X-Git-Url: https://git.distorted.org.uk/u/mdw/catacomb/blobdiff_plain/d3409d5ecf2492cff862616de72a580d1a8e8dc0..3563e36580c7dad68cd6d3f7eb82eef570fc0c76:/mpmont.h

diff --git a/mpmont.h b/mpmont.h
index 42aa17c..913f6f5 100644
--- a/mpmont.h
+++ b/mpmont.h
@@ -1,6 +1,6 @@
 /* -*-c-*-
  *
- * $Id: mpmont.h,v 1.1 1999/11/17 18:02:16 mdw Exp $
+ * $Id: mpmont.h,v 1.7 2004/04/01 12:50:09 mdw Exp $
  *
  * Montgomery reduction
  *
@@ -30,13 +30,38 @@
 /*----- Revision history --------------------------------------------------* 
  *
  * $Log: mpmont.h,v $
+ * Revision 1.7  2004/04/01 12:50:09  mdw
+ * Add cyclic group abstraction, with test code.  Separate off exponentation
+ * functions for better static linking.  Fix a buttload of bugs on the way.
+ * Generally ensure that negative exponents do inversion correctly.  Add
+ * table of standard prime-field subgroups.  (Binary field subgroups are
+ * currently unimplemented but easy to add if anyone ever finds a good one.)
+ *
+ * Revision 1.6  2002/01/13 13:49:25  mdw
+ * Make @const@-correct.
+ *
+ * Revision 1.5  2001/06/16 13:00:04  mdw
+ * Moved @mpmont_factor@ to <mp.h>.  Documented interface change to
+ * @mpmont_expr@ and @mpmont_mexpr@ -- the arguments are now in Montgomery
+ * form.
+ *
+ * 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 1.1  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 +69,11 @@
 
 /*----- 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 +82,9 @@
  * 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 +100,8 @@
  * 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 +113,8 @@
 
 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;
 
@@ -101,10 +128,105 @@ typedef struct mpmont {
  * 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*/);
 
+/* --- @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