/* -*-c-*-
*
- * $Id: prim.h,v 1.1 1999/12/22 15:58:59 mdw Exp $
+ * $Id: prim.h,v 1.3 2004/04/08 01:36:15 mdw Exp $
*
* Finding primitive elements
*
* MA 02111-1307, USA.
*/
-/*----- Revision history --------------------------------------------------*
- *
- * $Log: prim.h,v $
- * Revision 1.1 1999/12/22 15:58:59 mdw
- * Search for primitive elements using prime-search equipment.
- *
- */
-
#ifndef CATACOMB_PRIM_H
#define CATACOMB_PRIM_H
*
* 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 ------------------------------------------------*/