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   1 /* -*-c-*-
   2  *
   3  * $Id: mpbarrett.h,v 1.4 2004/04/01 12:50:09 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 1.4  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.)
  39  *
  40  * Revision 1.3  2001/06/16 12:58:47  mdw
  41  * Added simultaneous exponentiation with Barrett reduction.
  42  *
  43  * Revision 1.2  2000/10/08 12:03:44  mdw
  44  * (mpbarrett_reduce): Cope with negative numbers.
  45  *
  46  * Revision 1.1  1999/12/10 23:22:00  mdw
  47  * Barrett reduction support: works with even moduli.
  48  *
  49  */
  50
  51 /*----- Notes on Barrett reduction ----------------------------------------*
  52  *
  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.
  57  *
  58  * It's useful for slightly less heavy-duty work than Montgomery reduction
  59  * because the precomputation phase is rather simpler, involving a single
  60  * division operation.
  61  *
  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.
  66  */
  67
  68 #ifndef CATACOMB_MPBARRETT_H
  69 #define CATACOMB_MPBARRETT_H
  70
  71 #ifdef __cplusplus
  72   extern "C" {
  73 #endif
  74
  75 /*----- Header files ------------------------------------------------------*/
  76
  77 #ifndef CATACOMB_MP_H
  78 #  include "mp.h"
  79 #endif
  80
  81 /*----- Data structures ---------------------------------------------------*/
  82
  83 typedef struct mpbarrett {
  84   mp *m;
  85   mp *mu;
  86   size_t k;
  87 } mpbarrett;
  88
  89 /*----- Functions provided ------------------------------------------------*/
  90
  91 /* --- @mpbarrett_create@ --- *
  92  *
  93  * Arguments:   @mpbarrett *mb@ = pointer to Barrett reduction context
  94  *              @mp *m@ = modulus to work to
  95  *
  96  *
  97  * Returns:     ---
  98  *
  99  * Use:         Initializes a Barrett reduction context ready for use.
 100  */
 101
 102 extern void mpbarrett_create(mpbarrett */*mb*/, mp */*m*/);
 103
 104 /* --- @mpbarrett_destroy@ --- *
 105  *
 106  * Arguments:   @mpbarrett *mb@ = pointer to Barrett reduction context
 107  *
 108  * Returns:     ---
 109  *
 110  * Use:         Destroys a Barrett reduction context releasing any resources
 111  *              claimed.
 112  */
 113
 114 extern void mpbarrett_destroy(mpbarrett */*mb*/);
 115
 116 /* --- @mpbarrett_reduce@ --- *
 117  *
 118  * Arguments:   @mpbarrett *mb@ = pointer to Barrett reduction context
 119  *              @mp *d@ = destination for result
 120  *              @mp *m@ = number to reduce
 121  *
 122  * Returns:     The residue of @m@ modulo the number in the reduction
 123  *              context.
 124  *
 125  * Use:         Performs an efficient modular reduction.
 126  */
 127
 128 extern mp *mpbarrett_reduce(mpbarrett */*mb*/, mp */*d*/, mp */*m*/);
 129
 130 /* --- @mpbarrett_exp@ --- *
 131  *
 132  * Arguments:   @mpbarrett *mb@ = pointer to Barrett reduction context
 133  *              @mp *d@ = fake destination
 134  *              @mp *a@ = base
 135  *              @mp *e@ = exponent
 136  *
 137  * Returns:     Result, %$a^e \bmod m$%.
 138  */
 139
 140 extern mp *mpbarrett_exp(mpbarrett */*mb*/, mp */*d*/, mp */*a*/, mp */*e*/);
 141
 142 /* --- @mpbarrett_mexp@ --- *
 143  *
 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
 148  *
 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
 151  *              is:
 152  *
 153  *              %$g_0^{e_0} g_1^{e_1} \ldots g_{n-1}^{e_{n-1}} \bmod m$%
 154  */
 155
 156 extern mp *mpbarrett_mexp(mpbarrett */*mb*/, mp */*d*/,
 157                           const mp_expfactor */*f*/, size_t /*n*/);
 158
 159 /*----- That's all, folks -------------------------------------------------*/
 160
 161 #ifdef __cplusplus
 162   }
 163 #endif
 164
 165 #endif