chiark / gitweb /
math/mpmont.c: Factor out the computational core of the algorithm.
[catacomb] / math / mpbarrett.h
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21a7c4b1 1/* -*-c-*-
21a7c4b1 2 *
3 * Barrett modular reduction
4 *
5 * (c) 1999 Straylight/Edgeware
6 */
7
45c0fd36 8/*----- Licensing notice --------------------------------------------------*
21a7c4b1 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.
45c0fd36 16 *
21a7c4b1 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.
45c0fd36 21 *
21a7c4b1 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
21a7c4b1 28/*----- Notes on Barrett reduction ----------------------------------------*
29 *
30 * Barrett reduction is a technique for computing modular residues. Unlike
31 * Montgomery reduction, it doesn't have restrictions on the modulus (except
32 * that it be positive) and doesn't confuse matters by putting an extra
33 * factor all the way through your computation.
34 *
35 * It's useful for slightly less heavy-duty work than Montgomery reduction
36 * because the precomputation phase is rather simpler, involving a single
37 * division operation.
38 *
39 * Sometimes it's useful to exponentiate modulo an even number, so there's a
40 * modexp routine provided which uses Barrett reduction rather than
41 * Montgomery reduction. This is handy when you're working on indices in an
42 * even-order cyclic group or something.
fa17e5dc
MW
43 *
44 * In more detail: suppose that %$b^{k-1} \le m < b^k$%. Let %$\mu = {}$%
45 * %$\lfloor b^{2k}/m \rfloor$%; %$\mu$% is a scaled approximation to the
46 * reciprocal %$1/m$%. Now, suppose we're given some %$a$% with
47 * %$0 \le a < b^{2k}$%. The first step is to calculate an approximation
48 * %$q = \lfloor \mu \lfloor a/b^{k-1} \rfloor/b^{k+1} \rfloor$% to the
49 * quotient %$a/m$%. Then we have:
50 *
51 * %$\lfloor a/m - a/b^{2k} - b^{k-1}/m + 1/b^{k+1} \rfloor \le {}$%
52 * %$q \le \lfloor a/m \rfloor
53 *
54 * But by assumption %$a < b^{2k}$% and %$2^{k-1} \le m$% so
55 *
56 * %$\lfloor a/m \rfloor - 2 \le q \le \lfloor a/m \rfloor$%
57 *
58 * Now we approximate the remainder by calculating %$r = a - q m$%.
59 * Certainly %$r \equiv a \pmod{m}$%; and
60 *
61 * %$0 \le r \le (a - m \lfloor a/m \rfloor) + 2 m < 3 m$%.
62 *
63 * So the remainder can be fixed up with at most two conditional
64 * subtractions.
21a7c4b1 65 */
66
67#ifndef CATACOMB_MPBARRETT_H
68#define CATACOMB_MPBARRETT_H
69
70#ifdef __cplusplus
71 extern "C" {
72#endif
73
74/*----- Header files ------------------------------------------------------*/
75
76#ifndef CATACOMB_MP_H
77# include "mp.h"
78#endif
79
80/*----- Data structures ---------------------------------------------------*/
81
82typedef struct mpbarrett {
83 mp *m;
84 mp *mu;
85 size_t k;
86} mpbarrett;
87
88/*----- Functions provided ------------------------------------------------*/
89
90/* --- @mpbarrett_create@ --- *
91 *
92 * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context
93 * @mp *m@ = modulus to work to
94 *
f4535c64 95 * Returns: Zero on success, nonzero on error.
21a7c4b1 96 *
97 * Use: Initializes a Barrett reduction context ready for use.
98 */
99
f4535c64 100extern int mpbarrett_create(mpbarrett */*mb*/, mp */*m*/);
21a7c4b1 101
102/* --- @mpbarrett_destroy@ --- *
103 *
104 * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context
105 *
106 * Returns: ---
107 *
108 * Use: Destroys a Barrett reduction context releasing any resources
109 * claimed.
110 */
111
112extern void mpbarrett_destroy(mpbarrett */*mb*/);
113
114/* --- @mpbarrett_reduce@ --- *
115 *
116 * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context
117 * @mp *d@ = destination for result
118 * @mp *m@ = number to reduce
119 *
120 * Returns: The residue of @m@ modulo the number in the reduction
121 * context.
122 *
30cbe7a7 123 * Use: Performs an efficient modular reduction.
21a7c4b1 124 */
125
126extern mp *mpbarrett_reduce(mpbarrett */*mb*/, mp */*d*/, mp */*m*/);
127
128/* --- @mpbarrett_exp@ --- *
129 *
130 * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context
45c0fd36
MW
131 * @mp *d@ = fake destination
132 * @mp *a@ = base
133 * @mp *e@ = exponent
21a7c4b1 134 *
45c0fd36 135 * Returns: Result, %$a^e \bmod m$%.
21a7c4b1 136 */
137
138extern mp *mpbarrett_exp(mpbarrett */*mb*/, mp */*d*/, mp */*a*/, mp */*e*/);
139
ab0350a6 140/* --- @mpbarrett_mexp@ --- *
141 *
142 * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context
143 * @mp *d@ = fake destination
34e4f738 144 * @const mp_expfactor *f@ = pointer to array of factors
ab0350a6 145 * @size_t n@ = number of factors supplied
146 *
147 * Returns: If the bases are %$g_0, g_1, \ldots, g_{n-1}$% and the
148 * exponents are %$e_0, e_1, \ldots, e_{n-1}$% then the result
149 * is:
150 *
151 * %$g_0^{e_0} g_1^{e_1} \ldots g_{n-1}^{e_{n-1}} \bmod m$%
152 */
153
154extern mp *mpbarrett_mexp(mpbarrett */*mb*/, mp */*d*/,
34e4f738 155 const mp_expfactor */*f*/, size_t /*n*/);
ab0350a6 156
21a7c4b1 157/*----- That's all, folks -------------------------------------------------*/
158
159#ifdef __cplusplus
160 }
161#endif
162
163#endif