3 * $Id: prim.h,v 1.2 2000/07/29 09:57:42 mdw Exp $
5 * Finding primitive elements
7 * (c) 1999 Straylight/Edgeware
10 /*----- Licensing notice --------------------------------------------------*
12 * This file is part of Catacomb.
14 * Catacomb is free software; you can redistribute it and/or modify
15 * it under the terms of the GNU Library General Public License as
16 * published by the Free Software Foundation; either version 2 of the
17 * License, or (at your option) any later version.
19 * Catacomb is distributed in the hope that it will be useful,
20 * but WITHOUT ANY WARRANTY; without even the implied warranty of
21 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
22 * GNU Library General Public License for more details.
24 * You should have received a copy of the GNU Library General Public
25 * License along with Catacomb; if not, write to the Free
26 * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
30 /*----- Revision history --------------------------------------------------*
33 * Revision 1.2 2000/07/29 09:57:42 mdw
34 * Improve primitive-element testing a lot. Now much more sensible and
35 * orthogonal: you can find a generator for any given subgroup order by
36 * putting in the appropriate parameters.
38 * Revision 1.1 1999/12/22 15:58:59 mdw
39 * Search for primitive elements using prime-search equipment.
43 #ifndef CATACOMB_PRIM_H
44 #define CATACOMB_PRIM_H
50 /*----- Header files ------------------------------------------------------*/
58 #ifndef CATACOMB_MPMONT_H
62 #ifndef CATACOMB_PGEN_H
66 /*----- Data structures ---------------------------------------------------*/
68 /* --- @prim_ctx@ --- *
70 * All fields must be configured by the client. Set @n@ to zero to discover
71 * generators of the subgroup of order %$m / f$%.
73 * Let %$p = \prod q_i + 1$% be a prime number. In order to find an element
74 * %$g$% with order %$o$%, we choose elements %$h_j$% from %$\gf{p}^*$%,
75 * compute $%g_j = h_j^{p/o}$%, rejecting %$h_j$% where %$g_j = 1$%, and then
76 * for each proper prime factor %$q_i$% of %$p/o$% we check that
77 * %$g^{f_i} \ne 1$%, where the %$f_i$% are cofactors of the %$q_i$%
78 * (%$f_i q_i = p/o$%).
81 typedef struct prim_ctx
{
82 mpmont mm
; /* Montgomery context for modulus */
83 mp
*exp
; /* Exponent (%$p/o$%; may be zero) */
84 size_t n
; /* Number of cofactors */
85 mp
**f
; /* Array of cofactors */
88 /*----- Functions provided ------------------------------------------------*/
90 /* --- @prim_test@ --- */
92 extern int prim_test(int /*rq*/, pgen_event */
*ev*/
, void */
*p*/
);
94 /* --- @prim_step@ --- */
96 extern int prim_step(int /*rq*/, pgen_event */
*ev*/
, void */
*p*/
);
98 /*----- That's all, folks -------------------------------------------------*/