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

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+/* -*-c-*-
+ *
+ * Chinese Remainder Theorem computations (Gauss's algorithm)
+ *
+ * (c) 1999 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_MPCRT_H
+#define CATACOMB_MPCRT_H
+
+#ifdef __cplusplus
+  extern "C" {
+#endif
+
+/*----- Header files ------------------------------------------------------*/
+
+#include <stddef.h>
+
+#ifndef CATACOMB_MP_H
+#  include "mp.h"
+#endif
+
+#ifndef CATACOMB_MPBARRETT_H
+#  include "mpbarrett.h"
+#endif
+
+/*----- Data structures ---------------------------------------------------*/
+
+typedef struct mpcrt_mod {
+  mp *m;				/* %$n_i$% -- the modulus */
+  mp *n;				/* %$N_i = n / n_i$% */
+  mp *ni;				/* %$M_i = N_i^{-1} \bmod n_i$% */
+  mp *nni;				/* %$N_i M_i \bmod m$% */
+} mpcrt_mod;
+
+typedef struct mpcrt {
+  size_t k;				/* Number of distinct moduli */
+  mpbarrett mb;				/* Barrett context for product */
+  mpcrt_mod *v;				/* Vector of information for each */
+} mpcrt;
+
+/*----- Functions provided ------------------------------------------------*/
+
+/* --- @mpcrt_create@ --- *
+ *
+ * Arguments:	@mpcrt *c@ = pointer to CRT context
+ *		@mpcrt_mod *v@ = pointer to vector of moduli
+ *		@size_t k@ = number of moduli
+ *		@mp *n@ = product of all moduli (@MP_NEW@ if unknown)
+ *
+ * Returns:	---
+ *
+ * Use:		Initializes a context for solving Chinese Remainder Theorem
+ *		problems.  The vector of moduli can be incomplete.  Omitted
+ *		items must be left as null pointers.  Not all combinations of
+ *		missing things can be coped with, even if there is
+ *		technically enough information to cope.  For example, if @n@
+ *		is unspecified, all the @m@ values must be present, even if
+ *		there is one modulus with both @m@ and @n@ (from which the
+ *		product of all moduli could clearly be calculated).
+ */
+
+extern void mpcrt_create(mpcrt */*c*/, mpcrt_mod */*v*/,
+			 size_t /*k*/, mp */*n*/);
+
+/* --- @mpcrt_destroy@ --- *
+ *
+ * Arguments:	@mpcrt *c@ - pointer to CRT context
+ *
+ * Returns:	---
+ *
+ * Use:		Destroys a CRT context, releasing all the resources it holds.
+ */
+
+extern void mpcrt_destroy(mpcrt */*c*/);
+
+/* --- @mpcrt_solve@ --- *
+ *
+ * Arguments:	@mpcrt *c@ = pointer to CRT context
+ *		@mp *d@ = fake destination
+ *		@mp **v@ = array of residues
+ *
+ * Returns:	The unique solution modulo the product of the individual
+ *		moduli, which leaves the given residues.
+ *
+ * Use:		Constructs a result given its residue modulo an array of
+ *		coprime integers.  This can be used to improve performance of
+ *		RSA encryption or Blum-Blum-Shub generation if the factors
+ *		of the modulus are known, since results can be computed mod
+ *		each of the individual factors and then combined at the end.
+ *		This is rather faster than doing the full-scale modular
+ *		exponentiation.
+ */
+
+extern mp *mpcrt_solve(mpcrt */*c*/, mp */*d*/, mp **/*v*/);
+
+/*----- That's all, folks -------------------------------------------------*/
+
+#ifdef __cplusplus
+  }
+#endif
+
+#endif