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 binary polynomial 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 * Sheueling Chang-Shantz <sheueling.chang@sun.com>,
24 * Stephen Fung <fungstep@hotmail.com>, and
25 * Douglas Stebila <douglas@stebila.ca>, Sun Microsystems Laboratories.
26 *
27 * Alternatively, the contents of this file may be used under the terms of
28 * either the GNU General Public License Version 2 or later (the "GPL"), or
29 * the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
30 * in which case the provisions of the GPL or the LGPL are applicable instead
31 * of those above. If you wish to allow use of your version of this file only
32 * under the terms of either the GPL or the LGPL, and not to allow others to
33 * use your version of this file under the terms of the MPL, indicate your
34 * decision by deleting the provisions above and replace them with the notice
35 * and other provisions required by the GPL or the LGPL. If you do not delete
36 * the provisions above, a recipient may use your version of this file under
37 * the terms of any one of the MPL, the GPL or the LGPL.
38 *
39 * ***** END LICENSE BLOCK ***** */
40 /*
41 * Copyright 2007 Sun Microsystems, Inc. All rights reserved.
42 * Use is subject to license terms.
43 *
44 * Sun elects to use this software under the MPL license.
45 */
46
47 #include "ec2.h"
48 #include "mp_gf2m.h"
49 #include "mp_gf2m-priv.h"
50 #include "mpi.h"
51 #include "mpi-priv.h"
52 #ifndef _KERNEL
53 #include <stdlib.h>
54 #endif
55
56 /* Fast reduction for polynomials over a 233-bit curve. Assumes reduction
57 * polynomial with terms {233, 74, 0}. */
58 mp_err
ec_GF2m_233_mod(const mp_int * a,mp_int * r,const GFMethod * meth)59 ec_GF2m_233_mod(const mp_int *a, mp_int *r, const GFMethod *meth)
60 {
61 mp_err res = MP_OKAY;
62 mp_digit *u, z;
63
64 if (a != r) {
65 MP_CHECKOK(mp_copy(a, r));
66 }
67 #ifdef ECL_SIXTY_FOUR_BIT
68 if (MP_USED(r) < 8) {
69 MP_CHECKOK(s_mp_pad(r, 8));
70 }
71 u = MP_DIGITS(r);
72 MP_USED(r) = 8;
73
74 /* u[7] only has 18 significant bits */
75 z = u[7];
76 u[4] ^= (z << 33) ^ (z >> 41);
77 u[3] ^= (z << 23);
78 z = u[6];
79 u[4] ^= (z >> 31);
80 u[3] ^= (z << 33) ^ (z >> 41);
81 u[2] ^= (z << 23);
82 z = u[5];
83 u[3] ^= (z >> 31);
84 u[2] ^= (z << 33) ^ (z >> 41);
85 u[1] ^= (z << 23);
86 z = u[4];
87 u[2] ^= (z >> 31);
88 u[1] ^= (z << 33) ^ (z >> 41);
89 u[0] ^= (z << 23);
90 z = u[3] >> 41; /* z only has 23 significant bits */
91 u[1] ^= (z << 10);
92 u[0] ^= z;
93 /* clear bits above 233 */
94 u[7] = u[6] = u[5] = u[4] = 0;
95 u[3] ^= z << 41;
96 #else
97 if (MP_USED(r) < 15) {
98 MP_CHECKOK(s_mp_pad(r, 15));
99 }
100 u = MP_DIGITS(r);
101 MP_USED(r) = 15;
102
103 /* u[14] only has 18 significant bits */
104 z = u[14];
105 u[9] ^= (z << 1);
106 u[7] ^= (z >> 9);
107 u[6] ^= (z << 23);
108 z = u[13];
109 u[9] ^= (z >> 31);
110 u[8] ^= (z << 1);
111 u[6] ^= (z >> 9);
112 u[5] ^= (z << 23);
113 z = u[12];
114 u[8] ^= (z >> 31);
115 u[7] ^= (z << 1);
116 u[5] ^= (z >> 9);
117 u[4] ^= (z << 23);
118 z = u[11];
119 u[7] ^= (z >> 31);
120 u[6] ^= (z << 1);
121 u[4] ^= (z >> 9);
122 u[3] ^= (z << 23);
123 z = u[10];
124 u[6] ^= (z >> 31);
125 u[5] ^= (z << 1);
126 u[3] ^= (z >> 9);
127 u[2] ^= (z << 23);
128 z = u[9];
129 u[5] ^= (z >> 31);
130 u[4] ^= (z << 1);
131 u[2] ^= (z >> 9);
132 u[1] ^= (z << 23);
133 z = u[8];
134 u[4] ^= (z >> 31);
135 u[3] ^= (z << 1);
136 u[1] ^= (z >> 9);
137 u[0] ^= (z << 23);
138 z = u[7] >> 9; /* z only has 23 significant bits */
139 u[3] ^= (z >> 22);
140 u[2] ^= (z << 10);
141 u[0] ^= z;
142 /* clear bits above 233 */
143 u[14] = u[13] = u[12] = u[11] = u[10] = u[9] = u[8] = 0;
144 u[7] ^= z << 9;
145 #endif
146 s_mp_clamp(r);
147
148 CLEANUP:
149 return res;
150 }
151
152 /* Fast squaring for polynomials over a 233-bit curve. Assumes reduction
153 * polynomial with terms {233, 74, 0}. */
154 mp_err
ec_GF2m_233_sqr(const mp_int * a,mp_int * r,const GFMethod * meth)155 ec_GF2m_233_sqr(const mp_int *a, mp_int *r, const GFMethod *meth)
156 {
157 mp_err res = MP_OKAY;
158 mp_digit *u, *v;
159
160 v = MP_DIGITS(a);
161
162 #ifdef ECL_SIXTY_FOUR_BIT
163 if (MP_USED(a) < 4) {
164 return mp_bsqrmod(a, meth->irr_arr, r);
165 }
166 if (MP_USED(r) < 8) {
167 MP_CHECKOK(s_mp_pad(r, 8));
168 }
169 MP_USED(r) = 8;
170 #else
171 if (MP_USED(a) < 8) {
172 return mp_bsqrmod(a, meth->irr_arr, r);
173 }
174 if (MP_USED(r) < 15) {
175 MP_CHECKOK(s_mp_pad(r, 15));
176 }
177 MP_USED(r) = 15;
178 #endif
179 u = MP_DIGITS(r);
180
181 #ifdef ECL_THIRTY_TWO_BIT
182 u[14] = gf2m_SQR0(v[7]);
183 u[13] = gf2m_SQR1(v[6]);
184 u[12] = gf2m_SQR0(v[6]);
185 u[11] = gf2m_SQR1(v[5]);
186 u[10] = gf2m_SQR0(v[5]);
187 u[9] = gf2m_SQR1(v[4]);
188 u[8] = gf2m_SQR0(v[4]);
189 #endif
190 u[7] = gf2m_SQR1(v[3]);
191 u[6] = gf2m_SQR0(v[3]);
192 u[5] = gf2m_SQR1(v[2]);
193 u[4] = gf2m_SQR0(v[2]);
194 u[3] = gf2m_SQR1(v[1]);
195 u[2] = gf2m_SQR0(v[1]);
196 u[1] = gf2m_SQR1(v[0]);
197 u[0] = gf2m_SQR0(v[0]);
198 return ec_GF2m_233_mod(r, r, meth);
199
200 CLEANUP:
201 return res;
202 }
203
204 /* Fast multiplication for polynomials over a 233-bit curve. Assumes
205 * reduction polynomial with terms {233, 74, 0}. */
206 mp_err
ec_GF2m_233_mul(const mp_int * a,const mp_int * b,mp_int * r,const GFMethod * meth)207 ec_GF2m_233_mul(const mp_int *a, const mp_int *b, mp_int *r,
208 const GFMethod *meth)
209 {
210 mp_err res = MP_OKAY;
211 mp_digit a3 = 0, a2 = 0, a1 = 0, a0, b3 = 0, b2 = 0, b1 = 0, b0;
212
213 #ifdef ECL_THIRTY_TWO_BIT
214 mp_digit a7 = 0, a6 = 0, a5 = 0, a4 = 0, b7 = 0, b6 = 0, b5 = 0, b4 =
215 0;
216 mp_digit rm[8];
217 #endif
218
219 if (a == b) {
220 return ec_GF2m_233_sqr(a, r, meth);
221 } else {
222 switch (MP_USED(a)) {
223 #ifdef ECL_THIRTY_TWO_BIT
224 case 8:
225 a7 = MP_DIGIT(a, 7);
226 /* FALLTHROUGH */
227 case 7:
228 a6 = MP_DIGIT(a, 6);
229 /* FALLTHROUGH */
230 case 6:
231 a5 = MP_DIGIT(a, 5);
232 /* FALLTHROUGH */
233 case 5:
234 a4 = MP_DIGIT(a, 4);
235 #endif
236 /* FALLTHROUGH */
237 case 4:
238 a3 = MP_DIGIT(a, 3);
239 /* FALLTHROUGH */
240 case 3:
241 a2 = MP_DIGIT(a, 2);
242 /* FALLTHROUGH */
243 case 2:
244 a1 = MP_DIGIT(a, 1);
245 /* FALLTHROUGH */
246 default:
247 a0 = MP_DIGIT(a, 0);
248 }
249 switch (MP_USED(b)) {
250 #ifdef ECL_THIRTY_TWO_BIT
251 case 8:
252 b7 = MP_DIGIT(b, 7);
253 /* FALLTHROUGH */
254 case 7:
255 b6 = MP_DIGIT(b, 6);
256 /* FALLTHROUGH */
257 case 6:
258 b5 = MP_DIGIT(b, 5);
259 /* FALLTHROUGH */
260 case 5:
261 b4 = MP_DIGIT(b, 4);
262 #endif
263 /* FALLTHROUGH */
264 case 4:
265 b3 = MP_DIGIT(b, 3);
266 /* FALLTHROUGH */
267 case 3:
268 b2 = MP_DIGIT(b, 2);
269 /* FALLTHROUGH */
270 case 2:
271 b1 = MP_DIGIT(b, 1);
272 /* FALLTHROUGH */
273 default:
274 b0 = MP_DIGIT(b, 0);
275 }
276 #ifdef ECL_SIXTY_FOUR_BIT
277 MP_CHECKOK(s_mp_pad(r, 8));
278 s_bmul_4x4(MP_DIGITS(r), a3, a2, a1, a0, b3, b2, b1, b0);
279 MP_USED(r) = 8;
280 s_mp_clamp(r);
281 #else
282 MP_CHECKOK(s_mp_pad(r, 16));
283 s_bmul_4x4(MP_DIGITS(r) + 8, a7, a6, a5, a4, b7, b6, b5, b4);
284 s_bmul_4x4(MP_DIGITS(r), a3, a2, a1, a0, b3, b2, b1, b0);
285 s_bmul_4x4(rm, a7 ^ a3, a6 ^ a2, a5 ^ a1, a4 ^ a0, b7 ^ b3,
286 b6 ^ b2, b5 ^ b1, b4 ^ b0);
287 rm[7] ^= MP_DIGIT(r, 7) ^ MP_DIGIT(r, 15);
288 rm[6] ^= MP_DIGIT(r, 6) ^ MP_DIGIT(r, 14);
289 rm[5] ^= MP_DIGIT(r, 5) ^ MP_DIGIT(r, 13);
290 rm[4] ^= MP_DIGIT(r, 4) ^ MP_DIGIT(r, 12);
291 rm[3] ^= MP_DIGIT(r, 3) ^ MP_DIGIT(r, 11);
292 rm[2] ^= MP_DIGIT(r, 2) ^ MP_DIGIT(r, 10);
293 rm[1] ^= MP_DIGIT(r, 1) ^ MP_DIGIT(r, 9);
294 rm[0] ^= MP_DIGIT(r, 0) ^ MP_DIGIT(r, 8);
295 MP_DIGIT(r, 11) ^= rm[7];
296 MP_DIGIT(r, 10) ^= rm[6];
297 MP_DIGIT(r, 9) ^= rm[5];
298 MP_DIGIT(r, 8) ^= rm[4];
299 MP_DIGIT(r, 7) ^= rm[3];
300 MP_DIGIT(r, 6) ^= rm[2];
301 MP_DIGIT(r, 5) ^= rm[1];
302 MP_DIGIT(r, 4) ^= rm[0];
303 MP_USED(r) = 16;
304 s_mp_clamp(r);
305 #endif
306 return ec_GF2m_233_mod(r, r, meth);
307 }
308
309 CLEANUP:
310 return res;
311 }
312
313 /* Wire in fast field arithmetic for 233-bit curves. */
314 mp_err
ec_group_set_gf2m233(ECGroup * group,ECCurveName name)315 ec_group_set_gf2m233(ECGroup *group, ECCurveName name)
316 {
317 group->meth->field_mod = &ec_GF2m_233_mod;
318 group->meth->field_mul = &ec_GF2m_233_mul;
319 group->meth->field_sqr = &ec_GF2m_233_sqr;
320 return MP_OKAY;
321 }
322