3 * $Id: mpbarrett.h,v 1.5 2004/04/08 01:36:15 mdw Exp $
5 * Barrett modular reduction
7 * (c) 1999 Straylight/Edgeware
10 /*----- Licensing notice --------------------------------------------------*
12 * This file is part of Catacomb.
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.
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.
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,
30 /*----- Notes on Barrett reduction ----------------------------------------*
32 * Barrett reduction is a technique for computing modular residues. Unlike
33 * Montgomery reduction, it doesn't have restrictions on the modulus (except
34 * that it be positive) and doesn't confuse matters by putting an extra
35 * factor all the way through your computation.
37 * It's useful for slightly less heavy-duty work than Montgomery reduction
38 * because the precomputation phase is rather simpler, involving a single
41 * Sometimes it's useful to exponentiate modulo an even number, so there's a
42 * modexp routine provided which uses Barrett reduction rather than
43 * Montgomery reduction. This is handy when you're working on indices in an
44 * even-order cyclic group or something.
47 #ifndef CATACOMB_MPBARRETT_H
48 #define CATACOMB_MPBARRETT_H
54 /*----- Header files ------------------------------------------------------*/
60 /*----- Data structures ---------------------------------------------------*/
62 typedef struct mpbarrett
{
68 /*----- Functions provided ------------------------------------------------*/
70 /* --- @mpbarrett_create@ --- *
72 * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context
73 * @mp *m@ = modulus to work to
78 * Use: Initializes a Barrett reduction context ready for use.
81 extern void mpbarrett_create(mpbarrett */
*mb*/
, mp */
*m*/
);
83 /* --- @mpbarrett_destroy@ --- *
85 * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context
89 * Use: Destroys a Barrett reduction context releasing any resources
93 extern void mpbarrett_destroy(mpbarrett */
*mb*/
);
95 /* --- @mpbarrett_reduce@ --- *
97 * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context
98 * @mp *d@ = destination for result
99 * @mp *m@ = number to reduce
101 * Returns: The residue of @m@ modulo the number in the reduction
104 * Use: Performs an efficient modular reduction.
107 extern mp
*mpbarrett_reduce(mpbarrett */
*mb*/
, mp */
*d*/
, mp */
*m*/
);
109 /* --- @mpbarrett_exp@ --- *
111 * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context
112 * @mp *d@ = fake destination
116 * Returns: Result, %$a^e \bmod m$%.
119 extern mp
*mpbarrett_exp(mpbarrett */
*mb*/
, mp */
*d*/
, mp */
*a*/
, mp */
*e*/
);
121 /* --- @mpbarrett_mexp@ --- *
123 * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context
124 * @mp *d@ = fake destination
125 * @const mp_expfactor *f@ = pointer to array of factors
126 * @size_t n@ = number of factors supplied
128 * Returns: If the bases are %$g_0, g_1, \ldots, g_{n-1}$% and the
129 * exponents are %$e_0, e_1, \ldots, e_{n-1}$% then the result
132 * %$g_0^{e_0} g_1^{e_1} \ldots g_{n-1}^{e_{n-1}} \bmod m$%
135 extern mp
*mpbarrett_mexp(mpbarrett */
*mb*/
, mp */
*d*/
,
136 const mp_expfactor */
*f*/
, size_t /*n*/);
138 /*----- That's all, folks -------------------------------------------------*/