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1 | /* -*-c-*- |
2 | * |
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3 | * $Id$ |
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4 | * |
5 | * General cyclic group abstraction |
6 | * |
7 | * (c) 2004 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_GROUP_H |
31 | #define CATACOMB_GROUP_H |
32 | |
33 | #ifdef __cplusplus |
34 | extern "C" { |
35 | #endif |
36 | |
37 | /*----- Header files ------------------------------------------------------*/ |
38 | |
39 | #include <mLib/dstr.h> |
40 | |
41 | #ifndef CATACOMB_BUF_H |
42 | # include "buf.h" |
43 | #endif |
44 | |
45 | #ifndef CATACOMB_DH_H |
46 | # include "ec.h" |
47 | #endif |
48 | |
49 | #ifndef CATACOMB_GRAND_H |
50 | # include "grand.h" |
51 | #endif |
52 | |
53 | #ifndef CATACOMB_MP_H |
54 | # include "mp.h" |
55 | #endif |
56 | |
57 | #ifndef CATACOMB_QDPARSE_H |
58 | # include "qdparse.h" |
59 | #endif |
60 | |
61 | /*----- Data structures ---------------------------------------------------*/ |
62 | |
63 | #ifndef ge |
64 | typedef struct ge ge; /* Group element (abstract type) */ |
65 | #endif |
66 | |
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67 | typedef struct group_ { |
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68 | const struct group_ops *ops; /* Operations table */ |
69 | size_t nbits; /* Size of an element in bits */ |
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70 | size_t noctets; /* Size of raw element in octets */ |
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71 | ge *i; /* Identity element */ |
72 | ge *g; /* Generator element */ |
73 | mp *r; /* Order of the generator */ |
74 | mp *h; /* Cofactor */ |
75 | } group; |
76 | |
77 | typedef struct group_expfactor { |
78 | ge *base; /* The base */ |
79 | mp *exp; /* The exponent */ |
80 | } group_expfactor; |
81 | |
82 | typedef struct group_ops { |
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83 | |
84 | /* --- General information --- */ |
85 | |
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86 | unsigned ty; /* Type of this group */ |
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87 | const char *name; /* Textual name string */ |
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88 | |
89 | /* --- Memory management --- */ |
90 | |
91 | void (*destroygroup)(group */*g*/); |
92 | ge *(*create)(group */*g*/); |
93 | void (*copy)(group */*g*/, ge */*d*/, ge */*x*/); |
94 | void (*burn)(group */*g*/, ge */*x*/); |
95 | void (*destroy)(group */*g*/, ge */*e*/); |
96 | |
97 | /* --- Comparisons --- */ |
98 | |
99 | int (*samep)(group */*g*/, group */*h*/); |
100 | int (*eq)(group */*g*/, ge */*x*/, ge */*y*/); |
101 | int (*identp)(group */*g*/, ge */*x*/); |
102 | |
103 | /* --- Other stuff --- */ |
104 | |
105 | const char *(*check)(group */*g*/, grand */*gr*/); |
106 | |
107 | /* --- Arithmetic --- */ |
108 | |
109 | void (*mul)(group */*g*/, ge */*d*/, ge */*x*/, ge */*y*/); |
110 | void (*sqr)(group */*g*/, ge */*d*/, ge */*x*/); |
111 | void (*inv)(group */*g*/, ge */*d*/, ge */*x*/); |
112 | void (*div)(group */*g*/, ge */*d*/, ge */*x*/, ge */*y*/); |
113 | void (*exp)(group */*g*/, ge */*d*/, ge */*x*/, mp */*n*/); |
114 | void (*mexp)(group */*g*/, ge */*d*/, |
115 | const group_expfactor */*f*/, size_t /*n*/); |
116 | |
117 | /* --- Debugging --- */ |
118 | |
119 | int (*read)(group */*g*/, ge */*d*/, |
120 | const mptext_ops */*ops*/, void */*p*/); |
121 | int (*write)(group */*g*/, ge */*x*/, |
122 | const mptext_ops */*ops*/, void */*p*/); |
123 | |
124 | /* --- Conversions --- */ |
125 | |
126 | mp *(*toint)(group */*g*/, mp */*d*/, ge */*x*/); |
127 | int (*fromint)(group */*g*/, ge */*d*/, mp */*x*/); |
128 | int (*toec)(group */*g*/, ec */*d*/, ge */*x*/); |
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129 | int (*fromec)(group */*g*/, ge */*d*/, const ec */*p*/); |
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130 | int (*tobuf)(group */*h*/, buf */*b*/, ge */*x*/); |
131 | int (*frombuf)(group */*h*/, buf */*b*/, ge */*d*/); |
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132 | int (*toraw)(group */*h*/, buf */*b*/, ge */*x*/); |
133 | int (*fromraw)(group */*h*/, buf */*b*/, ge */*d*/); |
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134 | |
135 | } group_ops; |
136 | |
137 | enum { |
138 | GTY_PRIME, /* Prime field subgroup */ |
139 | GTY_BINARY, /* Binary feld subgroup */ |
140 | GTY_EC /* Elliptic curve group */ |
141 | }; |
142 | |
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143 | #define G_NAME(g) (g)->ops->name |
144 | #define G_TYPE(g) (g)->ops->ty |
145 | |
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146 | #define G_DESTROYGROUP(g) (g)->ops->destroygroup((g)) |
147 | #define G_CREATE(g) (g)->ops->create((g)) |
148 | #define G_COPY(g, d, x) (g)->ops->copy((g), (d), (x)) |
149 | #define G_BURN(g, x) (g)->ops->burn((g), (x)) |
150 | #define G_DESTROY(g, x) (g)->ops->destroy((g), (x)) |
151 | |
152 | #define G_SAMEP(g, h) (g)->ops->samep((g), (h)) |
153 | #define G_EQ(g, x, y) (g)->ops->eq((g), (x), (y)) |
154 | #define G_IDENTP(g, x) (g)->ops->identp((g), (x)) |
155 | |
156 | #define G_CHECK(g, gr) (g)->ops->check((g), (gr)) |
157 | |
158 | #define G_MUL(g, d, x, y) (g)->ops->mul((g), (d), (x), (y)) |
159 | #define G_SQR(g, d, x) (g)->ops->sqr((g), (d), (x)) |
160 | #define G_INV(g, d, x) (g)->ops->inv((g), (d), (x)) |
161 | #define G_DIV(g, d, x, y) (g)->ops->div((g), (d), (x), (y)) |
162 | #define G_EXP(g, d, x, n) (g)->ops->exp((g), (d), (x), (n)) |
163 | #define G_MEXP(g, d, f, n) (g)->ops->mexp((g), (d), (f), (n)) |
164 | |
165 | #define G_READ(g, d, o, p) (g)->ops->read((g), (d), (o), (p)) |
166 | #define G_WRITE(g, x, o, p) (g)->ops->write((g), (x), (o), (p)) |
167 | |
168 | #define G_TOINT(g, d, x) (g)->ops->toint((g), (d), (x)) |
169 | #define G_FROMINT(g, d, x) (g)->ops->fromint((g), (d), (x)) |
170 | #define G_TOEC(g, d, x) (g)->ops->toec((g), (d), (x)) |
171 | #define G_FROMEC(g, d, p) (g)->ops->fromec((g), (d), (p)) |
172 | #define G_TOBUF(g, b, x) (g)->ops->tobuf((g), (b), (x)) |
173 | #define G_FROMBUF(g, b, d) (g)->ops->frombuf((g), (b), (d)) |
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174 | #define G_TORAW(g, b, x) (g)->ops->toraw((g), (b), (x)) |
175 | #define G_FROMRAW(g, b, d) (g)->ops->fromraw((g), (b), (d)) |
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176 | |
177 | /*----- Handy functions ---------------------------------------------------*/ |
178 | |
179 | /* --- @group_check@ --- * |
180 | * |
181 | * Arguments: @group *g@ = an abstract group |
182 | * @ge *x@ = a group element |
183 | * |
184 | * Returns: Zero on success, nonzero for failure. |
185 | * |
186 | * Use: Checks that @x@ is a valid group element. This may take a |
187 | * while, since it checks that %$x^h \ne 1$%. |
188 | */ |
189 | |
190 | extern int group_check(group */*g*/, ge */*x*/); |
191 | |
192 | /* --- @group_samep@ --- * |
193 | * |
194 | * Arguments: @group *g, *h@ = two abstract groups |
195 | * |
196 | * Returns: Nonzero if the groups are in fact identical (not just |
197 | * isomorphic). |
198 | * |
199 | * Use: Checks to see whether two groups are actually the same. This |
200 | * function does the full check: the group operatrion @samep@ |
201 | * just does the group-specific details. |
202 | */ |
203 | |
204 | extern int group_samep(group */*g*/, group */*h*/); |
205 | |
206 | /*----- Textual I/O on group elements -------------------------------------*/ |
207 | |
208 | extern int group_readstring(group */*g*/, ge */*d*/, |
209 | const char */*p*/, char **/*end*/); |
210 | extern int group_writestring(group */*g*/, ge */*d*/, |
211 | char */*p*/, size_t /*sz*/); |
212 | |
213 | extern int group_readfile(group */*g*/, ge */*d*/, FILE */*fp*/); |
214 | extern int group_writefile(group */*g*/, ge */*x*/, FILE */*fp*/); |
215 | |
216 | extern int group_readdstr(group */*g*/, ge */*d*/, |
217 | dstr */*dd*/, size_t */*off*/); |
218 | extern int group_writedstr(group */*g*/, ge */*x*/, dstr */*d*/); |
219 | |
220 | /*----- Standard implementations ------------------------------------------*/ |
221 | |
222 | /* --- @group_stdidentp@ --- * |
223 | * |
224 | * Arguments: @group *g@ = abstract group |
225 | * @ge *x@ = group element |
226 | * |
227 | * Returns: Nonzero if %$x$% is the group identity. |
228 | */ |
229 | |
230 | extern int group_stdidentp(group */*g*/, ge */*x*/); |
231 | |
232 | /* --- @group_stdcheck@ --- * |
233 | * |
234 | * Arguments: @group *g@ = abstract group |
235 | * @grand *gr@ = random number source. |
236 | * |
237 | * Returns: Null on success, or a pointer to an error message. |
238 | */ |
239 | |
240 | extern const char *group_stdcheck(group */*g*/, grand */*gr*/); |
241 | |
242 | /* --- @group_stdsqr@ --- * |
243 | * |
244 | * Arguments: @group *g@ = abstract group |
245 | * @ge *d@ = destination pointer |
246 | * @ge *x@ = group element |
247 | * |
248 | * Returns: --- |
249 | * |
250 | * Use: Computes %$d = x^2$% as %$d = x x$%. |
251 | */ |
252 | |
253 | extern void group_stdsqr(group */*g*/, ge */*d*/, ge */*x*/); |
254 | |
255 | /* --- @group_stddiv@ --- * |
256 | * |
257 | * Arguments: @group *g@ = abstract group |
258 | * @ge *d@ = destination pointer |
259 | * @ge *x@ = dividend |
260 | * @ge *y@ = divisor |
261 | * |
262 | * Returns: --- |
263 | * |
264 | * Use: Computes %$d = x/y$% as %$d = x y^{-1}$%. |
265 | */ |
266 | |
267 | extern void group_stddiv(group */*g*/, ge */*d*/, ge */*x*/, ge */*y*/); |
268 | |
269 | /* --- @group_stdexp@ --- * |
270 | * |
271 | * Arguments: @group *g@ = abstract group |
272 | * @ge *d@ = destination pointer |
273 | * @ge *x@ = base element |
274 | * @mp *n@ = exponent |
275 | * |
276 | * Returns: --- |
277 | * |
278 | * Use: Computes %$d = x^n$% efficiently. |
279 | */ |
280 | |
281 | extern void group_stdexp(group */*g*/, ge */*d*/, ge */*x*/, mp */*n*/); |
282 | |
283 | /* --- @group_stdmexp@ --- * |
284 | * |
285 | * Arguments: @group *g@ = abstract group |
286 | * @ge *d@ = destination pointer |
287 | * @const group_expfactor *f@ = vector of factors |
288 | * @size_t n@ = number of factors |
289 | * |
290 | * Returns: --- |
291 | * |
292 | * Use: Computes %$d = g_0^{x_0} g_1^{x_1} \ldots$% efficiently. |
293 | */ |
294 | |
295 | extern void group_stdmexp(group */*g*/, ge */*d*/, |
296 | const group_expfactor */*f*/, size_t /*n*/); |
297 | |
298 | /* --- @group_stdtoec@ --- * |
299 | * |
300 | * Arguments: @group *g@ = abstract group |
301 | * @ec *d@ = destination point |
302 | * @ge *x@ = group element |
303 | * |
304 | * Returns: @-1@, indicating failure. |
305 | * |
306 | * Use: Fails to convert a group element to an elliptic curve point. |
307 | */ |
308 | |
309 | extern int group_stdtoec(group */*g*/, ec */*d*/, ge */*x*/); |
310 | |
311 | /* --- @group_stdfromec@ --- * |
312 | * |
313 | * Arguments: @group *g@ = abstract group |
314 | * @ge *d@ = destination pointer |
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315 | * @const ec *p@ = elliptic curve point |
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316 | * |
317 | * Returns: Zero for success, @-1@ on failure. |
318 | * |
319 | * Use: Converts %$p$% to a group element by converting its %$x$%- |
320 | * coordinate. |
321 | */ |
322 | |
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323 | extern int group_stdfromec(group */*g*/, ge */*d*/, const ec */*p*/); |
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324 | |
325 | /*----- Prime field subgroups ---------------------------------------------*/ |
326 | |
327 | typedef struct gprime_param { |
328 | mp *p, *q; /* Prime numbers %$p$% and %$q$% */ |
329 | mp *g; /* Generates order-%$q$% subgroup */ |
330 | } gprime_param; |
331 | |
332 | /* --- @group_prime@ --- * |
333 | * |
334 | * Arguments: @const gprime_param *gp@ = group parameters |
335 | * |
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336 | * Returns: A pointer to the group, or null. |
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337 | * |
338 | * Use: Constructs an abstract group interface for a subgroup of a |
339 | * prime field. Group elements are @mp *@ pointers. |
340 | */ |
341 | |
342 | group *group_prime(const gprime_param */*gp*/); |
343 | |
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344 | /*----- Binary field subgroups --------------------------------------------*/ |
345 | |
346 | typedef gprime_param gbin_param; |
347 | |
348 | /* --- @group_binary@ --- * |
349 | * |
350 | * Arguments: @const gbin_param *gb@ = group parameters |
351 | * |
352 | * Returns: A pointer to the group, or null. |
353 | * |
354 | * Use: Constructs an abstract group interface for a subgroup of a |
355 | * prime field. Group elements are @mp *@ pointers. |
356 | */ |
357 | |
358 | group *group_binary(const gbin_param */*gp*/); |
359 | |
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360 | /*----- Elliptic curve groups ---------------------------------------------*/ |
361 | |
362 | /* --- @group_ec@ --- * |
363 | * |
364 | * Arguments: @const ec_info *ei@ = elliptic curve parameters |
365 | * |
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366 | * Returns: A pointer to the group, or null. |
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367 | * |
368 | * Use: Constructs an abstract group interface for an elliptic curve |
369 | * group. Group elements are @ec@ structures. The contents of |
370 | * the @ec_info@ structure becomes the property of the @group@ |
371 | * object; you can (and should) free the structure itself, but |
372 | * calling @ec_freeinfo@ on it is not allowed. |
373 | */ |
374 | |
375 | group *group_ec(const ec_info */*ei*/); |
376 | |
377 | /*----- General group initialization --------------------------------------*/ |
378 | |
379 | /* --- @group_parse@ --- * |
380 | * |
381 | * Arguments: @qd_parse *qd@ = quick-and-dirty parser |
382 | * |
383 | * Returns: Group pointer, or null for failure. |
384 | * |
385 | * Use: Parses a group description and returns the group. This has |
386 | * the form `TYPE { SPEC }' where TYPE is `prime' or `ec', and |
387 | * SPEC is the appropriate kind of group specification of the |
388 | * given type. |
389 | */ |
390 | |
391 | extern group *group_parse(qd_parse */*qd*/); |
392 | |
393 | /* --- @group_fromstring@ --- * |
394 | * |
395 | * Arguments: @const char *p@ = pointer to string to read |
396 | * @group **gg@ = where to put the group pointer |
397 | * |
398 | * Returns: Null if OK, or an error string. |
399 | * |
400 | * Use: Parses a group spec from a string, and returns the group. |
401 | */ |
402 | |
403 | extern const char *group_fromstring(const char */*p*/, group **/*gg*/); |
404 | |
405 | /*----- That's all, folks -------------------------------------------------*/ |
406 | |
407 | #ifdef __cplusplus |
408 | } |
409 | #endif |
410 | |
411 | #endif |