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+/* -*-c-*-
+ *
+ * $Id: gfreduce.h,v 1.1.2.1 2004/03/21 22:39:46 mdw Exp $
+ *
+ * Reduction modulo sparse binary polynomials
+ *
+ * (c) 2004 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.
+ */
+
+/*----- Revision history --------------------------------------------------* 
+ *
+ * $Log: gfreduce.h,v $
+ * Revision 1.1.2.1  2004/03/21 22:39:46  mdw
+ * Elliptic curves on binary fields work.
+ *
+ */
+
+#ifndef CATACOMB_GFREDUCE_H
+#define CATACOMB_GFREDUCE_H
+
+#ifdef __cplusplus
+  extern "C" {
+#endif
+
+/*----- Header files ------------------------------------------------------*/
+
+#ifndef CATACOMB_GF_H
+#  include "gf.h"
+#endif
+
+/*----- Data structures ---------------------------------------------------*/
+
+typedef struct gfreduce_instr {
+  unsigned op;				/* Instruction opcode */
+  size_t arg;				/* Immediate argument */
+} gfreduce_instr;
+
+enum {
+  GFRI_LOAD,				/* Load @p[arg]@ */
+  GFRI_LSL,				/* XOR with @w << arg@ */
+  GFRI_LSR,				/* XOR with @w >> arg@ */
+  GFRI_STORE,				/* Store @p[arg]@ */
+  GFRI_MAX
+};
+
+typedef struct gfreduce {
+  size_t lim;				/* Word of degree bit */
+  mpw mask;				/* Mask for degree word */
+  mp *p;				/* Copy of the polynomial */
+  size_t in;				/* Number of instruction words */
+  gfreduce_instr *iv, *liv;		/* Vector of instructions */
+} gfreduce;
+
+/*----- Functions provided ------------------------------------------------*/
+
+/* --- @gfreduce_create@ --- *
+ *
+ * Arguments:	@gfreduce *r@ = structure to fill in
+ *		@mp *x@ = a (hopefully sparse) polynomial
+ *
+ * Returns:	---
+ *
+ * Use:		Initializes a context structure for reduction.
+ */
+
+extern void gfreduce_create(gfreduce */*r*/, mp */*p*/);
+
+/* --- @gfreduce_destroy@ --- *
+ *
+ * Arguments:	@gfreduce *r@ = structure to free
+ *
+ * Returns:	---
+ *
+ * Use:		Reclaims the resources from a reduction context.
+ */
+
+extern void gfreduce_destroy(gfreduce */*r*/);
+
+/* --- @gfreduce_dump@ --- *
+ *
+ * Arguments:	@gfreduce *r@ = structure to dump
+ *		@FILE *fp@ = file to dump on
+ *
+ * Returns:	---
+ *
+ * Use:		Dumps a reduction context.
+ */
+
+extern void gfreduce_dump(gfreduce */*r*/, FILE */*fp*/);
+
+/* --- @gfreduce_do@ --- *
+ *
+ * Arguments:	@gfreduce *r@ = reduction context
+ *		@mp *d@ = destination
+ *		@mp *x@ = source
+ *
+ * Returns:	Destination, @x@ reduced modulo the reduction poly.
+ */
+
+extern mp *gfreduce_do(gfreduce */*r*/, mp */*d*/, mp */*x*/);
+
+/* --- @gfreduce_sqrt@ --- *
+ *
+ * Arguments:	@gfreduce *r@ = pointer to reduction context
+ *		@mp *d@ = destination
+ *		@mp *x@ = some polynomial
+ *
+ * Returns:	The square root of @x@ modulo @r->p@, or null.
+ */
+
+extern mp *gfreduce_sqrt(gfreduce */*r*/, mp */*d*/, mp */*x*/);
+
+/* --- @gfreduce_trace@ --- *
+ *
+ * Arguments:	@gfreduce *r@ = pointer to reduction context
+ *		@mp *x@ = some polynomial
+ *
+ * Returns:	The trace of @x@. (%$\Tr(x)=x + x^2 + \cdots + x^{2^{m-1}}$%
+ *		if %$x \in \gf{2^m}$%).
+ */
+
+extern int gfreduce_trace(gfreduce */*r*/, mp */*x*/);
+
+/* --- @gfreduce_halftrace@ --- *
+ *
+ * Arguments:	@gfreduce *r@ = pointer to reduction context
+ *		@mp *d@ = destination
+ *		@mp *x@ = some polynomial
+ *
+ * Returns:	The half-trace of @x@.
+ *		(%$\HfTr(x)= x + x^{2^2} + \cdots + x^{2^{m-1}}$%
+ *		if %$x \in \gf{2^m}$% with %$m$% odd).
+ */
+
+extern mp *gfreduce_halftrace(gfreduce */*r*/, mp */*d*/, mp */*x*/);
+
+/* --- @gfreduce_quadsolve@ --- *
+ *
+ * Arguments:	@gfreduce *r@ = pointer to reduction context
+ *		@mp *d@ = destination
+ *		@mp *x@ = some polynomial
+ *
+ * Returns:	A polynomial @y@ such that %$y^2 + y = x$%, or null.
+ */
+
+extern mp *gfreduce_quadsolve(gfreduce */*r*/, mp */*d*/, mp */*x*/);
+
+/* --- @gfreduce_exp@ --- *
+ *
+ * Arguments:	@gfreduce *gr@ = pointer to reduction context
+ *              @mp *d@ = fake destination
+ *              @mp *a@ = base
+ *              @mp *e@ = exponent
+ *
+ * Returns:     Result, %$a^e \bmod m$%.
+ */
+
+extern mp *gfreduce_exp(gfreduce */*gr*/, mp */*d*/, mp */*a*/, mp */*e*/);
+
+/*----- That's all, folks -------------------------------------------------*/
+
+#ifdef __cplusplus
+  }
+#endif
+
+#endif