|
1 /* ********************************************************************* |
|
2 * |
|
3 * Sun elects to have this file available under and governed by the |
|
4 * Mozilla Public License Version 1.1 ("MPL") (see |
|
5 * http://www.mozilla.org/MPL/ for full license text). For the avoidance |
|
6 * of doubt and subject to the following, Sun also elects to allow |
|
7 * licensees to use this file under the MPL, the GNU General Public |
|
8 * License version 2 only or the Lesser General Public License version |
|
9 * 2.1 only. Any references to the "GNU General Public License version 2 |
|
10 * or later" or "GPL" in the following shall be construed to mean the |
|
11 * GNU General Public License version 2 only. Any references to the "GNU |
|
12 * Lesser General Public License version 2.1 or later" or "LGPL" in the |
|
13 * following shall be construed to mean the GNU Lesser General Public |
|
14 * License version 2.1 only. However, the following notice accompanied |
|
15 * the original version of this file: |
|
16 * |
|
17 * Version: MPL 1.1/GPL 2.0/LGPL 2.1 |
|
18 * |
|
19 * The contents of this file are subject to the Mozilla Public License Version |
|
20 * 1.1 (the "License"); you may not use this file except in compliance with |
|
21 * the License. You may obtain a copy of the License at |
|
22 * http://www.mozilla.org/MPL/ |
|
23 * |
|
24 * Software distributed under the License is distributed on an "AS IS" basis, |
|
25 * WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License |
|
26 * for the specific language governing rights and limitations under the |
|
27 * License. |
|
28 * |
|
29 * The Original Code is the elliptic curve math library for prime field curves. |
|
30 * |
|
31 * The Initial Developer of the Original Code is |
|
32 * Sun Microsystems, Inc. |
|
33 * Portions created by the Initial Developer are Copyright (C) 2003 |
|
34 * the Initial Developer. All Rights Reserved. |
|
35 * |
|
36 * Contributor(s): |
|
37 * Douglas Stebila <douglas@stebila.ca> |
|
38 * |
|
39 * Alternatively, the contents of this file may be used under the terms of |
|
40 * either the GNU General Public License Version 2 or later (the "GPL"), or |
|
41 * the GNU Lesser General Public License Version 2.1 or later (the "LGPL"), |
|
42 * in which case the provisions of the GPL or the LGPL are applicable instead |
|
43 * of those above. If you wish to allow use of your version of this file only |
|
44 * under the terms of either the GPL or the LGPL, and not to allow others to |
|
45 * use your version of this file under the terms of the MPL, indicate your |
|
46 * decision by deleting the provisions above and replace them with the notice |
|
47 * and other provisions required by the GPL or the LGPL. If you do not delete |
|
48 * the provisions above, a recipient may use your version of this file under |
|
49 * the terms of any one of the MPL, the GPL or the LGPL. |
|
50 * |
|
51 *********************************************************************** */ |
|
52 /* |
|
53 * Copyright 2007 Sun Microsystems, Inc. All rights reserved. |
|
54 * Use is subject to license terms. |
|
55 */ |
|
56 |
|
57 #pragma ident "%Z%%M% %I% %E% SMI" |
|
58 |
|
59 #include "ecp.h" |
|
60 #include "mpi.h" |
|
61 #include "mplogic.h" |
|
62 #include "mpi-priv.h" |
|
63 #ifndef _KERNEL |
|
64 #include <stdlib.h> |
|
65 #endif |
|
66 |
|
67 /* Fast modular reduction for p384 = 2^384 - 2^128 - 2^96 + 2^32 - 1. a can be r. |
|
68 * Uses algorithm 2.30 from Hankerson, Menezes, Vanstone. Guide to |
|
69 * Elliptic Curve Cryptography. */ |
|
70 mp_err |
|
71 ec_GFp_nistp384_mod(const mp_int *a, mp_int *r, const GFMethod *meth) |
|
72 { |
|
73 mp_err res = MP_OKAY; |
|
74 int a_bits = mpl_significant_bits(a); |
|
75 int i; |
|
76 |
|
77 /* m1, m2 are statically-allocated mp_int of exactly the size we need */ |
|
78 mp_int m[10]; |
|
79 |
|
80 #ifdef ECL_THIRTY_TWO_BIT |
|
81 mp_digit s[10][12]; |
|
82 for (i = 0; i < 10; i++) { |
|
83 MP_SIGN(&m[i]) = MP_ZPOS; |
|
84 MP_ALLOC(&m[i]) = 12; |
|
85 MP_USED(&m[i]) = 12; |
|
86 MP_DIGITS(&m[i]) = s[i]; |
|
87 } |
|
88 #else |
|
89 mp_digit s[10][6]; |
|
90 for (i = 0; i < 10; i++) { |
|
91 MP_SIGN(&m[i]) = MP_ZPOS; |
|
92 MP_ALLOC(&m[i]) = 6; |
|
93 MP_USED(&m[i]) = 6; |
|
94 MP_DIGITS(&m[i]) = s[i]; |
|
95 } |
|
96 #endif |
|
97 |
|
98 #ifdef ECL_THIRTY_TWO_BIT |
|
99 /* for polynomials larger than twice the field size or polynomials |
|
100 * not using all words, use regular reduction */ |
|
101 if ((a_bits > 768) || (a_bits <= 736)) { |
|
102 MP_CHECKOK(mp_mod(a, &meth->irr, r)); |
|
103 } else { |
|
104 for (i = 0; i < 12; i++) { |
|
105 s[0][i] = MP_DIGIT(a, i); |
|
106 } |
|
107 s[1][0] = 0; |
|
108 s[1][1] = 0; |
|
109 s[1][2] = 0; |
|
110 s[1][3] = 0; |
|
111 s[1][4] = MP_DIGIT(a, 21); |
|
112 s[1][5] = MP_DIGIT(a, 22); |
|
113 s[1][6] = MP_DIGIT(a, 23); |
|
114 s[1][7] = 0; |
|
115 s[1][8] = 0; |
|
116 s[1][9] = 0; |
|
117 s[1][10] = 0; |
|
118 s[1][11] = 0; |
|
119 for (i = 0; i < 12; i++) { |
|
120 s[2][i] = MP_DIGIT(a, i+12); |
|
121 } |
|
122 s[3][0] = MP_DIGIT(a, 21); |
|
123 s[3][1] = MP_DIGIT(a, 22); |
|
124 s[3][2] = MP_DIGIT(a, 23); |
|
125 for (i = 3; i < 12; i++) { |
|
126 s[3][i] = MP_DIGIT(a, i+9); |
|
127 } |
|
128 s[4][0] = 0; |
|
129 s[4][1] = MP_DIGIT(a, 23); |
|
130 s[4][2] = 0; |
|
131 s[4][3] = MP_DIGIT(a, 20); |
|
132 for (i = 4; i < 12; i++) { |
|
133 s[4][i] = MP_DIGIT(a, i+8); |
|
134 } |
|
135 s[5][0] = 0; |
|
136 s[5][1] = 0; |
|
137 s[5][2] = 0; |
|
138 s[5][3] = 0; |
|
139 s[5][4] = MP_DIGIT(a, 20); |
|
140 s[5][5] = MP_DIGIT(a, 21); |
|
141 s[5][6] = MP_DIGIT(a, 22); |
|
142 s[5][7] = MP_DIGIT(a, 23); |
|
143 s[5][8] = 0; |
|
144 s[5][9] = 0; |
|
145 s[5][10] = 0; |
|
146 s[5][11] = 0; |
|
147 s[6][0] = MP_DIGIT(a, 20); |
|
148 s[6][1] = 0; |
|
149 s[6][2] = 0; |
|
150 s[6][3] = MP_DIGIT(a, 21); |
|
151 s[6][4] = MP_DIGIT(a, 22); |
|
152 s[6][5] = MP_DIGIT(a, 23); |
|
153 s[6][6] = 0; |
|
154 s[6][7] = 0; |
|
155 s[6][8] = 0; |
|
156 s[6][9] = 0; |
|
157 s[6][10] = 0; |
|
158 s[6][11] = 0; |
|
159 s[7][0] = MP_DIGIT(a, 23); |
|
160 for (i = 1; i < 12; i++) { |
|
161 s[7][i] = MP_DIGIT(a, i+11); |
|
162 } |
|
163 s[8][0] = 0; |
|
164 s[8][1] = MP_DIGIT(a, 20); |
|
165 s[8][2] = MP_DIGIT(a, 21); |
|
166 s[8][3] = MP_DIGIT(a, 22); |
|
167 s[8][4] = MP_DIGIT(a, 23); |
|
168 s[8][5] = 0; |
|
169 s[8][6] = 0; |
|
170 s[8][7] = 0; |
|
171 s[8][8] = 0; |
|
172 s[8][9] = 0; |
|
173 s[8][10] = 0; |
|
174 s[8][11] = 0; |
|
175 s[9][0] = 0; |
|
176 s[9][1] = 0; |
|
177 s[9][2] = 0; |
|
178 s[9][3] = MP_DIGIT(a, 23); |
|
179 s[9][4] = MP_DIGIT(a, 23); |
|
180 s[9][5] = 0; |
|
181 s[9][6] = 0; |
|
182 s[9][7] = 0; |
|
183 s[9][8] = 0; |
|
184 s[9][9] = 0; |
|
185 s[9][10] = 0; |
|
186 s[9][11] = 0; |
|
187 |
|
188 MP_CHECKOK(mp_add(&m[0], &m[1], r)); |
|
189 MP_CHECKOK(mp_add(r, &m[1], r)); |
|
190 MP_CHECKOK(mp_add(r, &m[2], r)); |
|
191 MP_CHECKOK(mp_add(r, &m[3], r)); |
|
192 MP_CHECKOK(mp_add(r, &m[4], r)); |
|
193 MP_CHECKOK(mp_add(r, &m[5], r)); |
|
194 MP_CHECKOK(mp_add(r, &m[6], r)); |
|
195 MP_CHECKOK(mp_sub(r, &m[7], r)); |
|
196 MP_CHECKOK(mp_sub(r, &m[8], r)); |
|
197 MP_CHECKOK(mp_submod(r, &m[9], &meth->irr, r)); |
|
198 s_mp_clamp(r); |
|
199 } |
|
200 #else |
|
201 /* for polynomials larger than twice the field size or polynomials |
|
202 * not using all words, use regular reduction */ |
|
203 if ((a_bits > 768) || (a_bits <= 736)) { |
|
204 MP_CHECKOK(mp_mod(a, &meth->irr, r)); |
|
205 } else { |
|
206 for (i = 0; i < 6; i++) { |
|
207 s[0][i] = MP_DIGIT(a, i); |
|
208 } |
|
209 s[1][0] = 0; |
|
210 s[1][1] = 0; |
|
211 s[1][2] = (MP_DIGIT(a, 10) >> 32) | (MP_DIGIT(a, 11) << 32); |
|
212 s[1][3] = MP_DIGIT(a, 11) >> 32; |
|
213 s[1][4] = 0; |
|
214 s[1][5] = 0; |
|
215 for (i = 0; i < 6; i++) { |
|
216 s[2][i] = MP_DIGIT(a, i+6); |
|
217 } |
|
218 s[3][0] = (MP_DIGIT(a, 10) >> 32) | (MP_DIGIT(a, 11) << 32); |
|
219 s[3][1] = (MP_DIGIT(a, 11) >> 32) | (MP_DIGIT(a, 6) << 32); |
|
220 for (i = 2; i < 6; i++) { |
|
221 s[3][i] = (MP_DIGIT(a, i+4) >> 32) | (MP_DIGIT(a, i+5) << 32); |
|
222 } |
|
223 s[4][0] = (MP_DIGIT(a, 11) >> 32) << 32; |
|
224 s[4][1] = MP_DIGIT(a, 10) << 32; |
|
225 for (i = 2; i < 6; i++) { |
|
226 s[4][i] = MP_DIGIT(a, i+4); |
|
227 } |
|
228 s[5][0] = 0; |
|
229 s[5][1] = 0; |
|
230 s[5][2] = MP_DIGIT(a, 10); |
|
231 s[5][3] = MP_DIGIT(a, 11); |
|
232 s[5][4] = 0; |
|
233 s[5][5] = 0; |
|
234 s[6][0] = (MP_DIGIT(a, 10) << 32) >> 32; |
|
235 s[6][1] = (MP_DIGIT(a, 10) >> 32) << 32; |
|
236 s[6][2] = MP_DIGIT(a, 11); |
|
237 s[6][3] = 0; |
|
238 s[6][4] = 0; |
|
239 s[6][5] = 0; |
|
240 s[7][0] = (MP_DIGIT(a, 11) >> 32) | (MP_DIGIT(a, 6) << 32); |
|
241 for (i = 1; i < 6; i++) { |
|
242 s[7][i] = (MP_DIGIT(a, i+5) >> 32) | (MP_DIGIT(a, i+6) << 32); |
|
243 } |
|
244 s[8][0] = MP_DIGIT(a, 10) << 32; |
|
245 s[8][1] = (MP_DIGIT(a, 10) >> 32) | (MP_DIGIT(a, 11) << 32); |
|
246 s[8][2] = MP_DIGIT(a, 11) >> 32; |
|
247 s[8][3] = 0; |
|
248 s[8][4] = 0; |
|
249 s[8][5] = 0; |
|
250 s[9][0] = 0; |
|
251 s[9][1] = (MP_DIGIT(a, 11) >> 32) << 32; |
|
252 s[9][2] = MP_DIGIT(a, 11) >> 32; |
|
253 s[9][3] = 0; |
|
254 s[9][4] = 0; |
|
255 s[9][5] = 0; |
|
256 |
|
257 MP_CHECKOK(mp_add(&m[0], &m[1], r)); |
|
258 MP_CHECKOK(mp_add(r, &m[1], r)); |
|
259 MP_CHECKOK(mp_add(r, &m[2], r)); |
|
260 MP_CHECKOK(mp_add(r, &m[3], r)); |
|
261 MP_CHECKOK(mp_add(r, &m[4], r)); |
|
262 MP_CHECKOK(mp_add(r, &m[5], r)); |
|
263 MP_CHECKOK(mp_add(r, &m[6], r)); |
|
264 MP_CHECKOK(mp_sub(r, &m[7], r)); |
|
265 MP_CHECKOK(mp_sub(r, &m[8], r)); |
|
266 MP_CHECKOK(mp_submod(r, &m[9], &meth->irr, r)); |
|
267 s_mp_clamp(r); |
|
268 } |
|
269 #endif |
|
270 |
|
271 CLEANUP: |
|
272 return res; |
|
273 } |
|
274 |
|
275 /* Compute the square of polynomial a, reduce modulo p384. Store the |
|
276 * result in r. r could be a. Uses optimized modular reduction for p384. |
|
277 */ |
|
278 mp_err |
|
279 ec_GFp_nistp384_sqr(const mp_int *a, mp_int *r, const GFMethod *meth) |
|
280 { |
|
281 mp_err res = MP_OKAY; |
|
282 |
|
283 MP_CHECKOK(mp_sqr(a, r)); |
|
284 MP_CHECKOK(ec_GFp_nistp384_mod(r, r, meth)); |
|
285 CLEANUP: |
|
286 return res; |
|
287 } |
|
288 |
|
289 /* Compute the product of two polynomials a and b, reduce modulo p384. |
|
290 * Store the result in r. r could be a or b; a could be b. Uses |
|
291 * optimized modular reduction for p384. */ |
|
292 mp_err |
|
293 ec_GFp_nistp384_mul(const mp_int *a, const mp_int *b, mp_int *r, |
|
294 const GFMethod *meth) |
|
295 { |
|
296 mp_err res = MP_OKAY; |
|
297 |
|
298 MP_CHECKOK(mp_mul(a, b, r)); |
|
299 MP_CHECKOK(ec_GFp_nistp384_mod(r, r, meth)); |
|
300 CLEANUP: |
|
301 return res; |
|
302 } |
|
303 |
|
304 /* Wire in fast field arithmetic and precomputation of base point for |
|
305 * named curves. */ |
|
306 mp_err |
|
307 ec_group_set_gfp384(ECGroup *group, ECCurveName name) |
|
308 { |
|
309 if (name == ECCurve_NIST_P384) { |
|
310 group->meth->field_mod = &ec_GFp_nistp384_mod; |
|
311 group->meth->field_mul = &ec_GFp_nistp384_mul; |
|
312 group->meth->field_sqr = &ec_GFp_nistp384_sqr; |
|
313 } |
|
314 return MP_OKAY; |
|
315 } |