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