/* -*-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
*
/*----- 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.
*
*
* 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 ------------------------------------------------*/