3 * $Id: rho.h,v 1.1 2000/07/09 21:32:30 mdw Exp $
5 * Pollard's rho algorithm for discrete logs
7 * (c) 2000 Straylight/Edgeware
10 /*----- Licensing notice --------------------------------------------------*
12 * This file is part of Catacomb.
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.
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.
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,
30 /*----- Revision history --------------------------------------------------*
33 * Revision 1.1 2000/07/09 21:32:30 mdw
34 * Pollard's rho algorithm for computing discrete logs.
38 #ifndef CATACOMB_RHO_H
39 #define CATACOMB_RHO_H
45 /*----- Header files ------------------------------------------------------*/
51 /*----- Data structures ---------------------------------------------------*/
53 /* --- The group operations table --- */
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
);
63 /* --- The Pollard's rho context structure --- */
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 */
72 /*----- Functions provided ------------------------------------------------*/
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)
80 * Returns: The discrete logarithm %$\log_g a$%, or null if the algorithm
81 * failed. (This is unlikely, though possible.)
83 * Use: Uses Pollard's rho algorithm to compute discrete logs in the
84 * group %$G$% generated by %$g$%.
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 %$\alpha$%, %$\beta$%).
94 * Locating a cycle gives us a collision
96 * %$g^{\alpha} a^{\beta} = g^{\alpha'} a^{\beta'}$%
98 * Taking logs of both sides (to base %$g$%) gives us that
100 * %$\log a\equiv\frac{\alpha-\alpha'}{\beta'-\beta}\bmod{n}$%
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'
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.
111 * Finally, note that this function will free the input values
112 * when it's finished with them. This probably isn't a great
116 extern mp
*rho(rho_ctx */
*cc*/
, void */
*x*/
, void */
*y*/
,
117 mp */
*a*/
, mp */
*b*/
);
119 /* --- @rho_prime@ --- *
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
126 * Returns: The discrete logarithm %$\log_g a$%.
128 * Use: Computes discrete logarithms in a subgroup of a prime field.
131 extern mp
*rho_prime(mp */
*g*/
, mp */
*a*/
, mp */
*n*/
, mp */
*p*/
);
133 /*----- That's all, folks -------------------------------------------------*/