| 1 | /* -*-c-*- |
| 2 | * |
| 3 | * $Id: prim.h,v 1.2 2000/07/29 09:57:42 mdw Exp $ |
| 4 | * |
| 5 | * Finding primitive elements |
| 6 | * |
| 7 | * (c) 1999 Straylight/Edgeware |
| 8 | */ |
| 9 | |
| 10 | /*----- Licensing notice --------------------------------------------------* |
| 11 | * |
| 12 | * This file is part of Catacomb. |
| 13 | * |
| 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. |
| 18 | * |
| 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. |
| 23 | * |
| 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, |
| 27 | * MA 02111-1307, USA. |
| 28 | */ |
| 29 | |
| 30 | /*----- Revision history --------------------------------------------------* |
| 31 | * |
| 32 | * $Log: prim.h,v $ |
| 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. |
| 37 | * |
| 38 | * Revision 1.1 1999/12/22 15:58:59 mdw |
| 39 | * Search for primitive elements using prime-search equipment. |
| 40 | * |
| 41 | */ |
| 42 | |
| 43 | #ifndef CATACOMB_PRIM_H |
| 44 | #define CATACOMB_PRIM_H |
| 45 | |
| 46 | #ifdef __cplusplus |
| 47 | extern "C" { |
| 48 | #endif |
| 49 | |
| 50 | /*----- Header files ------------------------------------------------------*/ |
| 51 | |
| 52 | #include <stddef.h> |
| 53 | |
| 54 | #ifndef CATACOMB_MP_H |
| 55 | # include "mp.h" |
| 56 | #endif |
| 57 | |
| 58 | #ifndef CATACOMB_MPMONT_H |
| 59 | # include "mpmont.h" |
| 60 | #endif |
| 61 | |
| 62 | #ifndef CATACOMB_PGEN_H |
| 63 | # include "pgen.h" |
| 64 | #endif |
| 65 | |
| 66 | /*----- Data structures ---------------------------------------------------*/ |
| 67 | |
| 68 | /* --- @prim_ctx@ --- * |
| 69 | * |
| 70 | * All fields must be configured by the client. Set @n@ to zero to discover |
| 71 | * generators of the subgroup of order %$m / f$%. |
| 72 | * |
| 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 | * (%$f_i q_i = p/o$%). |
| 79 | */ |
| 80 | |
| 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 */ |
| 86 | } prim_ctx; |
| 87 | |
| 88 | /*----- Functions provided ------------------------------------------------*/ |
| 89 | |
| 90 | /* --- @prim_test@ --- */ |
| 91 | |
| 92 | extern int prim_test(int /*rq*/, pgen_event */*ev*/, void */*p*/); |
| 93 | |
| 94 | /* --- @prim_step@ --- */ |
| 95 | |
| 96 | extern int prim_step(int /*rq*/, pgen_event */*ev*/, void */*p*/); |
| 97 | |
| 98 | /*----- That's all, folks -------------------------------------------------*/ |
| 99 | |
| 100 | #ifdef __cplusplus |
| 101 | } |
| 102 | #endif |
| 103 | |
| 104 | #endif |