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1 | /* -*-c-*- |
2 | * |
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3 | * $Id: prim.h,v 1.2 2000/07/29 09:57:42 mdw Exp $ |
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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 $ |
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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 | * |
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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 %$m / f$%. |
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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 | * (%$f_i q_i = p/o$%). |
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79 | */ |
80 | |
81 | typedef struct prim_ctx { |
82 | mpmont mm; /* Montgomery context for modulus */ |
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83 | mp *exp; /* Exponent (%$p/o$%; may be zero) */ |
84 | size_t n; /* Number of cofactors */ |
85 | mp **f; /* Array of cofactors */ |
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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 |