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1 | /* -*-c-*- |
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2 | * |
3 | * Chinese Remainder Theorem computations (Gauss's algorithm) |
4 | * |
5 | * (c) 1999 Straylight/Edgeware |
6 | */ |
7 | |
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8 | /*----- Licensing notice --------------------------------------------------* |
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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. |
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16 | * |
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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. |
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21 | * |
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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 | |
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28 | #ifndef CATACOMB_MPCRT_H |
29 | #define CATACOMB_MPCRT_H |
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30 | |
31 | #ifdef __cplusplus |
32 | extern "C" { |
33 | #endif |
34 | |
35 | /*----- Header files ------------------------------------------------------*/ |
36 | |
37 | #include <stddef.h> |
38 | |
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39 | #ifndef CATACOMB_MP_H |
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40 | # include "mp.h" |
41 | #endif |
42 | |
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43 | #ifndef CATACOMB_MPBARRETT_H |
44 | # include "mpbarrett.h" |
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45 | #endif |
46 | |
47 | /*----- Data structures ---------------------------------------------------*/ |
48 | |
49 | typedef struct mpcrt_mod { |
50 | mp *m; /* %$n_i$% -- the modulus */ |
51 | mp *n; /* %$N_i = n / n_i$% */ |
52 | mp *ni; /* %$M_i = N_i^{-1} \bmod n_i$% */ |
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53 | mp *nni; /* %$N_i M_i \bmod m$% */ |
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54 | } mpcrt_mod; |
55 | |
56 | typedef struct mpcrt { |
57 | size_t k; /* Number of distinct moduli */ |
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58 | mpbarrett mb; /* Barrett context for product */ |
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59 | mpcrt_mod *v; /* Vector of information for each */ |
60 | } mpcrt; |
61 | |
62 | /*----- Functions provided ------------------------------------------------*/ |
63 | |
64 | /* --- @mpcrt_create@ --- * |
65 | * |
66 | * Arguments: @mpcrt *c@ = pointer to CRT context |
67 | * @mpcrt_mod *v@ = pointer to vector of moduli |
68 | * @size_t k@ = number of moduli |
69 | * @mp *n@ = product of all moduli (@MP_NEW@ if unknown) |
70 | * |
71 | * Returns: --- |
72 | * |
73 | * Use: Initializes a context for solving Chinese Remainder Theorem |
74 | * problems. The vector of moduli can be incomplete. Omitted |
75 | * items must be left as null pointers. Not all combinations of |
76 | * missing things can be coped with, even if there is |
77 | * technically enough information to cope. For example, if @n@ |
78 | * is unspecified, all the @m@ values must be present, even if |
79 | * there is one modulus with both @m@ and @n@ (from which the |
80 | * product of all moduli could clearly be calculated). |
81 | */ |
82 | |
83 | extern void mpcrt_create(mpcrt */*c*/, mpcrt_mod */*v*/, |
84 | size_t /*k*/, mp */*n*/); |
85 | |
86 | /* --- @mpcrt_destroy@ --- * |
87 | * |
88 | * Arguments: @mpcrt *c@ - pointer to CRT context |
89 | * |
90 | * Returns: --- |
91 | * |
92 | * Use: Destroys a CRT context, releasing all the resources it holds. |
93 | */ |
94 | |
95 | extern void mpcrt_destroy(mpcrt */*c*/); |
96 | |
97 | /* --- @mpcrt_solve@ --- * |
98 | * |
99 | * Arguments: @mpcrt *c@ = pointer to CRT context |
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100 | * @mp *d@ = fake destination |
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101 | * @mp **v@ = array of residues |
102 | * |
103 | * Returns: The unique solution modulo the product of the individual |
104 | * moduli, which leaves the given residues. |
105 | * |
106 | * Use: Constructs a result given its residue modulo an array of |
107 | * coprime integers. This can be used to improve performance of |
108 | * RSA encryption or Blum-Blum-Shub generation if the factors |
109 | * of the modulus are known, since results can be computed mod |
110 | * each of the individual factors and then combined at the end. |
111 | * This is rather faster than doing the full-scale modular |
112 | * exponentiation. |
113 | */ |
114 | |
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115 | extern mp *mpcrt_solve(mpcrt */*c*/, mp */*d*/, mp **/*v*/); |
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116 | |
117 | /*----- That's all, folks -------------------------------------------------*/ |
118 | |
119 | #ifdef __cplusplus |
120 | } |
121 | #endif |
122 | |
123 | #endif |