projects / u / mdw / catacomb / blob
? search:


105838ccef6a12e6cef6f8ac016209b3d25ada12
[u/mdw/catacomb] / ec.h
1 /* -*-c-*-
2 *
3 * $Id: ec.h,v 1.4 2003/05/15 23:25:59 mdw Exp $
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 $
33 * Revision 1.4 2003/05/15 23:25:59 mdw
34 * Make elliptic curve stuff build.
35 *
36 * Revision 1.3 2002/01/13 13:48:44 mdw
37 * Further progress.
38 *
39 * Revision 1.2 2001/05/07 17:29:44 mdw
40 * Treat projective coordinates as an internal representation. Various
41 * minor interface changes.
42 *
43 * Revision 1.1 2001/04/29 18:12:33 mdw
44 * Prototype version.
45 *
46 */
47
48 #ifndef CATACOMB_EC_H
49 #define CATACOMB_EC_H
50
51 #ifdef __cplusplus
52 extern "C" {
53 #endif
54
55 /*----- Header files ------------------------------------------------------*/
56
57 #include "field.h"
58 #include "mp.h"
59
60 /*----- Data structures ---------------------------------------------------*/
61
62 /* --- An elliptic curve representation --- */
63
64 typedef struct ec_curve {
65 const struct ec_ops *ops; /* Curve operations */
66 field *f; /* Underlying field structure */
67 } ec_curve;
68
69 /* --- An elliptic curve point --- */
70
71 typedef struct ec {
72 mp *x, *y; /* Point coordinates */
73 mp *z; /* Common denominator (or null) */
74 } ec;
75
76 /* --- A factor for simultaneous multiplication --- */
77
78 typedef struct ec_mulfactor {
79 ec base; /* The point */
80 mp *exp; /* The exponent */
81 } ec_mulfactor;
82
83 /* --- Elliptic curve operations --- */
84
85 typedef struct ec_ops {
86 void (*destroy)(ec_curve */*c*/);
87 ec *(*in)(ec_curve */*c*/, ec */*d*/, const ec */*p*/);
88 ec *(*out)(ec_curve */*c*/, ec */*d*/, const ec */*p*/);
89 ec *(*find)(ec_curve */*c*/, ec */*d*/, mp */*x*/);
90 ec *(*neg)(ec_curve */*c*/, ec */*d*/, const ec */*p*/);
91 ec *(*add)(ec_curve */*c*/, ec */*d*/, const ec */*p*/, const ec */*q*/);
92 ec *(*sub)(ec_curve */*c*/, ec */*d*/, const ec */*p*/, const ec */*q*/);
93 ec *(*dbl)(ec_curve */*c*/, ec */*d*/, const ec */*p*/);
94 } ec_ops;
95
96 #define EC_IN(c, d, p) (c)->ops->in((c), (d), (p))
97 #define EC_OUT(c, d, p) (c)->ops->in((c), (d), (p))
98
99 #define EC_FIND(c, d, x) (c)->ops->find((c), (d), (x))
100 #define EC_NEG(c, d, x) (c)->ops->neg((c), (d), (x))
101 #define EC_ADD(c, d, p, q) (c)->ops->add((c), (d), (p), (q))
102 #define EC_SUB(c, d, p, q) (c)->ops->sub((c), (d), (p), (q))
103 #define EC_DBL(c, d, p) (c)->ops->dbl((c), (d), (p))
104
105 /*----- Simple memory management things -----------------------------------*/
106
107 /* --- @ec_create@ --- *
108 *
109 * Arguments: @ec *p@ = pointer to an elliptic-curve point
110 *
111 * Returns: The argument @p@.
112 *
113 * Use: Initializes a new point. The initial value is the additive
114 * identity (which is universal for all curves).
115 */
116
117 #define EC_INIT { MP_NEW, MP_NEW, MP_NEW }
118
119 #define EC_CREATE(p) do { \
120 ec *_p = (p); \
121 _p->x = _p->y = _p->z = MP_NEW; \
122 } while (0)
123
124 extern ec *ec_create(ec */*p*/);
125
126 /* --- @ec_destroy@ --- *
127 *
128 * Arguments: @ec *p@ = pointer to an elliptic-curve point
129 *
130 * Returns: ---
131 *
132 * Use: Destroys a point, making it invalid.
133 */
134
135 #define EC_DESTROY(p) do { \
136 ec *_p = (p); \
137 if (!EC_ATINF(_p)) { \
138 MP_DROP(_p->x); \
139 MP_DROP(_p->y); \
140 if (_p->z) MP_DROP(_p->z); \
141 } \
142 } while (0)
143
144 extern void ec_destroy(ec */*p*/);
145
146 /* --- @ec_atinf@ --- *
147 *
148 * Arguments: @const ec *p@ = pointer to a point
149 *
150 * Returns: Nonzero if %$p = O$% is the point at infinity, zero
151 * otherwise.
152 */
153
154 #define EC_ATINF(p) ((p)->x == MP_NEW || (p)->x == MP_NEWSEC)
155
156 extern int ec_atinf(const ec */*p*/);
157
158 /* --- @ec_setinf@ --- *
159 *
160 * Arguments: @ec *p@ = pointer to a point
161 *
162 * Returns: The argument @p@.
163 *
164 * Use: Sets the given point to be the point %$O$% at infinity.
165 */
166
167 #define EC_SETINF(p) do { \
168 ec *_p = (p); \
169 if (!EC_ATINF(_p)) { \
170 MP_DROP(_p->x); \
171 MP_DROP(_p->y); \
172 if (_p->z) MP_DROP(_p->z); \
173 _p->x = _p->y = _p->z = MP_NEW; \
174 _p->y = MP_NEW; \
175 _p->z = MP_NEW; \
176 } \
177 } while (0)
178
179 extern ec *ec_setinf(ec */*p*/);
180
181 /* --- @ec_copy@ --- *
182 *
183 * Arguments: @ec *d@ = pointer to destination point
184 * @const ec *p@ = pointer to source point
185 *
186 * Returns: The destination @d@.
187 *
188 * Use: Creates a copy of an elliptic curve point.
189 */
190
191 #define EC_COPY(d, p) do { \
192 ec *_d = (d); \
193 const ec *_p = (p); \
194 if (d != p) { \
195 EC_DESTROY(d); \
196 if (EC_ATINF(p)) \
197 _d->x = _d->y = _d->z = MP_NEW; \
198 else { \
199 _d->x = MP_COPY(_p->x); \
200 _d->y = MP_COPY(_p->y); \
201 _d->z = _p->z ? MP_COPY(_p->z) : MP_NEW; \
202 } \
203 } \
204 } while (0)
205
206 extern ec *ec_copy(ec */*d*/, const ec */*p*/);
207
208 /*----- Interesting arithmetic --------------------------------------------*/
209
210 /* --- @ec_in@ --- *
211 *
212 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
213 * @ec *d@ = pointer to the destination point
214 * @const ec *p@ = pointer to the source point
215 *
216 * Returns: The destination point.
217 *
218 * Use: Converts a point to internal representation.
219 */
220
221 extern ec *ec_in(ec_curve */*c*/, ec */*d*/, const ec */*p*/);
222
223 /* --- @ec_out@ --- *
224 *
225 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
226 * @ec *d@ = pointer to the destination point
227 * @const ec *p@ = pointer to the source point
228 *
229 * Returns: The destination point.
230 *
231 * Use: Converts a point to external representation.
232 */
233
234 extern ec *ec_out(ec_curve */*c*/, ec */*d*/, const ec */*p*/);
235
236 /* --- @ec_find@ --- *
237 *
238 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
239 * @ec *d@ = pointer to the destination point
240 * @mp *x@ = a possible x-coordinate
241 *
242 * Returns: The destination if OK, or null if no point was found.
243 *
244 * Use: Finds a point on an elliptic curve with a given
245 * x-coordinate. If there is no point with the given
246 * %$x$%-coordinate, a null pointer is returned and the
247 * destination is left invalid.
248 */
249
250 extern ec *ec_find(ec_curve */*c*/, ec */*d*/, mp */*x*/);
251
252 /* --- @ec_neg@ --- *
253 *
254 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
255 * @ec *d@ = pointer to the destination point
256 * @const ec *p@ = pointer to the operand point
257 *
258 * Returns: The destination point.
259 *
260 * Use: Computes the negation of the given point.
261 */
262
263 extern ec *ec_neg(ec_curve */*c*/, ec */*d*/, const ec */*p*/);
264
265 /* --- @ec_add@ --- *
266 *
267 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
268 * @ec *d@ = pointer to the destination point
269 * @const ec *p, *q@ = pointers to the operand points
270 *
271 * Returns: The destination @d@.
272 *
273 * Use: Adds two points on an elliptic curve.
274 */
275
276 extern ec *ec_add(ec_curve */*c*/, ec */*d*/,
277 const ec */*p*/, const ec */*q*/);
278
279 /* --- @ec_sub@ --- *
280 *
281 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
282 * @ec *d@ = pointer to the destination point
283 * @const ec *p, *q@ = pointers to the operand points
284 *
285 * Returns: The destination @d@.
286 *
287 * Use: Subtracts one point from another on an elliptic curve.
288 */
289
290 extern ec *ec_sub(ec_curve */*c*/, ec */*d*/,
291 const ec */*p*/, const ec */*q*/);
292
293 /* --- @ec_dbl@ --- *
294 *
295 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
296 * @ec *d@ = pointer to the destination point
297 * @const ec *p@ = pointer to the operand point
298 *
299 * Returns: The destination @d@.
300 *
301 * Use: Doubles a point on an elliptic curve.
302 */
303
304 extern ec *ec_dbl(ec_curve */*c*/, ec */*d*/, const ec */*p*/);
305
306 /* --- @ec_mul@, @ec_imul@ --- *
307 *
308 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
309 * @ec *d@ = pointer to the destination point
310 * @const ec *p@ = pointer to the generator point
311 * @mp *n@ = integer multiplier
312 *
313 * Returns: The destination @d@.
314 *
315 * Use: Multiplies a point by a scalar, returning %$n p$%. The
316 * @imul@ variant uses internal representations for argument
317 * and result.
318 */
319
320 extern ec *ec_mul(ec_curve */*c*/, ec */*d*/, const ec */*p*/, mp */*n*/);
321 extern ec *ec_imul(ec_curve */*c*/, ec */*d*/, const ec */*p*/, mp */*n*/);
322
323 /* --- @ec_mmul@, @ec_immul@ --- *
324 *
325 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
326 * @ec *d@ = pointer to the destination point
327 * @const ec_mulfactor *f@ = pointer to vector of factors
328 * @size_t n@ = number of factors
329 *
330 * Returns: The destination @d@.
331 *
332 * Use: Does simultaneous point multiplication. The @immul@ variant
333 * uses internal representations for arguments and result.
334 */
335
336 extern ec *ec_mmul(ec_curve */*c*/, ec */*d*/,
337 const ec_mulfactor */*f*/, size_t /*n*/);
338 extern ec *ec_immul(ec_curve */*c*/, ec */*d*/,
339 const ec_mulfactor */*f*/, size_t /*n*/);
340
341 /*----- Standard curve operations -----------------------------------------*/
342
343 /* --- @ec_idin@, @ec_idout@ --- *
344 *
345 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
346 * @ec *d@ = pointer to the destination
347 * @const ec *p@ = pointer to a source point
348 *
349 * Returns: The destination @d@.
350 *
351 * Use: An identity operation if your curve has no internal
352 * representation. (The field internal representation is still
353 * used.)
354 */
355
356 extern ec *ec_idin(ec_curve */*c*/, ec */*d*/, const ec */*p*/);
357 extern ec *ec_idout(ec_curve */*c*/, ec */*d*/, const ec */*p*/);
358
359 /* --- @ec_projin@, @ec_projout@ --- *
360 *
361 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
362 * @ec *d@ = pointer to the destination
363 * @const ec *p@ = pointer to a source point
364 *
365 * Returns: The destination @d@.
366 *
367 * Use: Conversion functions if your curve operations use a
368 * projective representation.
369 */
370
371 extern ec *ec_projin(ec_curve */*c*/, ec */*d*/, const ec */*p*/);
372 extern ec *ec_projout(ec_curve */*c*/, ec */*d*/, const ec */*p*/);
373
374 /* --- @ec_stdsub@ --- *
375 *
376 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
377 * @ec *d@ = pointer to the destination
378 * @const ec *p, *q@ = the operand points
379 *
380 * Returns: The destination @d@.
381 *
382 * Use: Standard point subtraction operation, in terms of negation
383 * and addition. This isn't as efficient as a ready-made
384 * subtraction operator.
385 */
386
387 extern ec *ec_stdsub(ec_curve */*c*/, ec */*d*/,
388 const ec */*p*/, const ec */*q*/);
389
390 /*----- Creating curves ---------------------------------------------------*/
391
392 /* --- @ec_destroycurve@ --- *
393 *
394 * Arguments: @ec_curve *c@ = pointer to an ellptic curve
395 *
396 * Returns: ---
397 *
398 * Use: Destroys a description of an elliptic curve.
399 */
400
401 extern void ec_destroycurve(ec_curve */*c*/);
402
403 /* --- @ec_prime@, @ec_primeproj@ --- *
404 *
405 * Arguments: @field *f@ = the underyling field for this elliptic curve
406 * @mp *a, *b@ = the coefficients for this curve
407 *
408 * Returns: A pointer to the curve.
409 *
410 * Use: Creates a curve structure for an elliptic curve defined over
411 * a prime field. The @primeproj@ variant uses projective
412 * coordinates, which can be a win.
413 */
414
415 extern ec_curve *ec_prime(field */*f*/, mp */*a*/, mp */*b*/);
416 extern ec_curve *ec_primeproj(field */*f*/, mp */*a*/, mp */*b*/);
417
418 /* --- @ec_bin@ --- *
419 *
420 * Arguments: @field *f@ = the underlying field for this elliptic curve
421 * @mp *a, *b@ = the coefficients for this curve
422 *
423 * Returns: A pointer to the curve.
424 *
425 * Use: Creates a curve structure for a non-supersingular elliptic
426 * curve defined over a binary field.
427 */
428
429 extern ec_curve *ec_bin(field */*f*/, mp */*a*/, mp */*b*/);
430
431 /*----- That's all, folks -------------------------------------------------*/
432
433 #ifdef __cplusplus
434 }
435 #endif
436
437 #endif
Catacomb cryptographic library (downstream of http://git.distorted.org.uk/~mdw/catacomb/)