b0ab12e6 |
1 | /* -*-c-*- |
2 | * |
4edc47b8 |
3 | * $Id: field.h,v 1.10 2004/04/01 21:28:41 mdw Exp $ |
b0ab12e6 |
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 $ |
4edc47b8 |
33 | * Revision 1.10 2004/04/01 21:28:41 mdw |
34 | * Normal basis support (translates to poly basis internally). Rewrite |
35 | * EC and prime group table generators in awk, so that they can reuse data |
36 | * for repeated constants. |
37 | * |
34e4f738 |
38 | * Revision 1.9 2004/04/01 12:50:09 mdw |
39 | * Add cyclic group abstraction, with test code. Separate off exponentation |
40 | * functions for better static linking. Fix a buttload of bugs on the way. |
41 | * Generally ensure that negative exponents do inversion correctly. Add |
42 | * table of standard prime-field subgroups. (Binary field subgroups are |
43 | * currently unimplemented but easy to add if anyone ever finds a good one.) |
44 | * |
432c4e18 |
45 | * Revision 1.8 2004/03/27 17:54:11 mdw |
46 | * Standard curves and curve checking. |
47 | * |
f46efa79 |
48 | * Revision 1.7 2004/03/27 00:04:46 mdw |
49 | * Implement efficient reduction for pleasant-looking primes. |
50 | * |
bc985cef |
51 | * Revision 1.6 2004/03/23 15:19:32 mdw |
52 | * Test elliptic curves more thoroughly. |
53 | * |
9b8b6877 |
54 | * Revision 1.5 2004/03/23 12:08:26 mdw |
55 | * Random field-element selection. |
56 | * |
c3caa2fa |
57 | * Revision 1.4 2004/03/21 22:52:06 mdw |
58 | * Merge and close elliptic curve branch. |
59 | * |
ceb3f0c0 |
60 | * Revision 1.3.4.2 2004/03/21 22:39:46 mdw |
61 | * Elliptic curves on binary fields work. |
62 | * |
8823192f |
63 | * Revision 1.3.4.1 2004/03/20 00:13:31 mdw |
64 | * Projective coordinates for prime curves |
65 | * |
b085fd91 |
66 | * Revision 1.3 2002/01/13 13:48:44 mdw |
67 | * Further progress. |
68 | * |
2685767a |
69 | * Revision 1.2 2001/05/07 17:30:13 mdw |
70 | * Add an internal-representation no-op function. |
71 | * |
b0ab12e6 |
72 | * Revision 1.1 2001/04/29 18:12:33 mdw |
73 | * Prototype version. |
74 | * |
75 | */ |
76 | |
77 | #ifndef CATACOMB_FIELD_H |
78 | #define CATACOMB_FIELD_H |
79 | |
80 | #ifdef __cplusplus |
81 | extern "C" { |
82 | #endif |
83 | |
84 | /*----- Header files ------------------------------------------------------*/ |
85 | |
9b8b6877 |
86 | #ifndef CATACOMB_GRAND_H |
87 | # include "grand.h" |
88 | #endif |
89 | |
b0ab12e6 |
90 | #ifndef CATACOMB_MP_H |
91 | # include "mp.h" |
92 | #endif |
93 | |
432c4e18 |
94 | #ifndef CATACOMB_QDPARSE_H |
95 | # include "qdparse.h" |
96 | #endif |
97 | |
b0ab12e6 |
98 | /*----- Data structures ---------------------------------------------------*/ |
99 | |
100 | typedef struct field { |
101 | const struct field_ops *ops; /* Field operations */ |
102 | mp *zero, *one; /* Identities in the field */ |
432c4e18 |
103 | mp *m; /* Modulus (prime and binary) */ |
104 | unsigned long nbits; /* Length of field element in bits */ |
105 | size_t noctets; /* Length of element in octets */ |
b0ab12e6 |
106 | } field; |
107 | |
bc985cef |
108 | enum { |
109 | FTY_PRIME, |
110 | FTY_BINARY |
111 | }; |
112 | |
b0ab12e6 |
113 | typedef struct field_ops { |
114 | |
bc985cef |
115 | /* --- General information --- */ |
116 | |
117 | unsigned ty; /* What kind of field this is */ |
118 | const char *name; /* Human-readable name string */ |
119 | |
b0ab12e6 |
120 | /* --- Universal operations --- */ |
121 | |
122 | void (*destroy)(field */*f*/); |
9b8b6877 |
123 | mp *(*rand)(field */*f*/, mp */*d*/, grand */*r*/); |
34e4f738 |
124 | int (*samep)(field */*f*/, field */*g*/); |
b0ab12e6 |
125 | |
126 | mp *(*in)(field */*f*/, mp */*d*/, mp */*x*/); |
127 | mp *(*out)(field */*f*/, mp */*d*/, mp */*x*/); |
128 | |
8823192f |
129 | int (*zerop)(field */*f*/, mp */*x*/); |
b085fd91 |
130 | mp *(*neg)(field */*f*/, mp */*d*/, mp */*x*/); |
b0ab12e6 |
131 | mp *(*add)(field */*f*/, mp */*d*/, mp */*x*/, mp */*y*/); |
132 | mp *(*sub)(field */*f*/, mp */*d*/, mp */*x*/, mp */*y*/); |
133 | mp *(*mul)(field */*f*/, mp */*d*/, mp */*x*/, mp */*y*/); |
134 | mp *(*sqr)(field */*f*/, mp */*d*/, mp */*x*/); |
135 | mp *(*inv)(field */*f*/, mp */*d*/, mp */*x*/); |
136 | mp *(*reduce)(field */*f*/, mp */*d*/, mp */*x*/); |
ceb3f0c0 |
137 | mp *(*sqrt)(field */*f*/, mp */*d*/, mp */*x*/); |
138 | |
139 | /* --- Operations for binary fields only --- */ |
140 | |
141 | mp *(*quadsolve)(field */*f*/, mp */*d*/, mp */*x*/); |
b0ab12e6 |
142 | |
143 | /* --- Operations for prime fields only --- */ |
144 | |
145 | mp *(*dbl)(field */*f*/, mp */*d*/, mp */*x*/); |
146 | mp *(*tpl)(field */*f*/, mp */*d*/, mp */*x*/); |
8823192f |
147 | mp *(*qdl)(field */*f*/, mp */*d*/, mp */*x*/); |
148 | mp *(*hlv)(field */*f*/, mp */*d*/, mp */*x*/); |
b0ab12e6 |
149 | |
150 | } field_ops; |
151 | |
bc985cef |
152 | #define F_TYPE(f) (f)->ops->ty |
153 | #define F_NAME(f) (f)->ops->name |
154 | |
b0ab12e6 |
155 | #define F_DESTROY(f) (f)->ops->destroy((f)) |
bc985cef |
156 | #define F_RAND(f, d, r) (f)->ops->rand((f), (d), (r)) |
34e4f738 |
157 | #define F_SAMEP(f, g) (f)->ops->samep((f), (g)) |
b0ab12e6 |
158 | |
159 | #define F_IN(f, d, x) (f)->ops->in((f), (d), (x)) |
160 | #define F_OUT(f, d, x) (f)->ops->out((f), (d), (x)) |
8823192f |
161 | |
162 | #define F_ZEROP(f, x) (f)->ops->zerop((f), (x)) |
b085fd91 |
163 | #define F_NEG(f, d, x) (f)->ops->neg((f), (d), (x)) |
b0ab12e6 |
164 | #define F_ADD(f, d, x, y) (f)->ops->add((f), (d), (x), (y)) |
165 | #define F_SUB(f, d, x, y) (f)->ops->sub((f), (d), (x), (y)) |
166 | #define F_MUL(f, d, x, y) (f)->ops->mul((f), (d), (x), (y)) |
167 | #define F_SQR(f, d, x) (f)->ops->sqr((f), (d), (x)) |
168 | #define F_INV(f, d, x) (f)->ops->inv((f), (d), (x)) |
169 | #define F_REDUCE(f, d, x) (f)->ops->reduce((f), (d), (x)) |
ceb3f0c0 |
170 | #define F_SQRT(f, d, x) (f)->ops->sqrt((f), (d), (x)) |
171 | |
172 | #define F_QUADSOLVE(f, d, x) (f)->ops->quadsolve((f), (d), (x)) |
b0ab12e6 |
173 | |
174 | #define F_DBL(f, d, x) (f)->ops->dbl((f), (d), (x)) |
175 | #define F_TPL(f, d, x) (f)->ops->tpl((f), (d), (x)) |
8823192f |
176 | #define F_QDL(f, d, x) (f)->ops->qdl((f), (d), (x)) |
177 | #define F_HLV(f, d, x) (f)->ops->hlv((f), (d), (x)) |
b0ab12e6 |
178 | |
2685767a |
179 | /*----- Helpful field operations ------------------------------------------*/ |
180 | |
181 | /* --- @field_id@ --- * |
182 | * |
183 | * Arguments: @field *f@ = pointer to a field |
184 | * @mp *d@ = a destination element |
185 | * @mp *x@ = a source element |
186 | * |
187 | * Returns: The result element. |
188 | * |
189 | * Use: An identity operation which can be used if your field has no |
190 | * internal representation. |
191 | */ |
192 | |
193 | extern mp *field_id(field */*f*/, mp */*d*/, mp */*x*/); |
194 | |
34e4f738 |
195 | /* --- @field_samep@ --- * |
196 | * |
197 | * Arguments: @field *f, *g@ = two fields |
198 | * |
199 | * Returns: Nonzero if the fields are identical (not just isomorphic). |
200 | * |
201 | * Use: Checks for sameness of fields. This function does the full |
202 | * check, not just the field-type-specific check done by the |
203 | * @sampep@ field operation. |
204 | */ |
205 | |
206 | extern int field_samep(field */*f*/, field */*g*/); |
207 | |
208 | /* --- @field_stdsamep@ --- * |
209 | * |
210 | * Arguments: @field *f, *g@ = two fields |
211 | * |
212 | * Returns: Nonzero if the fields are identical (not just isomorphic). |
213 | * |
214 | * Use: Standard sameness check, based on equality of the @m@ |
215 | * member. |
216 | */ |
217 | |
218 | extern int field_stdsamep(field */*f*/, field */*g*/); |
219 | |
b0ab12e6 |
220 | /*----- Creating fields ---------------------------------------------------*/ |
221 | |
222 | /* --- @field_prime@ --- * |
223 | * |
224 | * Arguments: @mp *p@ = the characteristic of the field |
225 | * |
226 | * Returns: A pointer to the field. |
227 | * |
228 | * Use: Creates a field structure for a prime field of size %$p$%, |
229 | * using Montgomery reduction for arithmetic. |
230 | */ |
231 | |
232 | extern field *field_prime(mp */*p*/); |
233 | |
f46efa79 |
234 | /* --- @field_niceprime@ --- * |
235 | * |
236 | * Arguments: @mp *p@ = the characteristic of the field |
237 | * |
238 | * Returns: A pointer to the field. |
239 | * |
240 | * Use: Creates a field structure for a prime field of size %$p$%, |
241 | * using efficient reduction for nice primes. |
242 | */ |
243 | |
244 | extern field *field_niceprime(mp */*p*/); |
245 | |
b0ab12e6 |
246 | /* --- @field_binpoly@ --- * |
247 | * |
248 | * Arguments: @mp *p@ = an irreducible polynomial over %$\gf{2}$% |
249 | * |
250 | * Returns: A pointer to the field. |
251 | * |
252 | * Use: Creates a field structure for a binary field using naive |
253 | * arithmetic. |
254 | */ |
255 | |
256 | extern field *field_binpoly(mp */*p*/); |
257 | |
4edc47b8 |
258 | /* --- @field_binnorm@ --- * |
259 | * |
260 | * Arguments: @mp *p@ = the reduction polynomial |
261 | * @mp *beta@ = representation of normal point |
262 | * |
263 | * Returns: A pointer to the field. |
264 | * |
265 | * Use: Creates a field structure for a binary field mod @p@ which |
266 | * uses a normal basis representation externally. Computations |
267 | * are still done on a polynomial-basis representation. |
268 | */ |
269 | |
270 | extern field *field_binnorm(mp */*p*/, mp */*beta*/); |
271 | |
432c4e18 |
272 | /* --- @field_parse@ --- * |
273 | * |
274 | * Arguments: @qd_parse *qd@ = parser context |
275 | * |
276 | * Returns: Field pointer if OK, or null. |
277 | * |
278 | * Use: Parses a field description, which has the form |
279 | * |
4edc47b8 |
280 | * * `prime', `niceprime', `binpoly', or `binnorm' |
432c4e18 |
281 | * * an optional `:' |
282 | * * the field modulus |
4edc47b8 |
283 | * * for `binnorm', an optional `,' and the beta value |
432c4e18 |
284 | */ |
285 | |
286 | extern field *field_parse(qd_parse */*qd*/); |
287 | |
b0ab12e6 |
288 | /*----- That's all, folks -------------------------------------------------*/ |
289 | |
290 | #ifdef __cplusplus |
291 | } |
292 | #endif |
293 | |
294 | #endif |