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   1 /* -*-c-*-
   2  *
   3  * $Id: rho.h,v 1.1 2000/07/09 21:32:30 mdw Exp $
   4  *
   5  * Pollard's rho algorithm for discrete logs
   6  *
   7  * (c) 2000 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: rho.h,v $
  33  * Revision 1.1  2000/07/09 21:32:30  mdw
  34  * Pollard's rho algorithm for computing discrete logs.
  35  *
  36  */
  37
  38 #ifndef CATACOMB_RHO_H
  39 #define CATACOMB_RHO_H
  40
  41 #ifdef __cplusplus
  42   extern "C" {
  43 #endif
  44
  45 /*----- Header files ------------------------------------------------------*/
  46
  47 #ifndef CATACOMB_MP_H
  48 #  include "mp.h"
  49 #endif
  50
  51 /*----- Data structures ---------------------------------------------------*/
  52
  53 /* --- The group operations table --- */
  54
  55 typedef struct rho_ops {
  56   void (*sqr)(void *x, void *c);
  57   void (*mul)(void *x, void *y, void *c);
  58   int (*eq)(void *x, void *y);
  59   int (*split)(void *x);
  60   void (*drop)(void *x);
  61 } rho_ops;
  62
  63 /* --- The Pollard's rho context structure --- */
  64
  65 typedef struct rho_ctx {
  66   rho_ops *ops;                         /* Group operations table */
  67   void *c;                              /* Context for group operations */
  68   void *g, *a;                          /* Generator and argument for log */
  69   mp *n;                                /* Cyclic group order */
  70 } rho_ctx;
  71
  72 /*----- Functions provided ------------------------------------------------*/
  73
  74 /* --- @rho@ --- *
  75  *
  76  * Arguments:   @rho_ctx *cc@ = pointer to the context structure
  77  *              @void *x, *y@ = two (equal) base values (try 1)
  78  *              @mp *a, *b@ = logs of %$x$% (see below)
  79  *
  80  * Returns:     The discrete logarithm %$\log_g a$%, or null if the algorithm
  81  *              failed.  (This is unlikely, though possible.)
  82  *
  83  * Use:         Uses Pollard's rho algorithm to compute discrete logs in the
  84  *              group %$G$% generated by %$g$%.
  85  *
  86  *              The algorithm works by finding a cycle in a pseudo-random
  87  *              walk.  The function @ops->split@ should return an element
  88  *              from %$\{\,0, 1, 2\,\}$% according to its argument, in order
  89  *              to determine the walk.  At each step in the walk, we know a
  90  *              group element %$x \in G$% together with its representation as
  91  *              a product of powers of %$g$% and $%a$% (i.e., we know that
  92  *              %$x = g^\alpha a^\beta$% for some %$\alpha$%, %$\beta$%).
  93  *
  94  *              Locating a cycle gives us a collision
  95  *
  96  *                %$g^{\alpha} a^{\beta} = g^{\alpha'} a^{\beta'}$%
  97  *
  98  *              Taking logs of both sides (to base %$g$%) gives us that
  99  *
 100  *                %$\log a\equiv\frac{\alpha-\alpha'}{\beta'-\beta}\bmod{n}$%
 101  *
 102  *              Good initial values are %$x = y = 1$% (the multiplicative
 103  *              identity of %$G$%) and %$\alpha\equiv\beta\equiv0\bmod{n}$%.
 104  *              If that doesn't work then start choosing more `interesting'
 105  *              values.
 106  *
 107  *              Note that the algorithm requires minimal space but
 108  *              %$O(\sqrt{n})$% time.  Don't do this on large groups,
 109  *              particularly if you can find a decent factor base.
 110  *
 111  *              Finally, note that this function will free the input values
 112  *              when it's finished with them.  This probably isn't a great
 113  *              problem.
 114  */
 115
 116 extern mp *rho(rho_ctx */*cc*/, void */*x*/, void */*y*/,
 117                mp */*a*/, mp */*b*/);
 118
 119 /* --- @rho_prime@ --- *
 120  *
 121  * Arguments:   @mp *g@ = generator for the group
 122  *              @mp *a@ = value to find the logarithm of
 123  *              @mp *n@ = order of the group
 124  *              @mp *p@ = prime size of the underlying prime field
 125  *
 126  * Returns:     The discrete logarithm %$\log_g a$%.
 127  *
 128  * Use:         Computes discrete logarithms in a subgroup of a prime field.
 129  */
 130
 131 extern mp *rho_prime(mp */*g*/, mp */*a*/, mp */*n*/, mp */*p*/);
 132
 133 /*----- That's all, folks -------------------------------------------------*/
 134
 135 #ifdef __cplusplus
 136   }
 137 #endif
 138
 139 #endif