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1 | /* -*-c-*- |
2 | * |
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3 | * $Id: mpbarrett.h,v 1.3 2001/06/16 12:58:47 mdw Exp $ |
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4 | * |
5 | * Barrett modular reduction |
6 | * |
7 | * (c) 1999 Straylight/Edgeware |
8 | */ |
9 | |
10 | /*----- Licensing notice --------------------------------------------------* |
11 | * |
12 | * This file is part of Catacomb. |
13 | * |
14 | * Catacomb is free software; you can redistribute it and/or modify |
15 | * it under the terms of the GNU Library General Public License as |
16 | * published by the Free Software Foundation; either version 2 of the |
17 | * License, or (at your option) any later version. |
18 | * |
19 | * Catacomb is distributed in the hope that it will be useful, |
20 | * but WITHOUT ANY WARRANTY; without even the implied warranty of |
21 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
22 | * GNU Library General Public License for more details. |
23 | * |
24 | * You should have received a copy of the GNU Library General Public |
25 | * License along with Catacomb; if not, write to the Free |
26 | * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, |
27 | * MA 02111-1307, USA. |
28 | */ |
29 | |
30 | /*----- Revision history --------------------------------------------------* |
31 | * |
32 | * $Log: mpbarrett.h,v $ |
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33 | * Revision 1.3 2001/06/16 12:58:47 mdw |
34 | * Added simultaneous exponentiation with Barrett reduction. |
35 | * |
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36 | * Revision 1.2 2000/10/08 12:03:44 mdw |
37 | * (mpbarrett_reduce): Cope with negative numbers. |
38 | * |
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39 | * Revision 1.1 1999/12/10 23:22:00 mdw |
40 | * Barrett reduction support: works with even moduli. |
41 | * |
42 | */ |
43 | |
44 | /*----- Notes on Barrett reduction ----------------------------------------* |
45 | * |
46 | * Barrett reduction is a technique for computing modular residues. Unlike |
47 | * Montgomery reduction, it doesn't have restrictions on the modulus (except |
48 | * that it be positive) and doesn't confuse matters by putting an extra |
49 | * factor all the way through your computation. |
50 | * |
51 | * It's useful for slightly less heavy-duty work than Montgomery reduction |
52 | * because the precomputation phase is rather simpler, involving a single |
53 | * division operation. |
54 | * |
55 | * Sometimes it's useful to exponentiate modulo an even number, so there's a |
56 | * modexp routine provided which uses Barrett reduction rather than |
57 | * Montgomery reduction. This is handy when you're working on indices in an |
58 | * even-order cyclic group or something. |
59 | */ |
60 | |
61 | #ifndef CATACOMB_MPBARRETT_H |
62 | #define CATACOMB_MPBARRETT_H |
63 | |
64 | #ifdef __cplusplus |
65 | extern "C" { |
66 | #endif |
67 | |
68 | /*----- Header files ------------------------------------------------------*/ |
69 | |
70 | #ifndef CATACOMB_MP_H |
71 | # include "mp.h" |
72 | #endif |
73 | |
74 | /*----- Data structures ---------------------------------------------------*/ |
75 | |
76 | typedef struct mpbarrett { |
77 | mp *m; |
78 | mp *mu; |
79 | size_t k; |
80 | } mpbarrett; |
81 | |
82 | /*----- Functions provided ------------------------------------------------*/ |
83 | |
84 | /* --- @mpbarrett_create@ --- * |
85 | * |
86 | * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context |
87 | * @mp *m@ = modulus to work to |
88 | * |
89 | * |
90 | * Returns: --- |
91 | * |
92 | * Use: Initializes a Barrett reduction context ready for use. |
93 | */ |
94 | |
95 | extern void mpbarrett_create(mpbarrett */*mb*/, mp */*m*/); |
96 | |
97 | /* --- @mpbarrett_destroy@ --- * |
98 | * |
99 | * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context |
100 | * |
101 | * Returns: --- |
102 | * |
103 | * Use: Destroys a Barrett reduction context releasing any resources |
104 | * claimed. |
105 | */ |
106 | |
107 | extern void mpbarrett_destroy(mpbarrett */*mb*/); |
108 | |
109 | /* --- @mpbarrett_reduce@ --- * |
110 | * |
111 | * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context |
112 | * @mp *d@ = destination for result |
113 | * @mp *m@ = number to reduce |
114 | * |
115 | * Returns: The residue of @m@ modulo the number in the reduction |
116 | * context. |
117 | * |
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118 | * Use: Performs an efficient modular reduction. |
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119 | */ |
120 | |
121 | extern mp *mpbarrett_reduce(mpbarrett */*mb*/, mp */*d*/, mp */*m*/); |
122 | |
123 | /* --- @mpbarrett_exp@ --- * |
124 | * |
125 | * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context |
126 | * @mp *d@ = fake destination |
127 | * @mp *a@ = base |
128 | * @mp *e@ = exponent |
129 | * |
130 | * Returns: Result, %$a^e \bmod m$%. |
131 | */ |
132 | |
133 | extern mp *mpbarrett_exp(mpbarrett */*mb*/, mp */*d*/, mp */*a*/, mp */*e*/); |
134 | |
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135 | /* --- @mpbarrett_mexp@ --- * |
136 | * |
137 | * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context |
138 | * @mp *d@ = fake destination |
139 | * @mp_expfactor *f@ = pointer to array of factors |
140 | * @size_t n@ = number of factors supplied |
141 | * |
142 | * Returns: If the bases are %$g_0, g_1, \ldots, g_{n-1}$% and the |
143 | * exponents are %$e_0, e_1, \ldots, e_{n-1}$% then the result |
144 | * is: |
145 | * |
146 | * %$g_0^{e_0} g_1^{e_1} \ldots g_{n-1}^{e_{n-1}} \bmod m$% |
147 | */ |
148 | |
149 | extern mp *mpbarrett_mexp(mpbarrett */*mb*/, mp */*d*/, |
150 | mp_expfactor */*f*/, size_t /*n*/); |
151 | |
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152 | /*----- That's all, folks -------------------------------------------------*/ |
153 | |
154 | #ifdef __cplusplus |
155 | } |
156 | #endif |
157 | |
158 | #endif |