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 Netscape security libraries.
30 *
31 * The Initial Developer of the Original Code is
32 * Netscape Communications Corporation.
33 * Portions created by the Initial Developer are Copyright (C) 2000
34 * the Initial Developer. All Rights Reserved.
35 *
36 * Contributor(s):
37 * Sheueling Chang Shantz <sheueling.chang@sun.com>,
38 * Stephen Fung <stephen.fung@sun.com>, and
39 * Douglas Stebila <douglas@stebila.ca> of Sun Laboratories.
40 *
41 * Alternatively, the contents of this file may be used under the terms of
42 * either the GNU General Public License Version 2 or later (the "GPL"), or
43 * the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
44 * in which case the provisions of the GPL or the LGPL are applicable instead
45 * of those above. If you wish to allow use of your version of this file only
46 * under the terms of either the GPL or the LGPL, and not to allow others to
47 * use your version of this file under the terms of the MPL, indicate your
48 * decision by deleting the provisions above and replace them with the notice
49 * and other provisions required by the GPL or the LGPL. If you do not delete
50 * the provisions above, a recipient may use your version of this file under
51 * the terms of any one of the MPL, the GPL or the LGPL.
52 *
53 *********************************************************************** */
54 /*
55 * Copyright (c) 2007, Oracle and/or its affiliates. All rights reserved.
56 * Use is subject to license terms.
57 */
58
59 /* $Id: mpmontg.c,v 1.20 2006/08/29 02:41:38 nelson%bolyard.com Exp $ */
60
61 /* This file implements moduluar exponentiation using Montgomery's
62 * method for modular reduction. This file implements the method
63 * described as "Improvement 1" in the paper "A Cryptogrpahic Library for
64 * the Motorola DSP56000" by Stephen R. Dusse' and Burton S. Kaliski Jr.
65 * published in "Advances in Cryptology: Proceedings of EUROCRYPT '90"
66 * "Lecture Notes in Computer Science" volume 473, 1991, pg 230-244,
67 * published by Springer Verlag.
68 */
69
70 #define MP_USING_CACHE_SAFE_MOD_EXP 1
71 #ifndef _KERNEL
72 #include <string.h>
73 #include <stddef.h> /* ptrdiff_t */
74 #endif
75 #include "mpi-priv.h"
76 #include "mplogic.h"
77 #include "mpprime.h"
78 #ifdef MP_USING_MONT_MULF
79 #include "montmulf.h"
80 #endif
81
82 /* if MP_CHAR_STORE_SLOW is defined, we */
83 /* need to know endianness of this platform. */
84 #ifdef MP_CHAR_STORE_SLOW
85 #if !defined(MP_IS_BIG_ENDIAN) && !defined(MP_IS_LITTLE_ENDIAN)
86 #error "You must define MP_IS_BIG_ENDIAN or MP_IS_LITTLE_ENDIAN\n" \
87 " if you define MP_CHAR_STORE_SLOW."
88 #endif
89 #endif
90
91 #ifndef STATIC
92 #define STATIC
93 #endif
94
95 #define MAX_ODD_INTS 32 /* 2 ** (WINDOW_BITS - 1) */
96
97 #ifndef _KERNEL
98 #if defined(_WIN32_WCE)
99 #define ABORT res = MP_UNDEF; goto CLEANUP
100 #else
101 #define ABORT abort()
102 #endif
103 #else
104 #define ABORT res = MP_UNDEF; goto CLEANUP
105 #endif /* _KERNEL */
106
107 /* computes T = REDC(T), 2^b == R */
108 mp_err s_mp_redc(mp_int *T, mp_mont_modulus *mmm)
109 {
110 mp_err res;
111 mp_size i;
112
113 i = MP_USED(T) + MP_USED(&mmm->N) + 2;
114 MP_CHECKOK( s_mp_pad(T, i) );
115 for (i = 0; i < MP_USED(&mmm->N); ++i ) {
116 mp_digit m_i = MP_DIGIT(T, i) * mmm->n0prime;
117 /* T += N * m_i * (MP_RADIX ** i); */
118 MP_CHECKOK( s_mp_mul_d_add_offset(&mmm->N, m_i, T, i) );
119 }
120 s_mp_clamp(T);
121
122 /* T /= R */
123 s_mp_div_2d(T, mmm->b);
124
125 if ((res = s_mp_cmp(T, &mmm->N)) >= 0) {
126 /* T = T - N */
127 MP_CHECKOK( s_mp_sub(T, &mmm->N) );
128 #ifdef DEBUG
129 if ((res = mp_cmp(T, &mmm->N)) >= 0) {
130 res = MP_UNDEF;
131 goto CLEANUP;
132 }
133 #endif
134 }
135 res = MP_OKAY;
136 CLEANUP:
137 return res;
138 }
139
140 #if !defined(MP_ASSEMBLY_MUL_MONT) && !defined(MP_MONT_USE_MP_MUL)
141 mp_err s_mp_mul_mont(const mp_int *a, const mp_int *b, mp_int *c,
142 mp_mont_modulus *mmm)
143 {
144 mp_digit *pb;
145 mp_digit m_i;
146 mp_err res;
147 mp_size ib;
148 mp_size useda, usedb;
149
150 ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG);
151
152 if (MP_USED(a) < MP_USED(b)) {
153 const mp_int *xch = b; /* switch a and b, to do fewer outer loops */
154 b = a;
155 a = xch;
156 }
157
158 MP_USED(c) = 1; MP_DIGIT(c, 0) = 0;
159 ib = MP_USED(a) + MP_MAX(MP_USED(b), MP_USED(&mmm->N)) + 2;
160 if((res = s_mp_pad(c, ib)) != MP_OKAY)
161 goto CLEANUP;
162
163 useda = MP_USED(a);
164 pb = MP_DIGITS(b);
165 s_mpv_mul_d(MP_DIGITS(a), useda, *pb++, MP_DIGITS(c));
166 s_mp_setz(MP_DIGITS(c) + useda + 1, ib - (useda + 1));
167 m_i = MP_DIGIT(c, 0) * mmm->n0prime;
168 s_mp_mul_d_add_offset(&mmm->N, m_i, c, 0);
169
170 /* Outer loop: Digits of b */
171 usedb = MP_USED(b);
172 for (ib = 1; ib < usedb; ib++) {
173 mp_digit b_i = *pb++;
174
175 /* Inner product: Digits of a */
176 if (b_i)
177 s_mpv_mul_d_add_prop(MP_DIGITS(a), useda, b_i, MP_DIGITS(c) + ib);
178 m_i = MP_DIGIT(c, ib) * mmm->n0prime;
179 s_mp_mul_d_add_offset(&mmm->N, m_i, c, ib);
180 }
181 if (usedb < MP_USED(&mmm->N)) {
182 for (usedb = MP_USED(&mmm->N); ib < usedb; ++ib ) {
183 m_i = MP_DIGIT(c, ib) * mmm->n0prime;
184 s_mp_mul_d_add_offset(&mmm->N, m_i, c, ib);
185 }
186 }
187 s_mp_clamp(c);
188 s_mp_div_2d(c, mmm->b);
189 if (s_mp_cmp(c, &mmm->N) >= 0) {
190 MP_CHECKOK( s_mp_sub(c, &mmm->N) );
191 }
192 res = MP_OKAY;
193
194 CLEANUP:
195 return res;
196 }
197 #endif