/* -*-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.
*
* 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" {
/*----- 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
* 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@).
* 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.
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;
* 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 -------------------------------------------------*/
projects / u / mdw / catacomb / blobdiff