b0ab12e6 |
1 | /* -*-c-*- |
2 | * |
41cb1beb |
3 | * $Id: ec.h,v 1.4 2003/05/15 23:25:59 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 $ |
41cb1beb |
33 | * Revision 1.4 2003/05/15 23:25:59 mdw |
34 | * Make elliptic curve stuff build. |
35 | * |
b085fd91 |
36 | * Revision 1.3 2002/01/13 13:48:44 mdw |
37 | * Further progress. |
38 | * |
41a324a7 |
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 | * |
b0ab12e6 |
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 | |
b085fd91 |
62 | /* --- An elliptic curve representation --- */ |
63 | |
b0ab12e6 |
64 | typedef struct ec_curve { |
65 | const struct ec_ops *ops; /* Curve operations */ |
66 | field *f; /* Underlying field structure */ |
67 | } ec_curve; |
68 | |
b085fd91 |
69 | /* --- An elliptic curve point --- */ |
70 | |
b0ab12e6 |
71 | typedef struct ec { |
72 | mp *x, *y; /* Point coordinates */ |
73 | mp *z; /* Common denominator (or null) */ |
74 | } ec; |
75 | |
b085fd91 |
76 | /* --- A factor for simultaneous multiplication --- */ |
77 | |
78 | typedef struct ec_mulfactor { |
79 | ec base; /* The point */ |
41cb1beb |
80 | mp *exp; /* The exponent */ |
b085fd91 |
81 | } ec_mulfactor; |
82 | |
83 | /* --- Elliptic curve operations --- */ |
84 | |
b0ab12e6 |
85 | typedef struct ec_ops { |
86 | void (*destroy)(ec_curve */*c*/); |
41a324a7 |
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*/); |
b085fd91 |
90 | ec *(*neg)(ec_curve */*c*/, ec */*d*/, const ec */*p*/); |
41a324a7 |
91 | ec *(*add)(ec_curve */*c*/, ec */*d*/, const ec */*p*/, const ec */*q*/); |
b085fd91 |
92 | ec *(*sub)(ec_curve */*c*/, ec */*d*/, const ec */*p*/, const ec */*q*/); |
41a324a7 |
93 | ec *(*dbl)(ec_curve */*c*/, ec */*d*/, const ec */*p*/); |
b0ab12e6 |
94 | } ec_ops; |
95 | |
41a324a7 |
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 | |
b0ab12e6 |
99 | #define EC_FIND(c, d, x) (c)->ops->find((c), (d), (x)) |
b085fd91 |
100 | #define EC_NEG(c, d, x) (c)->ops->neg((c), (d), (x)) |
b0ab12e6 |
101 | #define EC_ADD(c, d, p, q) (c)->ops->add((c), (d), (p), (q)) |
b085fd91 |
102 | #define EC_SUB(c, d, p, q) (c)->ops->sub((c), (d), (p), (q)) |
b0ab12e6 |
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 | * |
41a324a7 |
111 | * Returns: The argument @p@. |
b0ab12e6 |
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 | |
41a324a7 |
124 | extern ec *ec_create(ec */*p*/); |
b0ab12e6 |
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 | * |
41a324a7 |
162 | * Returns: The argument @p@. |
b0ab12e6 |
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 | |
41a324a7 |
179 | extern ec *ec_setinf(ec */*p*/); |
b0ab12e6 |
180 | |
181 | /* --- @ec_copy@ --- * |
182 | * |
183 | * Arguments: @ec *d@ = pointer to destination point |
184 | * @const ec *p@ = pointer to source point |
185 | * |
41a324a7 |
186 | * Returns: The destination @d@. |
b0ab12e6 |
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 { \ |
b085fd91 |
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; \ |
b0ab12e6 |
202 | } \ |
203 | } \ |
204 | } while (0) |
205 | |
41a324a7 |
206 | extern ec *ec_copy(ec */*d*/, const ec */*p*/); |
b0ab12e6 |
207 | |
208 | /*----- Interesting arithmetic --------------------------------------------*/ |
209 | |
b085fd91 |
210 | /* --- @ec_in@ --- * |
b0ab12e6 |
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 | * |
b085fd91 |
216 | * Returns: The destination point. |
b0ab12e6 |
217 | * |
b085fd91 |
218 | * Use: Converts a point to internal representation. |
b0ab12e6 |
219 | */ |
220 | |
b085fd91 |
221 | extern ec *ec_in(ec_curve */*c*/, ec */*d*/, const ec */*p*/); |
b0ab12e6 |
222 | |
b085fd91 |
223 | /* --- @ec_out@ --- * |
b0ab12e6 |
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 | * |
b085fd91 |
229 | * Returns: The destination point. |
b0ab12e6 |
230 | * |
b085fd91 |
231 | * Use: Converts a point to external representation. |
b0ab12e6 |
232 | */ |
233 | |
b085fd91 |
234 | extern ec *ec_out(ec_curve */*c*/, ec */*d*/, const ec */*p*/); |
b0ab12e6 |
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 | * |
b085fd91 |
242 | * Returns: The destination if OK, or null if no point was found. |
b0ab12e6 |
243 | * |
b085fd91 |
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. |
b0ab12e6 |
248 | */ |
249 | |
b085fd91 |
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*/); |
b0ab12e6 |
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 | * |
41a324a7 |
271 | * Returns: The destination @d@. |
b0ab12e6 |
272 | * |
273 | * Use: Adds two points on an elliptic curve. |
274 | */ |
275 | |
41a324a7 |
276 | extern ec *ec_add(ec_curve */*c*/, ec */*d*/, |
277 | const ec */*p*/, const ec */*q*/); |
b0ab12e6 |
278 | |
b085fd91 |
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 | |
b0ab12e6 |
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 | * |
41a324a7 |
299 | * Returns: The destination @d@. |
b0ab12e6 |
300 | * |
301 | * Use: Doubles a point on an elliptic curve. |
302 | */ |
303 | |
41a324a7 |
304 | extern ec *ec_dbl(ec_curve */*c*/, ec */*d*/, const ec */*p*/); |
b0ab12e6 |
305 | |
b085fd91 |
306 | /* --- @ec_mul@, @ec_imul@ --- * |
b0ab12e6 |
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 | * |
41a324a7 |
313 | * Returns: The destination @d@. |
b0ab12e6 |
314 | * |
b085fd91 |
315 | * Use: Multiplies a point by a scalar, returning %$n p$%. The |
316 | * @imul@ variant uses internal representations for argument |
317 | * and result. |
b0ab12e6 |
318 | */ |
319 | |
41a324a7 |
320 | extern ec *ec_mul(ec_curve */*c*/, ec */*d*/, const ec */*p*/, mp */*n*/); |
b085fd91 |
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*/); |
41a324a7 |
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*/); |
b0ab12e6 |
373 | |
b085fd91 |
374 | /* --- @ec_stdsub@ --- * |
375 | * |
376 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
377 | * @ec *d@ = pointer to the destination |
41cb1beb |
378 | * @const ec *p, *q@ = the operand points |
b085fd91 |
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 | |
41cb1beb |
387 | extern ec *ec_stdsub(ec_curve */*c*/, ec */*d*/, |
388 | const ec */*p*/, const ec */*q*/); |
b085fd91 |
389 | |
b0ab12e6 |
390 | /*----- Creating curves ---------------------------------------------------*/ |
391 | |
b085fd91 |
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@ --- * |
b0ab12e6 |
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 |
b085fd91 |
411 | * a prime field. The @primeproj@ variant uses projective |
412 | * coordinates, which can be a win. |
b0ab12e6 |
413 | */ |
414 | |
415 | extern ec_curve *ec_prime(field */*f*/, mp */*a*/, mp */*b*/); |
b085fd91 |
416 | extern ec_curve *ec_primeproj(field */*f*/, mp */*a*/, mp */*b*/); |
b0ab12e6 |
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 |