b0ab12e6 |
1 | /* -*-c-*- |
2 | * |
391faf42 |
3 | * $Id: ec-prime.c,v 1.5 2004/03/22 02:19:10 mdw Exp $ |
b0ab12e6 |
4 | * |
5 | * Elliptic curves over prime fields |
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-prime.c,v $ |
391faf42 |
33 | * Revision 1.5 2004/03/22 02:19:10 mdw |
34 | * Rationalise the sliding-window threshold. Drop guarantee that right |
35 | * arguments to EC @add@ are canonical, and fix up projective implementations |
36 | * to cope. |
37 | * |
c3caa2fa |
38 | * Revision 1.4 2004/03/21 22:52:06 mdw |
39 | * Merge and close elliptic curve branch. |
40 | * |
ceb3f0c0 |
41 | * Revision 1.3.4.3 2004/03/21 22:39:46 mdw |
42 | * Elliptic curves on binary fields work. |
43 | * |
8823192f |
44 | * Revision 1.3.4.2 2004/03/20 00:13:31 mdw |
45 | * Projective coordinates for prime curves |
46 | * |
dbfee00a |
47 | * Revision 1.3.4.1 2003/06/10 13:43:53 mdw |
48 | * Simple (non-projective) curves over prime fields now seem to work. |
49 | * |
41cb1beb |
50 | * Revision 1.3 2003/05/15 23:25:59 mdw |
51 | * Make elliptic curve stuff build. |
52 | * |
b085fd91 |
53 | * Revision 1.2 2002/01/13 13:48:44 mdw |
54 | * Further progress. |
55 | * |
b0ab12e6 |
56 | * Revision 1.1 2001/04/29 18:12:33 mdw |
57 | * Prototype version. |
58 | * |
59 | */ |
60 | |
61 | /*----- Header files ------------------------------------------------------*/ |
62 | |
41cb1beb |
63 | #include <mLib/sub.h> |
64 | |
b0ab12e6 |
65 | #include "ec.h" |
66 | |
67 | /*----- Data structures ---------------------------------------------------*/ |
68 | |
69 | typedef struct ecctx { |
70 | ec_curve c; |
71 | mp *a, *b; |
72 | } ecctx; |
73 | |
dbfee00a |
74 | /*----- Simple prime curves -----------------------------------------------*/ |
b0ab12e6 |
75 | |
8823192f |
76 | static const ec_ops ec_primeops, ec_primeprojops, ec_primeprojxops; |
41cb1beb |
77 | |
78 | static ec *ecneg(ec_curve *c, ec *d, const ec *p) |
b085fd91 |
79 | { |
80 | EC_COPY(d, p); |
ceb3f0c0 |
81 | if (d->y) |
82 | d->y = F_NEG(c->f, d->y, d->y); |
b085fd91 |
83 | return (d); |
84 | } |
85 | |
8823192f |
86 | static ec *ecfind(ec_curve *c, ec *d, mp *x) |
87 | { |
88 | mp *p, *q; |
89 | ecctx *cc = (ecctx *)c; |
90 | field *f = c->f; |
91 | |
92 | q = F_SQR(f, MP_NEW, x); |
93 | p = F_MUL(f, MP_NEW, x, q); |
94 | q = F_MUL(f, q, x, cc->a); |
95 | p = F_ADD(f, p, p, q); |
96 | p = F_ADD(f, p, p, cc->b); |
97 | MP_DROP(q); |
98 | p = F_SQRT(f, p, p); |
99 | if (!p) |
100 | return (0); |
101 | EC_DESTROY(d); |
102 | d->x = MP_COPY(x); |
103 | d->y = p; |
104 | d->z = MP_COPY(f->one); |
b085fd91 |
105 | return (d); |
106 | } |
107 | |
108 | static ec *ecdbl(ec_curve *c, ec *d, const ec *a) |
b0ab12e6 |
109 | { |
b085fd91 |
110 | if (EC_ATINF(a)) |
111 | EC_SETINF(d); |
8823192f |
112 | else if (F_ZEROP(c->f, a->y)) |
b085fd91 |
113 | EC_COPY(d, a); |
114 | else { |
115 | field *f = c->f; |
116 | ecctx *cc = (ecctx *)c; |
117 | mp *lambda; |
118 | mp *dy, *dx; |
119 | |
8823192f |
120 | dx = F_SQR(f, MP_NEW, a->x); /* %$x^2$% */ |
121 | dy = F_DBL(f, MP_NEW, a->y); /* %$2 y$% */ |
122 | dx = F_TPL(f, dx, dx); /* %$3 x^2$% */ |
123 | dx = F_ADD(f, dx, dx, cc->a); /* %$3 x^2 + A$% */ |
124 | dy = F_INV(f, dy, dy); /* %$(2 y)^{-1}$% */ |
125 | lambda = F_MUL(f, MP_NEW, dx, dy); /* %$\lambda = (3 x^2 + A)/(2 y)$% */ |
b085fd91 |
126 | |
8823192f |
127 | dx = F_SQR(f, dx, lambda); /* %$\lambda^2$% */ |
128 | dy = F_DBL(f, dy, a->x); /* %$2 x$% */ |
129 | dx = F_SUB(f, dx, dx, dy); /* %$x' = \lambda^2 - 2 x */ |
130 | dy = F_SUB(f, dy, a->x, dx); /* %$x - x'$% */ |
131 | dy = F_MUL(f, dy, lambda, dy); /* %$\lambda (x - x')$% */ |
132 | dy = F_SUB(f, dy, dy, a->y); /* %$y' = \lambda (x - x') - y$% */ |
b0ab12e6 |
133 | |
b085fd91 |
134 | EC_DESTROY(d); |
135 | d->x = dx; |
136 | d->y = dy; |
137 | d->z = 0; |
138 | MP_DROP(lambda); |
139 | } |
140 | return (d); |
141 | } |
142 | |
8823192f |
143 | static ec *ecprojdbl(ec_curve *c, ec *d, const ec *a) |
144 | { |
145 | if (EC_ATINF(a)) |
146 | EC_SETINF(d); |
147 | else if (F_ZEROP(c->f, a->y)) |
148 | EC_COPY(d, a); |
149 | else { |
150 | field *f = c->f; |
151 | ecctx *cc = (ecctx *)c; |
152 | mp *p, *q, *m, *s, *dx, *dy, *dz; |
153 | |
154 | p = F_SQR(f, MP_NEW, a->z); /* %$z^2$% */ |
155 | q = F_SQR(f, MP_NEW, p); /* %$z^4$% */ |
156 | p = F_MUL(f, p, q, cc->a); /* %$A z^4$% */ |
157 | m = F_SQR(f, MP_NEW, a->x); /* %$x^2$% */ |
158 | m = F_TPL(f, m, m); /* %$3 x^2$% */ |
159 | m = F_ADD(f, m, m, p); /* %$m = 3 x^2 + A z^4$% */ |
160 | |
161 | q = F_DBL(f, q, a->y); /* %$2 y$% */ |
162 | dz = F_MUL(f, MP_NEW, q, a->z); /* %$z' = 2 y z$% */ |
163 | |
164 | p = F_SQR(f, p, q); /* %$4 y^2$% */ |
165 | s = F_MUL(f, MP_NEW, p, a->x); /* %$s = 4 x y^2$% */ |
166 | q = F_SQR(f, q, p); /* %$16 y^4$% */ |
167 | q = F_HLV(f, q, q); /* %$t = 8 y^4$% */ |
168 | |
169 | p = F_DBL(f, p, s); /* %$2 s$% */ |
170 | dx = F_SQR(f, MP_NEW, m); /* %$m^2$% */ |
171 | dx = F_SUB(f, dx, dx, p); /* %$x' = m^2 - 2 s$% */ |
172 | |
173 | s = F_SUB(f, s, s, dx); /* %$s - x'$% */ |
174 | dy = F_MUL(f, p, m, s); /* %$m (s - x')$% */ |
175 | dy = F_SUB(f, dy, dy, q); /* %$y' = m (s - x') - t$% */ |
176 | |
177 | EC_DESTROY(d); |
178 | d->x = dx; |
179 | d->y = dy; |
180 | d->z = dz; |
181 | MP_DROP(m); |
182 | MP_DROP(q); |
183 | MP_DROP(s); |
184 | } |
185 | return (d); |
186 | } |
187 | |
188 | static ec *ecprojxdbl(ec_curve *c, ec *d, const ec *a) |
189 | { |
190 | if (EC_ATINF(a)) |
191 | EC_SETINF(d); |
192 | else if (F_ZEROP(c->f, a->y)) |
193 | EC_COPY(d, a); |
194 | else { |
195 | field *f = c->f; |
196 | mp *p, *q, *m, *s, *dx, *dy, *dz; |
197 | |
198 | m = F_SQR(f, MP_NEW, a->z); /* %$z^2$% */ |
199 | p = F_SUB(f, MP_NEW, a->x, m); /* %$x - z^2$% */ |
200 | q = F_ADD(f, MP_NEW, a->x, m); /* %$x + z^2$% */ |
201 | m = F_MUL(f, m, p, q); /* %$x^2 - z^4$% */ |
202 | m = F_TPL(f, m, m); /* %$m = 3 x^2 - 3 z^4$% */ |
203 | |
204 | q = F_DBL(f, q, a->y); /* %$2 y$% */ |
205 | dz = F_MUL(f, MP_NEW, q, a->z); /* %$z' = 2 y z$% */ |
206 | |
207 | p = F_SQR(f, p, q); /* %$4 y^2$% */ |
208 | s = F_MUL(f, MP_NEW, p, a->x); /* %$s = 4 x y^2$% */ |
209 | q = F_SQR(f, q, p); /* %$16 y^4$% */ |
210 | q = F_HLV(f, q, q); /* %$t = 8 y^4$% */ |
211 | |
212 | p = F_DBL(f, p, s); /* %$2 s$% */ |
213 | dx = F_SQR(f, MP_NEW, m); /* %$m^2$% */ |
214 | dx = F_SUB(f, dx, dx, p); /* %$x' = m^2 - 2 s$% */ |
215 | |
216 | s = F_SUB(f, s, s, dx); /* %$s - x'$% */ |
217 | dy = F_MUL(f, p, m, s); /* %$m (s - x')$% */ |
218 | dy = F_SUB(f, dy, dy, q); /* %$y' = m (s - x') - t$% */ |
219 | |
220 | EC_DESTROY(d); |
221 | d->x = dx; |
222 | d->y = dy; |
223 | d->z = dz; |
224 | MP_DROP(m); |
225 | MP_DROP(q); |
226 | MP_DROP(s); |
227 | } |
228 | return (d); |
229 | } |
230 | |
b085fd91 |
231 | static ec *ecadd(ec_curve *c, ec *d, const ec *a, const ec *b) |
232 | { |
b0ab12e6 |
233 | if (a == b) |
234 | ecdbl(c, d, a); |
235 | else if (EC_ATINF(a)) |
236 | EC_COPY(d, b); |
237 | else if (EC_ATINF(b)) |
238 | EC_COPY(d, a); |
b085fd91 |
239 | else { |
240 | field *f = c->f; |
241 | mp *lambda; |
242 | mp *dy, *dx; |
243 | |
244 | if (!MP_EQ(a->x, b->x)) { |
8823192f |
245 | dy = F_SUB(f, MP_NEW, a->y, b->y); /* %$y_0 - y_1$% */ |
246 | dx = F_SUB(f, MP_NEW, a->x, b->x); /* %$x_0 - x_1$% */ |
247 | dx = F_INV(f, dx, dx); /* %$(x_0 - x_1)^{-1}$% */ |
b085fd91 |
248 | lambda = F_MUL(f, MP_NEW, dy, dx); |
8823192f |
249 | /* %$\lambda = (y_0 - y1)/(x_0 - x_1)$% */ |
250 | } else if (F_ZEROP(c->f, a->y) || !MP_EQ(a->y, b->y)) { |
b0ab12e6 |
251 | EC_SETINF(d); |
b085fd91 |
252 | return (d); |
253 | } else { |
254 | ecctx *cc = (ecctx *)c; |
8823192f |
255 | dx = F_SQR(f, MP_NEW, a->x); /* %$x_0^2$% */ |
256 | dx = F_TPL(f, dx, dx); /* %$3 x_0^2$% */ |
257 | dx = F_ADD(f, dx, dx, cc->a); /* %$3 x_0^2 + A$% */ |
258 | dy = F_DBL(f, MP_NEW, a->y); /* %$2 y_0$% */ |
259 | dy = F_INV(f, dy, dy); /* %$(2 y_0)^{-1}$% */ |
41cb1beb |
260 | lambda = F_MUL(f, MP_NEW, dx, dy); |
8823192f |
261 | /* %$\lambda = (3 x_0^2 + A)/(2 y_0)$% */ |
b085fd91 |
262 | } |
263 | |
8823192f |
264 | dx = F_SQR(f, dx, lambda); /* %$\lambda^2$% */ |
265 | dx = F_SUB(f, dx, dx, a->x); /* %$\lambda^2 - x_0$% */ |
266 | dx = F_SUB(f, dx, dx, b->x); /* %$x' = \lambda^2 - x_0 - x_1$% */ |
267 | dy = F_SUB(f, dy, b->x, dx); /* %$x_1 - x'$% */ |
268 | dy = F_MUL(f, dy, lambda, dy); /* %$\lambda (x_1 - x')$% */ |
ceb3f0c0 |
269 | dy = F_SUB(f, dy, dy, b->y); /* %$y' = \lambda (x_1 - x') - y_1$% */ |
b0ab12e6 |
270 | |
b085fd91 |
271 | EC_DESTROY(d); |
272 | d->x = dx; |
273 | d->y = dy; |
274 | d->z = 0; |
275 | MP_DROP(lambda); |
b0ab12e6 |
276 | } |
b085fd91 |
277 | return (d); |
b0ab12e6 |
278 | } |
279 | |
8823192f |
280 | static ec *ecprojadd(ec_curve *c, ec *d, const ec *a, const ec *b) |
281 | { |
282 | if (a == b) |
283 | c->ops->dbl(c, d, a); |
284 | else if (EC_ATINF(a)) |
285 | EC_COPY(d, b); |
286 | else if (EC_ATINF(b)) |
287 | EC_COPY(d, a); |
288 | else { |
289 | field *f = c->f; |
391faf42 |
290 | mp *p, *q, *r, *w, *u, *uu, *s, *ss, *dx, *dy, *dz; |
8823192f |
291 | |
292 | q = F_SQR(f, MP_NEW, a->z); /* %$z_0^2$% */ |
293 | u = F_MUL(f, MP_NEW, q, b->x); /* %$u = x_1 z_0^2$% */ |
294 | p = F_MUL(f, MP_NEW, q, b->y); /* %$y_1 z_0^2$% */ |
295 | s = F_MUL(f, q, p, a->z); /* %$s = y_1 z_0^3$% */ |
296 | |
391faf42 |
297 | q = F_SQR(f, MP_NEW, b->z); /* %$z_1^2$% */ |
298 | uu = F_MUL(f, MP_NEW, q, a->x); /* %$uu = x_0 z_1^2$%*/ |
299 | p = F_MUL(f, p, q, a->y); /* %$y_0 z_1^2$% */ |
300 | ss = F_MUL(f, q, p, b->z); /* %$ss = y_0 z_1^3$% */ |
301 | |
302 | w = F_SUB(f, p, uu, u); /* %$w = uu - u$% */ |
303 | r = F_SUB(f, MP_NEW, ss, s); /* %$r = ss - s$% */ |
8823192f |
304 | if (F_ZEROP(f, w)) { |
ceb3f0c0 |
305 | MP_DROP(w); |
306 | MP_DROP(u); |
307 | MP_DROP(s); |
391faf42 |
308 | MP_DROP(uu); |
309 | MP_DROP(ss); |
8823192f |
310 | if (F_ZEROP(f, r)) { |
8823192f |
311 | MP_DROP(r); |
8823192f |
312 | return (c->ops->dbl(c, d, a)); |
313 | } else { |
8823192f |
314 | MP_DROP(r); |
8823192f |
315 | EC_SETINF(d); |
316 | return (d); |
317 | } |
318 | } |
391faf42 |
319 | u = F_ADD(f, u, u, uu); /* %$t = uu + u$% */ |
320 | s = F_ADD(f, s, s, ss); /* %$m = ss + r$% */ |
8823192f |
321 | |
391faf42 |
322 | uu = F_MUL(f, uu, a->z, w); /* %$z_0 w$% */ |
323 | dz = F_MUL(f, ss, uu, b->z); /* %$z' = z_0 z_1 w$% */ |
8823192f |
324 | |
391faf42 |
325 | p = F_SQR(f, uu, w); /* %$w^2$% */ |
8823192f |
326 | q = F_MUL(f, MP_NEW, p, u); /* %$t w^2$% */ |
327 | u = F_MUL(f, u, p, w); /* %$w^3$% */ |
328 | p = F_MUL(f, p, u, s); /* %$m w^3$% */ |
329 | |
330 | dx = F_SQR(f, u, r); /* %$r^2$% */ |
331 | dx = F_SUB(f, dx, dx, q); /* %$x' = r^2 - t w^2$% */ |
332 | |
333 | s = F_DBL(f, s, dx); /* %$2 x'$% */ |
334 | q = F_SUB(f, q, q, s); /* %$v = t w^2 - 2 x'$% */ |
335 | dy = F_MUL(f, s, q, r); /* %$v r$% */ |
336 | dy = F_SUB(f, dy, dy, p); /* %$v r - m w^3$% */ |
337 | dy = F_HLV(f, dy, dy); /* %$y' = (v r - m w^3)/2$% */ |
338 | |
339 | EC_DESTROY(d); |
340 | d->x = dx; |
341 | d->y = dy; |
342 | d->z = dz; |
343 | MP_DROP(p); |
344 | MP_DROP(q); |
345 | MP_DROP(r); |
346 | MP_DROP(w); |
347 | } |
348 | return (d); |
349 | } |
350 | |
351 | static int eccheck(ec_curve *c, const ec *p) |
352 | { |
353 | ecctx *cc = (ecctx *)c; |
354 | field *f = c->f; |
355 | int rc; |
356 | mp *l = F_SQR(f, MP_NEW, p->y); |
357 | mp *x = F_SQR(f, MP_NEW, p->x); |
358 | mp *r = F_MUL(f, MP_NEW, x, p->x); |
359 | x = F_MUL(f, x, cc->a, p->x); |
360 | r = F_ADD(f, r, r, x); |
361 | r = F_ADD(f, r, r, cc->b); |
362 | rc = MP_EQ(l, r) ? 0 : -1; |
363 | mp_drop(l); |
364 | mp_drop(x); |
365 | mp_drop(r); |
366 | return (rc); |
367 | } |
368 | |
369 | static int ecprojcheck(ec_curve *c, const ec *p) |
370 | { |
371 | ec t = EC_INIT; |
372 | int rc; |
373 | |
374 | c->ops->fix(c, &t, p); |
375 | rc = eccheck(c, &t); |
376 | EC_DESTROY(&t); |
377 | return (rc); |
378 | } |
379 | |
41cb1beb |
380 | static void ecdestroy(ec_curve *c) |
381 | { |
382 | ecctx *cc = (ecctx *)c; |
383 | MP_DROP(cc->a); |
384 | MP_DROP(cc->b); |
385 | DESTROY(cc); |
386 | } |
387 | |
388 | /* --- @ec_prime@, @ec_primeproj@ --- * |
389 | * |
dbfee00a |
390 | * Arguments: @field *f@ = the underlying field for this elliptic curve |
41cb1beb |
391 | * @mp *a, *b@ = the coefficients for this curve |
392 | * |
393 | * Returns: A pointer to the curve. |
394 | * |
395 | * Use: Creates a curve structure for an elliptic curve defined over |
396 | * a prime field. The @primeproj@ variant uses projective |
397 | * coordinates, which can be a win. |
398 | */ |
399 | |
400 | extern ec_curve *ec_prime(field *f, mp *a, mp *b) |
401 | { |
402 | ecctx *cc = CREATE(ecctx); |
403 | cc->c.ops = &ec_primeops; |
404 | cc->c.f = f; |
dbfee00a |
405 | cc->a = F_IN(f, MP_NEW, a); |
406 | cc->b = F_IN(f, MP_NEW, b); |
41cb1beb |
407 | return (&cc->c); |
408 | } |
409 | |
8823192f |
410 | extern ec_curve *ec_primeproj(field *f, mp *a, mp *b) |
411 | { |
412 | ecctx *cc = CREATE(ecctx); |
413 | mp *ax; |
414 | |
415 | ax = mp_add(MP_NEW, a, MP_THREE); |
416 | ax = F_IN(f, ax, ax); |
417 | if (F_ZEROP(f, ax)) |
418 | cc->c.ops = &ec_primeprojxops; |
419 | else |
420 | cc->c.ops = &ec_primeprojops; |
421 | MP_DROP(ax); |
422 | cc->c.f = f; |
423 | cc->a = F_IN(f, MP_NEW, a); |
424 | cc->b = F_IN(f, MP_NEW, b); |
41cb1beb |
425 | return (&cc->c); |
426 | } |
427 | |
428 | static const ec_ops ec_primeops = { |
8823192f |
429 | ecdestroy, ec_idin, ec_idout, ec_idfix, |
430 | 0, ecneg, ecadd, ec_stdsub, ecdbl, eccheck |
431 | }; |
432 | |
433 | static const ec_ops ec_primeprojops = { |
434 | ecdestroy, ec_projin, ec_projout, ec_projfix, |
435 | 0, ecneg, ecprojadd, ec_stdsub, ecprojdbl, ecprojcheck |
436 | }; |
437 | |
438 | static const ec_ops ec_primeprojxops = { |
439 | ecdestroy, ec_projin, ec_projout, ec_projfix, |
440 | 0, ecneg, ecprojadd, ec_stdsub, ecprojxdbl, ecprojcheck |
41cb1beb |
441 | }; |
442 | |
443 | /*----- Test rig ----------------------------------------------------------*/ |
444 | |
445 | #ifdef TEST_RIG |
446 | |
447 | #define MP(x) mp_readstring(MP_NEW, #x, 0, 0) |
448 | |
ceb3f0c0 |
449 | int main(int argc, char *argv[]) |
41cb1beb |
450 | { |
451 | field *f; |
452 | ec_curve *c; |
453 | ec g = EC_INIT, d = EC_INIT; |
454 | mp *p, *a, *b, *r; |
ceb3f0c0 |
455 | int i, n = argc == 1 ? 1 : atoi(argv[1]); |
41cb1beb |
456 | |
dbfee00a |
457 | printf("ec-prime: "); |
458 | fflush(stdout); |
41cb1beb |
459 | a = MP(-3); |
460 | b = MP(0x64210519e59c80e70fa7e9ab72243049feb8deecc146b9b1); |
461 | p = MP(6277101735386680763835789423207666416083908700390324961279); |
dbfee00a |
462 | r = MP(6277101735386680763835789423176059013767194773182842284080); |
41cb1beb |
463 | |
464 | f = field_prime(p); |
ceb3f0c0 |
465 | c = ec_primeproj(f, a, b); |
41cb1beb |
466 | |
467 | g.x = MP(0x188da80eb03090f67cbf20eb43a18800f4ff0afd82ff1012); |
468 | g.y = MP(0x07192b95ffc8da78631011ed6b24cdd573f977a11e794811); |
469 | |
ceb3f0c0 |
470 | for (i = 0; i < n; i++) { |
471 | ec_mul(c, &d, &g, r); |
472 | if (EC_ATINF(&d)) { |
473 | fprintf(stderr, "zero too early\n"); |
474 | return (1); |
475 | } |
476 | ec_add(c, &d, &d, &g); |
477 | if (!EC_ATINF(&d)) { |
478 | fprintf(stderr, "didn't reach zero\n"); |
479 | MP_EPRINT("d.x", d.x); |
480 | MP_EPRINT("d.y", d.y); |
481 | return (1); |
482 | } |
483 | ec_destroy(&d); |
dbfee00a |
484 | } |
41cb1beb |
485 | ec_destroy(&g); |
486 | ec_destroycurve(c); |
487 | F_DESTROY(f); |
dbfee00a |
488 | MP_DROP(p); MP_DROP(a); MP_DROP(b); MP_DROP(r); |
489 | assert(!mparena_count(&mparena_global)); |
490 | printf("ok\n"); |
41cb1beb |
491 | return (0); |
492 | } |
493 | |
494 | #endif |
495 | |
b0ab12e6 |
496 | /*----- That's all, folks -------------------------------------------------*/ |