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.
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>, Sun Microsystems Laboratories
35 *
36 *********************************************************************** */
37
38/* Uses Montgomery reduction for field arithmetic. See mpi/mpmontg.c for
39 * code implementation. */
40
41#include "mpi.h"
42#include "mplogic.h"
43#include "mpi-priv.h"
44#include "ecl-priv.h"
45#include "ecp.h"
46#ifndef _KERNEL
47#include <stdlib.h>
48#include <stdio.h>
49#endif
50
51/* Construct a generic GFMethod for arithmetic over prime fields with
52 * irreducible irr. */
53GFMethod *
54GFMethod_consGFp_mont(const mp_int *irr)
55{
56 mp_err res = MP_OKAY;
57 int i;
58 GFMethod *meth = NULL;
59 mp_mont_modulus *mmm;
60
61 meth = GFMethod_consGFp(irr);
62 if (meth == NULL)
63 return NULL;
64
65#ifdef _KERNEL
66 mmm = (mp_mont_modulus *) kmem_alloc(sizeof(mp_mont_modulus),
67 FLAG(irr));
68#else
69 mmm = (mp_mont_modulus *) malloc(sizeof(mp_mont_modulus));
70#endif
71 if (mmm == NULL) {
72 res = MP_MEM;
73 goto CLEANUP;
74 }
75
76 meth->field_mul = &ec_GFp_mul_mont;
77 meth->field_sqr = &ec_GFp_sqr_mont;
78 meth->field_div = &ec_GFp_div_mont;
79 meth->field_enc = &ec_GFp_enc_mont;
80 meth->field_dec = &ec_GFp_dec_mont;
81 meth->extra1 = mmm;
82 meth->extra2 = NULL;
83 meth->extra_free = &ec_GFp_extra_free_mont;
84
85 mmm->N = meth->irr;
86 i = mpl_significant_bits(&meth->irr);
87 i += MP_DIGIT_BIT - 1;
88 mmm->b = i - i % MP_DIGIT_BIT;
89 mmm->n0prime = 0 - s_mp_invmod_radix(MP_DIGIT(&meth->irr, 0));
90
91 CLEANUP:
92 if (res != MP_OKAY) {
93 GFMethod_free(meth);
94 return NULL;
95 }
96 return meth;
97}
98
99/* Wrapper functions for generic prime field arithmetic. */
100
101/* Field multiplication using Montgomery reduction. */
102mp_err
103ec_GFp_mul_mont(const mp_int *a, const mp_int *b, mp_int *r,
104 const GFMethod *meth)
105{
106 mp_err res = MP_OKAY;
107
108#ifdef MP_MONT_USE_MP_MUL
109 /* if MP_MONT_USE_MP_MUL is defined, then the function s_mp_mul_mont
110 * is not implemented and we have to use mp_mul and s_mp_redc directly
111 */
112 MP_CHECKOK(mp_mul(a, b, r));
113 MP_CHECKOK(s_mp_redc(r, (mp_mont_modulus *) meth->extra1));
114#else
115 mp_int s;
116
117 MP_DIGITS(&s) = 0;
118 /* s_mp_mul_mont doesn't allow source and destination to be the same */
119 if ((a == r) || (b == r)) {
120 MP_CHECKOK(mp_init(&s, FLAG(a)));
121 MP_CHECKOK(s_mp_mul_mont
122 (a, b, &s, (mp_mont_modulus *) meth->extra1));
123 MP_CHECKOK(mp_copy(&s, r));
124 mp_clear(&s);
125 } else {
126 return s_mp_mul_mont(a, b, r, (mp_mont_modulus *) meth->extra1);
127 }
128#endif
129 CLEANUP:
130 return res;
131}
132
133/* Field squaring using Montgomery reduction. */
134mp_err
135ec_GFp_sqr_mont(const mp_int *a, mp_int *r, const GFMethod *meth)
136{
137 return ec_GFp_mul_mont(a, a, r, meth);
138}
139
140/* Field division using Montgomery reduction. */
141mp_err
142ec_GFp_div_mont(const mp_int *a, const mp_int *b, mp_int *r,
143 const GFMethod *meth)
144{
145 mp_err res = MP_OKAY;
146
147 /* if A=aZ represents a encoded in montgomery coordinates with Z and #
148 * and \ respectively represent multiplication and division in
149 * montgomery coordinates, then A\B = (a/b)Z = (A/B)Z and Binv =
150 * (1/b)Z = (1/B)(Z^2) where B # Binv = Z */
151 MP_CHECKOK(ec_GFp_div(a, b, r, meth));
152 MP_CHECKOK(ec_GFp_enc_mont(r, r, meth));
153 if (a == NULL) {
154 MP_CHECKOK(ec_GFp_enc_mont(r, r, meth));
155 }
156 CLEANUP:
157 return res;
158}
159
160/* Encode a field element in Montgomery form. See s_mp_to_mont in
161 * mpi/mpmontg.c */
162mp_err
163ec_GFp_enc_mont(const mp_int *a, mp_int *r, const GFMethod *meth)
164{
165 mp_mont_modulus *mmm;
166 mp_err res = MP_OKAY;
167
168 mmm = (mp_mont_modulus *) meth->extra1;
169 MP_CHECKOK(mpl_lsh(a, r, mmm->b));
170 MP_CHECKOK(mp_mod(r, &mmm->N, r));
171 CLEANUP:
172 return res;
173}
174
175/* Decode a field element from Montgomery form. */
176mp_err
177ec_GFp_dec_mont(const mp_int *a, mp_int *r, const GFMethod *meth)
178{
179 mp_err res = MP_OKAY;
180
181 if (a != r) {
182 MP_CHECKOK(mp_copy(a, r));
183 }
184 MP_CHECKOK(s_mp_redc(r, (mp_mont_modulus *) meth->extra1));
185 CLEANUP:
186 return res;
187}
188
189/* Free the memory allocated to the extra fields of Montgomery GFMethod
190 * object. */
191void
192ec_GFp_extra_free_mont(GFMethod *meth)
193{
194 if (meth->extra1 != NULL) {
195#ifdef _KERNEL
196 kmem_free(meth->extra1, sizeof(mp_mont_modulus));
197#else
198 free(meth->extra1);
199#endif
200 meth->extra1 = NULL;
201 }
202}
203