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[u/mdw/catacomb] / rho.h

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-/* -*-c-*-
- *
- * $Id: rho.h,v 1.3 2004/04/08 01:36:15 mdw Exp $
- *
- * Pollard's rho algorithm for discrete logs
- *
- * (c) 2000 Straylight/Edgeware
- */
-
-/*----- Licensing notice --------------------------------------------------*
- *
- * This file is part of Catacomb.
- *
- * Catacomb is free software; you can redistribute it and/or modify
- * it under the terms of the GNU Library General Public License as
- * published by the Free Software Foundation; either version 2 of the
- * License, or (at your option) any later version.
- *
- * Catacomb is distributed in the hope that it will be useful,
- * but WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
- * GNU Library General Public License for more details.
- *
- * You should have received a copy of the GNU Library General Public
- * License along with Catacomb; if not, write to the Free
- * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
- * MA 02111-1307, USA.
- */
-
-#ifndef CATACOMB_RHO_H
-#define CATACOMB_RHO_H
-
-#ifdef __cplusplus
-  extern "C" {
-#endif
-
-/*----- Header files ------------------------------------------------------*/
-
-#ifndef CATACOMB_MP_H
-#  include "mp.h"
-#endif
-
-/*----- Data structures ---------------------------------------------------*/
-
-/* --- The group operations table --- */
-
-typedef struct rho_ops {
-  void (*sqr)(void *x, void *c);
-  void (*mul)(void *x, void *y, void *c);
-  int (*eq)(void *x, void *y);
-  int (*split)(void *x);
-  void (*drop)(void *x);
-} rho_ops;
-
-/* --- The Pollard's rho context structure --- */
-
-typedef struct rho_ctx {
-  const rho_ops *ops;                  /* Group operations table */
-  void *c;                             /* Context for group operations */
-  void *g, *a;                         /* Generator and argument for log */
-  mp *n;                               /* Cyclic group order */
-} rho_ctx;
-
-/*----- Functions provided ------------------------------------------------*/
-
-/* --- @rho@ --- *
- *
- * Arguments:  @rho_ctx *cc@ = pointer to the context structure
- *             @void *x, *y@ = two (equal) base values (try 1)
- *             @mp *a, *b@ = logs of %$x$% (see below)
- *
- * Returns:    The discrete logarithm %$\log_g a$%, or null if the algorithm
- *             failed.  (This is unlikely, though possible.)
- *
- * Use:                Uses Pollard's rho algorithm to compute discrete logs in the
- *             group %$G$% generated by %$g$%.
- *
- *             The algorithm works by finding a cycle in a pseudo-random
- *             walk.  The function @ops->split@ should return an element
- *             from %$\{\,0, 1, 2\,\}$% according to its argument, in order
- *             to determine the walk.  At each step in the walk, we know a
- *             group element %$x \in G$% together with its representation as
- *             a product of powers of %$g$% and $%a$% (i.e., we know that
- *             %$x = g^\alpha a^\beta$% for some %$\alpha$%, %$\beta$%).
- *
- *             Locating a cycle gives us a collision
- *
- *               %$g^{\alpha} a^{\beta} = g^{\alpha'} a^{\beta'}$%
- *
- *             Taking logs of both sides (to base %$g$%) gives us that
- *
- *               %$\log a\equiv\frac{\alpha-\alpha'}{\beta'-\beta}\bmod{n}$%
- *
- *             Good initial values are %$x = y = 1$% (the multiplicative
- *             identity of %$G$%) and %$\alpha\equiv\beta\equiv0\bmod{n}$%.
- *             If that doesn't work then start choosing more `interesting'
- *             values.
- *
- *             Note that the algorithm requires minimal space but
- *             %$O(\sqrt{n})$% time.  Don't do this on large groups,
- *             particularly if you can find a decent factor base.
- *
- *             Finally, note that this function will free the input values
- *             when it's finished with them.  This probably isn't a great
- *             problem.
- */
-
-extern mp *rho(rho_ctx */*cc*/, void */*x*/, void */*y*/,
-              mp */*a*/, mp */*b*/);
-
-/* --- @rho_prime@ --- *
- *
- * Arguments:  @mp *g@ = generator for the group
- *             @mp *a@ = value to find the logarithm of
- *             @mp *n@ = order of the group
- *             @mp *p@ = prime size of the underlying prime field
- *
- * Returns:    The discrete logarithm %$\log_g a$%.
- *
- * Use:                Computes discrete logarithms in a subgroup of a prime field.
- */
-
-extern mp *rho_prime(mp */*g*/, mp */*a*/, mp */*n*/, mp */*p*/);
-
-/*----- That's all, folks -------------------------------------------------*/
-
-#ifdef __cplusplus
-  }
-#endif
-
-#endif