X-Git-Url: https://git.distorted.org.uk/u/mdw/catacomb/blobdiff_plain/ba6e6b64033b1f9de49feccb5c9cd438354481f7..0f00dc4c8eb47e67bc0f148c2dd109f73a451e0a:/math/rho.h

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+/* -*-c-*-
+ *
+ * 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