b0ab12e6 |
1 | /* -*-c-*- |
2 | * |
c3caa2fa |
3 | * $Id: ec.c,v 1.5 2004/03/21 22:52:06 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.c,v $ |
c3caa2fa |
33 | * Revision 1.5 2004/03/21 22:52:06 mdw |
34 | * Merge and close elliptic curve branch. |
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 | /*----- Header files ------------------------------------------------------*/ |
58 | |
59 | #include "ec.h" |
b085fd91 |
60 | #include "ec-exp.h" |
b0ab12e6 |
61 | |
62 | /*----- Trivial wrappers --------------------------------------------------*/ |
63 | |
64 | /* --- @ec_create@ --- * |
65 | * |
66 | * Arguments: @ec *p@ = pointer to an elliptic-curve point |
67 | * |
41cb1beb |
68 | * Returns: The argument @p@. |
b0ab12e6 |
69 | * |
70 | * Use: Initializes a new point. The initial value is the additive |
71 | * identity (which is universal for all curves). |
72 | */ |
73 | |
41cb1beb |
74 | ec *ec_create(ec *p) { EC_CREATE(p); return (p); } |
b0ab12e6 |
75 | |
76 | /* --- @ec_destroy@ --- * |
77 | * |
78 | * Arguments: @ec *p@ = pointer to an elliptic-curve point |
79 | * |
80 | * Returns: --- |
81 | * |
82 | * Use: Destroys a point, making it invalid. |
83 | */ |
84 | |
85 | void ec_destroy(ec *p) { EC_DESTROY(p); } |
86 | |
87 | /* --- @ec_atinf@ --- * |
88 | * |
89 | * Arguments: @const ec *p@ = pointer to a point |
90 | * |
91 | * Returns: Nonzero if %$p = O$% is the point at infinity, zero |
92 | * otherwise. |
93 | */ |
94 | |
95 | int ec_atinf(const ec *p) { return (EC_ATINF(p)); } |
96 | |
97 | /* --- @ec_setinf@ --- * |
98 | * |
99 | * Arguments: @ec *p@ = pointer to a point |
100 | * |
41cb1beb |
101 | * Returns: The argument @p@. |
b0ab12e6 |
102 | * |
103 | * Use: Sets the given point to be the point %$O$% at infinity. |
104 | */ |
105 | |
41cb1beb |
106 | ec *ec_setinf(ec *p) { EC_SETINF(p); return (p); } |
b0ab12e6 |
107 | |
108 | /* --- @ec_copy@ --- * |
109 | * |
110 | * Arguments: @ec *d@ = pointer to destination point |
111 | * @const ec *p@ = pointer to source point |
112 | * |
41cb1beb |
113 | * Returns: The destination @d@. |
b0ab12e6 |
114 | * |
115 | * Use: Creates a copy of an elliptic curve point. |
116 | */ |
117 | |
41cb1beb |
118 | ec *ec_copy(ec *d, const ec *p) { EC_COPY(d, p); return (d); } |
b0ab12e6 |
119 | |
41a324a7 |
120 | /*----- Standard curve operations -----------------------------------------*/ |
b0ab12e6 |
121 | |
8823192f |
122 | /* --- @ec_idin@, @ec_idout@, @ec_idfix@ --- * |
b0ab12e6 |
123 | * |
124 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
41a324a7 |
125 | * @ec *d@ = pointer to the destination |
126 | * @const ec *p@ = pointer to a source point |
b0ab12e6 |
127 | * |
41a324a7 |
128 | * Returns: The destination @d@. |
b0ab12e6 |
129 | * |
41a324a7 |
130 | * Use: An identity operation if your curve has no internal |
131 | * representation. (The field internal representation is still |
132 | * used.) |
b0ab12e6 |
133 | */ |
134 | |
41a324a7 |
135 | ec *ec_idin(ec_curve *c, ec *d, const ec *p) |
b0ab12e6 |
136 | { |
137 | if (EC_ATINF(p)) |
138 | EC_SETINF(d); |
139 | else { |
140 | field *f = c->f; |
141 | d->x = F_IN(f, d->x, p->x); |
142 | d->y = F_IN(f, d->y, p->y); |
41a324a7 |
143 | mp_drop(d->z); d->z = 0; |
144 | } |
145 | return (d); |
146 | } |
147 | |
148 | ec *ec_idout(ec_curve *c, ec *d, const ec *p) |
149 | { |
150 | if (EC_ATINF(p)) |
151 | EC_SETINF(d); |
152 | else { |
153 | field *f = c->f; |
154 | d->x = F_OUT(f, d->x, p->x); |
155 | d->y = F_OUT(f, d->y, p->y); |
156 | mp_drop(d->z); d->z = 0; |
b0ab12e6 |
157 | } |
41a324a7 |
158 | return (d); |
b0ab12e6 |
159 | } |
160 | |
8823192f |
161 | ec *ec_idfix(ec_curve *c, ec *d, const ec *p) |
162 | { |
163 | EC_COPY(d, p); |
164 | return (d); |
165 | } |
166 | |
41a324a7 |
167 | /* --- @ec_projin@, @ec_projout@ --- * |
b0ab12e6 |
168 | * |
169 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
41a324a7 |
170 | * @ec *d@ = pointer to the destination |
171 | * @const ec *p@ = pointer to a source point |
b0ab12e6 |
172 | * |
41a324a7 |
173 | * Returns: The destination @d@. |
b0ab12e6 |
174 | * |
41a324a7 |
175 | * Use: Conversion functions if your curve operations use a |
176 | * projective representation. |
b0ab12e6 |
177 | */ |
178 | |
41a324a7 |
179 | ec *ec_projin(ec_curve *c, ec *d, const ec *p) |
180 | { |
181 | if (EC_ATINF(p)) |
182 | EC_SETINF(d); |
183 | else { |
184 | field *f = c->f; |
185 | d->x = F_IN(f, d->x, p->x); |
186 | d->y = F_IN(f, d->y, p->y); |
187 | mp_drop(d->z); d->z = MP_COPY(f->one); |
188 | } |
189 | return (d); |
190 | } |
191 | |
192 | ec *ec_projout(ec_curve *c, ec *d, const ec *p) |
b0ab12e6 |
193 | { |
194 | if (EC_ATINF(p)) |
195 | EC_SETINF(d); |
196 | else { |
8823192f |
197 | mp *x, *y, *z, *zz; |
b0ab12e6 |
198 | field *f = c->f; |
199 | z = F_INV(f, MP_NEW, p->z); |
8823192f |
200 | zz = F_SQR(f, MP_NEW, z); |
201 | z = F_MUL(f, z, zz, z); |
202 | x = F_MUL(f, d->x, p->x, zz); |
b0ab12e6 |
203 | y = F_MUL(f, d->y, p->y, z); |
204 | mp_drop(z); |
8823192f |
205 | mp_drop(zz); |
b0ab12e6 |
206 | mp_drop(d->z); |
207 | d->x = F_OUT(f, x, x); |
208 | d->y = F_OUT(f, y, y); |
209 | d->z = 0; |
210 | } |
41a324a7 |
211 | return (d); |
b0ab12e6 |
212 | } |
213 | |
8823192f |
214 | ec *ec_projfix(ec_curve *c, ec *d, const ec *p) |
215 | { |
216 | if (EC_ATINF(p)) |
217 | EC_SETINF(d); |
218 | else if (d->z == c->f->one) |
219 | EC_COPY(d, p); |
220 | else { |
221 | mp *z, *zz; |
222 | field *f = c->f; |
223 | z = F_INV(f, MP_NEW, p->z); |
224 | zz = F_SQR(f, MP_NEW, z); |
225 | z = F_MUL(f, z, zz, z); |
226 | d->x = F_MUL(f, d->x, p->x, zz); |
227 | d->y = F_MUL(f, d->y, p->y, z); |
228 | mp_drop(z); |
229 | mp_drop(zz); |
230 | mp_drop(d->z); |
231 | d->z = MP_COPY(f->one); |
232 | } |
233 | return (d); |
234 | } |
235 | |
b085fd91 |
236 | /* --- @ec_stdsub@ --- * |
237 | * |
238 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
239 | * @ec *d@ = pointer to the destination |
41cb1beb |
240 | * @const ec *p, *q@ = the operand points |
b085fd91 |
241 | * |
242 | * Returns: The destination @d@. |
243 | * |
244 | * Use: Standard point subtraction operation, in terms of negation |
245 | * and addition. This isn't as efficient as a ready-made |
246 | * subtraction operator. |
247 | */ |
248 | |
41cb1beb |
249 | ec *ec_stdsub(ec_curve *c, ec *d, const ec *p, const ec *q) |
b085fd91 |
250 | { |
251 | ec t = EC_INIT; |
41cb1beb |
252 | EC_NEG(c, &t, q); |
8823192f |
253 | EC_FIX(c, &t, &t); |
41cb1beb |
254 | EC_ADD(c, d, p, &t); |
b085fd91 |
255 | EC_DESTROY(&t); |
256 | return (d); |
257 | } |
258 | |
41cb1beb |
259 | /*----- Creating curves ---------------------------------------------------*/ |
260 | |
261 | /* --- @ec_destroycurve@ --- * |
262 | * |
263 | * Arguments: @ec_curve *c@ = pointer to an ellptic curve |
264 | * |
265 | * Returns: --- |
266 | * |
267 | * Use: Destroys a description of an elliptic curve. |
268 | */ |
269 | |
270 | void ec_destroycurve(ec_curve *c) { c->ops->destroy(c); } |
271 | |
41a324a7 |
272 | /*----- Real arithmetic ---------------------------------------------------*/ |
273 | |
b0ab12e6 |
274 | /* --- @ec_find@ --- * |
275 | * |
276 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
277 | * @ec *d@ = pointer to the destination point |
278 | * @mp *x@ = a possible x-coordinate |
279 | * |
280 | * Returns: Zero if OK, nonzero if there isn't a point there. |
281 | * |
282 | * Use: Finds a point on an elliptic curve with a given x-coordinate. |
283 | */ |
284 | |
41a324a7 |
285 | ec *ec_find(ec_curve *c, ec *d, mp *x) |
b0ab12e6 |
286 | { |
b0ab12e6 |
287 | x = F_IN(c->f, MP_NEW, x); |
41a324a7 |
288 | if ((d = EC_FIND(c, d, x)) != 0) |
289 | EC_OUT(c, d, d); |
8823192f |
290 | MP_DROP(x); |
41a324a7 |
291 | return (d); |
b0ab12e6 |
292 | } |
293 | |
dbfee00a |
294 | /* --- @ec_neg@ --- * |
295 | * |
296 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
297 | * @ec *d@ = pointer to the destination point |
298 | * @const ec *p@ = pointer to the operand point |
299 | * |
300 | * Returns: The destination point. |
301 | * |
302 | * Use: Computes the negation of the given point. |
303 | */ |
304 | |
305 | ec *ec_neg(ec_curve *c, ec *d, const ec *p) |
306 | { |
307 | EC_IN(c, d, p); |
308 | EC_NEG(c, d, d); |
309 | return (EC_OUT(c, d, d)); |
310 | } |
311 | |
b0ab12e6 |
312 | /* --- @ec_add@ --- * |
313 | * |
314 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
315 | * @ec *d@ = pointer to the destination point |
316 | * @const ec *p, *q@ = pointers to the operand points |
317 | * |
318 | * Returns: --- |
319 | * |
320 | * Use: Adds two points on an elliptic curve. |
321 | */ |
322 | |
41a324a7 |
323 | ec *ec_add(ec_curve *c, ec *d, const ec *p, const ec *q) |
b0ab12e6 |
324 | { |
325 | ec pp = EC_INIT, qq = EC_INIT; |
41a324a7 |
326 | EC_IN(c, &pp, p); |
327 | EC_IN(c, &qq, q); |
b0ab12e6 |
328 | EC_ADD(c, d, &pp, &qq); |
41a324a7 |
329 | EC_OUT(c, d, d); |
b0ab12e6 |
330 | EC_DESTROY(&pp); |
331 | EC_DESTROY(&qq); |
41a324a7 |
332 | return (d); |
b0ab12e6 |
333 | } |
334 | |
dbfee00a |
335 | /* --- @ec_sub@ --- * |
336 | * |
337 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
338 | * @ec *d@ = pointer to the destination point |
339 | * @const ec *p, *q@ = pointers to the operand points |
340 | * |
341 | * Returns: The destination @d@. |
342 | * |
343 | * Use: Subtracts one point from another on an elliptic curve. |
344 | */ |
345 | |
346 | ec *ec_sub(ec_curve *c, ec *d, const ec *p, const ec *q) |
347 | { |
348 | ec pp, qq; |
349 | EC_IN(c, &pp, p); |
350 | EC_IN(c, &qq, q); |
351 | EC_SUB(c, d, &qq, &qq); |
352 | EC_OUT(c, d, d); |
353 | EC_DESTROY(&pp); |
354 | EC_DESTROY(&qq); |
355 | return (d); |
356 | } |
357 | |
b0ab12e6 |
358 | /* --- @ec_dbl@ --- * |
359 | * |
360 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
361 | * @ec *d@ = pointer to the destination point |
362 | * @const ec *p@ = pointer to the operand point |
363 | * |
364 | * Returns: --- |
365 | * |
366 | * Use: Doubles a point on an elliptic curve. |
367 | */ |
368 | |
41a324a7 |
369 | ec *ec_dbl(ec_curve *c, ec *d, const ec *p) |
b0ab12e6 |
370 | { |
41a324a7 |
371 | EC_IN(c, d, p); |
b0ab12e6 |
372 | EC_DBL(c, d, d); |
41a324a7 |
373 | return (EC_OUT(c, d, d)); |
b0ab12e6 |
374 | } |
375 | |
8823192f |
376 | /* --- @ec_check@ --- * |
377 | * |
378 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
379 | * @const ec *p@ = pointer to the point |
380 | * |
381 | * Returns: Zero if OK, nonzero if this is an invalid point. |
382 | * |
383 | * Use: Checks that a point is actually on an elliptic curve. |
384 | */ |
385 | |
386 | int ec_check(ec_curve *c, const ec *p) |
387 | { |
388 | ec t = EC_INIT; |
389 | int rc; |
390 | |
391 | if (EC_ATINF(p)) |
392 | return (0); |
393 | EC_IN(c, &t, p); |
394 | rc = EC_CHECK(c, &t); |
395 | EC_DESTROY(&t); |
396 | return (rc); |
397 | } |
398 | |
b085fd91 |
399 | /* --- @ec_imul@, @ec_mul@ --- * |
b0ab12e6 |
400 | * |
401 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
402 | * @ec *d@ = pointer to the destination point |
403 | * @const ec *p@ = pointer to the generator point |
404 | * @mp *n@ = integer multiplier |
405 | * |
b085fd91 |
406 | * Returns: The destination @d@. |
b0ab12e6 |
407 | * |
b085fd91 |
408 | * Use: Multiplies a point by a scalar, returning %$n p$%. The |
409 | * @imul@ variant uses internal representations for argument |
410 | * and result. |
b0ab12e6 |
411 | */ |
412 | |
b085fd91 |
413 | ec *ec_imul(ec_curve *c, ec *d, const ec *p, mp *n) |
b0ab12e6 |
414 | { |
b085fd91 |
415 | ec t = EC_INIT; |
b0ab12e6 |
416 | |
b085fd91 |
417 | EC_COPY(&t, p); |
418 | if (t.x && (n->f & MP_BURN)) |
419 | t.x->f |= MP_BURN; |
420 | MP_SHRINK(n); |
b0ab12e6 |
421 | EC_SETINF(d); |
b085fd91 |
422 | if (MP_LEN(n) == 0) |
423 | ; |
8823192f |
424 | else { |
425 | if (n->f & MP_NEG) |
426 | EC_NEG(c, &t, &t); |
427 | if (MP_LEN(n) < EXP_THRESH) |
428 | EXP_SIMPLE(*d, t, n); |
429 | else |
430 | EXP_WINDOW(*d, t, n); |
431 | } |
dbfee00a |
432 | EC_DESTROY(&t); |
b085fd91 |
433 | return (d); |
434 | } |
b0ab12e6 |
435 | |
b085fd91 |
436 | ec *ec_mul(ec_curve *c, ec *d, const ec *p, mp *n) |
437 | { |
438 | EC_IN(c, d, p); |
439 | ec_imul(c, d, d, n); |
41a324a7 |
440 | return (EC_OUT(c, d, d)); |
b0ab12e6 |
441 | } |
442 | |
443 | /*----- That's all, folks -------------------------------------------------*/ |