/* -*-c-*-
*
- * $Id: mpmont.h,v 1.2 1999/11/19 13:17:43 mdw Exp $
+ * $Id: mpmont.h,v 1.8 2004/04/08 01:36:15 mdw Exp $
*
* Montgomery reduction
*
* MA 02111-1307, USA.
*/
-/*----- Revision history --------------------------------------------------*
- *
- * $Log: mpmont.h,v $
- * Revision 1.2 1999/11/19 13:17:43 mdw
- * Add extra interface to exponentiation which returns a Montgomerized
- * result. Add simultaneous exponentiation interface.
- *
- * 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;
-/* --- A base/exponent pair for @mpmont_mexp@ --- */
-
-typedef struct mpmont_factor {
- mp *base;
- mp *exp;
-} mpmont_factor;
-
/*----- Functions provided ------------------------------------------------*/
/* --- @mpmont_create@ --- *
* Returns: ---
*
* Use: Initializes a Montgomery reduction context ready for use.
+ * The argument @m@ must be a positive odd integer.
*/
extern void mpmont_create(mpmont */*mm*/, mp */*m*/);
*
* Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
* @mp *d@ = destination
- * @const mp *a@ = source, assumed positive
+ * @mp *a@ = source, assumed positive
*
* Returns: Result, %$a R^{-1} \bmod m$%.
*/
-extern mp *mpmont_reduce(mpmont */*mm*/, mp */*d*/, const mp */*a*/);
+extern mp *mpmont_reduce(mpmont */*mm*/, mp */*d*/, mp */*a*/);
/* --- @mpmont_mul@ --- *
*
* Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
* @mp *d@ = destination
- * @const mp *a, *b@ = sources, assumed positive
+ * @mp *a, *b@ = sources, assumed positive
*
* Returns: Result, %$a b R^{-1} \bmod m$%.
*/
-extern mp *mpmont_mul(mpmont */*mm*/, mp */*d*/,
- const mp */*a*/, const mp */*b*/);
+extern mp *mpmont_mul(mpmont */*mm*/, mp */*d*/, mp */*a*/, mp */*b*/);
/* --- @mpmont_expr@ --- *
*
* Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
- * @const mp *a@ = base
- * @const mp *e@ = exponent
+ * @mp *d@ = fake destination
+ * @mp *a@ = base
+ * @mp *e@ = exponent
*
- * Returns: Result, %$a^e R \bmod m$%. This is useful if further modular
- * arithmetic is to be performed on the result.
+ * 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*/, const mp */*a*/, const mp */*e*/);
+extern mp *mpmont_expr(mpmont */*mm*/, mp */*d*/, mp */*a*/, mp */*e*/);
/* --- @mpmont_exp@ --- *
*
* Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
- * @const mp *a@ = base
- * @const mp *e@ = exponent
+ * @mp *d@ = fake destination
+ * @mp *a@ = base
+ * @mp *e@ = exponent
*
* Returns: Result, %$a^e \bmod m$%.
*/
-extern mp *mpmont_exp(mpmont */*mm*/, const mp */*a*/, const mp */*e*/);
+extern mp *mpmont_exp(mpmont */*mm*/, mp */*d*/, mp */*a*/, mp */*e*/);
/* --- @mpmont_mexpr@ --- *
*
* Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
- * @mpmont_factor *f@ = pointer to array of factors
+ * @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:
*
- * %$g_0^{e_0} g_1^{e_1} \ldots g_{n-1}^{e_{n-1}} R \bmod m$%
+ * %$g_0^{e_0} g_1^{e_1} \ldots g_{n-1}^{e_{n-1}} \bmod m$%
+ *
+ *
+ * except that the %$g_i$% and result are in Montgomery form.
*/
-extern mp *mpmont_mexpr(mpmont */*mm*/, mpmont_factor */*f*/, size_t /*n*/);
+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
- * @mpmont_factor *f@ = pointer to array of factors
+ * @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*/, mpmont_factor */*f*/, size_t /*n*/);
+extern mp *mpmont_mexp(mpmont */*mm*/, mp */*d*/,
+ const mp_expfactor */*f*/, size_t /*n*/);
/*----- That's all, folks -------------------------------------------------*/
projects / u / mdw / catacomb / blobdiff