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1 | /* -*-c-*- |
2 | * |
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3 | * $Id: field.h,v 1.9 2004/04/01 12:50:09 mdw Exp $ |
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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 | |
30 | /*----- Revision history --------------------------------------------------* |
31 | * |
32 | * $Log: field.h,v $ |
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33 | * Revision 1.9 2004/04/01 12:50:09 mdw |
34 | * Add cyclic group abstraction, with test code. Separate off exponentation |
35 | * functions for better static linking. Fix a buttload of bugs on the way. |
36 | * Generally ensure that negative exponents do inversion correctly. Add |
37 | * table of standard prime-field subgroups. (Binary field subgroups are |
38 | * currently unimplemented but easy to add if anyone ever finds a good one.) |
39 | * |
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40 | * Revision 1.8 2004/03/27 17:54:11 mdw |
41 | * Standard curves and curve checking. |
42 | * |
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43 | * Revision 1.7 2004/03/27 00:04:46 mdw |
44 | * Implement efficient reduction for pleasant-looking primes. |
45 | * |
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46 | * Revision 1.6 2004/03/23 15:19:32 mdw |
47 | * Test elliptic curves more thoroughly. |
48 | * |
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49 | * Revision 1.5 2004/03/23 12:08:26 mdw |
50 | * Random field-element selection. |
51 | * |
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52 | * Revision 1.4 2004/03/21 22:52:06 mdw |
53 | * Merge and close elliptic curve branch. |
54 | * |
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55 | * Revision 1.3.4.2 2004/03/21 22:39:46 mdw |
56 | * Elliptic curves on binary fields work. |
57 | * |
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58 | * Revision 1.3.4.1 2004/03/20 00:13:31 mdw |
59 | * Projective coordinates for prime curves |
60 | * |
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61 | * Revision 1.3 2002/01/13 13:48:44 mdw |
62 | * Further progress. |
63 | * |
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64 | * Revision 1.2 2001/05/07 17:30:13 mdw |
65 | * Add an internal-representation no-op function. |
66 | * |
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67 | * Revision 1.1 2001/04/29 18:12:33 mdw |
68 | * Prototype version. |
69 | * |
70 | */ |
71 | |
72 | #ifndef CATACOMB_FIELD_H |
73 | #define CATACOMB_FIELD_H |
74 | |
75 | #ifdef __cplusplus |
76 | extern "C" { |
77 | #endif |
78 | |
79 | /*----- Header files ------------------------------------------------------*/ |
80 | |
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81 | #ifndef CATACOMB_GRAND_H |
82 | # include "grand.h" |
83 | #endif |
84 | |
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85 | #ifndef CATACOMB_MP_H |
86 | # include "mp.h" |
87 | #endif |
88 | |
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89 | #ifndef CATACOMB_QDPARSE_H |
90 | # include "qdparse.h" |
91 | #endif |
92 | |
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93 | /*----- Data structures ---------------------------------------------------*/ |
94 | |
95 | typedef struct field { |
96 | const struct field_ops *ops; /* Field operations */ |
97 | mp *zero, *one; /* Identities in the field */ |
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98 | mp *m; /* Modulus (prime and binary) */ |
99 | unsigned long nbits; /* Length of field element in bits */ |
100 | size_t noctets; /* Length of element in octets */ |
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101 | } field; |
102 | |
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103 | enum { |
104 | FTY_PRIME, |
105 | FTY_BINARY |
106 | }; |
107 | |
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108 | typedef struct field_ops { |
109 | |
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110 | /* --- General information --- */ |
111 | |
112 | unsigned ty; /* What kind of field this is */ |
113 | const char *name; /* Human-readable name string */ |
114 | |
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115 | /* --- Universal operations --- */ |
116 | |
117 | void (*destroy)(field */*f*/); |
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118 | mp *(*rand)(field */*f*/, mp */*d*/, grand */*r*/); |
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119 | int (*samep)(field */*f*/, field */*g*/); |
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120 | |
121 | mp *(*in)(field */*f*/, mp */*d*/, mp */*x*/); |
122 | mp *(*out)(field */*f*/, mp */*d*/, mp */*x*/); |
123 | |
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124 | int (*zerop)(field */*f*/, mp */*x*/); |
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125 | mp *(*neg)(field */*f*/, mp */*d*/, mp */*x*/); |
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126 | mp *(*add)(field */*f*/, mp */*d*/, mp */*x*/, mp */*y*/); |
127 | mp *(*sub)(field */*f*/, mp */*d*/, mp */*x*/, mp */*y*/); |
128 | mp *(*mul)(field */*f*/, mp */*d*/, mp */*x*/, mp */*y*/); |
129 | mp *(*sqr)(field */*f*/, mp */*d*/, mp */*x*/); |
130 | mp *(*inv)(field */*f*/, mp */*d*/, mp */*x*/); |
131 | mp *(*reduce)(field */*f*/, mp */*d*/, mp */*x*/); |
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132 | mp *(*sqrt)(field */*f*/, mp */*d*/, mp */*x*/); |
133 | |
134 | /* --- Operations for binary fields only --- */ |
135 | |
136 | mp *(*quadsolve)(field */*f*/, mp */*d*/, mp */*x*/); |
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137 | |
138 | /* --- Operations for prime fields only --- */ |
139 | |
140 | mp *(*dbl)(field */*f*/, mp */*d*/, mp */*x*/); |
141 | mp *(*tpl)(field */*f*/, mp */*d*/, mp */*x*/); |
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142 | mp *(*qdl)(field */*f*/, mp */*d*/, mp */*x*/); |
143 | mp *(*hlv)(field */*f*/, mp */*d*/, mp */*x*/); |
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144 | |
145 | } field_ops; |
146 | |
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147 | #define F_TYPE(f) (f)->ops->ty |
148 | #define F_NAME(f) (f)->ops->name |
149 | |
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150 | #define F_DESTROY(f) (f)->ops->destroy((f)) |
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151 | #define F_RAND(f, d, r) (f)->ops->rand((f), (d), (r)) |
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152 | #define F_SAMEP(f, g) (f)->ops->samep((f), (g)) |
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153 | |
154 | #define F_IN(f, d, x) (f)->ops->in((f), (d), (x)) |
155 | #define F_OUT(f, d, x) (f)->ops->out((f), (d), (x)) |
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156 | |
157 | #define F_ZEROP(f, x) (f)->ops->zerop((f), (x)) |
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158 | #define F_NEG(f, d, x) (f)->ops->neg((f), (d), (x)) |
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159 | #define F_ADD(f, d, x, y) (f)->ops->add((f), (d), (x), (y)) |
160 | #define F_SUB(f, d, x, y) (f)->ops->sub((f), (d), (x), (y)) |
161 | #define F_MUL(f, d, x, y) (f)->ops->mul((f), (d), (x), (y)) |
162 | #define F_SQR(f, d, x) (f)->ops->sqr((f), (d), (x)) |
163 | #define F_INV(f, d, x) (f)->ops->inv((f), (d), (x)) |
164 | #define F_REDUCE(f, d, x) (f)->ops->reduce((f), (d), (x)) |
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165 | #define F_SQRT(f, d, x) (f)->ops->sqrt((f), (d), (x)) |
166 | |
167 | #define F_QUADSOLVE(f, d, x) (f)->ops->quadsolve((f), (d), (x)) |
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168 | |
169 | #define F_DBL(f, d, x) (f)->ops->dbl((f), (d), (x)) |
170 | #define F_TPL(f, d, x) (f)->ops->tpl((f), (d), (x)) |
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171 | #define F_QDL(f, d, x) (f)->ops->qdl((f), (d), (x)) |
172 | #define F_HLV(f, d, x) (f)->ops->hlv((f), (d), (x)) |
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173 | |
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174 | /*----- Helpful field operations ------------------------------------------*/ |
175 | |
176 | /* --- @field_id@ --- * |
177 | * |
178 | * Arguments: @field *f@ = pointer to a field |
179 | * @mp *d@ = a destination element |
180 | * @mp *x@ = a source element |
181 | * |
182 | * Returns: The result element. |
183 | * |
184 | * Use: An identity operation which can be used if your field has no |
185 | * internal representation. |
186 | */ |
187 | |
188 | extern mp *field_id(field */*f*/, mp */*d*/, mp */*x*/); |
189 | |
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190 | /* --- @field_samep@ --- * |
191 | * |
192 | * Arguments: @field *f, *g@ = two fields |
193 | * |
194 | * Returns: Nonzero if the fields are identical (not just isomorphic). |
195 | * |
196 | * Use: Checks for sameness of fields. This function does the full |
197 | * check, not just the field-type-specific check done by the |
198 | * @sampep@ field operation. |
199 | */ |
200 | |
201 | extern int field_samep(field */*f*/, field */*g*/); |
202 | |
203 | /* --- @field_stdsamep@ --- * |
204 | * |
205 | * Arguments: @field *f, *g@ = two fields |
206 | * |
207 | * Returns: Nonzero if the fields are identical (not just isomorphic). |
208 | * |
209 | * Use: Standard sameness check, based on equality of the @m@ |
210 | * member. |
211 | */ |
212 | |
213 | extern int field_stdsamep(field */*f*/, field */*g*/); |
214 | |
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215 | /*----- Creating fields ---------------------------------------------------*/ |
216 | |
217 | /* --- @field_prime@ --- * |
218 | * |
219 | * Arguments: @mp *p@ = the characteristic of the field |
220 | * |
221 | * Returns: A pointer to the field. |
222 | * |
223 | * Use: Creates a field structure for a prime field of size %$p$%, |
224 | * using Montgomery reduction for arithmetic. |
225 | */ |
226 | |
227 | extern field *field_prime(mp */*p*/); |
228 | |
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229 | /* --- @field_niceprime@ --- * |
230 | * |
231 | * Arguments: @mp *p@ = the characteristic of the field |
232 | * |
233 | * Returns: A pointer to the field. |
234 | * |
235 | * Use: Creates a field structure for a prime field of size %$p$%, |
236 | * using efficient reduction for nice primes. |
237 | */ |
238 | |
239 | extern field *field_niceprime(mp */*p*/); |
240 | |
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241 | /* --- @field_binpoly@ --- * |
242 | * |
243 | * Arguments: @mp *p@ = an irreducible polynomial over %$\gf{2}$% |
244 | * |
245 | * Returns: A pointer to the field. |
246 | * |
247 | * Use: Creates a field structure for a binary field using naive |
248 | * arithmetic. |
249 | */ |
250 | |
251 | extern field *field_binpoly(mp */*p*/); |
252 | |
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253 | /* --- @field_parse@ --- * |
254 | * |
255 | * Arguments: @qd_parse *qd@ = parser context |
256 | * |
257 | * Returns: Field pointer if OK, or null. |
258 | * |
259 | * Use: Parses a field description, which has the form |
260 | * |
261 | * * `prime', `niceprime' or `binpoly' |
262 | * * an optional `:' |
263 | * * the field modulus |
264 | */ |
265 | |
266 | extern field *field_parse(qd_parse */*qd*/); |
267 | |
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268 | /*----- That's all, folks -------------------------------------------------*/ |
269 | |
270 | #ifdef __cplusplus |
271 | } |
272 | #endif |
273 | |
274 | #endif |