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