git.distorted.org.uk Git - u/mdw/catacomb/blob - mpbarrett.h

   1 /* -*-c-*-
   2  *
   3  * $Id$
   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 /*----- Notes on Barrett reduction ----------------------------------------*
  31  *
  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.
  36  *
  37  * It's useful for slightly less heavy-duty work than Montgomery reduction
  38  * because the precomputation phase is rather simpler, involving a single
  39  * division operation.
  40  *
  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.
  45  */
  46
  47 #ifndef CATACOMB_MPBARRETT_H
  48 #define CATACOMB_MPBARRETT_H
  49
  50 #ifdef __cplusplus
  51   extern "C" {
  52 #endif
  53
  54 /*----- Header files ------------------------------------------------------*/
  55
  56 #ifndef CATACOMB_MP_H
  57 #  include "mp.h"
  58 #endif
  59
  60 /*----- Data structures ---------------------------------------------------*/
  61
  62 typedef struct mpbarrett {
  63   mp *m;
  64   mp *mu;
  65   size_t k;
  66 } mpbarrett;
  67
  68 /*----- Functions provided ------------------------------------------------*/
  69
  70 /* --- @mpbarrett_create@ --- *
  71  *
  72  * Arguments:   @mpbarrett *mb@ = pointer to Barrett reduction context
  73  *              @mp *m@ = modulus to work to
  74  *
  75  * Returns:     Zero on success, nonzero on error.
  76  *
  77  * Use:         Initializes a Barrett reduction context ready for use.
  78  */
  79
  80 extern int mpbarrett_create(mpbarrett */*mb*/, mp */*m*/);
  81
  82 /* --- @mpbarrett_destroy@ --- *
  83  *
  84  * Arguments:   @mpbarrett *mb@ = pointer to Barrett reduction context
  85  *
  86  * Returns:     ---
  87  *
  88  * Use:         Destroys a Barrett reduction context releasing any resources
  89  *              claimed.
  90  */
  91
  92 extern void mpbarrett_destroy(mpbarrett */*mb*/);
  93
  94 /* --- @mpbarrett_reduce@ --- *
  95  *
  96  * Arguments:   @mpbarrett *mb@ = pointer to Barrett reduction context
  97  *              @mp *d@ = destination for result
  98  *              @mp *m@ = number to reduce
  99  *
 100  * Returns:     The residue of @m@ modulo the number in the reduction
 101  *              context.
 102  *
 103  * Use:         Performs an efficient modular reduction.
 104  */
 105
 106 extern mp *mpbarrett_reduce(mpbarrett */*mb*/, mp */*d*/, mp */*m*/);
 107
 108 /* --- @mpbarrett_exp@ --- *
 109  *
 110  * Arguments:   @mpbarrett *mb@ = pointer to Barrett reduction context
 111  *              @mp *d@ = fake destination
 112  *              @mp *a@ = base
 113  *              @mp *e@ = exponent
 114  *
 115  * Returns:     Result, %$a^e \bmod m$%.
 116  */
 117
 118 extern mp *mpbarrett_exp(mpbarrett */*mb*/, mp */*d*/, mp */*a*/, mp */*e*/);
 119
 120 /* --- @mpbarrett_mexp@ --- *
 121  *
 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
 126  *
 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
 129  *              is:
 130  *
 131  *              %$g_0^{e_0} g_1^{e_1} \ldots g_{n-1}^{e_{n-1}} \bmod m$%
 132  */
 133
 134 extern mp *mpbarrett_mexp(mpbarrett */*mb*/, mp */*d*/,
 135                           const mp_expfactor */*f*/, size_t /*n*/);
 136
 137 /*----- That's all, folks -------------------------------------------------*/
 138
 139 #ifdef __cplusplus
 140   }
 141 #endif
 142
 143 #endif