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 Netscape security libraries.
27 *
28 * The Initial Developer of the Original Code is
29 * Netscape Communications Corporation.
30 * Portions created by the Initial Developer are Copyright (C) 2000
31 * the Initial Developer. All Rights Reserved.
32 *
33 * Contributor(s):
34 * Sheueling Chang Shantz <sheueling.chang@sun.com>,
35 * Stephen Fung <stephen.fung@sun.com>, and
36 * Douglas Stebila <douglas@stebila.ca> of Sun Laboratories.
37 *
38 *********************************************************************** */
39
40/* This file implements moduluar exponentiation using Montgomery's
41 * method for modular reduction. This file implements the method
42 * described as "Improvement 1" in the paper "A Cryptogrpahic Library for
43 * the Motorola DSP56000" by Stephen R. Dusse' and Burton S. Kaliski Jr.
44 * published in "Advances in Cryptology: Proceedings of EUROCRYPT '90"
45 * "Lecture Notes in Computer Science" volume 473, 1991, pg 230-244,
46 * published by Springer Verlag.
47 */
48
49#define MP_USING_CACHE_SAFE_MOD_EXP 1
50#ifndef _KERNEL
51#include <string.h>
52#include <stddef.h> /* ptrdiff_t */
53#endif
54#include "mpi-priv.h"
55#include "mplogic.h"
56#include "mpprime.h"
57#ifdef MP_USING_MONT_MULF
58#include "montmulf.h"
59#endif
60
61/* if MP_CHAR_STORE_SLOW is defined, we */
62/* need to know endianness of this platform. */
63#ifdef MP_CHAR_STORE_SLOW
64#if !defined(MP_IS_BIG_ENDIAN) && !defined(MP_IS_LITTLE_ENDIAN)
65#error "You must define MP_IS_BIG_ENDIAN or MP_IS_LITTLE_ENDIAN\n" \
66 " if you define MP_CHAR_STORE_SLOW."
67#endif
68#endif
69
70#ifndef STATIC
71#define STATIC
72#endif
73
74#define MAX_ODD_INTS 32 /* 2 ** (WINDOW_BITS - 1) */
75
76#ifndef _KERNEL
77#if defined(_WIN32_WCE)
78#define ABORT res = MP_UNDEF; goto CLEANUP
79#else
80#define ABORT abort()
81#endif
82#else
83#define ABORT res = MP_UNDEF; goto CLEANUP
84#endif /* _KERNEL */
85
86/* computes T = REDC(T), 2^b == R */
87mp_err s_mp_redc(mp_int *T, mp_mont_modulus *mmm)
88{
89 mp_err res;
90 mp_size i;
91
92 i = MP_USED(T) + MP_USED(&mmm->N) + 2;
93 MP_CHECKOK( s_mp_pad(T, i) );
94 for (i = 0; i < MP_USED(&mmm->N); ++i ) {
95 mp_digit m_i = MP_DIGIT(T, i) * mmm->n0prime;
96 /* T += N * m_i * (MP_RADIX ** i); */
97 MP_CHECKOK( s_mp_mul_d_add_offset(&mmm->N, m_i, T, i) );
98 }
99 s_mp_clamp(T);
100
101 /* T /= R */
102 s_mp_div_2d(T, mmm->b);
103
104 if ((res = s_mp_cmp(T, &mmm->N)) >= 0) {
105 /* T = T - N */
106 MP_CHECKOK( s_mp_sub(T, &mmm->N) );
107#ifdef DEBUG
108 if ((res = mp_cmp(T, &mmm->N)) >= 0) {
109 res = MP_UNDEF;
110 goto CLEANUP;
111 }
112#endif
113 }
114 res = MP_OKAY;
115CLEANUP:
116 return res;
117}
118
119#if !defined(MP_ASSEMBLY_MUL_MONT) && !defined(MP_MONT_USE_MP_MUL)
120mp_err s_mp_mul_mont(const mp_int *a, const mp_int *b, mp_int *c,
121 mp_mont_modulus *mmm)
122{
123 mp_digit *pb;
124 mp_digit m_i;
125 mp_err res;
126 mp_size ib;
127 mp_size useda, usedb;
128
129 ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG);
130
131 if (MP_USED(a) < MP_USED(b)) {
132 const mp_int *xch = b; /* switch a and b, to do fewer outer loops */
133 b = a;
134 a = xch;
135 }
136
137 MP_USED(c) = 1; MP_DIGIT(c, 0) = 0;
138 ib = MP_USED(a) + MP_MAX(MP_USED(b), MP_USED(&mmm->N)) + 2;
139 if((res = s_mp_pad(c, ib)) != MP_OKAY)
140 goto CLEANUP;
141
142 useda = MP_USED(a);
143 pb = MP_DIGITS(b);
144 s_mpv_mul_d(MP_DIGITS(a), useda, *pb++, MP_DIGITS(c));
145 s_mp_setz(MP_DIGITS(c) + useda + 1, ib - (useda + 1));
146 m_i = MP_DIGIT(c, 0) * mmm->n0prime;
147 s_mp_mul_d_add_offset(&mmm->N, m_i, c, 0);
148
149 /* Outer loop: Digits of b */
150 usedb = MP_USED(b);
151 for (ib = 1; ib < usedb; ib++) {
152 mp_digit b_i = *pb++;
153
154 /* Inner product: Digits of a */
155 if (b_i)
156 s_mpv_mul_d_add_prop(MP_DIGITS(a), useda, b_i, MP_DIGITS(c) + ib);
157 m_i = MP_DIGIT(c, ib) * mmm->n0prime;
158 s_mp_mul_d_add_offset(&mmm->N, m_i, c, ib);
159 }
160 if (usedb < MP_USED(&mmm->N)) {
161 for (usedb = MP_USED(&mmm->N); ib < usedb; ++ib ) {
162 m_i = MP_DIGIT(c, ib) * mmm->n0prime;
163 s_mp_mul_d_add_offset(&mmm->N, m_i, c, ib);
164 }
165 }
166 s_mp_clamp(c);
167 s_mp_div_2d(c, mmm->b);
168 if (s_mp_cmp(c, &mmm->N) >= 0) {
169 MP_CHECKOK( s_mp_sub(c, &mmm->N) );
170 }
171 res = MP_OKAY;
172
173CLEANUP:
174 return res;
175}
176#endif
177