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Projective coordinates for prime curves
[u/mdw/catacomb] / ec.h
1 /* -*-c-*-
2 *
3 * $Id: ec.h,v 1.4.4.2 2004/03/20 00:13:31 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 1.4.4.2 2004/03/20 00:13:31 mdw
34 * Projective coordinates for prime curves
35 *
36 * Revision 1.4.4.1 2003/06/10 13:43:53 mdw
37 * Simple (non-projective) curves over prime fields now seem to work.
38 *
39 * Revision 1.4 2003/05/15 23:25:59 mdw
40 * Make elliptic curve stuff build.
41 *
42 * Revision 1.3 2002/01/13 13:48:44 mdw
43 * Further progress.
44 *
45 * Revision 1.2 2001/05/07 17:29:44 mdw
46 * Treat projective coordinates as an internal representation. Various
47 * minor interface changes.
48 *
49 * Revision 1.1 2001/04/29 18:12:33 mdw
50 * Prototype version.
51 *
52 */
53
54 #ifndef CATACOMB_EC_H
55 #define CATACOMB_EC_H
56
57 #ifdef __cplusplus
58 extern "C" {
59 #endif
60
61 /*----- Header files ------------------------------------------------------*/
62
63 #include "field.h"
64 #include "mp.h"
65
66 /*----- Data structures ---------------------------------------------------*/
67
68 /* --- An elliptic curve representation --- */
69
70 typedef struct ec_curve {
71 const struct ec_ops *ops; /* Curve operations */
72 field *f; /* Underlying field structure */
73 } ec_curve;
74
75 /* --- An elliptic curve point --- */
76
77 typedef struct ec {
78 mp *x, *y; /* Point coordinates */
79 mp *z; /* Common denominator (or null) */
80 } ec;
81
82 /* --- A factor for simultaneous multiplication --- */
83
84 typedef struct ec_mulfactor {
85 ec base; /* The point */
86 mp *exp; /* The exponent */
87 } ec_mulfactor;
88
89 /* --- Elliptic curve operations --- *
90 *
91 * All operations (apart from @destroy@ and @in@) are guaranteed to be
92 * performed on internal representations of points. Moreover, the second
93 * argument to @add@ and @mul@ is guaranteed to be the output of @in@ or
94 * @fix@.
95 */
96
97 typedef struct ec_ops {
98 void (*destroy)(ec_curve */*c*/);
99 ec *(*in)(ec_curve */*c*/, ec */*d*/, const ec */*p*/);
100 ec *(*out)(ec_curve */*c*/, ec */*d*/, const ec */*p*/);
101 ec *(*fix)(ec_curve */*c*/, ec */*d*/, const ec */*p*/);
102 ec *(*find)(ec_curve */*c*/, ec */*d*/, mp */*x*/);
103 ec *(*neg)(ec_curve */*c*/, ec */*d*/, const ec */*p*/);
104 ec *(*add)(ec_curve */*c*/, ec */*d*/, const ec */*p*/, const ec */*q*/);
105 ec *(*sub)(ec_curve */*c*/, ec */*d*/, const ec */*p*/, const ec */*q*/);
106 ec *(*dbl)(ec_curve */*c*/, ec */*d*/, const ec */*p*/);
107 int (*check)(ec_curve */*c*/, const ec */*p*/);
108 } ec_ops;
109
110 #define EC_IN(c, d, p) (c)->ops->in((c), (d), (p))
111 #define EC_OUT(c, d, p) (c)->ops->out((c), (d), (p))
112 #define EC_FIX(c, d, p) (c)->ops->fix((c), (d), (p))
113
114 #define EC_FIND(c, d, x) (c)->ops->find((c), (d), (x))
115 #define EC_NEG(c, d, x) (c)->ops->neg((c), (d), (x))
116 #define EC_ADD(c, d, p, q) (c)->ops->add((c), (d), (p), (q))
117 #define EC_SUB(c, d, p, q) (c)->ops->sub((c), (d), (p), (q))
118 #define EC_DBL(c, d, p) (c)->ops->dbl((c), (d), (p))
119 #define EC_CHECK(c, p) (c)->ops->check((c), (p))
120
121 /*----- Simple memory management things -----------------------------------*/
122
123 /* --- @ec_create@ --- *
124 *
125 * Arguments: @ec *p@ = pointer to an elliptic-curve point
126 *
127 * Returns: The argument @p@.
128 *
129 * Use: Initializes a new point. The initial value is the additive
130 * identity (which is universal for all curves).
131 */
132
133 #define EC_INIT { MP_NEW, MP_NEW, MP_NEW }
134
135 #define EC_CREATE(p) do { \
136 ec *_p = (p); \
137 _p->x = _p->y = _p->z = MP_NEW; \
138 } while (0)
139
140 extern ec *ec_create(ec */*p*/);
141
142 /* --- @ec_destroy@ --- *
143 *
144 * Arguments: @ec *p@ = pointer to an elliptic-curve point
145 *
146 * Returns: ---
147 *
148 * Use: Destroys a point, making it invalid.
149 */
150
151 #define EC_DESTROY(p) do { \
152 ec *_p = (p); \
153 if (!EC_ATINF(_p)) { \
154 MP_DROP(_p->x); \
155 MP_DROP(_p->y); \
156 if (_p->z) MP_DROP(_p->z); \
157 } \
158 } while (0)
159
160 extern void ec_destroy(ec */*p*/);
161
162 /* --- @ec_atinf@ --- *
163 *
164 * Arguments: @const ec *p@ = pointer to a point
165 *
166 * Returns: Nonzero if %$p = O$% is the point at infinity, zero
167 * otherwise.
168 */
169
170 #define EC_ATINF(p) ((p)->x == MP_NEW || (p)->x == MP_NEWSEC)
171
172 extern int ec_atinf(const ec */*p*/);
173
174 /* --- @ec_setinf@ --- *
175 *
176 * Arguments: @ec *p@ = pointer to a point
177 *
178 * Returns: The argument @p@.
179 *
180 * Use: Sets the given point to be the point %$O$% at infinity.
181 */
182
183 #define EC_SETINF(p) do { \
184 ec *_p = (p); \
185 if (!EC_ATINF(_p)) { \
186 MP_DROP(_p->x); \
187 MP_DROP(_p->y); \
188 if (_p->z) MP_DROP(_p->z); \
189 _p->x = _p->y = _p->z = MP_NEW; \
190 _p->y = MP_NEW; \
191 _p->z = MP_NEW; \
192 } \
193 } while (0)
194
195 extern ec *ec_setinf(ec */*p*/);
196
197 /* --- @ec_copy@ --- *
198 *
199 * Arguments: @ec *d@ = pointer to destination point
200 * @const ec *p@ = pointer to source point
201 *
202 * Returns: The destination @d@.
203 *
204 * Use: Creates a copy of an elliptic curve point.
205 */
206
207 #define EC_COPY(d, p) do { \
208 ec *_d = (d); \
209 const ec *_p = (p); \
210 if (d != p) { \
211 EC_DESTROY(d); \
212 if (EC_ATINF(p)) \
213 _d->x = _d->y = _d->z = MP_NEW; \
214 else { \
215 _d->x = MP_COPY(_p->x); \
216 _d->y = MP_COPY(_p->y); \
217 _d->z = _p->z ? MP_COPY(_p->z) : MP_NEW; \
218 } \
219 } \
220 } while (0)
221
222 extern ec *ec_copy(ec */*d*/, const ec */*p*/);
223
224 /*----- Interesting arithmetic --------------------------------------------*/
225
226 /* --- @ec_find@ --- *
227 *
228 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
229 * @ec *d@ = pointer to the destination point
230 * @mp *x@ = a possible x-coordinate
231 *
232 * Returns: The destination if OK, or null if no point was found.
233 *
234 * Use: Finds a point on an elliptic curve with a given
235 * x-coordinate. If there is no point with the given
236 * %$x$%-coordinate, a null pointer is returned and the
237 * destination is left invalid.
238 */
239
240 extern ec *ec_find(ec_curve */*c*/, ec */*d*/, mp */*x*/);
241
242 /* --- @ec_neg@ --- *
243 *
244 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
245 * @ec *d@ = pointer to the destination point
246 * @const ec *p@ = pointer to the operand point
247 *
248 * Returns: The destination point.
249 *
250 * Use: Computes the negation of the given point.
251 */
252
253 extern ec *ec_neg(ec_curve */*c*/, ec */*d*/, const ec */*p*/);
254
255 /* --- @ec_add@ --- *
256 *
257 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
258 * @ec *d@ = pointer to the destination point
259 * @const ec *p, *q@ = pointers to the operand points
260 *
261 * Returns: The destination @d@.
262 *
263 * Use: Adds two points on an elliptic curve.
264 */
265
266 extern ec *ec_add(ec_curve */*c*/, ec */*d*/,
267 const ec */*p*/, const ec */*q*/);
268
269 /* --- @ec_sub@ --- *
270 *
271 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
272 * @ec *d@ = pointer to the destination point
273 * @const ec *p, *q@ = pointers to the operand points
274 *
275 * Returns: The destination @d@.
276 *
277 * Use: Subtracts one point from another on an elliptic curve.
278 */
279
280 extern ec *ec_sub(ec_curve */*c*/, ec */*d*/,
281 const ec */*p*/, const ec */*q*/);
282
283 /* --- @ec_dbl@ --- *
284 *
285 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
286 * @ec *d@ = pointer to the destination point
287 * @const ec *p@ = pointer to the operand point
288 *
289 * Returns: The destination @d@.
290 *
291 * Use: Doubles a point on an elliptic curve.
292 */
293
294 extern ec *ec_dbl(ec_curve */*c*/, ec */*d*/, const ec */*p*/);
295
296 /* --- @ec_check@ --- *
297 *
298 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
299 * @const ec *p@ = pointer to the point
300 *
301 * Returns: Zero if OK, nonzero if this is an invalid point.
302 *
303 * Use: Checks that a point is actually on an elliptic curve.
304 */
305
306 extern int ec_check(ec_curve */*c*/, const ec */*p*/);
307
308 /* --- @ec_mul@, @ec_imul@ --- *
309 *
310 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
311 * @ec *d@ = pointer to the destination point
312 * @const ec *p@ = pointer to the generator point
313 * @mp *n@ = integer multiplier
314 *
315 * Returns: The destination @d@.
316 *
317 * Use: Multiplies a point by a scalar, returning %$n p$%. The
318 * @imul@ variant uses internal representations for argument
319 * and result.
320 */
321
322 extern ec *ec_mul(ec_curve */*c*/, ec */*d*/, const ec */*p*/, mp */*n*/);
323 extern ec *ec_imul(ec_curve */*c*/, ec */*d*/, const ec */*p*/, mp */*n*/);
324
325 /* --- @ec_mmul@, @ec_immul@ --- *
326 *
327 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
328 * @ec *d@ = pointer to the destination point
329 * @const ec_mulfactor *f@ = pointer to vector of factors
330 * @size_t n@ = number of factors
331 *
332 * Returns: The destination @d@.
333 *
334 * Use: Does simultaneous point multiplication. The @immul@ variant
335 * uses internal representations for arguments and result.
336 */
337
338 extern ec *ec_mmul(ec_curve */*c*/, ec */*d*/,
339 const ec_mulfactor */*f*/, size_t /*n*/);
340 extern ec *ec_immul(ec_curve */*c*/, ec */*d*/,
341 const ec_mulfactor */*f*/, size_t /*n*/);
342
343 /*----- Standard curve operations -----------------------------------------*/
344
345 /* --- @ec_idin@, @ec_idout@, @ec_idfix@ --- *
346 *
347 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
348 * @ec *d@ = pointer to the destination
349 * @const ec *p@ = pointer to a source point
350 *
351 * Returns: The destination @d@.
352 *
353 * Use: An identity operation if your curve has no internal
354 * representation. (The field internal representation is still
355 * used.)
356 */
357
358 extern ec *ec_idin(ec_curve */*c*/, ec */*d*/, const ec */*p*/);
359 extern ec *ec_idout(ec_curve */*c*/, ec */*d*/, const ec */*p*/);
360 extern ec *ec_idfix(ec_curve */*c*/, ec */*d*/, const ec */*p*/);
361
362 /* --- @ec_projin@, @ec_projout@, @ec_projfix@ --- *
363 *
364 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
365 * @ec *d@ = pointer to the destination
366 * @const ec *p@ = pointer to a source point
367 *
368 * Returns: The destination @d@.
369 *
370 * Use: Conversion functions if your curve operations use a
371 * projective representation.
372 */
373
374 extern ec *ec_projin(ec_curve */*c*/, ec */*d*/, const ec */*p*/);
375 extern ec *ec_projout(ec_curve */*c*/, ec */*d*/, const ec */*p*/);
376 extern ec *ec_projfix(ec_curve */*c*/, ec */*d*/, const ec */*p*/);
377
378 /* --- @ec_stdsub@ --- *
379 *
380 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
381 * @ec *d@ = pointer to the destination
382 * @const ec *p, *q@ = the operand points
383 *
384 * Returns: The destination @d@.
385 *
386 * Use: Standard point subtraction operation, in terms of negation
387 * and addition. This isn't as efficient as a ready-made
388 * subtraction operator.
389 */
390
391 extern ec *ec_stdsub(ec_curve */*c*/, ec */*d*/,
392 const ec */*p*/, const ec */*q*/);
393
394 /*----- Creating curves ---------------------------------------------------*/
395
396 /* --- @ec_destroycurve@ --- *
397 *
398 * Arguments: @ec_curve *c@ = pointer to an ellptic curve
399 *
400 * Returns: ---
401 *
402 * Use: Destroys a description of an elliptic curve.
403 */
404
405 extern void ec_destroycurve(ec_curve */*c*/);
406
407 /* --- @ec_prime@, @ec_primeproj@ --- *
408 *
409 * Arguments: @field *f@ = the underlying field for this elliptic curve
410 * @mp *a, *b@ = the coefficients for this curve
411 *
412 * Returns: A pointer to the curve.
413 *
414 * Use: Creates a curve structure for an elliptic curve defined over
415 * a prime field. The @primeproj@ variant uses projective
416 * coordinates, which can be a win.
417 */
418
419 extern ec_curve *ec_prime(field */*f*/, mp */*a*/, mp */*b*/);
420 extern ec_curve *ec_primeproj(field */*f*/, mp */*a*/, mp */*b*/);
421
422 /* --- @ec_bin@ --- *
423 *
424 * Arguments: @field *f@ = the underlying field for this elliptic curve
425 * @mp *a, *b@ = the coefficients for this curve
426 *
427 * Returns: A pointer to the curve.
428 *
429 * Use: Creates a curve structure for a non-supersingular elliptic
430 * curve defined over a binary field.
431 */
432
433 extern ec_curve *ec_bin(field */*f*/, mp */*a*/, mp */*b*/);
434
435 /*----- That's all, folks -------------------------------------------------*/
436
437 #ifdef __cplusplus
438 }
439 #endif
440
441 #endif
Catacomb cryptographic library (downstream of http://git.distorted.org.uk/~mdw/catacomb/)