X-Git-Url: https://git.distorted.org.uk/u/mdw/catacomb/blobdiff_plain/d3409d5ecf2492cff862616de72a580d1a8e8dc0..cd6eca4375f46a35b93e2fea4b0428a23b451aa3:/mpmont.h diff --git a/mpmont.h b/mpmont.h index 42aa17c..745cf5a 100644 --- a/mpmont.h +++ b/mpmont.h @@ -1,13 +1,13 @@ /* -*-c-*- * - * $Id: mpmont.h,v 1.1 1999/11/17 18:02:16 mdw Exp $ + * $Id$ * * Montgomery reduction * * (c) 1999 Straylight/Edgeware */ -/*----- Licensing notice --------------------------------------------------* +/*----- Licensing notice --------------------------------------------------* * * This file is part of Catacomb. * @@ -15,28 +15,20 @@ * 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: mpmont.h,v $ - * Revision 1.1 1999/11/17 18:02:16 mdw - * New multiprecision integer arithmetic suite. - * - */ - -#ifndef MPMONT_H -#define MPMONT_H +#ifndef CATACOMB_MPMONT_H +#define CATACOMB_MPMONT_H #ifdef __cplusplus extern "C" { @@ -44,11 +36,11 @@ /*----- Header files ------------------------------------------------------*/ -#ifndef MP_H +#ifndef CATACOMB_MP_H # include "mp.h" #endif -/*----- What's going on here? ---------------------------------------------* +/*----- Notes on Montgomery reduction -------------------------------------* * * Given a little bit of precomputation, Montgomery reduction enables modular * reductions of products to be calculated rather rapidly, without recourse @@ -57,7 +49,9 @@ * 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. + * * %$m$%, 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@). @@ -73,8 +67,8 @@ * 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 %$(xR \cdot yR)R^{-1} \bmod m$%, - * which is just %$xyR \bmod m$%. Thanks to distributivity, even additions + * 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. @@ -86,8 +80,8 @@ typedef struct mpmont { mp *m; /* Modulus */ - mpw mi; /* %$-m^{-1} \bmod b$% */ - size_t shift; /* %$\log_2 R$% */ + mp *mi; /* %$-m^{-1} \bmod R$% */ + size_t n; /* %$\log_b R$% */ mp *r, *r2; /* %$R \bmod m$%, %$R^2 \bmod m$% */ } mpmont; @@ -98,12 +92,107 @@ typedef struct mpmont { * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context * @mp *m@ = modulus to use * - * Returns: --- + * 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 void mpmont_create(mpmont */*mm*/, mp */*m*/); +extern mp *mpmont_mexp(mpmont */*mm*/, mp */*d*/, + const mp_expfactor */*f*/, size_t /*n*/); /*----- That's all, folks -------------------------------------------------*/