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