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 prime 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 * Douglas Stebila <douglas@stebila.ca>
35 *
36 *********************************************************************** */
37
38#include "ecp.h"
39#include "mpi.h"
40#include "mplogic.h"
41#include "mpi-priv.h"
42#ifndef _KERNEL
43#include <stdlib.h>
44#endif
45
46/* Fast modular reduction for p384 = 2^384 - 2^128 - 2^96 + 2^32 - 1. a can be r.
47 * Uses algorithm 2.30 from Hankerson, Menezes, Vanstone. Guide to
48 * Elliptic Curve Cryptography. */
49mp_err
50ec_GFp_nistp384_mod(const mp_int *a, mp_int *r, const GFMethod *meth)
51{
52 mp_err res = MP_OKAY;
53 int a_bits = mpl_significant_bits(a);
54 int i;
55
56 /* m1, m2 are statically-allocated mp_int of exactly the size we need */
57 mp_int m[10];
58
59#ifdef ECL_THIRTY_TWO_BIT
60 mp_digit s[10][12];
61 for (i = 0; i < 10; i++) {
62 MP_SIGN(&m[i]) = MP_ZPOS;
63 MP_ALLOC(&m[i]) = 12;
64 MP_USED(&m[i]) = 12;
65 MP_DIGITS(&m[i]) = s[i];
66 }
67#else
68 mp_digit s[10][6];
69 for (i = 0; i < 10; i++) {
70 MP_SIGN(&m[i]) = MP_ZPOS;
71 MP_ALLOC(&m[i]) = 6;
72 MP_USED(&m[i]) = 6;
73 MP_DIGITS(&m[i]) = s[i];
74 }
75#endif
76
77#ifdef ECL_THIRTY_TWO_BIT
78 /* for polynomials larger than twice the field size or polynomials
79 * not using all words, use regular reduction */
80 if ((a_bits > 768) || (a_bits <= 736)) {
81 MP_CHECKOK(mp_mod(a, &meth->irr, r));
82 } else {
83 for (i = 0; i < 12; i++) {
84 s[0][i] = MP_DIGIT(a, i);
85 }
86 s[1][0] = 0;
87 s[1][1] = 0;
88 s[1][2] = 0;
89 s[1][3] = 0;
90 s[1][4] = MP_DIGIT(a, 21);
91 s[1][5] = MP_DIGIT(a, 22);
92 s[1][6] = MP_DIGIT(a, 23);
93 s[1][7] = 0;
94 s[1][8] = 0;
95 s[1][9] = 0;
96 s[1][10] = 0;
97 s[1][11] = 0;
98 for (i = 0; i < 12; i++) {
99 s[2][i] = MP_DIGIT(a, i+12);
100 }
101 s[3][0] = MP_DIGIT(a, 21);
102 s[3][1] = MP_DIGIT(a, 22);
103 s[3][2] = MP_DIGIT(a, 23);
104 for (i = 3; i < 12; i++) {
105 s[3][i] = MP_DIGIT(a, i+9);
106 }
107 s[4][0] = 0;
108 s[4][1] = MP_DIGIT(a, 23);
109 s[4][2] = 0;
110 s[4][3] = MP_DIGIT(a, 20);
111 for (i = 4; i < 12; i++) {
112 s[4][i] = MP_DIGIT(a, i+8);
113 }
114 s[5][0] = 0;
115 s[5][1] = 0;
116 s[5][2] = 0;
117 s[5][3] = 0;
118 s[5][4] = MP_DIGIT(a, 20);
119 s[5][5] = MP_DIGIT(a, 21);
120 s[5][6] = MP_DIGIT(a, 22);
121 s[5][7] = MP_DIGIT(a, 23);
122 s[5][8] = 0;
123 s[5][9] = 0;
124 s[5][10] = 0;
125 s[5][11] = 0;
126 s[6][0] = MP_DIGIT(a, 20);
127 s[6][1] = 0;
128 s[6][2] = 0;
129 s[6][3] = MP_DIGIT(a, 21);
130 s[6][4] = MP_DIGIT(a, 22);
131 s[6][5] = MP_DIGIT(a, 23);
132 s[6][6] = 0;
133 s[6][7] = 0;
134 s[6][8] = 0;
135 s[6][9] = 0;
136 s[6][10] = 0;
137 s[6][11] = 0;
138 s[7][0] = MP_DIGIT(a, 23);
139 for (i = 1; i < 12; i++) {
140 s[7][i] = MP_DIGIT(a, i+11);
141 }
142 s[8][0] = 0;
143 s[8][1] = MP_DIGIT(a, 20);
144 s[8][2] = MP_DIGIT(a, 21);
145 s[8][3] = MP_DIGIT(a, 22);
146 s[8][4] = MP_DIGIT(a, 23);
147 s[8][5] = 0;
148 s[8][6] = 0;
149 s[8][7] = 0;
150 s[8][8] = 0;
151 s[8][9] = 0;
152 s[8][10] = 0;
153 s[8][11] = 0;
154 s[9][0] = 0;
155 s[9][1] = 0;
156 s[9][2] = 0;
157 s[9][3] = MP_DIGIT(a, 23);
158 s[9][4] = MP_DIGIT(a, 23);
159 s[9][5] = 0;
160 s[9][6] = 0;
161 s[9][7] = 0;
162 s[9][8] = 0;
163 s[9][9] = 0;
164 s[9][10] = 0;
165 s[9][11] = 0;
166
167 MP_CHECKOK(mp_add(&m[0], &m[1], r));
168 MP_CHECKOK(mp_add(r, &m[1], r));
169 MP_CHECKOK(mp_add(r, &m[2], r));
170 MP_CHECKOK(mp_add(r, &m[3], r));
171 MP_CHECKOK(mp_add(r, &m[4], r));
172 MP_CHECKOK(mp_add(r, &m[5], r));
173 MP_CHECKOK(mp_add(r, &m[6], r));
174 MP_CHECKOK(mp_sub(r, &m[7], r));
175 MP_CHECKOK(mp_sub(r, &m[8], r));
176 MP_CHECKOK(mp_submod(r, &m[9], &meth->irr, r));
177 s_mp_clamp(r);
178 }
179#else
180 /* for polynomials larger than twice the field size or polynomials
181 * not using all words, use regular reduction */
182 if ((a_bits > 768) || (a_bits <= 736)) {
183 MP_CHECKOK(mp_mod(a, &meth->irr, r));
184 } else {
185 for (i = 0; i < 6; i++) {
186 s[0][i] = MP_DIGIT(a, i);
187 }
188 s[1][0] = 0;
189 s[1][1] = 0;
190 s[1][2] = (MP_DIGIT(a, 10) >> 32) | (MP_DIGIT(a, 11) << 32);
191 s[1][3] = MP_DIGIT(a, 11) >> 32;
192 s[1][4] = 0;
193 s[1][5] = 0;
194 for (i = 0; i < 6; i++) {
195 s[2][i] = MP_DIGIT(a, i+6);
196 }
197 s[3][0] = (MP_DIGIT(a, 10) >> 32) | (MP_DIGIT(a, 11) << 32);
198 s[3][1] = (MP_DIGIT(a, 11) >> 32) | (MP_DIGIT(a, 6) << 32);
199 for (i = 2; i < 6; i++) {
200 s[3][i] = (MP_DIGIT(a, i+4) >> 32) | (MP_DIGIT(a, i+5) << 32);
201 }
202 s[4][0] = (MP_DIGIT(a, 11) >> 32) << 32;
203 s[4][1] = MP_DIGIT(a, 10) << 32;
204 for (i = 2; i < 6; i++) {
205 s[4][i] = MP_DIGIT(a, i+4);
206 }
207 s[5][0] = 0;
208 s[5][1] = 0;
209 s[5][2] = MP_DIGIT(a, 10);
210 s[5][3] = MP_DIGIT(a, 11);
211 s[5][4] = 0;
212 s[5][5] = 0;
213 s[6][0] = (MP_DIGIT(a, 10) << 32) >> 32;
214 s[6][1] = (MP_DIGIT(a, 10) >> 32) << 32;
215 s[6][2] = MP_DIGIT(a, 11);
216 s[6][3] = 0;
217 s[6][4] = 0;
218 s[6][5] = 0;
219 s[7][0] = (MP_DIGIT(a, 11) >> 32) | (MP_DIGIT(a, 6) << 32);
220 for (i = 1; i < 6; i++) {
221 s[7][i] = (MP_DIGIT(a, i+5) >> 32) | (MP_DIGIT(a, i+6) << 32);
222 }
223 s[8][0] = MP_DIGIT(a, 10) << 32;
224 s[8][1] = (MP_DIGIT(a, 10) >> 32) | (MP_DIGIT(a, 11) << 32);
225 s[8][2] = MP_DIGIT(a, 11) >> 32;
226 s[8][3] = 0;
227 s[8][4] = 0;
228 s[8][5] = 0;
229 s[9][0] = 0;
230 s[9][1] = (MP_DIGIT(a, 11) >> 32) << 32;
231 s[9][2] = MP_DIGIT(a, 11) >> 32;
232 s[9][3] = 0;
233 s[9][4] = 0;
234 s[9][5] = 0;
235
236 MP_CHECKOK(mp_add(&m[0], &m[1], r));
237 MP_CHECKOK(mp_add(r, &m[1], r));
238 MP_CHECKOK(mp_add(r, &m[2], r));
239 MP_CHECKOK(mp_add(r, &m[3], r));
240 MP_CHECKOK(mp_add(r, &m[4], r));
241 MP_CHECKOK(mp_add(r, &m[5], r));
242 MP_CHECKOK(mp_add(r, &m[6], r));
243 MP_CHECKOK(mp_sub(r, &m[7], r));
244 MP_CHECKOK(mp_sub(r, &m[8], r));
245 MP_CHECKOK(mp_submod(r, &m[9], &meth->irr, r));
246 s_mp_clamp(r);
247 }
248#endif
249
250 CLEANUP:
251 return res;
252}
253
254/* Compute the square of polynomial a, reduce modulo p384. Store the
255 * result in r. r could be a. Uses optimized modular reduction for p384.
256 */
257mp_err
258ec_GFp_nistp384_sqr(const mp_int *a, mp_int *r, const GFMethod *meth)
259{
260 mp_err res = MP_OKAY;
261
262 MP_CHECKOK(mp_sqr(a, r));
263 MP_CHECKOK(ec_GFp_nistp384_mod(r, r, meth));
264 CLEANUP:
265 return res;
266}
267
268/* Compute the product of two polynomials a and b, reduce modulo p384.
269 * Store the result in r. r could be a or b; a could be b. Uses
270 * optimized modular reduction for p384. */
271mp_err
272ec_GFp_nistp384_mul(const mp_int *a, const mp_int *b, mp_int *r,
273 const GFMethod *meth)
274{
275 mp_err res = MP_OKAY;
276
277 MP_CHECKOK(mp_mul(a, b, r));
278 MP_CHECKOK(ec_GFp_nistp384_mod(r, r, meth));
279 CLEANUP:
280 return res;
281}
282
283/* Wire in fast field arithmetic and precomputation of base point for
284 * named curves. */
285mp_err
286ec_group_set_gfp384(ECGroup *group, ECCurveName name)
287{
288 if (name == ECCurve_NIST_P384) {
289 group->meth->field_mod = &ec_GFp_nistp384_mod;
290 group->meth->field_mul = &ec_GFp_nistp384_mul;
291 group->meth->field_sqr = &ec_GFp_nistp384_sqr;
292 }
293 return MP_OKAY;
294}
295