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,
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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
75 * Returns: Zero on success, nonzero on error.
77 * Use: Initializes a Barrett reduction context ready for use.
80 extern int mpbarrett_create(mpbarrett */
*mb*/
, mp */
*m*/
);
82 /* --- @mpbarrett_destroy@ --- *
84 * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context
88 * Use: Destroys a Barrett reduction context releasing any resources
92 extern void mpbarrett_destroy(mpbarrett */
*mb*/
);
94 /* --- @mpbarrett_reduce@ --- *
96 * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context
97 * @mp *d@ = destination for result
98 * @mp *m@ = number to reduce
100 * Returns: The residue of @m@ modulo the number in the reduction
103 * Use: Performs an efficient modular reduction.
106 extern mp
*mpbarrett_reduce(mpbarrett */
*mb*/
, mp */
*d*/
, mp */
*m*/
);
108 /* --- @mpbarrett_exp@ --- *
110 * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context
111 * @mp *d@ = fake destination
115 * Returns: Result, %$a^e \bmod m$%.
118 extern mp
*mpbarrett_exp(mpbarrett */
*mb*/
, mp */
*d*/
, mp */
*a*/
, mp */
*e*/
);
120 /* --- @mpbarrett_mexp@ --- *
122 * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context
123 * @mp *d@ = fake destination
124 * @const mp_expfactor *f@ = pointer to array of factors
125 * @size_t n@ = number of factors supplied
127 * Returns: If the bases are %$g_0, g_1, \ldots, g_{n-1}$% and the
128 * exponents are %$e_0, e_1, \ldots, e_{n-1}$% then the result
131 * %$g_0^{e_0} g_1^{e_1} \ldots g_{n-1}^{e_{n-1}} \bmod m$%
134 extern mp
*mpbarrett_mexp(mpbarrett */
*mb*/
, mp */
*d*/
,
135 const mp_expfactor */
*f*/
, size_t /*n*/);
137 /*----- That's all, folks -------------------------------------------------*/