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

   1 /* -*-c-*-
   2  *
   3  * Barrett modular reduction
   4  *
   5  * (c) 1999 Straylight/Edgeware
   6  */
   7
   8 /*----- Licensing notice --------------------------------------------------*
   9  *
  10  * This file is part of Catacomb.
  11  *
  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
  15  * License, or (at your option) any later version.
  16  *
  17  * Catacomb is distributed in the hope that it will be useful,
  18  * but WITHOUT ANY WARRANTY; without even the implied warranty of
  19  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  20  * GNU Library General Public License for more details.
  21  *
  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,
  25  * MA 02111-1307, USA.
  26  */
  27
  28 /*----- Notes on Barrett reduction ----------------------------------------*
  29  *
  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.
  34  *
  35  * It's useful for slightly less heavy-duty work than Montgomery reduction
  36  * because the precomputation phase is rather simpler, involving a single
  37  * division operation.
  38  *
  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.
  43  */
  44
  45 #ifndef CATACOMB_MPBARRETT_H
  46 #define CATACOMB_MPBARRETT_H
  47
  48 #ifdef __cplusplus
  49   extern "C" {
  50 #endif
  51
  52 /*----- Header files ------------------------------------------------------*/
  53
  54 #ifndef CATACOMB_MP_H
  55 #  include "mp.h"
  56 #endif
  57
  58 /*----- Data structures ---------------------------------------------------*/
  59
  60 typedef struct mpbarrett {
  61   mp *m;
  62   mp *mu;
  63   size_t k;
  64 } mpbarrett;
  65
  66 /*----- Functions provided ------------------------------------------------*/
  67
  68 /* --- @mpbarrett_create@ --- *
  69  *
  70  * Arguments:   @mpbarrett *mb@ = pointer to Barrett reduction context
  71  *              @mp *m@ = modulus to work to
  72  *
  73  * Returns:     Zero on success, nonzero on error.
  74  *
  75  * Use:         Initializes a Barrett reduction context ready for use.
  76  */
  77
  78 extern int mpbarrett_create(mpbarrett */*mb*/, mp */*m*/);
  79
  80 /* --- @mpbarrett_destroy@ --- *
  81  *
  82  * Arguments:   @mpbarrett *mb@ = pointer to Barrett reduction context
  83  *
  84  * Returns:     ---
  85  *
  86  * Use:         Destroys a Barrett reduction context releasing any resources
  87  *              claimed.
  88  */
  89
  90 extern void mpbarrett_destroy(mpbarrett */*mb*/);
  91
  92 /* --- @mpbarrett_reduce@ --- *
  93  *
  94  * Arguments:   @mpbarrett *mb@ = pointer to Barrett reduction context
  95  *              @mp *d@ = destination for result
  96  *              @mp *m@ = number to reduce
  97  *
  98  * Returns:     The residue of @m@ modulo the number in the reduction
  99  *              context.
 100  *
 101  * Use:         Performs an efficient modular reduction.
 102  */
 103
 104 extern mp *mpbarrett_reduce(mpbarrett */*mb*/, mp */*d*/, mp */*m*/);
 105
 106 /* --- @mpbarrett_exp@ --- *
 107  *
 108  * Arguments:   @mpbarrett *mb@ = pointer to Barrett reduction context
 109  *              @mp *d@ = fake destination
 110  *              @mp *a@ = base
 111  *              @mp *e@ = exponent
 112  *
 113  * Returns:     Result, %$a^e \bmod m$%.
 114  */
 115
 116 extern mp *mpbarrett_exp(mpbarrett */*mb*/, mp */*d*/, mp */*a*/, mp */*e*/);
 117
 118 /* --- @mpbarrett_mexp@ --- *
 119  *
 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
 124  *
 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
 127  *              is:
 128  *
 129  *              %$g_0^{e_0} g_1^{e_1} \ldots g_{n-1}^{e_{n-1}} \bmod m$%
 130  */
 131
 132 extern mp *mpbarrett_mexp(mpbarrett */*mb*/, mp */*d*/,
 133                           const mp_expfactor */*f*/, size_t /*n*/);
 134
 135 /*----- That's all, folks -------------------------------------------------*/
 136
 137 #ifdef __cplusplus
 138   }
 139 #endif
 140
 141 #endif