git.distorted.org.uk Git - u/mdw/catacomb/blob - math/prim.h

   1 /* -*-c-*-
   2  *
   3  * Finding primitive elements
   4  *
   5  * (c) 1999 Straylight/Edgeware
   6  */
   7
   8 /*----- Licensing notice --------------------------------------------------*
   9  *
  10  * This file is part of Catacomb.
  11  *
  12  * Catacomb is free software; you can redistribute it and/or modify
  13  * it under the terms of the GNU Library General Public License as
  14  * published by the Free Software Foundation; either version 2 of the
  15  * License, or (at your option) any later version.
  16  *
  17  * Catacomb is distributed in the hope that it will be useful,
  18  * but WITHOUT ANY WARRANTY; without even the implied warranty of
  19  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  20  * GNU Library General Public License for more details.
  21  *
  22  * You should have received a copy of the GNU Library General Public
  23  * License along with Catacomb; if not, write to the Free
  24  * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
  25  * MA 02111-1307, USA.
  26  */
  27
  28 #ifndef CATACOMB_PRIM_H
  29 #define CATACOMB_PRIM_H
  30
  31 #ifdef __cplusplus
  32   extern "C" {
  33 #endif
  34
  35 /*----- Header files ------------------------------------------------------*/
  36
  37 #include <stddef.h>
  38
  39 #ifndef CATACOMB_MP_H
  40 #  include "mp.h"
  41 #endif
  42
  43 #ifndef CATACOMB_MPMONT_H
  44 #  include "mpmont.h"
  45 #endif
  46
  47 #ifndef CATACOMB_PGEN_H
  48 #  include "pgen.h"
  49 #endif
  50
  51 /*----- Data structures ---------------------------------------------------*/
  52
  53 /* --- @prim_ctx@ --- *
  54  *
  55  * All fields must be configured by the client.  Set @n@ to zero to discover
  56  * generators of the subgroup of order %$m / f$%.
  57  *
  58  * Let %$p = \prod q_i + 1$% be a prime number.  In order to find an element
  59  * %$g$% with order %$o$%, we choose elements %$h_j$% from %$\gf{p}^*$%,
  60  * compute $%g_j = h_j^{p/o}$%, rejecting %$h_j$% where %$g_j = 1$%, and then
  61  * for each proper prime factor %$q_i$% of %$p/o$% we check that
  62  * %$g^{f_i} \ne 1$%, where the %$f_i$% are cofactors of the %$q_i$%
  63  * (%$f_i q_i = p/o$%).
  64  */
  65
  66 typedef struct prim_ctx {
  67   mpmont mm;                            /* Montgomery context for modulus */
  68   mp *exp;                              /* Exponent (%$p/o$%; may be zero) */
  69   size_t n;                             /* Number of cofactors */
  70   mp **f;                               /* Array of cofactors */
  71 } prim_ctx;
  72
  73 /*----- Functions provided ------------------------------------------------*/
  74
  75 /* --- @prim_test@ --- */
  76
  77 extern pgen_proc prim_test;
  78
  79 /* --- @prim_step@ --- */
  80
  81 extern pgen_proc prim_step;
  82
  83 /*----- That's all, folks -------------------------------------------------*/
  84
  85 #ifdef __cplusplus
  86   }
  87 #endif
  88
  89 #endif