b0ab12e6 |
1 | /* -*-c-*- |
2 | * |
34e4f738 |
3 | * $Id: ec-prime.c,v 1.9 2004/04/01 12:50:09 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 $ |
34e4f738 |
33 | * Revision 1.9 2004/04/01 12:50:09 mdw |
34 | * Add cyclic group abstraction, with test code. Separate off exponentation |
35 | * functions for better static linking. Fix a buttload of bugs on the way. |
36 | * Generally ensure that negative exponents do inversion correctly. Add |
37 | * table of standard prime-field subgroups. (Binary field subgroups are |
38 | * currently unimplemented but easy to add if anyone ever finds a good one.) |
39 | * |
432c4e18 |
40 | * Revision 1.8 2004/03/27 17:54:11 mdw |
41 | * Standard curves and curve checking. |
42 | * |
f46efa79 |
43 | * Revision 1.7 2004/03/27 00:04:46 mdw |
44 | * Implement efficient reduction for pleasant-looking primes. |
45 | * |
bc985cef |
46 | * Revision 1.6 2004/03/23 15:19:32 mdw |
47 | * Test elliptic curves more thoroughly. |
48 | * |
391faf42 |
49 | * Revision 1.5 2004/03/22 02:19:10 mdw |
50 | * Rationalise the sliding-window threshold. Drop guarantee that right |
51 | * arguments to EC @add@ are canonical, and fix up projective implementations |
52 | * to cope. |
53 | * |
c3caa2fa |
54 | * Revision 1.4 2004/03/21 22:52:06 mdw |
55 | * Merge and close elliptic curve branch. |
56 | * |
ceb3f0c0 |
57 | * Revision 1.3.4.3 2004/03/21 22:39:46 mdw |
58 | * Elliptic curves on binary fields work. |
59 | * |
8823192f |
60 | * Revision 1.3.4.2 2004/03/20 00:13:31 mdw |
61 | * Projective coordinates for prime curves |
62 | * |
dbfee00a |
63 | * Revision 1.3.4.1 2003/06/10 13:43:53 mdw |
64 | * Simple (non-projective) curves over prime fields now seem to work. |
65 | * |
41cb1beb |
66 | * Revision 1.3 2003/05/15 23:25:59 mdw |
67 | * Make elliptic curve stuff build. |
68 | * |
b085fd91 |
69 | * Revision 1.2 2002/01/13 13:48:44 mdw |
70 | * Further progress. |
71 | * |
b0ab12e6 |
72 | * Revision 1.1 2001/04/29 18:12:33 mdw |
73 | * Prototype version. |
74 | * |
75 | */ |
76 | |
77 | /*----- Header files ------------------------------------------------------*/ |
78 | |
41cb1beb |
79 | #include <mLib/sub.h> |
80 | |
b0ab12e6 |
81 | #include "ec.h" |
82 | |
dbfee00a |
83 | /*----- Simple prime curves -----------------------------------------------*/ |
b0ab12e6 |
84 | |
8823192f |
85 | static const ec_ops ec_primeops, ec_primeprojops, ec_primeprojxops; |
41cb1beb |
86 | |
87 | static ec *ecneg(ec_curve *c, ec *d, const ec *p) |
b085fd91 |
88 | { |
89 | EC_COPY(d, p); |
ceb3f0c0 |
90 | if (d->y) |
91 | d->y = F_NEG(c->f, d->y, d->y); |
b085fd91 |
92 | return (d); |
93 | } |
94 | |
8823192f |
95 | static ec *ecfind(ec_curve *c, ec *d, mp *x) |
96 | { |
97 | mp *p, *q; |
8823192f |
98 | field *f = c->f; |
99 | |
100 | q = F_SQR(f, MP_NEW, x); |
101 | p = F_MUL(f, MP_NEW, x, q); |
432c4e18 |
102 | q = F_MUL(f, q, x, c->a); |
8823192f |
103 | p = F_ADD(f, p, p, q); |
432c4e18 |
104 | p = F_ADD(f, p, p, c->b); |
8823192f |
105 | MP_DROP(q); |
106 | p = F_SQRT(f, p, p); |
107 | if (!p) |
108 | return (0); |
109 | EC_DESTROY(d); |
110 | d->x = MP_COPY(x); |
111 | d->y = p; |
112 | d->z = MP_COPY(f->one); |
b085fd91 |
113 | return (d); |
114 | } |
115 | |
116 | static ec *ecdbl(ec_curve *c, ec *d, const ec *a) |
b0ab12e6 |
117 | { |
b085fd91 |
118 | if (EC_ATINF(a)) |
119 | EC_SETINF(d); |
8823192f |
120 | else if (F_ZEROP(c->f, a->y)) |
b085fd91 |
121 | EC_COPY(d, a); |
122 | else { |
123 | field *f = c->f; |
b085fd91 |
124 | mp *lambda; |
125 | mp *dy, *dx; |
126 | |
8823192f |
127 | dx = F_SQR(f, MP_NEW, a->x); /* %$x^2$% */ |
128 | dy = F_DBL(f, MP_NEW, a->y); /* %$2 y$% */ |
129 | dx = F_TPL(f, dx, dx); /* %$3 x^2$% */ |
432c4e18 |
130 | dx = F_ADD(f, dx, dx, c->a); /* %$3 x^2 + A$% */ |
8823192f |
131 | dy = F_INV(f, dy, dy); /* %$(2 y)^{-1}$% */ |
132 | lambda = F_MUL(f, MP_NEW, dx, dy); /* %$\lambda = (3 x^2 + A)/(2 y)$% */ |
b085fd91 |
133 | |
8823192f |
134 | dx = F_SQR(f, dx, lambda); /* %$\lambda^2$% */ |
135 | dy = F_DBL(f, dy, a->x); /* %$2 x$% */ |
136 | dx = F_SUB(f, dx, dx, dy); /* %$x' = \lambda^2 - 2 x */ |
137 | dy = F_SUB(f, dy, a->x, dx); /* %$x - x'$% */ |
138 | dy = F_MUL(f, dy, lambda, dy); /* %$\lambda (x - x')$% */ |
139 | dy = F_SUB(f, dy, dy, a->y); /* %$y' = \lambda (x - x') - y$% */ |
b0ab12e6 |
140 | |
b085fd91 |
141 | EC_DESTROY(d); |
142 | d->x = dx; |
143 | d->y = dy; |
144 | d->z = 0; |
145 | MP_DROP(lambda); |
146 | } |
147 | return (d); |
148 | } |
149 | |
8823192f |
150 | static ec *ecprojdbl(ec_curve *c, ec *d, const ec *a) |
151 | { |
152 | if (EC_ATINF(a)) |
153 | EC_SETINF(d); |
154 | else if (F_ZEROP(c->f, a->y)) |
155 | EC_COPY(d, a); |
156 | else { |
157 | field *f = c->f; |
8823192f |
158 | mp *p, *q, *m, *s, *dx, *dy, *dz; |
159 | |
160 | p = F_SQR(f, MP_NEW, a->z); /* %$z^2$% */ |
161 | q = F_SQR(f, MP_NEW, p); /* %$z^4$% */ |
432c4e18 |
162 | p = F_MUL(f, p, q, c->a); /* %$A z^4$% */ |
8823192f |
163 | m = F_SQR(f, MP_NEW, a->x); /* %$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 { |
8823192f |
260 | dx = F_SQR(f, MP_NEW, a->x); /* %$x_0^2$% */ |
261 | dx = F_TPL(f, dx, dx); /* %$3 x_0^2$% */ |
432c4e18 |
262 | dx = F_ADD(f, dx, dx, c->a); /* %$3 x_0^2 + A$% */ |
8823192f |
263 | dy = F_DBL(f, MP_NEW, a->y); /* %$2 y_0$% */ |
264 | dy = F_INV(f, dy, dy); /* %$(2 y_0)^{-1}$% */ |
41cb1beb |
265 | lambda = F_MUL(f, MP_NEW, dx, dy); |
8823192f |
266 | /* %$\lambda = (3 x_0^2 + A)/(2 y_0)$% */ |
b085fd91 |
267 | } |
268 | |
8823192f |
269 | dx = F_SQR(f, dx, lambda); /* %$\lambda^2$% */ |
270 | dx = F_SUB(f, dx, dx, a->x); /* %$\lambda^2 - x_0$% */ |
271 | dx = F_SUB(f, dx, dx, b->x); /* %$x' = \lambda^2 - x_0 - x_1$% */ |
272 | dy = F_SUB(f, dy, b->x, dx); /* %$x_1 - x'$% */ |
273 | dy = F_MUL(f, dy, lambda, dy); /* %$\lambda (x_1 - x')$% */ |
ceb3f0c0 |
274 | dy = F_SUB(f, dy, dy, b->y); /* %$y' = \lambda (x_1 - x') - y_1$% */ |
b0ab12e6 |
275 | |
b085fd91 |
276 | EC_DESTROY(d); |
277 | d->x = dx; |
278 | d->y = dy; |
279 | d->z = 0; |
280 | MP_DROP(lambda); |
b0ab12e6 |
281 | } |
b085fd91 |
282 | return (d); |
b0ab12e6 |
283 | } |
284 | |
8823192f |
285 | static ec *ecprojadd(ec_curve *c, ec *d, const ec *a, const ec *b) |
286 | { |
287 | if (a == b) |
288 | c->ops->dbl(c, d, a); |
289 | else if (EC_ATINF(a)) |
290 | EC_COPY(d, b); |
291 | else if (EC_ATINF(b)) |
292 | EC_COPY(d, a); |
293 | else { |
294 | field *f = c->f; |
391faf42 |
295 | mp *p, *q, *r, *w, *u, *uu, *s, *ss, *dx, *dy, *dz; |
8823192f |
296 | |
297 | q = F_SQR(f, MP_NEW, a->z); /* %$z_0^2$% */ |
298 | u = F_MUL(f, MP_NEW, q, b->x); /* %$u = x_1 z_0^2$% */ |
299 | p = F_MUL(f, MP_NEW, q, b->y); /* %$y_1 z_0^2$% */ |
300 | s = F_MUL(f, q, p, a->z); /* %$s = y_1 z_0^3$% */ |
301 | |
391faf42 |
302 | q = F_SQR(f, MP_NEW, b->z); /* %$z_1^2$% */ |
303 | uu = F_MUL(f, MP_NEW, q, a->x); /* %$uu = x_0 z_1^2$%*/ |
304 | p = F_MUL(f, p, q, a->y); /* %$y_0 z_1^2$% */ |
305 | ss = F_MUL(f, q, p, b->z); /* %$ss = y_0 z_1^3$% */ |
306 | |
307 | w = F_SUB(f, p, uu, u); /* %$w = uu - u$% */ |
308 | r = F_SUB(f, MP_NEW, ss, s); /* %$r = ss - s$% */ |
8823192f |
309 | if (F_ZEROP(f, w)) { |
ceb3f0c0 |
310 | MP_DROP(w); |
311 | MP_DROP(u); |
312 | MP_DROP(s); |
391faf42 |
313 | MP_DROP(uu); |
314 | MP_DROP(ss); |
8823192f |
315 | if (F_ZEROP(f, r)) { |
8823192f |
316 | MP_DROP(r); |
8823192f |
317 | return (c->ops->dbl(c, d, a)); |
318 | } else { |
8823192f |
319 | MP_DROP(r); |
8823192f |
320 | EC_SETINF(d); |
321 | return (d); |
322 | } |
323 | } |
391faf42 |
324 | u = F_ADD(f, u, u, uu); /* %$t = uu + u$% */ |
325 | s = F_ADD(f, s, s, ss); /* %$m = ss + r$% */ |
8823192f |
326 | |
391faf42 |
327 | uu = F_MUL(f, uu, a->z, w); /* %$z_0 w$% */ |
328 | dz = F_MUL(f, ss, uu, b->z); /* %$z' = z_0 z_1 w$% */ |
8823192f |
329 | |
391faf42 |
330 | p = F_SQR(f, uu, w); /* %$w^2$% */ |
8823192f |
331 | q = F_MUL(f, MP_NEW, p, u); /* %$t w^2$% */ |
332 | u = F_MUL(f, u, p, w); /* %$w^3$% */ |
333 | p = F_MUL(f, p, u, s); /* %$m w^3$% */ |
334 | |
335 | dx = F_SQR(f, u, r); /* %$r^2$% */ |
336 | dx = F_SUB(f, dx, dx, q); /* %$x' = r^2 - t w^2$% */ |
337 | |
338 | s = F_DBL(f, s, dx); /* %$2 x'$% */ |
339 | q = F_SUB(f, q, q, s); /* %$v = t w^2 - 2 x'$% */ |
340 | dy = F_MUL(f, s, q, r); /* %$v r$% */ |
341 | dy = F_SUB(f, dy, dy, p); /* %$v r - m w^3$% */ |
342 | dy = F_HLV(f, dy, dy); /* %$y' = (v r - m w^3)/2$% */ |
343 | |
344 | EC_DESTROY(d); |
345 | d->x = dx; |
346 | d->y = dy; |
347 | d->z = dz; |
348 | MP_DROP(p); |
349 | MP_DROP(q); |
350 | MP_DROP(r); |
351 | MP_DROP(w); |
352 | } |
353 | return (d); |
354 | } |
355 | |
356 | static int eccheck(ec_curve *c, const ec *p) |
357 | { |
8823192f |
358 | field *f = c->f; |
34e4f738 |
359 | mp *l, *x, *r; |
8823192f |
360 | int rc; |
34e4f738 |
361 | if (EC_ATINF(p)) return (0); |
362 | l = F_SQR(f, MP_NEW, p->y); |
363 | x = F_SQR(f, MP_NEW, p->x); |
364 | r = F_MUL(f, MP_NEW, x, p->x); |
432c4e18 |
365 | x = F_MUL(f, x, c->a, p->x); |
8823192f |
366 | r = F_ADD(f, r, r, x); |
432c4e18 |
367 | r = F_ADD(f, r, r, c->b); |
8823192f |
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 | { |
432c4e18 |
388 | MP_DROP(c->a); |
389 | MP_DROP(c->b); |
390 | DESTROY(c); |
41cb1beb |
391 | } |
392 | |
393 | /* --- @ec_prime@, @ec_primeproj@ --- * |
394 | * |
dbfee00a |
395 | * Arguments: @field *f@ = the underlying field for this elliptic curve |
41cb1beb |
396 | * @mp *a, *b@ = the coefficients for this curve |
397 | * |
398 | * Returns: A pointer to the curve. |
399 | * |
400 | * Use: Creates a curve structure for an elliptic curve defined over |
401 | * a prime field. The @primeproj@ variant uses projective |
402 | * coordinates, which can be a win. |
403 | */ |
404 | |
405 | extern ec_curve *ec_prime(field *f, mp *a, mp *b) |
406 | { |
432c4e18 |
407 | ec_curve *c = CREATE(ec_curve); |
408 | c->ops = &ec_primeops; |
409 | c->f = f; |
410 | c->a = F_IN(f, MP_NEW, a); |
411 | c->b = F_IN(f, MP_NEW, b); |
412 | return (c); |
41cb1beb |
413 | } |
414 | |
8823192f |
415 | extern ec_curve *ec_primeproj(field *f, mp *a, mp *b) |
416 | { |
432c4e18 |
417 | ec_curve *c = CREATE(ec_curve); |
8823192f |
418 | mp *ax; |
419 | |
420 | ax = mp_add(MP_NEW, a, MP_THREE); |
421 | ax = F_IN(f, ax, ax); |
422 | if (F_ZEROP(f, ax)) |
432c4e18 |
423 | c->ops = &ec_primeprojxops; |
8823192f |
424 | else |
432c4e18 |
425 | c->ops = &ec_primeprojops; |
8823192f |
426 | MP_DROP(ax); |
432c4e18 |
427 | c->f = f; |
428 | c->a = F_IN(f, MP_NEW, a); |
429 | c->b = F_IN(f, MP_NEW, b); |
430 | return (c); |
41cb1beb |
431 | } |
432 | |
433 | static const ec_ops ec_primeops = { |
34e4f738 |
434 | ecdestroy, ec_stdsamep, ec_idin, ec_idout, ec_idfix, |
bc985cef |
435 | ecfind, ecneg, ecadd, ec_stdsub, ecdbl, eccheck |
8823192f |
436 | }; |
437 | |
438 | static const ec_ops ec_primeprojops = { |
34e4f738 |
439 | ecdestroy, ec_stdsamep, ec_projin, ec_projout, ec_projfix, |
bc985cef |
440 | ecfind, ecneg, ecprojadd, ec_stdsub, ecprojdbl, ecprojcheck |
8823192f |
441 | }; |
442 | |
443 | static const ec_ops ec_primeprojxops = { |
34e4f738 |
444 | ecdestroy, ec_stdsamep, ec_projin, ec_projout, ec_projfix, |
bc985cef |
445 | ecfind, ecneg, ecprojadd, ec_stdsub, ecprojxdbl, ecprojcheck |
41cb1beb |
446 | }; |
447 | |
448 | /*----- Test rig ----------------------------------------------------------*/ |
449 | |
450 | #ifdef TEST_RIG |
451 | |
452 | #define MP(x) mp_readstring(MP_NEW, #x, 0, 0) |
453 | |
ceb3f0c0 |
454 | int main(int argc, char *argv[]) |
41cb1beb |
455 | { |
456 | field *f; |
457 | ec_curve *c; |
458 | ec g = EC_INIT, d = EC_INIT; |
459 | mp *p, *a, *b, *r; |
ceb3f0c0 |
460 | int i, n = argc == 1 ? 1 : atoi(argv[1]); |
41cb1beb |
461 | |
dbfee00a |
462 | printf("ec-prime: "); |
463 | fflush(stdout); |
41cb1beb |
464 | a = MP(-3); |
432c4e18 |
465 | b = MP(0xb3312fa7e23ee7e4988e056be3f82d19181d9c6efe8141120314088f5013875ac656398d8a2ed19d2a85c8edd3ec2aef); |
466 | p = MP(39402006196394479212279040100143613805079739270465446667948293404245721771496870329047266088258938001861606973112319); |
467 | r = MP(39402006196394479212279040100143613805079739270465446667946905279627659399113263569398956308152294913554433653942642); |
41cb1beb |
468 | |
f46efa79 |
469 | f = field_niceprime(p); |
ceb3f0c0 |
470 | c = ec_primeproj(f, a, b); |
41cb1beb |
471 | |
432c4e18 |
472 | g.x = MP(0xaa87ca22be8b05378eb1c71ef320ad746e1d3b628ba79b9859f741e082542a385502f25dbf55296c3a545e3872760ab7); |
473 | g.y = MP(0x3617de4a96262c6f5d9e98bf9292dc29f8f41dbd289a147ce9da3113b5f0b8c00a60b1ce1d7e819d7a431d7c90ea0e5f); |
41cb1beb |
474 | |
ceb3f0c0 |
475 | for (i = 0; i < n; i++) { |
476 | ec_mul(c, &d, &g, r); |
477 | if (EC_ATINF(&d)) { |
478 | fprintf(stderr, "zero too early\n"); |
479 | return (1); |
480 | } |
481 | ec_add(c, &d, &d, &g); |
482 | if (!EC_ATINF(&d)) { |
483 | fprintf(stderr, "didn't reach zero\n"); |
484 | MP_EPRINT("d.x", d.x); |
485 | MP_EPRINT("d.y", d.y); |
486 | return (1); |
487 | } |
488 | ec_destroy(&d); |
dbfee00a |
489 | } |
41cb1beb |
490 | ec_destroy(&g); |
491 | ec_destroycurve(c); |
492 | F_DESTROY(f); |
dbfee00a |
493 | MP_DROP(p); MP_DROP(a); MP_DROP(b); MP_DROP(r); |
494 | assert(!mparena_count(&mparena_global)); |
495 | printf("ok\n"); |
41cb1beb |
496 | return (0); |
497 | } |
498 | |
499 | #endif |
500 | |
b0ab12e6 |
501 | /*----- That's all, folks -------------------------------------------------*/ |