b0ab12e6 |
1 | /* -*-c-*- |
2 | * |
02d7884d |
3 | * $Id: ec.h,v 1.10 2004/04/03 03:32:05 mdw Exp $ |
b0ab12e6 |
4 | * |
5 | * Elliptic curve definitions |
6 | * |
7 | * (c) 2001 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: ec.h,v $ |
02d7884d |
33 | * Revision 1.10 2004/04/03 03:32:05 mdw |
34 | * General robustification. |
35 | * |
34e4f738 |
36 | * Revision 1.9 2004/04/01 12:50:09 mdw |
37 | * Add cyclic group abstraction, with test code. Separate off exponentation |
38 | * functions for better static linking. Fix a buttload of bugs on the way. |
39 | * Generally ensure that negative exponents do inversion correctly. Add |
40 | * table of standard prime-field subgroups. (Binary field subgroups are |
41 | * currently unimplemented but easy to add if anyone ever finds a good one.) |
42 | * |
432c4e18 |
43 | * Revision 1.8 2004/03/27 17:54:11 mdw |
44 | * Standard curves and curve checking. |
45 | * |
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46 | * Revision 1.7 2004/03/23 15:19:32 mdw |
47 | * Test elliptic curves more thoroughly. |
48 | * |
391faf42 |
49 | * Revision 1.6 2004/03/22 02:19:10 mdw |
50 | * Rationalise the sliding-window threshold. Drop guarantee that right |
51 | * arguments to EC @add@ are canonical, and fix up projective implementations |
52 | * to cope. |
53 | * |
c3caa2fa |
54 | * Revision 1.5 2004/03/21 22:52:06 mdw |
55 | * Merge and close elliptic curve branch. |
56 | * |
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57 | * Revision 1.4.4.3 2004/03/21 22:39:46 mdw |
58 | * Elliptic curves on binary fields work. |
59 | * |
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60 | * Revision 1.4.4.2 2004/03/20 00:13:31 mdw |
61 | * Projective coordinates for prime curves |
62 | * |
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63 | * Revision 1.4.4.1 2003/06/10 13:43:53 mdw |
64 | * Simple (non-projective) curves over prime fields now seem to work. |
65 | * |
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66 | * Revision 1.4 2003/05/15 23:25:59 mdw |
67 | * Make elliptic curve stuff build. |
68 | * |
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69 | * Revision 1.3 2002/01/13 13:48:44 mdw |
70 | * Further progress. |
71 | * |
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72 | * Revision 1.2 2001/05/07 17:29:44 mdw |
73 | * Treat projective coordinates as an internal representation. Various |
74 | * minor interface changes. |
75 | * |
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76 | * Revision 1.1 2001/04/29 18:12:33 mdw |
77 | * Prototype version. |
78 | * |
79 | */ |
80 | |
81 | #ifndef CATACOMB_EC_H |
82 | #define CATACOMB_EC_H |
83 | |
84 | #ifdef __cplusplus |
85 | extern "C" { |
86 | #endif |
87 | |
88 | /*----- Header files ------------------------------------------------------*/ |
89 | |
432c4e18 |
90 | #ifndef CATACOMB_FIELD_H |
91 | # include "field.h" |
92 | #endif |
93 | |
94 | #ifndef CATACOMB_MP_H |
95 | # include "mp.h" |
96 | #endif |
97 | |
98 | #ifndef CATACOMB_QDPARSE_H |
99 | # include "qdparse.h" |
100 | #endif |
b0ab12e6 |
101 | |
102 | /*----- Data structures ---------------------------------------------------*/ |
103 | |
b085fd91 |
104 | /* --- An elliptic curve representation --- */ |
105 | |
b0ab12e6 |
106 | typedef struct ec_curve { |
107 | const struct ec_ops *ops; /* Curve operations */ |
108 | field *f; /* Underlying field structure */ |
432c4e18 |
109 | mp *a, *b; /* Standard params (internal form) */ |
b0ab12e6 |
110 | } ec_curve; |
111 | |
b085fd91 |
112 | /* --- An elliptic curve point --- */ |
113 | |
b0ab12e6 |
114 | typedef struct ec { |
115 | mp *x, *y; /* Point coordinates */ |
116 | mp *z; /* Common denominator (or null) */ |
117 | } ec; |
118 | |
b085fd91 |
119 | /* --- A factor for simultaneous multiplication --- */ |
120 | |
121 | typedef struct ec_mulfactor { |
122 | ec base; /* The point */ |
41cb1beb |
123 | mp *exp; /* The exponent */ |
b085fd91 |
124 | } ec_mulfactor; |
125 | |
8823192f |
126 | /* --- Elliptic curve operations --- * |
127 | * |
128 | * All operations (apart from @destroy@ and @in@) are guaranteed to be |
391faf42 |
129 | * performed on internal representations of points. |
130 | * |
131 | * (Historical note. We used to guarantee that the second to @add@ and @mul@ |
132 | * was the output of @in@ or @fix@, but this canonification turned out to |
133 | * make the precomputation in @ec_exp@ too slow. Projective implementations |
134 | * must therefore cope with a pair of arbitrary points.) |
8823192f |
135 | */ |
b085fd91 |
136 | |
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137 | typedef struct ec_ops { |
138 | void (*destroy)(ec_curve */*c*/); |
34e4f738 |
139 | int (*samep)(ec_curve */*c*/, ec_curve */*d*/); |
41a324a7 |
140 | ec *(*in)(ec_curve */*c*/, ec */*d*/, const ec */*p*/); |
141 | ec *(*out)(ec_curve */*c*/, ec */*d*/, const ec */*p*/); |
8823192f |
142 | ec *(*fix)(ec_curve */*c*/, ec */*d*/, const ec */*p*/); |
41a324a7 |
143 | ec *(*find)(ec_curve */*c*/, ec */*d*/, mp */*x*/); |
b085fd91 |
144 | ec *(*neg)(ec_curve */*c*/, ec */*d*/, const ec */*p*/); |
41a324a7 |
145 | ec *(*add)(ec_curve */*c*/, ec */*d*/, const ec */*p*/, const ec */*q*/); |
b085fd91 |
146 | ec *(*sub)(ec_curve */*c*/, ec */*d*/, const ec */*p*/, const ec */*q*/); |
41a324a7 |
147 | ec *(*dbl)(ec_curve */*c*/, ec */*d*/, const ec */*p*/); |
8823192f |
148 | int (*check)(ec_curve */*c*/, const ec */*p*/); |
b0ab12e6 |
149 | } ec_ops; |
150 | |
34e4f738 |
151 | #define EC_SAMEP(c, d) (c)->ops->samep((c), (d)) |
41a324a7 |
152 | #define EC_IN(c, d, p) (c)->ops->in((c), (d), (p)) |
dbfee00a |
153 | #define EC_OUT(c, d, p) (c)->ops->out((c), (d), (p)) |
8823192f |
154 | #define EC_FIX(c, d, p) (c)->ops->fix((c), (d), (p)) |
41a324a7 |
155 | |
b0ab12e6 |
156 | #define EC_FIND(c, d, x) (c)->ops->find((c), (d), (x)) |
b085fd91 |
157 | #define EC_NEG(c, d, x) (c)->ops->neg((c), (d), (x)) |
b0ab12e6 |
158 | #define EC_ADD(c, d, p, q) (c)->ops->add((c), (d), (p), (q)) |
b085fd91 |
159 | #define EC_SUB(c, d, p, q) (c)->ops->sub((c), (d), (p), (q)) |
b0ab12e6 |
160 | #define EC_DBL(c, d, p) (c)->ops->dbl((c), (d), (p)) |
8823192f |
161 | #define EC_CHECK(c, p) (c)->ops->check((c), (p)) |
b0ab12e6 |
162 | |
432c4e18 |
163 | /* --- Elliptic curve parameters --- */ |
164 | |
165 | typedef struct ec_info { |
166 | ec_curve *c; /* The actual curve */ |
167 | ec g; /* The common point */ |
168 | mp *r; /* Order of %$g$% */ |
169 | mp *h; /* Cofactor %$h = \#E/r$% */ |
170 | } ec_info; |
171 | |
b0ab12e6 |
172 | /*----- Simple memory management things -----------------------------------*/ |
173 | |
174 | /* --- @ec_create@ --- * |
175 | * |
176 | * Arguments: @ec *p@ = pointer to an elliptic-curve point |
177 | * |
41a324a7 |
178 | * Returns: The argument @p@. |
b0ab12e6 |
179 | * |
180 | * Use: Initializes a new point. The initial value is the additive |
181 | * identity (which is universal for all curves). |
182 | */ |
183 | |
184 | #define EC_INIT { MP_NEW, MP_NEW, MP_NEW } |
185 | |
186 | #define EC_CREATE(p) do { \ |
187 | ec *_p = (p); \ |
188 | _p->x = _p->y = _p->z = MP_NEW; \ |
189 | } while (0) |
190 | |
41a324a7 |
191 | extern ec *ec_create(ec */*p*/); |
b0ab12e6 |
192 | |
193 | /* --- @ec_destroy@ --- * |
194 | * |
195 | * Arguments: @ec *p@ = pointer to an elliptic-curve point |
196 | * |
197 | * Returns: --- |
198 | * |
199 | * Use: Destroys a point, making it invalid. |
200 | */ |
201 | |
202 | #define EC_DESTROY(p) do { \ |
203 | ec *_p = (p); \ |
204 | if (!EC_ATINF(_p)) { \ |
205 | MP_DROP(_p->x); \ |
206 | MP_DROP(_p->y); \ |
207 | if (_p->z) MP_DROP(_p->z); \ |
208 | } \ |
209 | } while (0) |
210 | |
211 | extern void ec_destroy(ec */*p*/); |
212 | |
213 | /* --- @ec_atinf@ --- * |
214 | * |
215 | * Arguments: @const ec *p@ = pointer to a point |
216 | * |
217 | * Returns: Nonzero if %$p = O$% is the point at infinity, zero |
218 | * otherwise. |
219 | */ |
220 | |
221 | #define EC_ATINF(p) ((p)->x == MP_NEW || (p)->x == MP_NEWSEC) |
222 | |
223 | extern int ec_atinf(const ec */*p*/); |
224 | |
225 | /* --- @ec_setinf@ --- * |
226 | * |
227 | * Arguments: @ec *p@ = pointer to a point |
228 | * |
41a324a7 |
229 | * Returns: The argument @p@. |
b0ab12e6 |
230 | * |
231 | * Use: Sets the given point to be the point %$O$% at infinity. |
232 | */ |
233 | |
234 | #define EC_SETINF(p) do { \ |
235 | ec *_p = (p); \ |
236 | if (!EC_ATINF(_p)) { \ |
237 | MP_DROP(_p->x); \ |
238 | MP_DROP(_p->y); \ |
239 | if (_p->z) MP_DROP(_p->z); \ |
240 | _p->x = _p->y = _p->z = MP_NEW; \ |
241 | _p->y = MP_NEW; \ |
242 | _p->z = MP_NEW; \ |
243 | } \ |
244 | } while (0) |
245 | |
41a324a7 |
246 | extern ec *ec_setinf(ec */*p*/); |
b0ab12e6 |
247 | |
248 | /* --- @ec_copy@ --- * |
249 | * |
250 | * Arguments: @ec *d@ = pointer to destination point |
251 | * @const ec *p@ = pointer to source point |
252 | * |
41a324a7 |
253 | * Returns: The destination @d@. |
b0ab12e6 |
254 | * |
255 | * Use: Creates a copy of an elliptic curve point. |
256 | */ |
257 | |
258 | #define EC_COPY(d, p) do { \ |
259 | ec *_d = (d); \ |
260 | const ec *_p = (p); \ |
261 | if (d != p) { \ |
262 | EC_DESTROY(d); \ |
263 | if (EC_ATINF(p)) \ |
264 | _d->x = _d->y = _d->z = MP_NEW; \ |
265 | else { \ |
b085fd91 |
266 | _d->x = MP_COPY(_p->x); \ |
267 | _d->y = MP_COPY(_p->y); \ |
268 | _d->z = _p->z ? MP_COPY(_p->z) : MP_NEW; \ |
b0ab12e6 |
269 | } \ |
270 | } \ |
271 | } while (0) |
272 | |
41a324a7 |
273 | extern ec *ec_copy(ec */*d*/, const ec */*p*/); |
b0ab12e6 |
274 | |
bc985cef |
275 | /* --- @ec_eq@ --- * |
276 | * |
277 | * Arguments: @const ec *p, *q@ = two points |
278 | * |
279 | * Returns: Nonzero if the points are equal. Compares external-format |
280 | * points. |
281 | */ |
282 | |
283 | #define EC_EQ(p, q) \ |
284 | ((EC_ATINF(p) && EC_ATINF(q)) || \ |
285 | (!EC_ATINF(p) && !EC_ATINF(q) && \ |
286 | MP_EQ((p)->x, (q)->x) && \ |
287 | MP_EQ((p)->y, (q)->y))) |
288 | |
289 | extern int ec_eq(const ec *p, const ec *q); |
290 | |
b0ab12e6 |
291 | /*----- Interesting arithmetic --------------------------------------------*/ |
292 | |
34e4f738 |
293 | /* --- @ec_samep@ --- * |
294 | * |
295 | * Arguments: @ec_curve *c, *d@ = two elliptic curves |
296 | * |
297 | * Returns: Nonzero if the curves are identical (not just isomorphic). |
298 | * |
299 | * Use: Checks for sameness of curves. This function does the full |
300 | * check, not just the curve-type-specific check done by the |
301 | * @sampep@ field operation. |
302 | */ |
303 | |
304 | extern int ec_samep(ec_curve */*c*/, ec_curve */*d*/); |
305 | |
b0ab12e6 |
306 | /* --- @ec_find@ --- * |
307 | * |
308 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
309 | * @ec *d@ = pointer to the destination point |
310 | * @mp *x@ = a possible x-coordinate |
311 | * |
b085fd91 |
312 | * Returns: The destination if OK, or null if no point was found. |
b0ab12e6 |
313 | * |
b085fd91 |
314 | * Use: Finds a point on an elliptic curve with a given |
315 | * x-coordinate. If there is no point with the given |
316 | * %$x$%-coordinate, a null pointer is returned and the |
317 | * destination is left invalid. |
b0ab12e6 |
318 | */ |
319 | |
b085fd91 |
320 | extern ec *ec_find(ec_curve */*c*/, ec */*d*/, mp */*x*/); |
321 | |
bc985cef |
322 | /* --- @ec_rand@ --- * |
323 | * |
324 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
325 | * @ec *d@ = pointer to the destination point |
326 | * @grand *r@ = random number source |
327 | * |
328 | * Returns: The destination @d@. |
329 | * |
330 | * Use: Finds a random point on the given curve. |
331 | */ |
332 | |
333 | extern ec *ec_rand(ec_curve */*c*/, ec */*d*/, grand */*r*/); |
334 | |
b085fd91 |
335 | /* --- @ec_neg@ --- * |
336 | * |
337 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
338 | * @ec *d@ = pointer to the destination point |
339 | * @const ec *p@ = pointer to the operand point |
340 | * |
341 | * Returns: The destination point. |
342 | * |
343 | * Use: Computes the negation of the given point. |
344 | */ |
345 | |
346 | extern ec *ec_neg(ec_curve */*c*/, ec */*d*/, const ec */*p*/); |
b0ab12e6 |
347 | |
348 | /* --- @ec_add@ --- * |
349 | * |
350 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
351 | * @ec *d@ = pointer to the destination point |
352 | * @const ec *p, *q@ = pointers to the operand points |
353 | * |
41a324a7 |
354 | * Returns: The destination @d@. |
b0ab12e6 |
355 | * |
356 | * Use: Adds two points on an elliptic curve. |
357 | */ |
358 | |
41a324a7 |
359 | extern ec *ec_add(ec_curve */*c*/, ec */*d*/, |
360 | const ec */*p*/, const ec */*q*/); |
b0ab12e6 |
361 | |
b085fd91 |
362 | /* --- @ec_sub@ --- * |
363 | * |
364 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
365 | * @ec *d@ = pointer to the destination point |
366 | * @const ec *p, *q@ = pointers to the operand points |
367 | * |
368 | * Returns: The destination @d@. |
369 | * |
370 | * Use: Subtracts one point from another on an elliptic curve. |
371 | */ |
372 | |
373 | extern ec *ec_sub(ec_curve */*c*/, ec */*d*/, |
374 | const ec */*p*/, const ec */*q*/); |
375 | |
b0ab12e6 |
376 | /* --- @ec_dbl@ --- * |
377 | * |
378 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
379 | * @ec *d@ = pointer to the destination point |
380 | * @const ec *p@ = pointer to the operand point |
381 | * |
41a324a7 |
382 | * Returns: The destination @d@. |
b0ab12e6 |
383 | * |
384 | * Use: Doubles a point on an elliptic curve. |
385 | */ |
386 | |
41a324a7 |
387 | extern ec *ec_dbl(ec_curve */*c*/, ec */*d*/, const ec */*p*/); |
b0ab12e6 |
388 | |
8823192f |
389 | /* --- @ec_check@ --- * |
390 | * |
391 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
392 | * @const ec *p@ = pointer to the point |
393 | * |
394 | * Returns: Zero if OK, nonzero if this is an invalid point. |
395 | * |
396 | * Use: Checks that a point is actually on an elliptic curve. |
397 | */ |
398 | |
399 | extern int ec_check(ec_curve */*c*/, const ec */*p*/); |
400 | |
b085fd91 |
401 | /* --- @ec_mul@, @ec_imul@ --- * |
b0ab12e6 |
402 | * |
403 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
404 | * @ec *d@ = pointer to the destination point |
405 | * @const ec *p@ = pointer to the generator point |
406 | * @mp *n@ = integer multiplier |
407 | * |
41a324a7 |
408 | * Returns: The destination @d@. |
b0ab12e6 |
409 | * |
b085fd91 |
410 | * Use: Multiplies a point by a scalar, returning %$n p$%. The |
411 | * @imul@ variant uses internal representations for argument |
412 | * and result. |
b0ab12e6 |
413 | */ |
414 | |
41a324a7 |
415 | extern ec *ec_mul(ec_curve */*c*/, ec */*d*/, const ec */*p*/, mp */*n*/); |
b085fd91 |
416 | extern ec *ec_imul(ec_curve */*c*/, ec */*d*/, const ec */*p*/, mp */*n*/); |
417 | |
418 | /* --- @ec_mmul@, @ec_immul@ --- * |
419 | * |
420 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
421 | * @ec *d@ = pointer to the destination point |
422 | * @const ec_mulfactor *f@ = pointer to vector of factors |
423 | * @size_t n@ = number of factors |
424 | * |
425 | * Returns: The destination @d@. |
426 | * |
427 | * Use: Does simultaneous point multiplication. The @immul@ variant |
428 | * uses internal representations for arguments and result. |
429 | */ |
430 | |
431 | extern ec *ec_mmul(ec_curve */*c*/, ec */*d*/, |
432 | const ec_mulfactor */*f*/, size_t /*n*/); |
433 | extern ec *ec_immul(ec_curve */*c*/, ec */*d*/, |
434 | const ec_mulfactor */*f*/, size_t /*n*/); |
41a324a7 |
435 | |
436 | /*----- Standard curve operations -----------------------------------------*/ |
437 | |
34e4f738 |
438 | /* --- @ec_stdsamep@ --- * |
439 | * |
440 | * Arguments: @ec_curve *c, *d@ = two elliptic curves |
441 | * |
442 | * Returns: Nonzero if the curves are identical (not just isomorphic). |
443 | * |
444 | * Use: Simple sameness check on @a@ and @b@ curve members. |
445 | */ |
446 | |
447 | extern int ec_stdsamep(ec_curve */*c*/, ec_curve */*d*/); |
448 | |
8823192f |
449 | /* --- @ec_idin@, @ec_idout@, @ec_idfix@ --- * |
41a324a7 |
450 | * |
451 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
452 | * @ec *d@ = pointer to the destination |
453 | * @const ec *p@ = pointer to a source point |
454 | * |
455 | * Returns: The destination @d@. |
456 | * |
457 | * Use: An identity operation if your curve has no internal |
458 | * representation. (The field internal representation is still |
459 | * used.) |
460 | */ |
461 | |
462 | extern ec *ec_idin(ec_curve */*c*/, ec */*d*/, const ec */*p*/); |
463 | extern ec *ec_idout(ec_curve */*c*/, ec */*d*/, const ec */*p*/); |
8823192f |
464 | extern ec *ec_idfix(ec_curve */*c*/, ec */*d*/, const ec */*p*/); |
41a324a7 |
465 | |
8823192f |
466 | /* --- @ec_projin@, @ec_projout@, @ec_projfix@ --- * |
41a324a7 |
467 | * |
468 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
469 | * @ec *d@ = pointer to the destination |
470 | * @const ec *p@ = pointer to a source point |
471 | * |
472 | * Returns: The destination @d@. |
473 | * |
474 | * Use: Conversion functions if your curve operations use a |
475 | * projective representation. |
476 | */ |
477 | |
478 | extern ec *ec_projin(ec_curve */*c*/, ec */*d*/, const ec */*p*/); |
479 | extern ec *ec_projout(ec_curve */*c*/, ec */*d*/, const ec */*p*/); |
8823192f |
480 | extern ec *ec_projfix(ec_curve */*c*/, ec */*d*/, const ec */*p*/); |
b0ab12e6 |
481 | |
b085fd91 |
482 | /* --- @ec_stdsub@ --- * |
483 | * |
484 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
485 | * @ec *d@ = pointer to the destination |
41cb1beb |
486 | * @const ec *p, *q@ = the operand points |
b085fd91 |
487 | * |
488 | * Returns: The destination @d@. |
489 | * |
490 | * Use: Standard point subtraction operation, in terms of negation |
491 | * and addition. This isn't as efficient as a ready-made |
492 | * subtraction operator. |
493 | */ |
494 | |
41cb1beb |
495 | extern ec *ec_stdsub(ec_curve */*c*/, ec */*d*/, |
496 | const ec */*p*/, const ec */*q*/); |
b085fd91 |
497 | |
b0ab12e6 |
498 | /*----- Creating curves ---------------------------------------------------*/ |
499 | |
b085fd91 |
500 | /* --- @ec_destroycurve@ --- * |
501 | * |
502 | * Arguments: @ec_curve *c@ = pointer to an ellptic curve |
503 | * |
504 | * Returns: --- |
505 | * |
506 | * Use: Destroys a description of an elliptic curve. |
507 | */ |
508 | |
509 | extern void ec_destroycurve(ec_curve */*c*/); |
510 | |
511 | /* --- @ec_prime@, @ec_primeproj@ --- * |
b0ab12e6 |
512 | * |
dbfee00a |
513 | * Arguments: @field *f@ = the underlying field for this elliptic curve |
b0ab12e6 |
514 | * @mp *a, *b@ = the coefficients for this curve |
515 | * |
02d7884d |
516 | * Returns: A pointer to the curve, or null. |
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517 | * |
518 | * Use: Creates a curve structure for an elliptic curve defined over |
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519 | * a prime field. The @primeproj@ variant uses projective |
520 | * coordinates, which can be a win. |
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521 | */ |
522 | |
523 | extern ec_curve *ec_prime(field */*f*/, mp */*a*/, mp */*b*/); |
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524 | extern ec_curve *ec_primeproj(field */*f*/, mp */*a*/, mp */*b*/); |
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525 | |
ceb3f0c0 |
526 | /* --- @ec_bin@, @ec_binproj@ --- * |
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527 | * |
528 | * Arguments: @field *f@ = the underlying field for this elliptic curve |
529 | * @mp *a, *b@ = the coefficients for this curve |
530 | * |
02d7884d |
531 | * Returns: A pointer to the curve, or null. |
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532 | * |
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533 | * Use: Creates a curve structure for an elliptic curve defined over |
534 | * a binary field. The @binproj@ variant uses projective |
535 | * coordinates, which can be a win. |
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536 | */ |
537 | |
538 | extern ec_curve *ec_bin(field */*f*/, mp */*a*/, mp */*b*/); |
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539 | extern ec_curve *ec_binproj(field */*f*/, mp */*a*/, mp */*b*/); |
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540 | |
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541 | /*----- Curve parameter sets ----------------------------------------------*/ |
542 | |
543 | /* --- @ec_curveparse@ --- * |
544 | * |
545 | * Arguments: @qd_parse *qd@ = parser context |
546 | * |
547 | * Returns: Elliptic curve pointer if OK, or null. |
548 | * |
549 | * Use: Parses an elliptic curve description, which has the form |
550 | * |
551 | * * a field description |
552 | * * an optional `/' |
553 | * * `prime', `primeproj', `bin', or `binproj' |
554 | * * an optional `:' |
555 | * * the %$a$% parameter |
556 | * * an optional `,' |
557 | * * the %$b$% parameter |
558 | */ |
559 | |
560 | extern ec_curve *ec_curveparse(qd_parse */*qd*/); |
561 | |
562 | /* --- @ec_ptparse@ --- * |
563 | * |
564 | * Arguments: @qd_parse *qd@ = parser context |
565 | * @ec *p@ = where to put the point |
566 | * |
567 | * Returns: The point address, or null. |
568 | * |
569 | * Use: Parses an elliptic curve point. This has the form |
570 | * |
571 | * * %$x$%-coordinate |
572 | * * optional `,' |
573 | * * %$y$%-coordinate |
574 | */ |
575 | |
576 | extern ec *ec_ptparse(qd_parse */*qd*/, ec */*p*/); |
577 | |
578 | /* --- @ec_infoparse@ --- * |
579 | * |
580 | * Arguments: @qd_parse *qd@ = parser context |
581 | * @ec_info *ei@ = curve information block, currently |
582 | * uninitialized |
583 | * |
584 | * Returns: Zero on success, nonzero on failure. |
585 | * |
586 | * Use: Parses an elliptic curve information string, and stores the |
587 | * information in @ei@. This has the form |
588 | * |
589 | * * elliptic curve description |
590 | * * optional `/' |
591 | * * common point |
592 | * * optional `:' |
593 | * * group order |
594 | * * optional `*' |
595 | * * cofactor |
596 | */ |
597 | |
598 | extern int ec_infoparse(qd_parse */*qd*/, ec_info */*ei*/); |
599 | |
600 | /* --- @ec_getinfo@ --- * |
601 | * |
602 | * Arguments: @ec_info *ei@ = where to write the information |
603 | * @const char *p@ = string describing a curve |
604 | * |
605 | * Returns: Null on success, or a pointer to an error message. |
606 | * |
607 | * Use: Parses out information about a curve. The string is either a |
608 | * standard curve name, or a curve info string. |
609 | */ |
610 | |
611 | extern const char *ec_getinfo(ec_info */*ei*/, const char */*p*/); |
612 | |
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613 | /* --- @ec_sameinfop@ --- * |
614 | * |
615 | * Arguments: @ec_info *ei, *ej@ = two elliptic curve parameter sets |
616 | * |
617 | * Returns: Nonzero if the curves are identical (not just isomorphic). |
618 | * |
619 | * Use: Checks for sameness of curve parameters. |
620 | */ |
621 | |
622 | extern int ec_sameinfop(ec_info */*ei*/, ec_info */*ej*/); |
623 | |
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624 | /* --- @ec_freeinfo@ --- * |
625 | * |
626 | * Arguments: @ec_info *ei@ = elliptic curve information block to free |
627 | * |
628 | * Returns: --- |
629 | * |
630 | * Use: Frees the information block. |
631 | */ |
632 | |
633 | extern void ec_freeinfo(ec_info */*ei*/); |
634 | |
635 | /* --- @ec_checkinfo@ --- * |
636 | * |
637 | * Arguments: @const ec_info *ei@ = elliptic curve information block |
638 | * |
639 | * Returns: Null if OK, or pointer to error message. |
640 | * |
641 | * Use: Checks an elliptic curve according to the rules in SEC1. |
642 | */ |
643 | |
644 | extern const char *ec_checkinfo(const ec_info */*ei*/, grand */*gr*/); |
645 | |
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646 | /*----- That's all, folks -------------------------------------------------*/ |
647 | |
648 | #ifdef __cplusplus |
649 | } |
650 | #endif |
651 | |
652 | #endif |