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