b0ab12e6 |
1 | /* -*-c-*- |
2 | * |
8823192f |
3 | * $Id: ec.h,v 1.4.4.2 2004/03/20 00:13:31 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 $ |
8823192f |
33 | * Revision 1.4.4.2 2004/03/20 00:13:31 mdw |
34 | * Projective coordinates for prime curves |
35 | * |
dbfee00a |
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 | * |
41cb1beb |
39 | * Revision 1.4 2003/05/15 23:25:59 mdw |
40 | * Make elliptic curve stuff build. |
41 | * |
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42 | * Revision 1.3 2002/01/13 13:48:44 mdw |
43 | * Further progress. |
44 | * |
41a324a7 |
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 | * |
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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 | |
b085fd91 |
68 | /* --- An elliptic curve representation --- */ |
69 | |
b0ab12e6 |
70 | typedef struct ec_curve { |
71 | const struct ec_ops *ops; /* Curve operations */ |
72 | field *f; /* Underlying field structure */ |
73 | } ec_curve; |
74 | |
b085fd91 |
75 | /* --- An elliptic curve point --- */ |
76 | |
b0ab12e6 |
77 | typedef struct ec { |
78 | mp *x, *y; /* Point coordinates */ |
79 | mp *z; /* Common denominator (or null) */ |
80 | } ec; |
81 | |
b085fd91 |
82 | /* --- A factor for simultaneous multiplication --- */ |
83 | |
84 | typedef struct ec_mulfactor { |
85 | ec base; /* The point */ |
41cb1beb |
86 | mp *exp; /* The exponent */ |
b085fd91 |
87 | } ec_mulfactor; |
88 | |
8823192f |
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 | */ |
b085fd91 |
96 | |
b0ab12e6 |
97 | typedef struct ec_ops { |
98 | void (*destroy)(ec_curve */*c*/); |
41a324a7 |
99 | ec *(*in)(ec_curve */*c*/, ec */*d*/, const ec */*p*/); |
100 | ec *(*out)(ec_curve */*c*/, ec */*d*/, const ec */*p*/); |
8823192f |
101 | ec *(*fix)(ec_curve */*c*/, ec */*d*/, const ec */*p*/); |
41a324a7 |
102 | ec *(*find)(ec_curve */*c*/, ec */*d*/, mp */*x*/); |
b085fd91 |
103 | ec *(*neg)(ec_curve */*c*/, ec */*d*/, const ec */*p*/); |
41a324a7 |
104 | ec *(*add)(ec_curve */*c*/, ec */*d*/, const ec */*p*/, const ec */*q*/); |
b085fd91 |
105 | ec *(*sub)(ec_curve */*c*/, ec */*d*/, const ec */*p*/, const ec */*q*/); |
41a324a7 |
106 | ec *(*dbl)(ec_curve */*c*/, ec */*d*/, const ec */*p*/); |
8823192f |
107 | int (*check)(ec_curve */*c*/, const ec */*p*/); |
b0ab12e6 |
108 | } ec_ops; |
109 | |
41a324a7 |
110 | #define EC_IN(c, d, p) (c)->ops->in((c), (d), (p)) |
dbfee00a |
111 | #define EC_OUT(c, d, p) (c)->ops->out((c), (d), (p)) |
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112 | #define EC_FIX(c, d, p) (c)->ops->fix((c), (d), (p)) |
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113 | |
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114 | #define EC_FIND(c, d, x) (c)->ops->find((c), (d), (x)) |
b085fd91 |
115 | #define EC_NEG(c, d, x) (c)->ops->neg((c), (d), (x)) |
b0ab12e6 |
116 | #define EC_ADD(c, d, p, q) (c)->ops->add((c), (d), (p), (q)) |
b085fd91 |
117 | #define EC_SUB(c, d, p, q) (c)->ops->sub((c), (d), (p), (q)) |
b0ab12e6 |
118 | #define EC_DBL(c, d, p) (c)->ops->dbl((c), (d), (p)) |
8823192f |
119 | #define EC_CHECK(c, p) (c)->ops->check((c), (p)) |
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120 | |
121 | /*----- Simple memory management things -----------------------------------*/ |
122 | |
123 | /* --- @ec_create@ --- * |
124 | * |
125 | * Arguments: @ec *p@ = pointer to an elliptic-curve point |
126 | * |
41a324a7 |
127 | * Returns: The argument @p@. |
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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 | |
41a324a7 |
140 | extern ec *ec_create(ec */*p*/); |
b0ab12e6 |
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 | * |
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178 | * Returns: The argument @p@. |
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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 | |
41a324a7 |
195 | extern ec *ec_setinf(ec */*p*/); |
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196 | |
197 | /* --- @ec_copy@ --- * |
198 | * |
199 | * Arguments: @ec *d@ = pointer to destination point |
200 | * @const ec *p@ = pointer to source point |
201 | * |
41a324a7 |
202 | * Returns: The destination @d@. |
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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 { \ |
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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; \ |
b0ab12e6 |
218 | } \ |
219 | } \ |
220 | } while (0) |
221 | |
41a324a7 |
222 | extern ec *ec_copy(ec */*d*/, const ec */*p*/); |
b0ab12e6 |
223 | |
224 | /*----- Interesting arithmetic --------------------------------------------*/ |
225 | |
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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 | * |
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232 | * Returns: The destination if OK, or null if no point was found. |
b0ab12e6 |
233 | * |
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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. |
b0ab12e6 |
238 | */ |
239 | |
b085fd91 |
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*/); |
b0ab12e6 |
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 | * |
41a324a7 |
261 | * Returns: The destination @d@. |
b0ab12e6 |
262 | * |
263 | * Use: Adds two points on an elliptic curve. |
264 | */ |
265 | |
41a324a7 |
266 | extern ec *ec_add(ec_curve */*c*/, ec */*d*/, |
267 | const ec */*p*/, const ec */*q*/); |
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268 | |
b085fd91 |
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 | |
b0ab12e6 |
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 | * |
41a324a7 |
289 | * Returns: The destination @d@. |
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290 | * |
291 | * Use: Doubles a point on an elliptic curve. |
292 | */ |
293 | |
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294 | extern ec *ec_dbl(ec_curve */*c*/, ec */*d*/, const ec */*p*/); |
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295 | |
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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 | |
b085fd91 |
308 | /* --- @ec_mul@, @ec_imul@ --- * |
b0ab12e6 |
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 | * |
41a324a7 |
315 | * Returns: The destination @d@. |
b0ab12e6 |
316 | * |
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317 | * Use: Multiplies a point by a scalar, returning %$n p$%. The |
318 | * @imul@ variant uses internal representations for argument |
319 | * and result. |
b0ab12e6 |
320 | */ |
321 | |
41a324a7 |
322 | extern ec *ec_mul(ec_curve */*c*/, ec */*d*/, const ec */*p*/, mp */*n*/); |
b085fd91 |
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*/); |
41a324a7 |
342 | |
343 | /*----- Standard curve operations -----------------------------------------*/ |
344 | |
8823192f |
345 | /* --- @ec_idin@, @ec_idout@, @ec_idfix@ --- * |
41a324a7 |
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*/); |
8823192f |
360 | extern ec *ec_idfix(ec_curve */*c*/, ec */*d*/, const ec */*p*/); |
41a324a7 |
361 | |
8823192f |
362 | /* --- @ec_projin@, @ec_projout@, @ec_projfix@ --- * |
41a324a7 |
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*/); |
8823192f |
376 | extern ec *ec_projfix(ec_curve */*c*/, ec */*d*/, const ec */*p*/); |
b0ab12e6 |
377 | |
b085fd91 |
378 | /* --- @ec_stdsub@ --- * |
379 | * |
380 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
381 | * @ec *d@ = pointer to the destination |
41cb1beb |
382 | * @const ec *p, *q@ = the operand points |
b085fd91 |
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 | |
41cb1beb |
391 | extern ec *ec_stdsub(ec_curve */*c*/, ec */*d*/, |
392 | const ec */*p*/, const ec */*q*/); |
b085fd91 |
393 | |
b0ab12e6 |
394 | /*----- Creating curves ---------------------------------------------------*/ |
395 | |
b085fd91 |
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@ --- * |
b0ab12e6 |
408 | * |
dbfee00a |
409 | * Arguments: @field *f@ = the underlying field for this elliptic curve |
b0ab12e6 |
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 |
b085fd91 |
415 | * a prime field. The @primeproj@ variant uses projective |
416 | * coordinates, which can be a win. |
b0ab12e6 |
417 | */ |
418 | |
419 | extern ec_curve *ec_prime(field */*f*/, mp */*a*/, mp */*b*/); |
b085fd91 |
420 | extern ec_curve *ec_primeproj(field */*f*/, mp */*a*/, mp */*b*/); |
b0ab12e6 |
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 |