21a7c4b1 |
1 | /* -*-c-*- |
2 | * |
34e4f738 |
3 | * $Id: mpbarrett.h,v 1.4 2004/04/01 12:50:09 mdw Exp $ |
21a7c4b1 |
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 $ |
34e4f738 |
33 | * Revision 1.4 2004/04/01 12:50:09 mdw |
34 | * Add cyclic group abstraction, with test code. Separate off exponentation |
35 | * functions for better static linking. Fix a buttload of bugs on the way. |
36 | * Generally ensure that negative exponents do inversion correctly. Add |
37 | * table of standard prime-field subgroups. (Binary field subgroups are |
38 | * currently unimplemented but easy to add if anyone ever finds a good one.) |
39 | * |
ab0350a6 |
40 | * Revision 1.3 2001/06/16 12:58:47 mdw |
41 | * Added simultaneous exponentiation with Barrett reduction. |
42 | * |
30cbe7a7 |
43 | * Revision 1.2 2000/10/08 12:03:44 mdw |
44 | * (mpbarrett_reduce): Cope with negative numbers. |
45 | * |
21a7c4b1 |
46 | * Revision 1.1 1999/12/10 23:22:00 mdw |
47 | * Barrett reduction support: works with even moduli. |
48 | * |
49 | */ |
50 | |
51 | /*----- Notes on Barrett reduction ----------------------------------------* |
52 | * |
53 | * Barrett reduction is a technique for computing modular residues. Unlike |
54 | * Montgomery reduction, it doesn't have restrictions on the modulus (except |
55 | * that it be positive) and doesn't confuse matters by putting an extra |
56 | * factor all the way through your computation. |
57 | * |
58 | * It's useful for slightly less heavy-duty work than Montgomery reduction |
59 | * because the precomputation phase is rather simpler, involving a single |
60 | * division operation. |
61 | * |
62 | * Sometimes it's useful to exponentiate modulo an even number, so there's a |
63 | * modexp routine provided which uses Barrett reduction rather than |
64 | * Montgomery reduction. This is handy when you're working on indices in an |
65 | * even-order cyclic group or something. |
66 | */ |
67 | |
68 | #ifndef CATACOMB_MPBARRETT_H |
69 | #define CATACOMB_MPBARRETT_H |
70 | |
71 | #ifdef __cplusplus |
72 | extern "C" { |
73 | #endif |
74 | |
75 | /*----- Header files ------------------------------------------------------*/ |
76 | |
77 | #ifndef CATACOMB_MP_H |
78 | # include "mp.h" |
79 | #endif |
80 | |
81 | /*----- Data structures ---------------------------------------------------*/ |
82 | |
83 | typedef struct mpbarrett { |
84 | mp *m; |
85 | mp *mu; |
86 | size_t k; |
87 | } mpbarrett; |
88 | |
89 | /*----- Functions provided ------------------------------------------------*/ |
90 | |
91 | /* --- @mpbarrett_create@ --- * |
92 | * |
93 | * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context |
94 | * @mp *m@ = modulus to work to |
95 | * |
96 | * |
97 | * Returns: --- |
98 | * |
99 | * Use: Initializes a Barrett reduction context ready for use. |
100 | */ |
101 | |
102 | extern void mpbarrett_create(mpbarrett */*mb*/, mp */*m*/); |
103 | |
104 | /* --- @mpbarrett_destroy@ --- * |
105 | * |
106 | * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context |
107 | * |
108 | * Returns: --- |
109 | * |
110 | * Use: Destroys a Barrett reduction context releasing any resources |
111 | * claimed. |
112 | */ |
113 | |
114 | extern void mpbarrett_destroy(mpbarrett */*mb*/); |
115 | |
116 | /* --- @mpbarrett_reduce@ --- * |
117 | * |
118 | * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context |
119 | * @mp *d@ = destination for result |
120 | * @mp *m@ = number to reduce |
121 | * |
122 | * Returns: The residue of @m@ modulo the number in the reduction |
123 | * context. |
124 | * |
30cbe7a7 |
125 | * Use: Performs an efficient modular reduction. |
21a7c4b1 |
126 | */ |
127 | |
128 | extern mp *mpbarrett_reduce(mpbarrett */*mb*/, mp */*d*/, mp */*m*/); |
129 | |
130 | /* --- @mpbarrett_exp@ --- * |
131 | * |
132 | * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context |
133 | * @mp *d@ = fake destination |
134 | * @mp *a@ = base |
135 | * @mp *e@ = exponent |
136 | * |
137 | * Returns: Result, %$a^e \bmod m$%. |
138 | */ |
139 | |
140 | extern mp *mpbarrett_exp(mpbarrett */*mb*/, mp */*d*/, mp */*a*/, mp */*e*/); |
141 | |
ab0350a6 |
142 | /* --- @mpbarrett_mexp@ --- * |
143 | * |
144 | * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context |
145 | * @mp *d@ = fake destination |
34e4f738 |
146 | * @const mp_expfactor *f@ = pointer to array of factors |
ab0350a6 |
147 | * @size_t n@ = number of factors supplied |
148 | * |
149 | * Returns: If the bases are %$g_0, g_1, \ldots, g_{n-1}$% and the |
150 | * exponents are %$e_0, e_1, \ldots, e_{n-1}$% then the result |
151 | * is: |
152 | * |
153 | * %$g_0^{e_0} g_1^{e_1} \ldots g_{n-1}^{e_{n-1}} \bmod m$% |
154 | */ |
155 | |
156 | extern mp *mpbarrett_mexp(mpbarrett */*mb*/, mp */*d*/, |
34e4f738 |
157 | const mp_expfactor */*f*/, size_t /*n*/); |
ab0350a6 |
158 | |
21a7c4b1 |
159 | /*----- That's all, folks -------------------------------------------------*/ |
160 | |
161 | #ifdef __cplusplus |
162 | } |
163 | #endif |
164 | |
165 | #endif |