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New interface for computing products of many (small) integers.
[u/mdw/catacomb]
/
mpmont.h
diff --git
a/mpmont.h
b/mpmont.h
index
20ae0ac
..
120fa92
100644
(file)
--- a/
mpmont.h
+++ b/
mpmont.h
@@
-1,6
+1,6
@@
/* -*-c-*-
*
/* -*-c-*-
*
- * $Id: mpmont.h,v 1.
2 1999/11/19 13:17:43
mdw Exp $
+ * $Id: mpmont.h,v 1.
4 1999/12/11 01:51:14
mdw Exp $
*
* Montgomery reduction
*
*
* Montgomery reduction
*
@@
-30,6
+30,12
@@
/*----- Revision history --------------------------------------------------*
*
* $Log: mpmont.h,v $
/*----- Revision history --------------------------------------------------*
*
* $Log: mpmont.h,v $
+ * Revision 1.4 1999/12/11 01:51:14 mdw
+ * Use a Karatsuba-based reduction for large moduli.
+ *
+ * Revision 1.3 1999/12/10 23:29:48 mdw
+ * Change header file guard names.
+ *
* 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 1.2 1999/11/19 13:17:43 mdw
* Add extra interface to exponentiation which returns a Montgomerized
* result. Add simultaneous exponentiation interface.
@@
-39,8
+45,8
@@
*
*/
*
*/
-#ifndef MPMONT_H
-#define MPMONT_H
+#ifndef
CATACOMB_
MPMONT_H
+#define
CATACOMB_
MPMONT_H
#ifdef __cplusplus
extern "C" {
#ifdef __cplusplus
extern "C" {
@@
-48,11
+54,11
@@
/*----- Header files ------------------------------------------------------*/
/*----- Header files ------------------------------------------------------*/
-#ifndef MP_H
+#ifndef
CATACOMB_
MP_H
# include "mp.h"
#endif
# 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
*
* Given a little bit of precomputation, Montgomery reduction enables modular
* reductions of products to be calculated rather rapidly, without recourse
@@
-61,7
+67,9
@@
* Before starting, you need to do a little work. In particular, the
* following things need to be worked out:
*
* 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@).
*
* * %$b$%, the radix of the number system you're in (here, it's
* @MPW_MAX + 1@).
@@
-77,8
+85,8
@@
* 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
* 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 %$(x
R \cdot yR)
R^{-1} \bmod m$%,
- * which is just %$x
y
R \bmod m$%. 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.
* 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.
@@
-90,8
+98,8
@@
typedef struct mpmont {
mp *m; /* Modulus */
typedef struct mpmont {
mp *m; /* Modulus */
- mp
w 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$% */
} mpmont;
mp *r, *r2; /* %$R \bmod m$%, %$R^2 \bmod m$% */
} mpmont;
@@
-112,6
+120,7
@@
typedef struct mpmont_factor {
* Returns: ---
*
* Use: Initializes a Montgomery reduction context ready for use.
* Returns: ---
*
* Use: Initializes a Montgomery reduction context ready for use.
+ * The argument @m@ must be a positive odd integer.
*/
extern void mpmont_create(mpmont */*mm*/, mp */*m*/);
*/
extern void mpmont_create(mpmont */*mm*/, mp */*m*/);
@@
-132,51
+141,53
@@
extern void mpmont_destroy(mpmont */*mm*/);
*
* Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
* @mp *d@ = destination
*
* Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
* @mp *d@ = destination
- * @
const
mp *a@ = source, assumed positive
+ * @mp *a@ = source, assumed positive
*
* Returns: Result, %$a R^{-1} \bmod m$%.
*/
*
* Returns: Result, %$a R^{-1} \bmod m$%.
*/
-extern mp *mpmont_reduce(mpmont */*mm*/, mp */*d*/,
const
mp */*a*/);
+extern mp *mpmont_reduce(mpmont */*mm*/, mp */*d*/, mp */*a*/);
/* --- @mpmont_mul@ --- *
*
* Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
* @mp *d@ = destination
/* --- @mpmont_mul@ --- *
*
* Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
* @mp *d@ = destination
- * @
const
mp *a, *b@ = sources, assumed positive
+ * @mp *a, *b@ = sources, assumed positive
*
* Returns: Result, %$a b R^{-1} \bmod m$%.
*/
*
* Returns: Result, %$a b R^{-1} \bmod m$%.
*/
-extern mp *mpmont_mul(mpmont */*mm*/, mp */*d*/,
- const mp */*a*/, const mp */*b*/);
+extern mp *mpmont_mul(mpmont */*mm*/, mp */*d*/, mp */*a*/, mp */*b*/);
/* --- @mpmont_expr@ --- *
*
* Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
/* --- @mpmont_expr@ --- *
*
* Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
- * @const mp *a@ = base
- * @const mp *e@ = exponent
+ * @mp *d@ = fake destination
+ * @mp *a@ = base
+ * @mp *e@ = exponent
*
* Returns: Result, %$a^e R \bmod m$%. This is useful if further modular
* arithmetic is to be performed on the result.
*/
*
* Returns: Result, %$a^e R \bmod m$%. This is useful if further modular
* arithmetic is to be performed on the result.
*/
-extern mp *mpmont_expr(mpmont */*mm*/,
const mp */*a*/, const
mp */*e*/);
+extern mp *mpmont_expr(mpmont */*mm*/,
mp */*d*/, mp */*a*/,
mp */*e*/);
/* --- @mpmont_exp@ --- *
*
* Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
/* --- @mpmont_exp@ --- *
*
* Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
- * @const mp *a@ = base
- * @const mp *e@ = exponent
+ * @mp *d@ = fake destination
+ * @mp *a@ = base
+ * @mp *e@ = exponent
*
* Returns: Result, %$a^e \bmod m$%.
*/
*
* Returns: Result, %$a^e \bmod m$%.
*/
-extern mp *mpmont_exp(mpmont */*mm*/,
const mp */*a*/, const
mp */*e*/);
+extern mp *mpmont_exp(mpmont */*mm*/,
mp */*d*/, mp */*a*/,
mp */*e*/);
/* --- @mpmont_mexpr@ --- *
*
* Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
/* --- @mpmont_mexpr@ --- *
*
* Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
+ * @mp *d@ = fake destination
* @mpmont_factor *f@ = pointer to array of factors
* @size_t n@ = number of factors supplied
*
* @mpmont_factor *f@ = pointer to array of factors
* @size_t n@ = number of factors supplied
*
@@
-187,11
+198,13
@@
extern mp *mpmont_exp(mpmont */*mm*/, const mp */*a*/, const mp */*e*/);
* %$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}} R \bmod m$%
*/
-extern mp *mpmont_mexpr(mpmont */*mm*/, mpmont_factor */*f*/, size_t /*n*/);
+extern mp *mpmont_mexpr(mpmont */*mm*/, mp */*d*/,
+ mpmont_factor */*f*/, size_t /*n*/);
/* --- @mpmont_mexp@ --- *
*
* Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
/* --- @mpmont_mexp@ --- *
*
* Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
+ * @mp *d@ = fake destination
* @mpmont_factor *f@ = pointer to array of factors
* @size_t n@ = number of factors supplied
*
* @mpmont_factor *f@ = pointer to array of factors
* @size_t n@ = number of factors supplied
*
@@
-200,7
+213,8
@@
extern mp *mpmont_mexpr(mpmont */*mm*/, mpmont_factor */*f*/, size_t /*n*/);
* Use: Convenient interface over @mpmont_mexpr@.
*/
* 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*/,
+ mpmont_factor */*f*/, size_t /*n*/);
/*----- That's all, folks -------------------------------------------------*/
/*----- That's all, folks -------------------------------------------------*/