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1 | /* -*-c-*- |
2 | * |
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3 | * $Id$ |
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4 | * |
5 | * Definitions for field arithmetic |
6 | * |
7 | * (c) 2000 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 | |
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30 | #ifndef CATACOMB_FIELD_H |
31 | #define CATACOMB_FIELD_H |
32 | |
33 | #ifdef __cplusplus |
34 | extern "C" { |
35 | #endif |
36 | |
37 | /*----- Header files ------------------------------------------------------*/ |
38 | |
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39 | #ifndef CATACOMB_GRAND_H |
40 | # include "grand.h" |
41 | #endif |
42 | |
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43 | #ifndef CATACOMB_MP_H |
44 | # include "mp.h" |
45 | #endif |
46 | |
432c4e18 |
47 | #ifndef CATACOMB_QDPARSE_H |
48 | # include "qdparse.h" |
49 | #endif |
50 | |
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51 | /*----- Data structures ---------------------------------------------------*/ |
52 | |
53 | typedef struct field { |
54 | const struct field_ops *ops; /* Field operations */ |
55 | mp *zero, *one; /* Identities in the field */ |
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56 | mp *m; /* Modulus (prime and binary) */ |
57 | unsigned long nbits; /* Length of field element in bits */ |
58 | size_t noctets; /* Length of element in octets */ |
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59 | mp *q; /* Number of elements in field */ |
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60 | } field; |
61 | |
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62 | enum { |
63 | FTY_PRIME, |
64 | FTY_BINARY |
65 | }; |
66 | |
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67 | typedef struct field_ops { |
68 | |
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69 | /* --- General information --- */ |
70 | |
71 | unsigned ty; /* What kind of field this is */ |
72 | const char *name; /* Human-readable name string */ |
73 | |
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74 | /* --- Universal operations --- */ |
75 | |
76 | void (*destroy)(field */*f*/); |
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77 | mp *(*rand)(field */*f*/, mp */*d*/, grand */*r*/); |
34e4f738 |
78 | int (*samep)(field */*f*/, field */*g*/); |
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79 | |
80 | mp *(*in)(field */*f*/, mp */*d*/, mp */*x*/); |
81 | mp *(*out)(field */*f*/, mp */*d*/, mp */*x*/); |
82 | |
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83 | int (*zerop)(field */*f*/, mp */*x*/); |
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84 | mp *(*neg)(field */*f*/, mp */*d*/, mp */*x*/); |
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85 | mp *(*add)(field */*f*/, mp */*d*/, mp */*x*/, mp */*y*/); |
86 | mp *(*sub)(field */*f*/, mp */*d*/, mp */*x*/, mp */*y*/); |
87 | mp *(*mul)(field */*f*/, mp */*d*/, mp */*x*/, mp */*y*/); |
88 | mp *(*sqr)(field */*f*/, mp */*d*/, mp */*x*/); |
89 | mp *(*inv)(field */*f*/, mp */*d*/, mp */*x*/); |
90 | mp *(*reduce)(field */*f*/, mp */*d*/, mp */*x*/); |
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91 | mp *(*sqrt)(field */*f*/, mp */*d*/, mp */*x*/); |
92 | |
93 | /* --- Operations for binary fields only --- */ |
94 | |
95 | mp *(*quadsolve)(field */*f*/, mp */*d*/, mp */*x*/); |
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96 | |
97 | /* --- Operations for prime fields only --- */ |
98 | |
99 | mp *(*dbl)(field */*f*/, mp */*d*/, mp */*x*/); |
100 | mp *(*tpl)(field */*f*/, mp */*d*/, mp */*x*/); |
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101 | mp *(*qdl)(field */*f*/, mp */*d*/, mp */*x*/); |
102 | mp *(*hlv)(field */*f*/, mp */*d*/, mp */*x*/); |
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103 | |
104 | } field_ops; |
105 | |
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106 | #define F_TYPE(f) (f)->ops->ty |
107 | #define F_NAME(f) (f)->ops->name |
108 | |
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109 | #define F_DESTROY(f) (f)->ops->destroy((f)) |
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110 | #define F_RAND(f, d, r) (f)->ops->rand((f), (d), (r)) |
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111 | #define F_SAMEP(f, g) (f)->ops->samep((f), (g)) |
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112 | |
113 | #define F_IN(f, d, x) (f)->ops->in((f), (d), (x)) |
114 | #define F_OUT(f, d, x) (f)->ops->out((f), (d), (x)) |
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115 | |
116 | #define F_ZEROP(f, x) (f)->ops->zerop((f), (x)) |
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117 | #define F_NEG(f, d, x) (f)->ops->neg((f), (d), (x)) |
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118 | #define F_ADD(f, d, x, y) (f)->ops->add((f), (d), (x), (y)) |
119 | #define F_SUB(f, d, x, y) (f)->ops->sub((f), (d), (x), (y)) |
120 | #define F_MUL(f, d, x, y) (f)->ops->mul((f), (d), (x), (y)) |
121 | #define F_SQR(f, d, x) (f)->ops->sqr((f), (d), (x)) |
122 | #define F_INV(f, d, x) (f)->ops->inv((f), (d), (x)) |
123 | #define F_REDUCE(f, d, x) (f)->ops->reduce((f), (d), (x)) |
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124 | #define F_SQRT(f, d, x) (f)->ops->sqrt((f), (d), (x)) |
125 | |
126 | #define F_QUADSOLVE(f, d, x) (f)->ops->quadsolve((f), (d), (x)) |
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127 | |
128 | #define F_DBL(f, d, x) (f)->ops->dbl((f), (d), (x)) |
129 | #define F_TPL(f, d, x) (f)->ops->tpl((f), (d), (x)) |
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130 | #define F_QDL(f, d, x) (f)->ops->qdl((f), (d), (x)) |
131 | #define F_HLV(f, d, x) (f)->ops->hlv((f), (d), (x)) |
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132 | |
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133 | /*----- Helpful field operations ------------------------------------------*/ |
134 | |
135 | /* --- @field_id@ --- * |
136 | * |
137 | * Arguments: @field *f@ = pointer to a field |
138 | * @mp *d@ = a destination element |
139 | * @mp *x@ = a source element |
140 | * |
141 | * Returns: The result element. |
142 | * |
143 | * Use: An identity operation which can be used if your field has no |
144 | * internal representation. |
145 | */ |
146 | |
147 | extern mp *field_id(field */*f*/, mp */*d*/, mp */*x*/); |
148 | |
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149 | /* --- @field_samep@ --- * |
150 | * |
151 | * Arguments: @field *f, *g@ = two fields |
152 | * |
153 | * Returns: Nonzero if the fields are identical (not just isomorphic). |
154 | * |
155 | * Use: Checks for sameness of fields. This function does the full |
156 | * check, not just the field-type-specific check done by the |
157 | * @sampep@ field operation. |
158 | */ |
159 | |
160 | extern int field_samep(field */*f*/, field */*g*/); |
161 | |
162 | /* --- @field_stdsamep@ --- * |
163 | * |
164 | * Arguments: @field *f, *g@ = two fields |
165 | * |
166 | * Returns: Nonzero if the fields are identical (not just isomorphic). |
167 | * |
168 | * Use: Standard sameness check, based on equality of the @m@ |
169 | * member. |
170 | */ |
171 | |
172 | extern int field_stdsamep(field */*f*/, field */*g*/); |
173 | |
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174 | /*----- Arithmetic --------------------------------------------------------*/ |
175 | |
176 | /* --- @field_exp@ --- * |
177 | * |
178 | * Arguments: @field *f@ = pointer to field |
179 | * @mp *d@ = fake destination |
180 | * @mp *a@ = base |
181 | * @mp *e@ = exponent |
182 | * |
183 | * Returns: Result, %$a^e$%. |
184 | * |
185 | * Use: Exponentiation in a finite field. Note that all quantities |
186 | * are in internal format. This is a generic implementation |
187 | * suitable for use with all fields and is not intended to be |
188 | * optimal. |
189 | */ |
190 | |
191 | extern mp *field_exp(field */*f*/, mp */*d*/, mp */*a*/, mp */*e*/); |
192 | |
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193 | /*----- Creating fields ---------------------------------------------------*/ |
194 | |
195 | /* --- @field_prime@ --- * |
196 | * |
197 | * Arguments: @mp *p@ = the characteristic of the field |
198 | * |
199 | * Returns: A pointer to the field. |
200 | * |
201 | * Use: Creates a field structure for a prime field of size %$p$%, |
202 | * using Montgomery reduction for arithmetic. |
203 | */ |
204 | |
205 | extern field *field_prime(mp */*p*/); |
206 | |
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207 | /* --- @field_niceprime@ --- * |
208 | * |
209 | * Arguments: @mp *p@ = the characteristic of the field |
210 | * |
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211 | * Returns: A pointer to the field, or null. |
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212 | * |
213 | * Use: Creates a field structure for a prime field of size %$p$%, |
214 | * using efficient reduction for nice primes. |
215 | */ |
216 | |
217 | extern field *field_niceprime(mp */*p*/); |
218 | |
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219 | /* --- @field_binpoly@ --- * |
220 | * |
221 | * Arguments: @mp *p@ = an irreducible polynomial over %$\gf{2}$% |
222 | * |
223 | * Returns: A pointer to the field. |
224 | * |
225 | * Use: Creates a field structure for a binary field using naive |
226 | * arithmetic. |
227 | */ |
228 | |
229 | extern field *field_binpoly(mp */*p*/); |
230 | |
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231 | /* --- @field_binnorm@ --- * |
232 | * |
233 | * Arguments: @mp *p@ = the reduction polynomial |
234 | * @mp *beta@ = representation of normal point |
235 | * |
236 | * Returns: A pointer to the field. |
237 | * |
238 | * Use: Creates a field structure for a binary field mod @p@ which |
239 | * uses a normal basis representation externally. Computations |
240 | * are still done on a polynomial-basis representation. |
241 | */ |
242 | |
243 | extern field *field_binnorm(mp */*p*/, mp */*beta*/); |
244 | |
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245 | /* --- @field_parse@ --- * |
246 | * |
247 | * Arguments: @qd_parse *qd@ = parser context |
248 | * |
249 | * Returns: Field pointer if OK, or null. |
250 | * |
251 | * Use: Parses a field description, which has the form |
252 | * |
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253 | * * `prime', `niceprime', `binpoly', or `binnorm' |
432c4e18 |
254 | * * an optional `:' |
255 | * * the field modulus |
4edc47b8 |
256 | * * for `binnorm', an optional `,' and the beta value |
432c4e18 |
257 | */ |
258 | |
259 | extern field *field_parse(qd_parse */*qd*/); |
260 | |
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261 | /*----- That's all, folks -------------------------------------------------*/ |
262 | |
263 | #ifdef __cplusplus |
264 | } |
265 | #endif |
266 | |
267 | #endif |