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 prime 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 * Douglas Stebila <douglas@stebila.ca>
24 *
25 * Alternatively, the contents of this file may be used under the terms of
26 * either the GNU General Public License Version 2 or later (the "GPL"), or
27 * the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
28 * in which case the provisions of the GPL or the LGPL are applicable instead
29 * of those above. If you wish to allow use of your version of this file only
30 * under the terms of either the GPL or the LGPL, and not to allow others to
31 * use your version of this file under the terms of the MPL, indicate your
32 * decision by deleting the provisions above and replace them with the notice
33 * and other provisions required by the GPL or the LGPL. If you do not delete
34 * the provisions above, a recipient may use your version of this file under
35 * the terms of any one of the MPL, the GPL or the LGPL.
36 *
37 * ***** END LICENSE BLOCK ***** */
38 /*
39 * Copyright 2007 Sun Microsystems, Inc. All rights reserved.
40 * Use is subject to license terms.
41 *
42 * Sun elects to use this software under the MPL license.
43 */
44
45 #include "ecp.h"
46 #include "mpi.h"
47 #include "mplogic.h"
48 #include "mpi-priv.h"
49 #ifndef _KERNEL
50 #include <stdlib.h>
51 #endif
52
53 #define ECP521_DIGITS ECL_CURVE_DIGITS(521)
54
55 /* Fast modular reduction for p521 = 2^521 - 1. a can be r. Uses
56 * algorithm 2.31 from Hankerson, Menezes, Vanstone. Guide to
57 * Elliptic Curve Cryptography. */
58 mp_err
ec_GFp_nistp521_mod(const mp_int * a,mp_int * r,const GFMethod * meth)59 ec_GFp_nistp521_mod(const mp_int *a, mp_int *r, const GFMethod *meth)
60 {
61 mp_err res = MP_OKAY;
62 int a_bits = mpl_significant_bits(a);
63 int i;
64
65 /* m1, m2 are statically-allocated mp_int of exactly the size we need */
66 mp_int m1;
67
68 mp_digit s1[ECP521_DIGITS] = { 0 };
69
70 MP_SIGN(&m1) = MP_ZPOS;
71 MP_ALLOC(&m1) = ECP521_DIGITS;
72 MP_USED(&m1) = ECP521_DIGITS;
73 MP_DIGITS(&m1) = s1;
74
75 if (a_bits < 521) {
76 if (a==r) return MP_OKAY;
77 return mp_copy(a, r);
78 }
79 /* for polynomials larger than twice the field size or polynomials
80 * not using all words, use regular reduction */
81 if (a_bits > (521*2)) {
82 MP_CHECKOK(mp_mod(a, &meth->irr, r));
83 } else {
84 #define FIRST_DIGIT (ECP521_DIGITS-1)
85 for (i = FIRST_DIGIT; i < MP_USED(a)-1; i++) {
86 s1[i-FIRST_DIGIT] = (MP_DIGIT(a, i) >> 9)
87 | (MP_DIGIT(a, 1+i) << (MP_DIGIT_BIT-9));
88 }
89 s1[i-FIRST_DIGIT] = MP_DIGIT(a, i) >> 9;
90
91 if ( a != r ) {
92 MP_CHECKOK(s_mp_pad(r,ECP521_DIGITS));
93 for (i = 0; i < ECP521_DIGITS; i++) {
94 MP_DIGIT(r,i) = MP_DIGIT(a, i);
95 }
96 }
97 MP_USED(r) = ECP521_DIGITS;
98 MP_DIGIT(r,FIRST_DIGIT) &= 0x1FF;
99
100 MP_CHECKOK(s_mp_add(r, &m1));
101 if (MP_DIGIT(r, FIRST_DIGIT) & 0x200) {
102 MP_CHECKOK(s_mp_add_d(r,1));
103 MP_DIGIT(r,FIRST_DIGIT) &= 0x1FF;
104 } else if (s_mp_cmp(r, &meth->irr) == 0) {
105 mp_zero(r);
106 }
107 s_mp_clamp(r);
108 }
109
110 CLEANUP:
111 return res;
112 }
113
114 /* Compute the square of polynomial a, reduce modulo p521. Store the
115 * result in r. r could be a. Uses optimized modular reduction for p521.
116 */
117 mp_err
ec_GFp_nistp521_sqr(const mp_int * a,mp_int * r,const GFMethod * meth)118 ec_GFp_nistp521_sqr(const mp_int *a, mp_int *r, const GFMethod *meth)
119 {
120 mp_err res = MP_OKAY;
121
122 MP_CHECKOK(mp_sqr(a, r));
123 MP_CHECKOK(ec_GFp_nistp521_mod(r, r, meth));
124 CLEANUP:
125 return res;
126 }
127
128 /* Compute the product of two polynomials a and b, reduce modulo p521.
129 * Store the result in r. r could be a or b; a could be b. Uses
130 * optimized modular reduction for p521. */
131 mp_err
ec_GFp_nistp521_mul(const mp_int * a,const mp_int * b,mp_int * r,const GFMethod * meth)132 ec_GFp_nistp521_mul(const mp_int *a, const mp_int *b, mp_int *r,
133 const GFMethod *meth)
134 {
135 mp_err res = MP_OKAY;
136
137 MP_CHECKOK(mp_mul(a, b, r));
138 MP_CHECKOK(ec_GFp_nistp521_mod(r, r, meth));
139 CLEANUP:
140 return res;
141 }
142
143 /* Divides two field elements. If a is NULL, then returns the inverse of
144 * b. */
145 mp_err
ec_GFp_nistp521_div(const mp_int * a,const mp_int * b,mp_int * r,const GFMethod * meth)146 ec_GFp_nistp521_div(const mp_int *a, const mp_int *b, mp_int *r,
147 const GFMethod *meth)
148 {
149 mp_err res = MP_OKAY;
150 mp_int t;
151
152 /* If a is NULL, then return the inverse of b, otherwise return a/b. */
153 if (a == NULL) {
154 return mp_invmod(b, &meth->irr, r);
155 } else {
156 /* MPI doesn't support divmod, so we implement it using invmod and
157 * mulmod. */
158 MP_CHECKOK(mp_init(&t, FLAG(b)));
159 MP_CHECKOK(mp_invmod(b, &meth->irr, &t));
160 MP_CHECKOK(mp_mul(a, &t, r));
161 MP_CHECKOK(ec_GFp_nistp521_mod(r, r, meth));
162 CLEANUP:
163 mp_clear(&t);
164 return res;
165 }
166 }
167
168 /* Wire in fast field arithmetic and precomputation of base point for
169 * named curves. */
170 mp_err
ec_group_set_gfp521(ECGroup * group,ECCurveName name)171 ec_group_set_gfp521(ECGroup *group, ECCurveName name)
172 {
173 if (name == ECCurve_NIST_P521) {
174 group->meth->field_mod = &ec_GFp_nistp521_mod;
175 group->meth->field_mul = &ec_GFp_nistp521_mul;
176 group->meth->field_sqr = &ec_GFp_nistp521_sqr;
177 group->meth->field_div = &ec_GFp_nistp521_div;
178 }
179 return MP_OKAY;
180 }
181