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

diff --git a/mpmont.h b/mpmont.h
deleted file mode 100644
index 745cf5a..0000000
--- a/mpmont.h
+++ /dev/null
@@ -1,203 +0,0 @@
-/* -*-c-*-
- *
- * $Id$
- *
- * Montgomery reduction
- *
- * (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_MPMONT_H
-#define CATACOMB_MPMONT_H
-
-#ifdef __cplusplus
-  extern "C" {
-#endif
-
-/*----- Header files ------------------------------------------------------*/
-
-#ifndef CATACOMB_MP_H
-#  include "mp.h"
-#endif
-
-/*----- Notes on Montgomery reduction -------------------------------------*
- *
- * Given a little bit of precomputation, Montgomery reduction enables modular
- * reductions of products to be calculated rather rapidly, without recourse
- * to annoying things like division.
- *
- * Before starting, you need to do a little work.  In particular, the
- * following things need to be worked out:
- *
- *   * %$m$%, which is the modulus you'll be working with.  This must be odd,
- *     otherwise the whole thing doesn't work.  You're better off using
- *     Barrett reduction if your modulus might be even.
- *
- *   * %$b$%, the radix of the number system you're in (here, it's
- *     @MPW_MAX + 1@).
- *
- *   * %$-m^{-1} \bmod b$%, a useful number for the reduction step.  (This
- *     means that the modulus mustn't be even.  This shouldn't be a problem.)
- *
- *   * %$R = b^n > m > b^{n - 1}$%, or at least %$\log_2 R$%.
- *
- *   * %$R \bmod m$% and %$R^2 \bmod m$%, which are useful when doing
- *     calculations such as exponentiation.
- *
- * The result of a Montgomery reduction of %$x$% is %$x R^{-1} \bmod m$%,
- * which doesn't look ever-so useful.  The trick is to initially apply a
- * factor of %$R$% to all of your numbers so that when you multiply and
- * perform a Montgomery reduction you get %$(x R \cdot y R) R^{-1} \bmod m$%,
- * which is just %$x y R \bmod m$%.  Thanks to distributivity, even additions
- * and subtractions can be performed on numbers in this form -- the extra
- * factor of %$R$% just runs through all the calculations until it's finally
- * stripped out by a final reduction operation.
- */
-
-/*----- Data structures ---------------------------------------------------*/
-
-/* --- A Montgomery reduction context --- */
-
-typedef struct mpmont {
-  mp *m;				/* Modulus */
-  mp *mi;				/* %$-m^{-1} \bmod R$% */
-  size_t n;				/* %$\log_b R$% */
-  mp *r, *r2;				/* %$R \bmod m$%, %$R^2 \bmod m$% */
-} mpmont;
-
-/*----- Functions provided ------------------------------------------------*/
-
-/* --- @mpmont_create@ --- *
- *
- * Arguments:	@mpmont *mm@ = pointer to Montgomery reduction context
- *		@mp *m@ = modulus to use
- *
- * Returns:	Zero on success, nonzero on error.
- *
- * Use:		Initializes a Montgomery reduction context ready for use.
- *		The argument @m@ must be a positive odd integer.
- */
-
-extern int mpmont_create(mpmont */*mm*/, mp */*m*/);
-
-/* --- @mpmont_destroy@ --- *
- *
- * Arguments:	@mpmont *mm@ = pointer to a Montgomery reduction context
- *
- * Returns:	---
- *
- * Use:		Disposes of a context when it's no longer of any use to
- *		anyone.
- */
-
-extern void mpmont_destroy(mpmont */*mm*/);
-
-/* --- @mpmont_reduce@ --- *
- *
- * Arguments:	@mpmont *mm@ = pointer to Montgomery reduction context
- *		@mp *d@ = destination
- *		@mp *a@ = source, assumed positive
- *
- * Returns:	Result, %$a R^{-1} \bmod m$%.
- */
-
-extern mp *mpmont_reduce(mpmont */*mm*/, mp */*d*/, mp */*a*/);
-
-/* --- @mpmont_mul@ --- *
- *
- * Arguments:	@mpmont *mm@ = pointer to Montgomery reduction context
- *		@mp *d@ = destination
- *		@mp *a, *b@ = sources, assumed positive
- *
- * Returns:	Result, %$a b R^{-1} \bmod m$%.
- */
-
-extern mp *mpmont_mul(mpmont */*mm*/, mp */*d*/, mp */*a*/, mp */*b*/);
-
-/* --- @mpmont_expr@ --- *
- *
- * Arguments:	@mpmont *mm@ = pointer to Montgomery reduction context
- *		@mp *d@ = fake destination
- *		@mp *a@ = base
- *		@mp *e@ = exponent
- *
- * Returns:	Result, %$(a R^{-1})^e R \bmod m$%.  This is useful if
- *		further modular arithmetic is to be performed on the result.
- */
-
-extern mp *mpmont_expr(mpmont */*mm*/, mp */*d*/, mp */*a*/, mp */*e*/);
-
-/* --- @mpmont_exp@ --- *
- *
- * Arguments:	@mpmont *mm@ = pointer to Montgomery reduction context
- *		@mp *d@ = fake destination
- *		@mp *a@ = base
- *		@mp *e@ = exponent
- *
- * Returns:	Result, %$a^e \bmod m$%.
- */
-
-extern mp *mpmont_exp(mpmont */*mm*/, mp */*d*/, mp */*a*/, mp */*e*/);
-
-/* --- @mpmont_mexpr@ --- *
- *
- * Arguments:	@mpmont *mm@ = pointer to Montgomery reduction context
- *		@mp *d@ = fake destination
- *		@const mp_expfactor *f@ = pointer to array of factors
- *		@size_t n@ = number of factors supplied
- *
- * Returns:	If the bases are %$g_0, g_1, \ldots, g_{n-1}$% and the
- *		exponents are %$e_0, e_1, \ldots, e_{n-1}$% then the result
- *		is:
- *
- *		%$g_0^{e_0} g_1^{e_1} \ldots g_{n-1}^{e_{n-1}} \bmod m$%
- *
- *
- *		except that the %$g_i$% and result are in Montgomery form.
- */
-
-extern mp *mpmont_mexpr(mpmont */*mm*/, mp */*d*/,
-			const mp_expfactor */*f*/, size_t /*n*/);
-
-/* --- @mpmont_mexp@ --- *
- *
- * Arguments:	@mpmont *mm@ = pointer to Montgomery reduction context
- *		@mp *d@ = fake destination
- *		@const mp_expfactor *f@ = pointer to array of factors
- *		@size_t n@ = number of factors supplied
- *
- * Returns:	Product of bases raised to exponents, all mod @m@.
- *
- * Use:		Convenient interface over @mpmont_mexpr@.
- */
-
-extern mp *mpmont_mexp(mpmont */*mm*/, mp */*d*/,
-		       const mp_expfactor */*f*/, size_t /*n*/);
-
-/*----- That's all, folks -------------------------------------------------*/
-
-#ifdef __cplusplus
-  }
-#endif
-
-#endif