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 193-bit curve. Assumes reduction
50 * polynomial with terms {193, 15, 0}. */
51mp_err
52ec_GF2m_193_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) < 7) {
62 MP_CHECKOK(s_mp_pad(r, 7));
63 }
64 u = MP_DIGITS(r);
65 MP_USED(r) = 7;
66
67 /* u[6] only has 2 significant bits */
68 z = u[6];
69 u[3] ^= (z << 14) ^ (z >> 1);
70 u[2] ^= (z << 63);
71 z = u[5];
72 u[3] ^= (z >> 50);
73 u[2] ^= (z << 14) ^ (z >> 1);
74 u[1] ^= (z << 63);
75 z = u[4];
76 u[2] ^= (z >> 50);
77 u[1] ^= (z << 14) ^ (z >> 1);
78 u[0] ^= (z << 63);
79 z = u[3] >> 1; /* z only has 63 significant bits */
80 u[1] ^= (z >> 49);
81 u[0] ^= (z << 15) ^ z;
82 /* clear bits above 193 */
83 u[6] = u[5] = u[4] = 0;
84 u[3] ^= z << 1;
85#else
86 if (MP_USED(r) < 13) {
87 MP_CHECKOK(s_mp_pad(r, 13));
88 }
89 u = MP_DIGITS(r);
90 MP_USED(r) = 13;
91
92 /* u[12] only has 2 significant bits */
93 z = u[12];
94 u[6] ^= (z << 14) ^ (z >> 1);
95 u[5] ^= (z << 31);
96 z = u[11];
97 u[6] ^= (z >> 18);
98 u[5] ^= (z << 14) ^ (z >> 1);
99 u[4] ^= (z << 31);
100 z = u[10];
101 u[5] ^= (z >> 18);
102 u[4] ^= (z << 14) ^ (z >> 1);
103 u[3] ^= (z << 31);
104 z = u[9];
105 u[4] ^= (z >> 18);
106 u[3] ^= (z << 14) ^ (z >> 1);
107 u[2] ^= (z << 31);
108 z = u[8];
109 u[3] ^= (z >> 18);
110 u[2] ^= (z << 14) ^ (z >> 1);
111 u[1] ^= (z << 31);
112 z = u[7];
113 u[2] ^= (z >> 18);
114 u[1] ^= (z << 14) ^ (z >> 1);
115 u[0] ^= (z << 31);
116 z = u[6] >> 1; /* z only has 31 significant bits */
117 u[1] ^= (z >> 17);
118 u[0] ^= (z << 15) ^ z;
119 /* clear bits above 193 */
120 u[12] = u[11] = u[10] = u[9] = u[8] = u[7] = 0;
121 u[6] ^= z << 1;
122#endif
123 s_mp_clamp(r);
124
125 CLEANUP:
126 return res;
127}
128
129/* Fast squaring for polynomials over a 193-bit curve. Assumes reduction
130 * polynomial with terms {193, 15, 0}. */
131mp_err
132ec_GF2m_193_sqr(const mp_int *a, mp_int *r, const GFMethod *meth)
133{
134 mp_err res = MP_OKAY;
135 mp_digit *u, *v;
136
137 v = MP_DIGITS(a);
138
139#ifdef ECL_SIXTY_FOUR_BIT
140 if (MP_USED(a) < 4) {
141 return mp_bsqrmod(a, meth->irr_arr, r);
142 }
143 if (MP_USED(r) < 7) {
144 MP_CHECKOK(s_mp_pad(r, 7));
145 }
146 MP_USED(r) = 7;
147#else
148 if (MP_USED(a) < 7) {
149 return mp_bsqrmod(a, meth->irr_arr, r);
150 }
151 if (MP_USED(r) < 13) {
152 MP_CHECKOK(s_mp_pad(r, 13));
153 }
154 MP_USED(r) = 13;
155#endif
156 u = MP_DIGITS(r);
157
158#ifdef ECL_THIRTY_TWO_BIT
159 u[12] = gf2m_SQR0(v[6]);
160 u[11] = gf2m_SQR1(v[5]);
161 u[10] = gf2m_SQR0(v[5]);
162 u[9] = gf2m_SQR1(v[4]);
163 u[8] = gf2m_SQR0(v[4]);
164 u[7] = gf2m_SQR1(v[3]);
165#endif
166 u[6] = gf2m_SQR0(v[3]);
167 u[5] = gf2m_SQR1(v[2]);
168 u[4] = gf2m_SQR0(v[2]);
169 u[3] = gf2m_SQR1(v[1]);
170 u[2] = gf2m_SQR0(v[1]);
171 u[1] = gf2m_SQR1(v[0]);
172 u[0] = gf2m_SQR0(v[0]);
173 return ec_GF2m_193_mod(r, r, meth);
174
175 CLEANUP:
176 return res;
177}
178
179/* Fast multiplication for polynomials over a 193-bit curve. Assumes
180 * reduction polynomial with terms {193, 15, 0}. */
181mp_err
182ec_GF2m_193_mul(const mp_int *a, const mp_int *b, mp_int *r,
183 const GFMethod *meth)
184{
185 mp_err res = MP_OKAY;
186 mp_digit a3 = 0, a2 = 0, a1 = 0, a0, b3 = 0, b2 = 0, b1 = 0, b0;
187
188#ifdef ECL_THIRTY_TWO_BIT
189 mp_digit a6 = 0, a5 = 0, a4 = 0, b6 = 0, b5 = 0, b4 = 0;
190 mp_digit rm[8];
191#endif
192
193 if (a == b) {
194 return ec_GF2m_193_sqr(a, r, meth);
195 } else {
196 switch (MP_USED(a)) {
197#ifdef ECL_THIRTY_TWO_BIT
198 case 7:
199 a6 = MP_DIGIT(a, 6);
200 case 6:
201 a5 = MP_DIGIT(a, 5);
202 case 5:
203 a4 = MP_DIGIT(a, 4);
204#endif
205 case 4:
206 a3 = MP_DIGIT(a, 3);
207 case 3:
208 a2 = MP_DIGIT(a, 2);
209 case 2:
210 a1 = MP_DIGIT(a, 1);
211 default:
212 a0 = MP_DIGIT(a, 0);
213 }
214 switch (MP_USED(b)) {
215#ifdef ECL_THIRTY_TWO_BIT
216 case 7:
217 b6 = MP_DIGIT(b, 6);
218 case 6:
219 b5 = MP_DIGIT(b, 5);
220 case 5:
221 b4 = MP_DIGIT(b, 4);
222#endif
223 case 4:
224 b3 = MP_DIGIT(b, 3);
225 case 3:
226 b2 = MP_DIGIT(b, 2);
227 case 2:
228 b1 = MP_DIGIT(b, 1);
229 default:
230 b0 = MP_DIGIT(b, 0);
231 }
232#ifdef ECL_SIXTY_FOUR_BIT
233 MP_CHECKOK(s_mp_pad(r, 8));
234 s_bmul_4x4(MP_DIGITS(r), a3, a2, a1, a0, b3, b2, b1, b0);
235 MP_USED(r) = 8;
236 s_mp_clamp(r);
237#else
238 MP_CHECKOK(s_mp_pad(r, 14));
239 s_bmul_3x3(MP_DIGITS(r) + 8, a6, a5, a4, b6, b5, b4);
240 s_bmul_4x4(MP_DIGITS(r), a3, a2, a1, a0, b3, b2, b1, b0);
241 s_bmul_4x4(rm, a3, a6 ^ a2, a5 ^ a1, a4 ^ a0, b3, b6 ^ b2, b5 ^ b1,
242 b4 ^ b0);
243 rm[7] ^= MP_DIGIT(r, 7);
244 rm[6] ^= MP_DIGIT(r, 6);
245 rm[5] ^= MP_DIGIT(r, 5) ^ MP_DIGIT(r, 13);
246 rm[4] ^= MP_DIGIT(r, 4) ^ MP_DIGIT(r, 12);
247 rm[3] ^= MP_DIGIT(r, 3) ^ MP_DIGIT(r, 11);
248 rm[2] ^= MP_DIGIT(r, 2) ^ MP_DIGIT(r, 10);
249 rm[1] ^= MP_DIGIT(r, 1) ^ MP_DIGIT(r, 9);
250 rm[0] ^= MP_DIGIT(r, 0) ^ MP_DIGIT(r, 8);
251 MP_DIGIT(r, 11) ^= rm[7];
252 MP_DIGIT(r, 10) ^= rm[6];
253 MP_DIGIT(r, 9) ^= rm[5];
254 MP_DIGIT(r, 8) ^= rm[4];
255 MP_DIGIT(r, 7) ^= rm[3];
256 MP_DIGIT(r, 6) ^= rm[2];
257 MP_DIGIT(r, 5) ^= rm[1];
258 MP_DIGIT(r, 4) ^= rm[0];
259 MP_USED(r) = 14;
260 s_mp_clamp(r);
261#endif
262 return ec_GF2m_193_mod(r, r, meth);
263 }
264
265 CLEANUP:
266 return res;
267}
268
269/* Wire in fast field arithmetic for 193-bit curves. */
270mp_err
271ec_group_set_gf2m193(ECGroup *group, ECCurveName name)
272{
273 group->meth->field_mod = &ec_GF2m_193_mod;
274 group->meth->field_mul = &ec_GF2m_193_mul;
275 group->meth->field_sqr = &ec_GF2m_193_sqr;
276 return MP_OKAY;
277}
278