Improve primitive-element testing a lot. Now much more sensible and

[u/mdw/catacomb] / prim.h

diff --git a/prim.h b/prim.h
index 30392cd..90b1156 100644 (file)
--- a/prim.h
+++ b/prim.h
@@ -1,6 +1,6 @@
 /* -*-c-*-
  *
- * $Id: prim.h,v 1.1 1999/12/22 15:58:59 mdw Exp $
+ * $Id: prim.h,v 1.2 2000/07/29 09:57:42 mdw Exp $
  *
  * Finding primitive elements
  *
@@ -30,6 +30,11 @@
 /*----- Revision history --------------------------------------------------* 
  *
  * $Log: prim.h,v $
+ * Revision 1.2  2000/07/29 09:57:42  mdw
+ * Improve primitive-element testing a lot.  Now much more sensible and
+ * orthogonal: you can find a generator for any given subgroup order by
+ * putting in the appropriate parameters.
+ *
  * Revision 1.1  1999/12/22 15:58:59  mdw
  * Search for primitive elements using prime-search equipment.
  *
@@ -64,12 +69,20 @@
  *
  * All fields must be configured by the client.  Set @n@ to zero to discover
  * generators of the subgroup of order %$m / f$%.
+ *
+ * Let %$p = \prod q_i + 1$% be a prime number.  In order to find an element
+ * %$g$% with order %$o$%, we choose elements %$h_j$% from %$\gf{p}^*$%,
+ * compute $%g_j = h_j^{p/o}$%, rejecting %$h_j$% where %$g_j = 1$%, and then
+ * for each proper prime factor %$q_i$% of %$p/o$% we check that
+ * %$g^{f_i} \ne 1$%, where the %$f_i$% are cofactors of the %$q_i$%
+ * (%$f_i q_i = p/o$%).
  */
 
 typedef struct prim_ctx {
   mpmont mm;                           /* Montgomery context for modulus */
-  mp *f;                               /* Array of factors */
-  size_t n;                            /* Number of factors */
+  mp *exp;                             /* Exponent (%$p/o$%; may be zero) */
+  size_t n;                            /* Number of cofactors */
+  mp **f;                              /* Array of cofactors */
 } prim_ctx;
 
 /*----- Functions provided ------------------------------------------------*/