+++ /dev/null
-/* -*-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
projects / u / mdw / catacomb / blobdiff