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ceb3f0c0 | 1 | /* -*-c-*- |
ceb3f0c0 | 2 | * |
3 | * Reduction modulo sparse binary polynomials | |
4 | * | |
5 | * (c) 2004 Straylight/Edgeware | |
6 | */ | |
7 | ||
45c0fd36 | 8 | /*----- Licensing notice --------------------------------------------------* |
ceb3f0c0 | 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 | * |
ceb3f0c0 | 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 | * |
ceb3f0c0 | 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 | ||
ceb3f0c0 | 28 | #ifndef CATACOMB_GFREDUCE_H |
29 | #define CATACOMB_GFREDUCE_H | |
30 | ||
31 | #ifdef __cplusplus | |
32 | extern "C" { | |
33 | #endif | |
34 | ||
35 | /*----- Header files ------------------------------------------------------*/ | |
36 | ||
12208248 MW |
37 | #include <stdio.h> |
38 | ||
ceb3f0c0 | 39 | #ifndef CATACOMB_GF_H |
40 | # include "gf.h" | |
41 | #endif | |
42 | ||
43 | /*----- Data structures ---------------------------------------------------*/ | |
44 | ||
45 | typedef struct gfreduce_instr { | |
46 | unsigned op; /* Instruction opcode */ | |
47 | size_t arg; /* Immediate argument */ | |
48 | } gfreduce_instr; | |
49 | ||
50 | enum { | |
51 | GFRI_LOAD, /* Load @p[arg]@ */ | |
52 | GFRI_LSL, /* XOR with @w << arg@ */ | |
53 | GFRI_LSR, /* XOR with @w >> arg@ */ | |
54 | GFRI_STORE, /* Store @p[arg]@ */ | |
55 | GFRI_MAX | |
56 | }; | |
57 | ||
58 | typedef struct gfreduce { | |
59 | size_t lim; /* Word of degree bit */ | |
60 | mpw mask; /* Mask for degree word */ | |
61 | mp *p; /* Copy of the polynomial */ | |
62 | size_t in; /* Number of instruction words */ | |
d153d02e MW |
63 | gfreduce_instr *iv; /* Vector of instructions */ |
64 | gfreduce_instr *fiv; /* Final-pass instruction suffix */ | |
ceb3f0c0 | 65 | } gfreduce; |
66 | ||
67 | /*----- Functions provided ------------------------------------------------*/ | |
68 | ||
69 | /* --- @gfreduce_create@ --- * | |
70 | * | |
71 | * Arguments: @gfreduce *r@ = structure to fill in | |
72 | * @mp *x@ = a (hopefully sparse) polynomial | |
73 | * | |
74 | * Returns: --- | |
75 | * | |
76 | * Use: Initializes a context structure for reduction. | |
77 | */ | |
78 | ||
79 | extern void gfreduce_create(gfreduce */*r*/, mp */*p*/); | |
80 | ||
81 | /* --- @gfreduce_destroy@ --- * | |
82 | * | |
83 | * Arguments: @gfreduce *r@ = structure to free | |
84 | * | |
85 | * Returns: --- | |
86 | * | |
87 | * Use: Reclaims the resources from a reduction context. | |
88 | */ | |
89 | ||
90 | extern void gfreduce_destroy(gfreduce */*r*/); | |
91 | ||
92 | /* --- @gfreduce_dump@ --- * | |
93 | * | |
94 | * Arguments: @gfreduce *r@ = structure to dump | |
95 | * @FILE *fp@ = file to dump on | |
96 | * | |
97 | * Returns: --- | |
98 | * | |
99 | * Use: Dumps a reduction context. | |
100 | */ | |
101 | ||
102 | extern void gfreduce_dump(gfreduce */*r*/, FILE */*fp*/); | |
103 | ||
104 | /* --- @gfreduce_do@ --- * | |
105 | * | |
106 | * Arguments: @gfreduce *r@ = reduction context | |
107 | * @mp *d@ = destination | |
108 | * @mp *x@ = source | |
109 | * | |
110 | * Returns: Destination, @x@ reduced modulo the reduction poly. | |
111 | */ | |
112 | ||
113 | extern mp *gfreduce_do(gfreduce */*r*/, mp */*d*/, mp */*x*/); | |
114 | ||
115 | /* --- @gfreduce_sqrt@ --- * | |
116 | * | |
117 | * Arguments: @gfreduce *r@ = pointer to reduction context | |
118 | * @mp *d@ = destination | |
119 | * @mp *x@ = some polynomial | |
120 | * | |
121 | * Returns: The square root of @x@ modulo @r->p@, or null. | |
122 | */ | |
123 | ||
124 | extern mp *gfreduce_sqrt(gfreduce */*r*/, mp */*d*/, mp */*x*/); | |
125 | ||
126 | /* --- @gfreduce_trace@ --- * | |
127 | * | |
128 | * Arguments: @gfreduce *r@ = pointer to reduction context | |
129 | * @mp *x@ = some polynomial | |
130 | * | |
131 | * Returns: The trace of @x@. (%$\Tr(x)=x + x^2 + \cdots + x^{2^{m-1}}$% | |
5a19b5df MW |
132 | * if %$x \in \gf{2^m}$%). Since the trace is invariant under |
133 | * the Frobenius automorphism (i.e., %$\Tr(x)^2 = \Tr(x)$%), it | |
134 | * must be an element of the base field, i.e., %$\gf{2}$%, and | |
135 | * we only need a single bit to represent it. | |
ceb3f0c0 | 136 | */ |
137 | ||
138 | extern int gfreduce_trace(gfreduce */*r*/, mp */*x*/); | |
139 | ||
140 | /* --- @gfreduce_halftrace@ --- * | |
141 | * | |
142 | * Arguments: @gfreduce *r@ = pointer to reduction context | |
143 | * @mp *d@ = destination | |
144 | * @mp *x@ = some polynomial | |
145 | * | |
146 | * Returns: The half-trace of @x@. | |
147 | * (%$\HfTr(x)= x + x^{2^2} + \cdots + x^{2^{m-1}}$% | |
148 | * if %$x \in \gf{2^m}$% with %$m$% odd). | |
149 | */ | |
150 | ||
151 | extern mp *gfreduce_halftrace(gfreduce */*r*/, mp */*d*/, mp */*x*/); | |
152 | ||
153 | /* --- @gfreduce_quadsolve@ --- * | |
154 | * | |
155 | * Arguments: @gfreduce *r@ = pointer to reduction context | |
156 | * @mp *d@ = destination | |
157 | * @mp *x@ = some polynomial | |
158 | * | |
159 | * Returns: A polynomial @y@ such that %$y^2 + y = x$%, or null. | |
5a19b5df MW |
160 | * |
161 | * Use: Solves quadratic equations in a field with characteristic 2. | |
162 | * Suppose we have an equation %$y^2 + A y + B = 0$% where | |
163 | * %$A \ne 0$%. (If %$A = 0$% then %$y = \sqrt{B}$% and you | |
164 | * want @gfreduce_sqrt@ instead.) Use this function to solve | |
165 | * %$z^2 + z = B/A^2$%; then set %$y = A z$%, since | |
166 | * %$y^2 + y = A^2 z^2 + A^2 z = A^2 (z^2 + z) = B$% as | |
167 | * required. | |
168 | * | |
169 | * The two roots are %$z$% and %$z + 1$%; this function always | |
170 | * returns the one with zero scalar coefficient. | |
ceb3f0c0 | 171 | */ |
172 | ||
173 | extern mp *gfreduce_quadsolve(gfreduce */*r*/, mp */*d*/, mp */*x*/); | |
174 | ||
175 | /* --- @gfreduce_exp@ --- * | |
176 | * | |
177 | * Arguments: @gfreduce *gr@ = pointer to reduction context | |
45c0fd36 MW |
178 | * @mp *d@ = fake destination |
179 | * @mp *a@ = base | |
180 | * @mp *e@ = exponent | |
ceb3f0c0 | 181 | * |
45c0fd36 | 182 | * Returns: Result, %$a^e \bmod m$%. |
ceb3f0c0 | 183 | */ |
184 | ||
185 | extern mp *gfreduce_exp(gfreduce */*gr*/, mp */*d*/, mp */*a*/, mp */*e*/); | |
186 | ||
187 | /*----- That's all, folks -------------------------------------------------*/ | |
188 | ||
189 | #ifdef __cplusplus | |
190 | } | |
191 | #endif | |
192 | ||
193 | #endif |