);
78        u[1] ^= (z << 23);
79        z = u[4];
80        u[2] ^= (z >> 31);
81        u[1] ^= (z << 33) ^ (z >> 41);
82        u[0] ^= (z << 23);
83        z = u[3] >> 41;                         /* z only has 23 significant bits */
84        u[1] ^= (z << 10);
85        u[0] ^= z;
86        /* clear bits above 233 */
87        u[7] = u[6] = u[5] = u[4] = 0;
88        u[3] ^= z << 41;
89#else
90        if (MP_USED(r) < 15) {
91                MP_CHECKOK(s_mp_pad(r, 15));
92        }
93        u = MP_DIGITS(r);
94        MP_USED(r) = 15;
95
96        /* u[14] only has 18 significant bits */
97        z = u[14];
98        u[9] ^= (z << 1);
99        u[7] ^= (z >> 9);
100        u[6] ^= (z << 23);
101        z = u[13];
102        u[9] ^= (z >> 31);
103        u[8] ^= (z << 1);
104        u[6] ^= (z >> 9);
105        u[5] ^= (z << 23);
106        z = u[12];
107        u[8] ^= (z >> 31);
108        u[7] ^= (z << 1);
109        u[5] ^= (z >> 9);
110        u[4] ^= (z << 23);
111        z = u[11];
112        u[7] ^= (z >> 31);
113        u[6] ^= (z << 1);
114        u[4] ^= (z >> 9);
115        u[3] ^= (z << 23);
116        z = u[10];
117        u[6] ^= (z >> 31);
118        u[5] ^= (z << 1);
119        u[3] ^= (z >> 9);
120        u[2] ^= (z << 23);
121        z = u[9];
122        u[5] ^= (z >> 31);
123        u[4] ^= (z << 1);
124        u[2] ^= (z >> 9);
125        u[1] ^= (z << 23);
126        z = u[8];
127        u[4] ^= (z >> 31);
128        u[3] ^= (z << 1);
129        u[1] ^= (z >> 9);
130        u[0] ^= (z << 23);
131        z = u[7] >> 9;                          /* z only has 23 significant bits */
132        u[3] ^= (z >> 22);
133        u[2] ^= (z << 10);
134        u[0] ^= z;
135        /* clear bits above 233 */
136        u[14] = u[13] = u[12] = u[11] = u[10] = u[9] = u[8] = 0;
137        u[7] ^= z << 9;
138#endif
139        s_mp_clamp(r);
140
141  CLEANUP:
142        return res;
143}
144
145/* Fast squaring for polynomials over a 233-bit curve. Assumes reduction
146 * polynomial with terms {233, 74, 0}. */
147mp_err
148ec_GF2m_233_sqr(const mp_int *a, mp_int *r, const GFMethod *meth)
149{
150        mp_err res = MP_OKAY;
151        mp_digit *u, *v;
152
153        v = MP_DIGITS(a);
154
155#ifdef ECL_SIXTY_FOUR_BIT
156        if (MP_USED(a) < 4) {
157                return mp_bsqrmod(a, meth->irr_arr, r);
158        }
159        if (MP_USED(r) < 8) {
160                MP_CHECKOK(s_mp_pad(r, 8));
161        }
162        MP_USED(r) = 8;
163#else
164        if (MP_USED(a) < 8) {
165                return mp_bsqrmod(a, meth->irr_arr, r);
166        }
167        if (MP_USED(r) < 15) {
168                MP_CHECKOK(s_mp_pad(r, 15));
169        }
170        MP_USED(r) = 15;
171#endif
172        u = MP_DIGITS(r);
173
174#ifdef ECL_THIRTY_TWO_BIT
175        u[14] = gf2m_SQR0(v[7]);
176        u[13] = gf2m_SQR1(v[6]);
177        u[12] = gf2m_SQR0(v[6]);
178        u[11] = gf2m_SQR1(v[5]);
179        u[10] = gf2m_SQR0(v[5]);
180        u[9] = gf2m_SQR1(v[4]);
181        u[8] = gf2m_SQR0(v[4]);
182#endif
183        u[7] = gf2m_SQR1(v[3]);
184        u[6] = gf2m_SQR0(v[3]);
185        u[5] = gf2m_SQR1(v[2]);
186        u[4] = gf2m_SQR0(v[2]);
187        u[3] = gf2m_SQR1(v[1]);
188        u[2] = gf2m_SQR0(v[1]);
189        u[1] = gf2m_SQR1(v[0]);
190        u[0] = gf2m_SQR0(v[0]);
191        return ec_GF2m_233_mod(r, r, meth);
192
193  CLEANUP:
194        return res;
195}
196
197/* Fast multiplication for polynomials over a 233-bit curve. Assumes
198 * reduction polynomial with terms {233, 74, 0}. */
199mp_err
200ec_GF2m_233_mul(const mp_int *a, const mp_int *b, mp_int *r,
201                                const GFMethod *meth)
202{
203        mp_err res = MP_OKAY;
204        mp_digit a3 = 0, a2 = 0, a1 = 0, a0, b3 = 0, b2 = 0, b1 = 0, b0;
205
206#ifdef ECL_THIRTY_TWO_BIT
207        mp_digit a7 = 0, a6 = 0, a5 = 0, a4 = 0, b7 = 0, b6 = 0, b5 = 0, b4 =
208                0;
209        mp_digit rm[8];
210#endif
211
212        if (a == b) {
213                return ec_GF2m_233_sqr(a, r, meth);
214        } else {
215                switch (MP_USED(a)) {
216#ifdef ECL_THIRTY_TWO_BIT
217                case 8:
218                        a7 = MP_DIGIT(a, 7);
219                case 7:
220                        a6 = MP_DIGIT(a, 6);
221                case 6:
222                        a5 = MP_DIGIT(a, 5);
223                case 5:
224                        a4 = MP_DIGIT(a, 4);
225#endif
226                case 4:
227                        a3 = MP_DIGIT(a, 3);
228                case 3:
229                        a2 = MP_DIGIT(a, 2);
230                case 2:
231                        a1 = MP_DIGIT(a, 1);
232                default:
233                        a0 = MP_DIGIT(a, 0);
234                }
235                switch (MP_USED(b)) {
236#ifdef ECL_THIRTY_TWO_BIT
237                case 8:
238                        b7 = MP_DIGIT(b, 7);
239                case 7:
240                        b6 = MP_DIGIT(b, 6);
241                case 6:
242                        b5 = MP_DIGIT(b, 5);
243                case 5:
244                        b4 = MP_DIGIT(b, 4);
245#endif
246                case 4:
247                        b3 = MP_DIGIT(b, 3);
248                case 3:
249                        b2 = MP_DIGIT(b, 2);
250                case 2:
251                        b1 = MP_DIGIT(b, 1);
252                default:
253                        b0 = MP_DIGIT(b, 0);
254                }
255#ifdef ECL_SIXTY_FOUR_BIT
256                MP_CHECKOK(s_mp_pad(r, 8));
257                s_bmul_4x4(MP_DIGITS(r), a3, a2, a1, a0, b3, b2, b1, b0);
258                MP_USED(r) = 8;
259                s_mp_clamp(r);
260#else
261                MP_CHECKOK(s_mp_pad(r, 16));
262                s_bmul_4x4(MP_DIGITS(r) + 8, a7, a6, a5, a4, b7, b6, b5, b4);
263                s_bmul_4x4(MP_DIGITS(r), a3, a2, a1, a0, b3, b2, b1, b0);
264                s_bmul_4x4(rm, a7 ^ a3, a6 ^ a2, a5 ^ a1, a4 ^ a0, b7 ^ b3,
265                                   b6 ^ b2, b5 ^ b1, b4 ^ b0);
266                rm[7] ^= MP_DIGIT(r, 7) ^ MP_DIGIT(r, 15);
267                rm[6] ^= MP_DIGIT(r, 6) ^ MP_DIGIT(r, 14);
268                rm[5] ^= MP_DIGIT(r, 5) ^ MP_DIGIT(r, 13);
269                rm[4] ^= MP_DIGIT(r, 4) ^ MP_DIGIT(r, 12);
270                rm[3] ^= MP_DIGIT(r, 3) ^ MP_DIGIT(r, 11);
271                rm[2] ^= MP_DIGIT(r, 2) ^ MP_DIGIT(r, 10);
272                rm[1] ^= MP_DIGIT(r, 1) ^ MP_DIGIT(r, 9);
273                rm[0] ^= MP_DIGIT(r, 0) ^ MP_DIGIT(r, 8);
274                MP_DIGIT(r, 11) ^= rm[7];
275                MP_DIGIT(r, 10) ^= rm[6];
276                MP_DIGIT(r, 9) ^= rm[5];
277                MP_DIGIT(r, 8) ^= rm[4];
278                MP_DIGIT(r, 7) ^= rm[3];
279                MP_DIGIT(r, 6) ^= rm[2];
280                MP_DIGIT(r, 5) ^= rm[1];
281                MP_DIGIT(r, 4) ^= rm[0];
282                MP_USED(r) = 16;
283                s_mp_clamp(r);
284#endif
285                return ec_GF2m_233_mod(r, r, meth);
286        }
287
288  CLEANUP:
289        return res;
290}
291
292/* Wire in fast field arithmetic for 233-bit curves. */
293mp_err
294ec_group_set_gf2m233(ECGroup *group, ECCurveName name)
295{
296        group->meth->field_mod = &ec_GF2m_233_mod;
297        group->meth->field_mul = &ec_GF2m_233_mul;
298        group->meth->field_sqr = &ec_GF2m_233_sqr;
299        return MP_OKAY;
300}
301