3 * Barrett modular reduction
5 * (c) 1999 Straylight/Edgeware
8 /*----- Licensing notice --------------------------------------------------*
10 * This file is part of Catacomb.
12 * Catacomb is free software; you can redistribute it and/or modify
13 * it under the terms of the GNU Library General Public License as
14 * published by the Free Software Foundation; either version 2 of the
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17 * Catacomb is distributed in the hope that it will be useful,
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19 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
20 * GNU Library General Public License for more details.
22 * You should have received a copy of the GNU Library General Public
23 * License along with Catacomb; if not, write to the Free
24 * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
28 /*----- Notes on Barrett reduction ----------------------------------------*
30 * Barrett reduction is a technique for computing modular residues. Unlike
31 * Montgomery reduction, it doesn't have restrictions on the modulus (except
32 * that it be positive) and doesn't confuse matters by putting an extra
33 * factor all the way through your computation.
35 * It's useful for slightly less heavy-duty work than Montgomery reduction
36 * because the precomputation phase is rather simpler, involving a single
39 * Sometimes it's useful to exponentiate modulo an even number, so there's a
40 * modexp routine provided which uses Barrett reduction rather than
41 * Montgomery reduction. This is handy when you're working on indices in an
42 * even-order cyclic group or something.
45 #ifndef CATACOMB_MPBARRETT_H
46 #define CATACOMB_MPBARRETT_H
52 /*----- Header files ------------------------------------------------------*/
58 /*----- Data structures ---------------------------------------------------*/
60 typedef struct mpbarrett {
66 /*----- Functions provided ------------------------------------------------*/
68 /* --- @mpbarrett_create@ --- *
70 * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context
71 * @mp *m@ = modulus to work to
73 * Returns: Zero on success, nonzero on error.
75 * Use: Initializes a Barrett reduction context ready for use.
78 extern int mpbarrett_create(mpbarrett */*mb*/, mp */*m*/);
80 /* --- @mpbarrett_destroy@ --- *
82 * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context
86 * Use: Destroys a Barrett reduction context releasing any resources
90 extern void mpbarrett_destroy(mpbarrett */*mb*/);
92 /* --- @mpbarrett_reduce@ --- *
94 * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context
95 * @mp *d@ = destination for result
96 * @mp *m@ = number to reduce
98 * Returns: The residue of @m@ modulo the number in the reduction
101 * Use: Performs an efficient modular reduction.
104 extern mp *mpbarrett_reduce(mpbarrett */*mb*/, mp */*d*/, mp */*m*/);
106 /* --- @mpbarrett_exp@ --- *
108 * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context
109 * @mp *d@ = fake destination
113 * Returns: Result, %$a^e \bmod m$%.
116 extern mp *mpbarrett_exp(mpbarrett */*mb*/, mp */*d*/, mp */*a*/, mp */*e*/);
118 /* --- @mpbarrett_mexp@ --- *
120 * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context
121 * @mp *d@ = fake destination
122 * @const mp_expfactor *f@ = pointer to array of factors
123 * @size_t n@ = number of factors supplied
125 * Returns: If the bases are %$g_0, g_1, \ldots, g_{n-1}$% and the
126 * exponents are %$e_0, e_1, \ldots, e_{n-1}$% then the result
129 * %$g_0^{e_0} g_1^{e_1} \ldots g_{n-1}^{e_{n-1}} \bmod m$%
132 extern mp *mpbarrett_mexp(mpbarrett */*mb*/, mp */*d*/,
133 const mp_expfactor */*f*/, size_t /*n*/);
135 /*----- That's all, folks -------------------------------------------------*/