b0ab12e6 |
1 | /* -*-c-*- |
2 | * |
ceb3f0c0 |
3 | * $Id: ec.h,v 1.4.4.3 2004/03/21 22:39:46 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 $ |
ceb3f0c0 |
33 | * Revision 1.4.4.3 2004/03/21 22:39:46 mdw |
34 | * Elliptic curves on binary fields work. |
35 | * |
8823192f |
36 | * Revision 1.4.4.2 2004/03/20 00:13:31 mdw |
37 | * Projective coordinates for prime curves |
38 | * |
dbfee00a |
39 | * Revision 1.4.4.1 2003/06/10 13:43:53 mdw |
40 | * Simple (non-projective) curves over prime fields now seem to work. |
41 | * |
41cb1beb |
42 | * Revision 1.4 2003/05/15 23:25:59 mdw |
43 | * Make elliptic curve stuff build. |
44 | * |
b085fd91 |
45 | * Revision 1.3 2002/01/13 13:48:44 mdw |
46 | * Further progress. |
47 | * |
41a324a7 |
48 | * Revision 1.2 2001/05/07 17:29:44 mdw |
49 | * Treat projective coordinates as an internal representation. Various |
50 | * minor interface changes. |
51 | * |
b0ab12e6 |
52 | * Revision 1.1 2001/04/29 18:12:33 mdw |
53 | * Prototype version. |
54 | * |
55 | */ |
56 | |
57 | #ifndef CATACOMB_EC_H |
58 | #define CATACOMB_EC_H |
59 | |
60 | #ifdef __cplusplus |
61 | extern "C" { |
62 | #endif |
63 | |
64 | /*----- Header files ------------------------------------------------------*/ |
65 | |
66 | #include "field.h" |
67 | #include "mp.h" |
68 | |
69 | /*----- Data structures ---------------------------------------------------*/ |
70 | |
b085fd91 |
71 | /* --- An elliptic curve representation --- */ |
72 | |
b0ab12e6 |
73 | typedef struct ec_curve { |
74 | const struct ec_ops *ops; /* Curve operations */ |
75 | field *f; /* Underlying field structure */ |
76 | } ec_curve; |
77 | |
b085fd91 |
78 | /* --- An elliptic curve point --- */ |
79 | |
b0ab12e6 |
80 | typedef struct ec { |
81 | mp *x, *y; /* Point coordinates */ |
82 | mp *z; /* Common denominator (or null) */ |
83 | } ec; |
84 | |
b085fd91 |
85 | /* --- A factor for simultaneous multiplication --- */ |
86 | |
87 | typedef struct ec_mulfactor { |
88 | ec base; /* The point */ |
41cb1beb |
89 | mp *exp; /* The exponent */ |
b085fd91 |
90 | } ec_mulfactor; |
91 | |
8823192f |
92 | /* --- Elliptic curve operations --- * |
93 | * |
94 | * All operations (apart from @destroy@ and @in@) are guaranteed to be |
95 | * performed on internal representations of points. Moreover, the second |
96 | * argument to @add@ and @mul@ is guaranteed to be the output of @in@ or |
97 | * @fix@. |
98 | */ |
b085fd91 |
99 | |
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100 | typedef struct ec_ops { |
101 | void (*destroy)(ec_curve */*c*/); |
41a324a7 |
102 | ec *(*in)(ec_curve */*c*/, ec */*d*/, const ec */*p*/); |
103 | ec *(*out)(ec_curve */*c*/, ec */*d*/, const ec */*p*/); |
8823192f |
104 | ec *(*fix)(ec_curve */*c*/, ec */*d*/, const ec */*p*/); |
41a324a7 |
105 | ec *(*find)(ec_curve */*c*/, ec */*d*/, mp */*x*/); |
b085fd91 |
106 | ec *(*neg)(ec_curve */*c*/, ec */*d*/, const ec */*p*/); |
41a324a7 |
107 | ec *(*add)(ec_curve */*c*/, ec */*d*/, const ec */*p*/, const ec */*q*/); |
b085fd91 |
108 | ec *(*sub)(ec_curve */*c*/, ec */*d*/, const ec */*p*/, const ec */*q*/); |
41a324a7 |
109 | ec *(*dbl)(ec_curve */*c*/, ec */*d*/, const ec */*p*/); |
8823192f |
110 | int (*check)(ec_curve */*c*/, const ec */*p*/); |
b0ab12e6 |
111 | } ec_ops; |
112 | |
41a324a7 |
113 | #define EC_IN(c, d, p) (c)->ops->in((c), (d), (p)) |
dbfee00a |
114 | #define EC_OUT(c, d, p) (c)->ops->out((c), (d), (p)) |
8823192f |
115 | #define EC_FIX(c, d, p) (c)->ops->fix((c), (d), (p)) |
41a324a7 |
116 | |
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117 | #define EC_FIND(c, d, x) (c)->ops->find((c), (d), (x)) |
b085fd91 |
118 | #define EC_NEG(c, d, x) (c)->ops->neg((c), (d), (x)) |
b0ab12e6 |
119 | #define EC_ADD(c, d, p, q) (c)->ops->add((c), (d), (p), (q)) |
b085fd91 |
120 | #define EC_SUB(c, d, p, q) (c)->ops->sub((c), (d), (p), (q)) |
b0ab12e6 |
121 | #define EC_DBL(c, d, p) (c)->ops->dbl((c), (d), (p)) |
8823192f |
122 | #define EC_CHECK(c, p) (c)->ops->check((c), (p)) |
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123 | |
124 | /*----- Simple memory management things -----------------------------------*/ |
125 | |
126 | /* --- @ec_create@ --- * |
127 | * |
128 | * Arguments: @ec *p@ = pointer to an elliptic-curve point |
129 | * |
41a324a7 |
130 | * Returns: The argument @p@. |
b0ab12e6 |
131 | * |
132 | * Use: Initializes a new point. The initial value is the additive |
133 | * identity (which is universal for all curves). |
134 | */ |
135 | |
136 | #define EC_INIT { MP_NEW, MP_NEW, MP_NEW } |
137 | |
138 | #define EC_CREATE(p) do { \ |
139 | ec *_p = (p); \ |
140 | _p->x = _p->y = _p->z = MP_NEW; \ |
141 | } while (0) |
142 | |
41a324a7 |
143 | extern ec *ec_create(ec */*p*/); |
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144 | |
145 | /* --- @ec_destroy@ --- * |
146 | * |
147 | * Arguments: @ec *p@ = pointer to an elliptic-curve point |
148 | * |
149 | * Returns: --- |
150 | * |
151 | * Use: Destroys a point, making it invalid. |
152 | */ |
153 | |
154 | #define EC_DESTROY(p) do { \ |
155 | ec *_p = (p); \ |
156 | if (!EC_ATINF(_p)) { \ |
157 | MP_DROP(_p->x); \ |
158 | MP_DROP(_p->y); \ |
159 | if (_p->z) MP_DROP(_p->z); \ |
160 | } \ |
161 | } while (0) |
162 | |
163 | extern void ec_destroy(ec */*p*/); |
164 | |
165 | /* --- @ec_atinf@ --- * |
166 | * |
167 | * Arguments: @const ec *p@ = pointer to a point |
168 | * |
169 | * Returns: Nonzero if %$p = O$% is the point at infinity, zero |
170 | * otherwise. |
171 | */ |
172 | |
173 | #define EC_ATINF(p) ((p)->x == MP_NEW || (p)->x == MP_NEWSEC) |
174 | |
175 | extern int ec_atinf(const ec */*p*/); |
176 | |
177 | /* --- @ec_setinf@ --- * |
178 | * |
179 | * Arguments: @ec *p@ = pointer to a point |
180 | * |
41a324a7 |
181 | * Returns: The argument @p@. |
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182 | * |
183 | * Use: Sets the given point to be the point %$O$% at infinity. |
184 | */ |
185 | |
186 | #define EC_SETINF(p) do { \ |
187 | ec *_p = (p); \ |
188 | if (!EC_ATINF(_p)) { \ |
189 | MP_DROP(_p->x); \ |
190 | MP_DROP(_p->y); \ |
191 | if (_p->z) MP_DROP(_p->z); \ |
192 | _p->x = _p->y = _p->z = MP_NEW; \ |
193 | _p->y = MP_NEW; \ |
194 | _p->z = MP_NEW; \ |
195 | } \ |
196 | } while (0) |
197 | |
41a324a7 |
198 | extern ec *ec_setinf(ec */*p*/); |
b0ab12e6 |
199 | |
200 | /* --- @ec_copy@ --- * |
201 | * |
202 | * Arguments: @ec *d@ = pointer to destination point |
203 | * @const ec *p@ = pointer to source point |
204 | * |
41a324a7 |
205 | * Returns: The destination @d@. |
b0ab12e6 |
206 | * |
207 | * Use: Creates a copy of an elliptic curve point. |
208 | */ |
209 | |
210 | #define EC_COPY(d, p) do { \ |
211 | ec *_d = (d); \ |
212 | const ec *_p = (p); \ |
213 | if (d != p) { \ |
214 | EC_DESTROY(d); \ |
215 | if (EC_ATINF(p)) \ |
216 | _d->x = _d->y = _d->z = MP_NEW; \ |
217 | else { \ |
b085fd91 |
218 | _d->x = MP_COPY(_p->x); \ |
219 | _d->y = MP_COPY(_p->y); \ |
220 | _d->z = _p->z ? MP_COPY(_p->z) : MP_NEW; \ |
b0ab12e6 |
221 | } \ |
222 | } \ |
223 | } while (0) |
224 | |
41a324a7 |
225 | extern ec *ec_copy(ec */*d*/, const ec */*p*/); |
b0ab12e6 |
226 | |
227 | /*----- Interesting arithmetic --------------------------------------------*/ |
228 | |
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229 | /* --- @ec_find@ --- * |
230 | * |
231 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
232 | * @ec *d@ = pointer to the destination point |
233 | * @mp *x@ = a possible x-coordinate |
234 | * |
b085fd91 |
235 | * Returns: The destination if OK, or null if no point was found. |
b0ab12e6 |
236 | * |
b085fd91 |
237 | * Use: Finds a point on an elliptic curve with a given |
238 | * x-coordinate. If there is no point with the given |
239 | * %$x$%-coordinate, a null pointer is returned and the |
240 | * destination is left invalid. |
b0ab12e6 |
241 | */ |
242 | |
b085fd91 |
243 | extern ec *ec_find(ec_curve */*c*/, ec */*d*/, mp */*x*/); |
244 | |
245 | /* --- @ec_neg@ --- * |
246 | * |
247 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
248 | * @ec *d@ = pointer to the destination point |
249 | * @const ec *p@ = pointer to the operand point |
250 | * |
251 | * Returns: The destination point. |
252 | * |
253 | * Use: Computes the negation of the given point. |
254 | */ |
255 | |
256 | extern ec *ec_neg(ec_curve */*c*/, ec */*d*/, const ec */*p*/); |
b0ab12e6 |
257 | |
258 | /* --- @ec_add@ --- * |
259 | * |
260 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
261 | * @ec *d@ = pointer to the destination point |
262 | * @const ec *p, *q@ = pointers to the operand points |
263 | * |
41a324a7 |
264 | * Returns: The destination @d@. |
b0ab12e6 |
265 | * |
266 | * Use: Adds two points on an elliptic curve. |
267 | */ |
268 | |
41a324a7 |
269 | extern ec *ec_add(ec_curve */*c*/, ec */*d*/, |
270 | const ec */*p*/, const ec */*q*/); |
b0ab12e6 |
271 | |
b085fd91 |
272 | /* --- @ec_sub@ --- * |
273 | * |
274 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
275 | * @ec *d@ = pointer to the destination point |
276 | * @const ec *p, *q@ = pointers to the operand points |
277 | * |
278 | * Returns: The destination @d@. |
279 | * |
280 | * Use: Subtracts one point from another on an elliptic curve. |
281 | */ |
282 | |
283 | extern ec *ec_sub(ec_curve */*c*/, ec */*d*/, |
284 | const ec */*p*/, const ec */*q*/); |
285 | |
b0ab12e6 |
286 | /* --- @ec_dbl@ --- * |
287 | * |
288 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
289 | * @ec *d@ = pointer to the destination point |
290 | * @const ec *p@ = pointer to the operand point |
291 | * |
41a324a7 |
292 | * Returns: The destination @d@. |
b0ab12e6 |
293 | * |
294 | * Use: Doubles a point on an elliptic curve. |
295 | */ |
296 | |
41a324a7 |
297 | extern ec *ec_dbl(ec_curve */*c*/, ec */*d*/, const ec */*p*/); |
b0ab12e6 |
298 | |
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299 | /* --- @ec_check@ --- * |
300 | * |
301 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
302 | * @const ec *p@ = pointer to the point |
303 | * |
304 | * Returns: Zero if OK, nonzero if this is an invalid point. |
305 | * |
306 | * Use: Checks that a point is actually on an elliptic curve. |
307 | */ |
308 | |
309 | extern int ec_check(ec_curve */*c*/, const ec */*p*/); |
310 | |
b085fd91 |
311 | /* --- @ec_mul@, @ec_imul@ --- * |
b0ab12e6 |
312 | * |
313 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
314 | * @ec *d@ = pointer to the destination point |
315 | * @const ec *p@ = pointer to the generator point |
316 | * @mp *n@ = integer multiplier |
317 | * |
41a324a7 |
318 | * Returns: The destination @d@. |
b0ab12e6 |
319 | * |
b085fd91 |
320 | * Use: Multiplies a point by a scalar, returning %$n p$%. The |
321 | * @imul@ variant uses internal representations for argument |
322 | * and result. |
b0ab12e6 |
323 | */ |
324 | |
41a324a7 |
325 | extern ec *ec_mul(ec_curve */*c*/, ec */*d*/, const ec */*p*/, mp */*n*/); |
b085fd91 |
326 | extern ec *ec_imul(ec_curve */*c*/, ec */*d*/, const ec */*p*/, mp */*n*/); |
327 | |
328 | /* --- @ec_mmul@, @ec_immul@ --- * |
329 | * |
330 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
331 | * @ec *d@ = pointer to the destination point |
332 | * @const ec_mulfactor *f@ = pointer to vector of factors |
333 | * @size_t n@ = number of factors |
334 | * |
335 | * Returns: The destination @d@. |
336 | * |
337 | * Use: Does simultaneous point multiplication. The @immul@ variant |
338 | * uses internal representations for arguments and result. |
339 | */ |
340 | |
341 | extern ec *ec_mmul(ec_curve */*c*/, ec */*d*/, |
342 | const ec_mulfactor */*f*/, size_t /*n*/); |
343 | extern ec *ec_immul(ec_curve */*c*/, ec */*d*/, |
344 | const ec_mulfactor */*f*/, size_t /*n*/); |
41a324a7 |
345 | |
346 | /*----- Standard curve operations -----------------------------------------*/ |
347 | |
8823192f |
348 | /* --- @ec_idin@, @ec_idout@, @ec_idfix@ --- * |
41a324a7 |
349 | * |
350 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
351 | * @ec *d@ = pointer to the destination |
352 | * @const ec *p@ = pointer to a source point |
353 | * |
354 | * Returns: The destination @d@. |
355 | * |
356 | * Use: An identity operation if your curve has no internal |
357 | * representation. (The field internal representation is still |
358 | * used.) |
359 | */ |
360 | |
361 | extern ec *ec_idin(ec_curve */*c*/, ec */*d*/, const ec */*p*/); |
362 | extern ec *ec_idout(ec_curve */*c*/, ec */*d*/, const ec */*p*/); |
8823192f |
363 | extern ec *ec_idfix(ec_curve */*c*/, ec */*d*/, const ec */*p*/); |
41a324a7 |
364 | |
8823192f |
365 | /* --- @ec_projin@, @ec_projout@, @ec_projfix@ --- * |
41a324a7 |
366 | * |
367 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
368 | * @ec *d@ = pointer to the destination |
369 | * @const ec *p@ = pointer to a source point |
370 | * |
371 | * Returns: The destination @d@. |
372 | * |
373 | * Use: Conversion functions if your curve operations use a |
374 | * projective representation. |
375 | */ |
376 | |
377 | extern ec *ec_projin(ec_curve */*c*/, ec */*d*/, const ec */*p*/); |
378 | extern ec *ec_projout(ec_curve */*c*/, ec */*d*/, const ec */*p*/); |
8823192f |
379 | extern ec *ec_projfix(ec_curve */*c*/, ec */*d*/, const ec */*p*/); |
b0ab12e6 |
380 | |
b085fd91 |
381 | /* --- @ec_stdsub@ --- * |
382 | * |
383 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
384 | * @ec *d@ = pointer to the destination |
41cb1beb |
385 | * @const ec *p, *q@ = the operand points |
b085fd91 |
386 | * |
387 | * Returns: The destination @d@. |
388 | * |
389 | * Use: Standard point subtraction operation, in terms of negation |
390 | * and addition. This isn't as efficient as a ready-made |
391 | * subtraction operator. |
392 | */ |
393 | |
41cb1beb |
394 | extern ec *ec_stdsub(ec_curve */*c*/, ec */*d*/, |
395 | const ec */*p*/, const ec */*q*/); |
b085fd91 |
396 | |
b0ab12e6 |
397 | /*----- Creating curves ---------------------------------------------------*/ |
398 | |
b085fd91 |
399 | /* --- @ec_destroycurve@ --- * |
400 | * |
401 | * Arguments: @ec_curve *c@ = pointer to an ellptic curve |
402 | * |
403 | * Returns: --- |
404 | * |
405 | * Use: Destroys a description of an elliptic curve. |
406 | */ |
407 | |
408 | extern void ec_destroycurve(ec_curve */*c*/); |
409 | |
410 | /* --- @ec_prime@, @ec_primeproj@ --- * |
b0ab12e6 |
411 | * |
dbfee00a |
412 | * Arguments: @field *f@ = the underlying field for this elliptic curve |
b0ab12e6 |
413 | * @mp *a, *b@ = the coefficients for this curve |
414 | * |
415 | * Returns: A pointer to the curve. |
416 | * |
417 | * Use: Creates a curve structure for an elliptic curve defined over |
b085fd91 |
418 | * a prime field. The @primeproj@ variant uses projective |
419 | * coordinates, which can be a win. |
b0ab12e6 |
420 | */ |
421 | |
422 | extern ec_curve *ec_prime(field */*f*/, mp */*a*/, mp */*b*/); |
b085fd91 |
423 | extern ec_curve *ec_primeproj(field */*f*/, mp */*a*/, mp */*b*/); |
b0ab12e6 |
424 | |
ceb3f0c0 |
425 | /* --- @ec_bin@, @ec_binproj@ --- * |
b0ab12e6 |
426 | * |
427 | * Arguments: @field *f@ = the underlying field for this elliptic curve |
428 | * @mp *a, *b@ = the coefficients for this curve |
429 | * |
430 | * Returns: A pointer to the curve. |
431 | * |
ceb3f0c0 |
432 | * Use: Creates a curve structure for an elliptic curve defined over |
433 | * a binary field. The @binproj@ variant uses projective |
434 | * coordinates, which can be a win. |
b0ab12e6 |
435 | */ |
436 | |
437 | extern ec_curve *ec_bin(field */*f*/, mp */*a*/, mp */*b*/); |
ceb3f0c0 |
438 | extern ec_curve *ec_binproj(field */*f*/, mp */*a*/, mp */*b*/); |
b0ab12e6 |
439 | |
440 | /*----- That's all, folks -------------------------------------------------*/ |
441 | |
442 | #ifdef __cplusplus |
443 | } |
444 | #endif |
445 | |
446 | #endif |