3 * $Id: mpbarrett.h,v 1.4 2004/04/01 12:50:09 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 /*----- Revision history --------------------------------------------------*
32 * $Log: mpbarrett.h,v $
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.)
40 * Revision 1.3 2001/06/16 12:58:47 mdw
41 * Added simultaneous exponentiation with Barrett reduction.
43 * Revision 1.2 2000/10/08 12:03:44 mdw
44 * (mpbarrett_reduce): Cope with negative numbers.
46 * Revision 1.1 1999/12/10 23:22:00 mdw
47 * Barrett reduction support: works with even moduli.
51 /*----- Notes on Barrett reduction ----------------------------------------*
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.
58 * It's useful for slightly less heavy-duty work than Montgomery reduction
59 * because the precomputation phase is rather simpler, involving a single
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.
68 #ifndef CATACOMB_MPBARRETT_H
69 #define CATACOMB_MPBARRETT_H
75 /*----- Header files ------------------------------------------------------*/
81 /*----- Data structures ---------------------------------------------------*/
83 typedef struct mpbarrett
{
89 /*----- Functions provided ------------------------------------------------*/
91 /* --- @mpbarrett_create@ --- *
93 * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context
94 * @mp *m@ = modulus to work to
99 * Use: Initializes a Barrett reduction context ready for use.
102 extern void mpbarrett_create(mpbarrett */
*mb*/
, mp */
*m*/
);
104 /* --- @mpbarrett_destroy@ --- *
106 * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context
110 * Use: Destroys a Barrett reduction context releasing any resources
114 extern void mpbarrett_destroy(mpbarrett */
*mb*/
);
116 /* --- @mpbarrett_reduce@ --- *
118 * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context
119 * @mp *d@ = destination for result
120 * @mp *m@ = number to reduce
122 * Returns: The residue of @m@ modulo the number in the reduction
125 * Use: Performs an efficient modular reduction.
128 extern mp
*mpbarrett_reduce(mpbarrett */
*mb*/
, mp */
*d*/
, mp */
*m*/
);
130 /* --- @mpbarrett_exp@ --- *
132 * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context
133 * @mp *d@ = fake destination
137 * Returns: Result, %$a^e \bmod m$%.
140 extern mp
*mpbarrett_exp(mpbarrett */
*mb*/
, mp */
*d*/
, mp */
*a*/
, mp */
*e*/
);
142 /* --- @mpbarrett_mexp@ --- *
144 * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context
145 * @mp *d@ = fake destination
146 * @const mp_expfactor *f@ = pointer to array of factors
147 * @size_t n@ = number of factors supplied
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
153 * %$g_0^{e_0} g_1^{e_1} \ldots g_{n-1}^{e_{n-1}} \bmod m$%
156 extern mp
*mpbarrett_mexp(mpbarrett */
*mb*/
, mp */
*d*/
,
157 const mp_expfactor */
*f*/
, size_t /*n*/);
159 /*----- That's all, folks -------------------------------------------------*/