b0ab12e6 |
1 | /* -*-c-*- |
2 | * |
f46efa79 |
3 | * $Id: ec-prime.c,v 1.7 2004/03/27 00:04:46 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 $ |
f46efa79 |
33 | * Revision 1.7 2004/03/27 00:04:46 mdw |
34 | * Implement efficient reduction for pleasant-looking primes. |
35 | * |
bc985cef |
36 | * Revision 1.6 2004/03/23 15:19:32 mdw |
37 | * Test elliptic curves more thoroughly. |
38 | * |
391faf42 |
39 | * Revision 1.5 2004/03/22 02:19:10 mdw |
40 | * Rationalise the sliding-window threshold. Drop guarantee that right |
41 | * arguments to EC @add@ are canonical, and fix up projective implementations |
42 | * to cope. |
43 | * |
c3caa2fa |
44 | * Revision 1.4 2004/03/21 22:52:06 mdw |
45 | * Merge and close elliptic curve branch. |
46 | * |
ceb3f0c0 |
47 | * Revision 1.3.4.3 2004/03/21 22:39:46 mdw |
48 | * Elliptic curves on binary fields work. |
49 | * |
8823192f |
50 | * Revision 1.3.4.2 2004/03/20 00:13:31 mdw |
51 | * Projective coordinates for prime curves |
52 | * |
dbfee00a |
53 | * Revision 1.3.4.1 2003/06/10 13:43:53 mdw |
54 | * Simple (non-projective) curves over prime fields now seem to work. |
55 | * |
41cb1beb |
56 | * Revision 1.3 2003/05/15 23:25:59 mdw |
57 | * Make elliptic curve stuff build. |
58 | * |
b085fd91 |
59 | * Revision 1.2 2002/01/13 13:48:44 mdw |
60 | * Further progress. |
61 | * |
b0ab12e6 |
62 | * Revision 1.1 2001/04/29 18:12:33 mdw |
63 | * Prototype version. |
64 | * |
65 | */ |
66 | |
67 | /*----- Header files ------------------------------------------------------*/ |
68 | |
41cb1beb |
69 | #include <mLib/sub.h> |
70 | |
b0ab12e6 |
71 | #include "ec.h" |
72 | |
73 | /*----- Data structures ---------------------------------------------------*/ |
74 | |
75 | typedef struct ecctx { |
76 | ec_curve c; |
77 | mp *a, *b; |
78 | } ecctx; |
79 | |
dbfee00a |
80 | /*----- Simple prime curves -----------------------------------------------*/ |
b0ab12e6 |
81 | |
8823192f |
82 | static const ec_ops ec_primeops, ec_primeprojops, ec_primeprojxops; |
41cb1beb |
83 | |
84 | static ec *ecneg(ec_curve *c, ec *d, const ec *p) |
b085fd91 |
85 | { |
86 | EC_COPY(d, p); |
ceb3f0c0 |
87 | if (d->y) |
88 | d->y = F_NEG(c->f, d->y, d->y); |
b085fd91 |
89 | return (d); |
90 | } |
91 | |
8823192f |
92 | static ec *ecfind(ec_curve *c, ec *d, mp *x) |
93 | { |
94 | mp *p, *q; |
95 | ecctx *cc = (ecctx *)c; |
96 | field *f = c->f; |
97 | |
98 | q = F_SQR(f, MP_NEW, x); |
99 | p = F_MUL(f, MP_NEW, x, q); |
100 | q = F_MUL(f, q, x, cc->a); |
101 | p = F_ADD(f, p, p, q); |
102 | p = F_ADD(f, p, p, cc->b); |
103 | MP_DROP(q); |
104 | p = F_SQRT(f, p, p); |
105 | if (!p) |
106 | return (0); |
107 | EC_DESTROY(d); |
108 | d->x = MP_COPY(x); |
109 | d->y = p; |
110 | d->z = MP_COPY(f->one); |
b085fd91 |
111 | return (d); |
112 | } |
113 | |
114 | static ec *ecdbl(ec_curve *c, ec *d, const ec *a) |
b0ab12e6 |
115 | { |
b085fd91 |
116 | if (EC_ATINF(a)) |
117 | EC_SETINF(d); |
8823192f |
118 | else if (F_ZEROP(c->f, a->y)) |
b085fd91 |
119 | EC_COPY(d, a); |
120 | else { |
121 | field *f = c->f; |
122 | ecctx *cc = (ecctx *)c; |
123 | mp *lambda; |
124 | mp *dy, *dx; |
125 | |
8823192f |
126 | dx = F_SQR(f, MP_NEW, a->x); /* %$x^2$% */ |
127 | dy = F_DBL(f, MP_NEW, a->y); /* %$2 y$% */ |
128 | dx = F_TPL(f, dx, dx); /* %$3 x^2$% */ |
129 | dx = F_ADD(f, dx, dx, cc->a); /* %$3 x^2 + A$% */ |
130 | dy = F_INV(f, dy, dy); /* %$(2 y)^{-1}$% */ |
131 | lambda = F_MUL(f, MP_NEW, dx, dy); /* %$\lambda = (3 x^2 + A)/(2 y)$% */ |
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132 | |
8823192f |
133 | dx = F_SQR(f, dx, lambda); /* %$\lambda^2$% */ |
134 | dy = F_DBL(f, dy, a->x); /* %$2 x$% */ |
135 | dx = F_SUB(f, dx, dx, dy); /* %$x' = \lambda^2 - 2 x */ |
136 | dy = F_SUB(f, dy, a->x, dx); /* %$x - x'$% */ |
137 | dy = F_MUL(f, dy, lambda, dy); /* %$\lambda (x - x')$% */ |
138 | dy = F_SUB(f, dy, dy, a->y); /* %$y' = \lambda (x - x') - y$% */ |
b0ab12e6 |
139 | |
b085fd91 |
140 | EC_DESTROY(d); |
141 | d->x = dx; |
142 | d->y = dy; |
143 | d->z = 0; |
144 | MP_DROP(lambda); |
145 | } |
146 | return (d); |
147 | } |
148 | |
8823192f |
149 | static ec *ecprojdbl(ec_curve *c, ec *d, const ec *a) |
150 | { |
151 | if (EC_ATINF(a)) |
152 | EC_SETINF(d); |
153 | else if (F_ZEROP(c->f, a->y)) |
154 | EC_COPY(d, a); |
155 | else { |
156 | field *f = c->f; |
157 | ecctx *cc = (ecctx *)c; |
158 | mp *p, *q, *m, *s, *dx, *dy, *dz; |
159 | |
160 | p = F_SQR(f, MP_NEW, a->z); /* %$z^2$% */ |
161 | q = F_SQR(f, MP_NEW, p); /* %$z^4$% */ |
162 | p = F_MUL(f, p, q, cc->a); /* %$A z^4$% */ |
163 | m = F_SQR(f, MP_NEW, a->x); /* %$x^2$% */ |
164 | m = F_TPL(f, m, m); /* %$3 x^2$% */ |
165 | m = F_ADD(f, m, m, p); /* %$m = 3 x^2 + A z^4$% */ |
166 | |
167 | q = F_DBL(f, q, a->y); /* %$2 y$% */ |
168 | dz = F_MUL(f, MP_NEW, q, a->z); /* %$z' = 2 y z$% */ |
169 | |
170 | p = F_SQR(f, p, q); /* %$4 y^2$% */ |
171 | s = F_MUL(f, MP_NEW, p, a->x); /* %$s = 4 x y^2$% */ |
172 | q = F_SQR(f, q, p); /* %$16 y^4$% */ |
173 | q = F_HLV(f, q, q); /* %$t = 8 y^4$% */ |
174 | |
175 | p = F_DBL(f, p, s); /* %$2 s$% */ |
176 | dx = F_SQR(f, MP_NEW, m); /* %$m^2$% */ |
177 | dx = F_SUB(f, dx, dx, p); /* %$x' = m^2 - 2 s$% */ |
178 | |
179 | s = F_SUB(f, s, s, dx); /* %$s - x'$% */ |
180 | dy = F_MUL(f, p, m, s); /* %$m (s - x')$% */ |
181 | dy = F_SUB(f, dy, dy, q); /* %$y' = m (s - x') - t$% */ |
182 | |
183 | EC_DESTROY(d); |
184 | d->x = dx; |
185 | d->y = dy; |
186 | d->z = dz; |
187 | MP_DROP(m); |
188 | MP_DROP(q); |
189 | MP_DROP(s); |
190 | } |
191 | return (d); |
192 | } |
193 | |
194 | static ec *ecprojxdbl(ec_curve *c, ec *d, const ec *a) |
195 | { |
196 | if (EC_ATINF(a)) |
197 | EC_SETINF(d); |
198 | else if (F_ZEROP(c->f, a->y)) |
199 | EC_COPY(d, a); |
200 | else { |
201 | field *f = c->f; |
202 | mp *p, *q, *m, *s, *dx, *dy, *dz; |
203 | |
204 | m = F_SQR(f, MP_NEW, a->z); /* %$z^2$% */ |
205 | p = F_SUB(f, MP_NEW, a->x, m); /* %$x - z^2$% */ |
206 | q = F_ADD(f, MP_NEW, a->x, m); /* %$x + z^2$% */ |
207 | m = F_MUL(f, m, p, q); /* %$x^2 - z^4$% */ |
208 | m = F_TPL(f, m, m); /* %$m = 3 x^2 - 3 z^4$% */ |
209 | |
210 | q = F_DBL(f, q, a->y); /* %$2 y$% */ |
211 | dz = F_MUL(f, MP_NEW, q, a->z); /* %$z' = 2 y z$% */ |
212 | |
213 | p = F_SQR(f, p, q); /* %$4 y^2$% */ |
214 | s = F_MUL(f, MP_NEW, p, a->x); /* %$s = 4 x y^2$% */ |
215 | q = F_SQR(f, q, p); /* %$16 y^4$% */ |
216 | q = F_HLV(f, q, q); /* %$t = 8 y^4$% */ |
217 | |
218 | p = F_DBL(f, p, s); /* %$2 s$% */ |
219 | dx = F_SQR(f, MP_NEW, m); /* %$m^2$% */ |
220 | dx = F_SUB(f, dx, dx, p); /* %$x' = m^2 - 2 s$% */ |
221 | |
222 | s = F_SUB(f, s, s, dx); /* %$s - x'$% */ |
223 | dy = F_MUL(f, p, m, s); /* %$m (s - x')$% */ |
224 | dy = F_SUB(f, dy, dy, q); /* %$y' = m (s - x') - t$% */ |
225 | |
226 | EC_DESTROY(d); |
227 | d->x = dx; |
228 | d->y = dy; |
229 | d->z = dz; |
230 | MP_DROP(m); |
231 | MP_DROP(q); |
232 | MP_DROP(s); |
233 | } |
234 | return (d); |
235 | } |
236 | |
b085fd91 |
237 | static ec *ecadd(ec_curve *c, ec *d, const ec *a, const ec *b) |
238 | { |
b0ab12e6 |
239 | if (a == b) |
240 | ecdbl(c, d, a); |
241 | else if (EC_ATINF(a)) |
242 | EC_COPY(d, b); |
243 | else if (EC_ATINF(b)) |
244 | EC_COPY(d, a); |
b085fd91 |
245 | else { |
246 | field *f = c->f; |
247 | mp *lambda; |
248 | mp *dy, *dx; |
249 | |
250 | if (!MP_EQ(a->x, b->x)) { |
8823192f |
251 | dy = F_SUB(f, MP_NEW, a->y, b->y); /* %$y_0 - y_1$% */ |
252 | dx = F_SUB(f, MP_NEW, a->x, b->x); /* %$x_0 - x_1$% */ |
253 | dx = F_INV(f, dx, dx); /* %$(x_0 - x_1)^{-1}$% */ |
b085fd91 |
254 | lambda = F_MUL(f, MP_NEW, dy, dx); |
8823192f |
255 | /* %$\lambda = (y_0 - y1)/(x_0 - x_1)$% */ |
256 | } else if (F_ZEROP(c->f, a->y) || !MP_EQ(a->y, b->y)) { |
b0ab12e6 |
257 | EC_SETINF(d); |
b085fd91 |
258 | return (d); |
259 | } else { |
260 | ecctx *cc = (ecctx *)c; |
8823192f |
261 | dx = F_SQR(f, MP_NEW, a->x); /* %$x_0^2$% */ |
262 | dx = F_TPL(f, dx, dx); /* %$3 x_0^2$% */ |
263 | dx = F_ADD(f, dx, dx, cc->a); /* %$3 x_0^2 + A$% */ |
264 | dy = F_DBL(f, MP_NEW, a->y); /* %$2 y_0$% */ |
265 | dy = F_INV(f, dy, dy); /* %$(2 y_0)^{-1}$% */ |
41cb1beb |
266 | lambda = F_MUL(f, MP_NEW, dx, dy); |
8823192f |
267 | /* %$\lambda = (3 x_0^2 + A)/(2 y_0)$% */ |
b085fd91 |
268 | } |
269 | |
8823192f |
270 | dx = F_SQR(f, dx, lambda); /* %$\lambda^2$% */ |
271 | dx = F_SUB(f, dx, dx, a->x); /* %$\lambda^2 - x_0$% */ |
272 | dx = F_SUB(f, dx, dx, b->x); /* %$x' = \lambda^2 - x_0 - x_1$% */ |
273 | dy = F_SUB(f, dy, b->x, dx); /* %$x_1 - x'$% */ |
274 | dy = F_MUL(f, dy, lambda, dy); /* %$\lambda (x_1 - x')$% */ |
ceb3f0c0 |
275 | dy = F_SUB(f, dy, dy, b->y); /* %$y' = \lambda (x_1 - x') - y_1$% */ |
b0ab12e6 |
276 | |
b085fd91 |
277 | EC_DESTROY(d); |
278 | d->x = dx; |
279 | d->y = dy; |
280 | d->z = 0; |
281 | MP_DROP(lambda); |
b0ab12e6 |
282 | } |
b085fd91 |
283 | return (d); |
b0ab12e6 |
284 | } |
285 | |
8823192f |
286 | static ec *ecprojadd(ec_curve *c, ec *d, const ec *a, const ec *b) |
287 | { |
288 | if (a == b) |
289 | c->ops->dbl(c, d, a); |
290 | else if (EC_ATINF(a)) |
291 | EC_COPY(d, b); |
292 | else if (EC_ATINF(b)) |
293 | EC_COPY(d, a); |
294 | else { |
295 | field *f = c->f; |
391faf42 |
296 | mp *p, *q, *r, *w, *u, *uu, *s, *ss, *dx, *dy, *dz; |
8823192f |
297 | |
298 | q = F_SQR(f, MP_NEW, a->z); /* %$z_0^2$% */ |
299 | u = F_MUL(f, MP_NEW, q, b->x); /* %$u = x_1 z_0^2$% */ |
300 | p = F_MUL(f, MP_NEW, q, b->y); /* %$y_1 z_0^2$% */ |
301 | s = F_MUL(f, q, p, a->z); /* %$s = y_1 z_0^3$% */ |
302 | |
391faf42 |
303 | q = F_SQR(f, MP_NEW, b->z); /* %$z_1^2$% */ |
304 | uu = F_MUL(f, MP_NEW, q, a->x); /* %$uu = x_0 z_1^2$%*/ |
305 | p = F_MUL(f, p, q, a->y); /* %$y_0 z_1^2$% */ |
306 | ss = F_MUL(f, q, p, b->z); /* %$ss = y_0 z_1^3$% */ |
307 | |
308 | w = F_SUB(f, p, uu, u); /* %$w = uu - u$% */ |
309 | r = F_SUB(f, MP_NEW, ss, s); /* %$r = ss - s$% */ |
8823192f |
310 | if (F_ZEROP(f, w)) { |
ceb3f0c0 |
311 | MP_DROP(w); |
312 | MP_DROP(u); |
313 | MP_DROP(s); |
391faf42 |
314 | MP_DROP(uu); |
315 | MP_DROP(ss); |
8823192f |
316 | if (F_ZEROP(f, r)) { |
8823192f |
317 | MP_DROP(r); |
8823192f |
318 | return (c->ops->dbl(c, d, a)); |
319 | } else { |
8823192f |
320 | MP_DROP(r); |
8823192f |
321 | EC_SETINF(d); |
322 | return (d); |
323 | } |
324 | } |
391faf42 |
325 | u = F_ADD(f, u, u, uu); /* %$t = uu + u$% */ |
326 | s = F_ADD(f, s, s, ss); /* %$m = ss + r$% */ |
8823192f |
327 | |
391faf42 |
328 | uu = F_MUL(f, uu, a->z, w); /* %$z_0 w$% */ |
329 | dz = F_MUL(f, ss, uu, b->z); /* %$z' = z_0 z_1 w$% */ |
8823192f |
330 | |
391faf42 |
331 | p = F_SQR(f, uu, w); /* %$w^2$% */ |
8823192f |
332 | q = F_MUL(f, MP_NEW, p, u); /* %$t w^2$% */ |
333 | u = F_MUL(f, u, p, w); /* %$w^3$% */ |
334 | p = F_MUL(f, p, u, s); /* %$m w^3$% */ |
335 | |
336 | dx = F_SQR(f, u, r); /* %$r^2$% */ |
337 | dx = F_SUB(f, dx, dx, q); /* %$x' = r^2 - t w^2$% */ |
338 | |
339 | s = F_DBL(f, s, dx); /* %$2 x'$% */ |
340 | q = F_SUB(f, q, q, s); /* %$v = t w^2 - 2 x'$% */ |
341 | dy = F_MUL(f, s, q, r); /* %$v r$% */ |
342 | dy = F_SUB(f, dy, dy, p); /* %$v r - m w^3$% */ |
343 | dy = F_HLV(f, dy, dy); /* %$y' = (v r - m w^3)/2$% */ |
344 | |
345 | EC_DESTROY(d); |
346 | d->x = dx; |
347 | d->y = dy; |
348 | d->z = dz; |
349 | MP_DROP(p); |
350 | MP_DROP(q); |
351 | MP_DROP(r); |
352 | MP_DROP(w); |
353 | } |
354 | return (d); |
355 | } |
356 | |
357 | static int eccheck(ec_curve *c, const ec *p) |
358 | { |
359 | ecctx *cc = (ecctx *)c; |
360 | field *f = c->f; |
361 | int rc; |
362 | mp *l = F_SQR(f, MP_NEW, p->y); |
363 | mp *x = F_SQR(f, MP_NEW, p->x); |
364 | mp *r = F_MUL(f, MP_NEW, x, p->x); |
365 | x = F_MUL(f, x, cc->a, p->x); |
366 | r = F_ADD(f, r, r, x); |
367 | r = F_ADD(f, r, r, cc->b); |
368 | rc = MP_EQ(l, r) ? 0 : -1; |
369 | mp_drop(l); |
370 | mp_drop(x); |
371 | mp_drop(r); |
372 | return (rc); |
373 | } |
374 | |
375 | static int ecprojcheck(ec_curve *c, const ec *p) |
376 | { |
377 | ec t = EC_INIT; |
378 | int rc; |
379 | |
380 | c->ops->fix(c, &t, p); |
381 | rc = eccheck(c, &t); |
382 | EC_DESTROY(&t); |
383 | return (rc); |
384 | } |
385 | |
41cb1beb |
386 | static void ecdestroy(ec_curve *c) |
387 | { |
388 | ecctx *cc = (ecctx *)c; |
389 | MP_DROP(cc->a); |
390 | MP_DROP(cc->b); |
391 | DESTROY(cc); |
392 | } |
393 | |
394 | /* --- @ec_prime@, @ec_primeproj@ --- * |
395 | * |
dbfee00a |
396 | * Arguments: @field *f@ = the underlying field for this elliptic curve |
41cb1beb |
397 | * @mp *a, *b@ = the coefficients for this curve |
398 | * |
399 | * Returns: A pointer to the curve. |
400 | * |
401 | * Use: Creates a curve structure for an elliptic curve defined over |
402 | * a prime field. The @primeproj@ variant uses projective |
403 | * coordinates, which can be a win. |
404 | */ |
405 | |
406 | extern ec_curve *ec_prime(field *f, mp *a, mp *b) |
407 | { |
408 | ecctx *cc = CREATE(ecctx); |
409 | cc->c.ops = &ec_primeops; |
410 | cc->c.f = f; |
dbfee00a |
411 | cc->a = F_IN(f, MP_NEW, a); |
412 | cc->b = F_IN(f, MP_NEW, b); |
41cb1beb |
413 | return (&cc->c); |
414 | } |
415 | |
8823192f |
416 | extern ec_curve *ec_primeproj(field *f, mp *a, mp *b) |
417 | { |
418 | ecctx *cc = CREATE(ecctx); |
419 | mp *ax; |
420 | |
421 | ax = mp_add(MP_NEW, a, MP_THREE); |
422 | ax = F_IN(f, ax, ax); |
423 | if (F_ZEROP(f, ax)) |
424 | cc->c.ops = &ec_primeprojxops; |
425 | else |
426 | cc->c.ops = &ec_primeprojops; |
427 | MP_DROP(ax); |
428 | cc->c.f = f; |
429 | cc->a = F_IN(f, MP_NEW, a); |
430 | cc->b = F_IN(f, MP_NEW, b); |
41cb1beb |
431 | return (&cc->c); |
432 | } |
433 | |
434 | static const ec_ops ec_primeops = { |
8823192f |
435 | ecdestroy, ec_idin, ec_idout, ec_idfix, |
bc985cef |
436 | ecfind, ecneg, ecadd, ec_stdsub, ecdbl, eccheck |
8823192f |
437 | }; |
438 | |
439 | static const ec_ops ec_primeprojops = { |
440 | ecdestroy, ec_projin, ec_projout, ec_projfix, |
bc985cef |
441 | ecfind, ecneg, ecprojadd, ec_stdsub, ecprojdbl, ecprojcheck |
8823192f |
442 | }; |
443 | |
444 | static const ec_ops ec_primeprojxops = { |
445 | ecdestroy, ec_projin, ec_projout, ec_projfix, |
bc985cef |
446 | ecfind, ecneg, ecprojadd, ec_stdsub, ecprojxdbl, ecprojcheck |
41cb1beb |
447 | }; |
448 | |
449 | /*----- Test rig ----------------------------------------------------------*/ |
450 | |
451 | #ifdef TEST_RIG |
452 | |
453 | #define MP(x) mp_readstring(MP_NEW, #x, 0, 0) |
454 | |
ceb3f0c0 |
455 | int main(int argc, char *argv[]) |
41cb1beb |
456 | { |
457 | field *f; |
458 | ec_curve *c; |
459 | ec g = EC_INIT, d = EC_INIT; |
460 | mp *p, *a, *b, *r; |
ceb3f0c0 |
461 | int i, n = argc == 1 ? 1 : atoi(argv[1]); |
41cb1beb |
462 | |
dbfee00a |
463 | printf("ec-prime: "); |
464 | fflush(stdout); |
41cb1beb |
465 | a = MP(-3); |
466 | b = MP(0x64210519e59c80e70fa7e9ab72243049feb8deecc146b9b1); |
467 | p = MP(6277101735386680763835789423207666416083908700390324961279); |
dbfee00a |
468 | r = MP(6277101735386680763835789423176059013767194773182842284080); |
41cb1beb |
469 | |
f46efa79 |
470 | f = field_niceprime(p); |
ceb3f0c0 |
471 | c = ec_primeproj(f, a, b); |
41cb1beb |
472 | |
473 | g.x = MP(0x188da80eb03090f67cbf20eb43a18800f4ff0afd82ff1012); |
474 | g.y = MP(0x07192b95ffc8da78631011ed6b24cdd573f977a11e794811); |
475 | |
ceb3f0c0 |
476 | for (i = 0; i < n; i++) { |
477 | ec_mul(c, &d, &g, r); |
478 | if (EC_ATINF(&d)) { |
479 | fprintf(stderr, "zero too early\n"); |
480 | return (1); |
481 | } |
482 | ec_add(c, &d, &d, &g); |
483 | if (!EC_ATINF(&d)) { |
484 | fprintf(stderr, "didn't reach zero\n"); |
485 | MP_EPRINT("d.x", d.x); |
486 | MP_EPRINT("d.y", d.y); |
487 | return (1); |
488 | } |
489 | ec_destroy(&d); |
dbfee00a |
490 | } |
41cb1beb |
491 | ec_destroy(&g); |
492 | ec_destroycurve(c); |
493 | F_DESTROY(f); |
dbfee00a |
494 | MP_DROP(p); MP_DROP(a); MP_DROP(b); MP_DROP(r); |
495 | assert(!mparena_count(&mparena_global)); |
496 | printf("ok\n"); |
41cb1beb |
497 | return (0); |
498 | } |
499 | |
500 | #endif |
501 | |
b0ab12e6 |
502 | /*----- That's all, folks -------------------------------------------------*/ |