b0ab12e6 |
1 | /* -*-c-*- |
2 | * |
02d7884d |
3 | * $Id: ec-prime.c,v 1.10 2004/04/03 03:32:05 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 $ |
02d7884d |
33 | * Revision 1.10 2004/04/03 03:32:05 mdw |
34 | * General robustification. |
35 | * |
34e4f738 |
36 | * Revision 1.9 2004/04/01 12:50:09 mdw |
37 | * Add cyclic group abstraction, with test code. Separate off exponentation |
38 | * functions for better static linking. Fix a buttload of bugs on the way. |
39 | * Generally ensure that negative exponents do inversion correctly. Add |
40 | * table of standard prime-field subgroups. (Binary field subgroups are |
41 | * currently unimplemented but easy to add if anyone ever finds a good one.) |
42 | * |
432c4e18 |
43 | * Revision 1.8 2004/03/27 17:54:11 mdw |
44 | * Standard curves and curve checking. |
45 | * |
f46efa79 |
46 | * Revision 1.7 2004/03/27 00:04:46 mdw |
47 | * Implement efficient reduction for pleasant-looking primes. |
48 | * |
bc985cef |
49 | * Revision 1.6 2004/03/23 15:19:32 mdw |
50 | * Test elliptic curves more thoroughly. |
51 | * |
391faf42 |
52 | * Revision 1.5 2004/03/22 02:19:10 mdw |
53 | * Rationalise the sliding-window threshold. Drop guarantee that right |
54 | * arguments to EC @add@ are canonical, and fix up projective implementations |
55 | * to cope. |
56 | * |
c3caa2fa |
57 | * Revision 1.4 2004/03/21 22:52:06 mdw |
58 | * Merge and close elliptic curve branch. |
59 | * |
ceb3f0c0 |
60 | * Revision 1.3.4.3 2004/03/21 22:39:46 mdw |
61 | * Elliptic curves on binary fields work. |
62 | * |
8823192f |
63 | * Revision 1.3.4.2 2004/03/20 00:13:31 mdw |
64 | * Projective coordinates for prime curves |
65 | * |
dbfee00a |
66 | * Revision 1.3.4.1 2003/06/10 13:43:53 mdw |
67 | * Simple (non-projective) curves over prime fields now seem to work. |
68 | * |
41cb1beb |
69 | * Revision 1.3 2003/05/15 23:25:59 mdw |
70 | * Make elliptic curve stuff build. |
71 | * |
b085fd91 |
72 | * Revision 1.2 2002/01/13 13:48:44 mdw |
73 | * Further progress. |
74 | * |
b0ab12e6 |
75 | * Revision 1.1 2001/04/29 18:12:33 mdw |
76 | * Prototype version. |
77 | * |
78 | */ |
79 | |
80 | /*----- Header files ------------------------------------------------------*/ |
81 | |
41cb1beb |
82 | #include <mLib/sub.h> |
83 | |
b0ab12e6 |
84 | #include "ec.h" |
85 | |
dbfee00a |
86 | /*----- Simple prime curves -----------------------------------------------*/ |
b0ab12e6 |
87 | |
8823192f |
88 | static const ec_ops ec_primeops, ec_primeprojops, ec_primeprojxops; |
41cb1beb |
89 | |
90 | static ec *ecneg(ec_curve *c, ec *d, const ec *p) |
b085fd91 |
91 | { |
92 | EC_COPY(d, p); |
ceb3f0c0 |
93 | if (d->y) |
94 | d->y = F_NEG(c->f, d->y, d->y); |
b085fd91 |
95 | return (d); |
96 | } |
97 | |
8823192f |
98 | static ec *ecfind(ec_curve *c, ec *d, mp *x) |
99 | { |
100 | mp *p, *q; |
8823192f |
101 | field *f = c->f; |
102 | |
103 | q = F_SQR(f, MP_NEW, x); |
104 | p = F_MUL(f, MP_NEW, x, q); |
432c4e18 |
105 | q = F_MUL(f, q, x, c->a); |
8823192f |
106 | p = F_ADD(f, p, p, q); |
432c4e18 |
107 | p = F_ADD(f, p, p, c->b); |
8823192f |
108 | MP_DROP(q); |
109 | p = F_SQRT(f, p, p); |
110 | if (!p) |
111 | return (0); |
112 | EC_DESTROY(d); |
113 | d->x = MP_COPY(x); |
114 | d->y = p; |
115 | d->z = MP_COPY(f->one); |
b085fd91 |
116 | return (d); |
117 | } |
118 | |
119 | static ec *ecdbl(ec_curve *c, ec *d, const ec *a) |
b0ab12e6 |
120 | { |
b085fd91 |
121 | if (EC_ATINF(a)) |
122 | EC_SETINF(d); |
8823192f |
123 | else if (F_ZEROP(c->f, a->y)) |
b085fd91 |
124 | EC_COPY(d, a); |
125 | else { |
126 | field *f = c->f; |
b085fd91 |
127 | mp *lambda; |
128 | mp *dy, *dx; |
129 | |
8823192f |
130 | dx = F_SQR(f, MP_NEW, a->x); /* %$x^2$% */ |
131 | dy = F_DBL(f, MP_NEW, a->y); /* %$2 y$% */ |
132 | dx = F_TPL(f, dx, dx); /* %$3 x^2$% */ |
432c4e18 |
133 | dx = F_ADD(f, dx, dx, c->a); /* %$3 x^2 + A$% */ |
8823192f |
134 | dy = F_INV(f, dy, dy); /* %$(2 y)^{-1}$% */ |
135 | lambda = F_MUL(f, MP_NEW, dx, dy); /* %$\lambda = (3 x^2 + A)/(2 y)$% */ |
b085fd91 |
136 | |
8823192f |
137 | dx = F_SQR(f, dx, lambda); /* %$\lambda^2$% */ |
138 | dy = F_DBL(f, dy, a->x); /* %$2 x$% */ |
139 | dx = F_SUB(f, dx, dx, dy); /* %$x' = \lambda^2 - 2 x */ |
140 | dy = F_SUB(f, dy, a->x, dx); /* %$x - x'$% */ |
141 | dy = F_MUL(f, dy, lambda, dy); /* %$\lambda (x - x')$% */ |
142 | dy = F_SUB(f, dy, dy, a->y); /* %$y' = \lambda (x - x') - y$% */ |
b0ab12e6 |
143 | |
b085fd91 |
144 | EC_DESTROY(d); |
145 | d->x = dx; |
146 | d->y = dy; |
147 | d->z = 0; |
148 | MP_DROP(lambda); |
149 | } |
150 | return (d); |
151 | } |
152 | |
8823192f |
153 | static ec *ecprojdbl(ec_curve *c, ec *d, const ec *a) |
154 | { |
155 | if (EC_ATINF(a)) |
156 | EC_SETINF(d); |
157 | else if (F_ZEROP(c->f, a->y)) |
158 | EC_COPY(d, a); |
159 | else { |
160 | field *f = c->f; |
8823192f |
161 | mp *p, *q, *m, *s, *dx, *dy, *dz; |
162 | |
163 | p = F_SQR(f, MP_NEW, a->z); /* %$z^2$% */ |
164 | q = F_SQR(f, MP_NEW, p); /* %$z^4$% */ |
432c4e18 |
165 | p = F_MUL(f, p, q, c->a); /* %$A z^4$% */ |
8823192f |
166 | m = F_SQR(f, MP_NEW, a->x); /* %$x^2$% */ |
167 | m = F_TPL(f, m, m); /* %$3 x^2$% */ |
168 | m = F_ADD(f, m, m, p); /* %$m = 3 x^2 + A z^4$% */ |
169 | |
170 | q = F_DBL(f, q, a->y); /* %$2 y$% */ |
171 | dz = F_MUL(f, MP_NEW, q, a->z); /* %$z' = 2 y z$% */ |
172 | |
173 | p = F_SQR(f, p, q); /* %$4 y^2$% */ |
174 | s = F_MUL(f, MP_NEW, p, a->x); /* %$s = 4 x y^2$% */ |
175 | q = F_SQR(f, q, p); /* %$16 y^4$% */ |
176 | q = F_HLV(f, q, q); /* %$t = 8 y^4$% */ |
177 | |
178 | p = F_DBL(f, p, s); /* %$2 s$% */ |
179 | dx = F_SQR(f, MP_NEW, m); /* %$m^2$% */ |
180 | dx = F_SUB(f, dx, dx, p); /* %$x' = m^2 - 2 s$% */ |
181 | |
182 | s = F_SUB(f, s, s, dx); /* %$s - x'$% */ |
183 | dy = F_MUL(f, p, m, s); /* %$m (s - x')$% */ |
184 | dy = F_SUB(f, dy, dy, q); /* %$y' = m (s - x') - t$% */ |
185 | |
186 | EC_DESTROY(d); |
187 | d->x = dx; |
188 | d->y = dy; |
189 | d->z = dz; |
190 | MP_DROP(m); |
191 | MP_DROP(q); |
192 | MP_DROP(s); |
193 | } |
194 | return (d); |
195 | } |
196 | |
197 | static ec *ecprojxdbl(ec_curve *c, ec *d, const ec *a) |
198 | { |
199 | if (EC_ATINF(a)) |
200 | EC_SETINF(d); |
201 | else if (F_ZEROP(c->f, a->y)) |
202 | EC_COPY(d, a); |
203 | else { |
204 | field *f = c->f; |
205 | mp *p, *q, *m, *s, *dx, *dy, *dz; |
206 | |
207 | m = F_SQR(f, MP_NEW, a->z); /* %$z^2$% */ |
208 | p = F_SUB(f, MP_NEW, a->x, m); /* %$x - z^2$% */ |
209 | q = F_ADD(f, MP_NEW, a->x, m); /* %$x + z^2$% */ |
210 | m = F_MUL(f, m, p, q); /* %$x^2 - z^4$% */ |
211 | m = F_TPL(f, m, m); /* %$m = 3 x^2 - 3 z^4$% */ |
212 | |
213 | q = F_DBL(f, q, a->y); /* %$2 y$% */ |
214 | dz = F_MUL(f, MP_NEW, q, a->z); /* %$z' = 2 y z$% */ |
215 | |
216 | p = F_SQR(f, p, q); /* %$4 y^2$% */ |
217 | s = F_MUL(f, MP_NEW, p, a->x); /* %$s = 4 x y^2$% */ |
218 | q = F_SQR(f, q, p); /* %$16 y^4$% */ |
219 | q = F_HLV(f, q, q); /* %$t = 8 y^4$% */ |
220 | |
221 | p = F_DBL(f, p, s); /* %$2 s$% */ |
222 | dx = F_SQR(f, MP_NEW, m); /* %$m^2$% */ |
223 | dx = F_SUB(f, dx, dx, p); /* %$x' = m^2 - 2 s$% */ |
224 | |
225 | s = F_SUB(f, s, s, dx); /* %$s - x'$% */ |
226 | dy = F_MUL(f, p, m, s); /* %$m (s - x')$% */ |
227 | dy = F_SUB(f, dy, dy, q); /* %$y' = m (s - x') - t$% */ |
228 | |
229 | EC_DESTROY(d); |
230 | d->x = dx; |
231 | d->y = dy; |
232 | d->z = dz; |
233 | MP_DROP(m); |
234 | MP_DROP(q); |
235 | MP_DROP(s); |
236 | } |
237 | return (d); |
238 | } |
239 | |
b085fd91 |
240 | static ec *ecadd(ec_curve *c, ec *d, const ec *a, const ec *b) |
241 | { |
b0ab12e6 |
242 | if (a == b) |
243 | ecdbl(c, d, a); |
244 | else if (EC_ATINF(a)) |
245 | EC_COPY(d, b); |
246 | else if (EC_ATINF(b)) |
247 | EC_COPY(d, a); |
b085fd91 |
248 | else { |
249 | field *f = c->f; |
250 | mp *lambda; |
251 | mp *dy, *dx; |
252 | |
253 | if (!MP_EQ(a->x, b->x)) { |
8823192f |
254 | dy = F_SUB(f, MP_NEW, a->y, b->y); /* %$y_0 - y_1$% */ |
255 | dx = F_SUB(f, MP_NEW, a->x, b->x); /* %$x_0 - x_1$% */ |
256 | dx = F_INV(f, dx, dx); /* %$(x_0 - x_1)^{-1}$% */ |
b085fd91 |
257 | lambda = F_MUL(f, MP_NEW, dy, dx); |
8823192f |
258 | /* %$\lambda = (y_0 - y1)/(x_0 - x_1)$% */ |
259 | } else if (F_ZEROP(c->f, a->y) || !MP_EQ(a->y, b->y)) { |
b0ab12e6 |
260 | EC_SETINF(d); |
b085fd91 |
261 | return (d); |
262 | } else { |
8823192f |
263 | dx = F_SQR(f, MP_NEW, a->x); /* %$x_0^2$% */ |
264 | dx = F_TPL(f, dx, dx); /* %$3 x_0^2$% */ |
432c4e18 |
265 | dx = F_ADD(f, dx, dx, c->a); /* %$3 x_0^2 + A$% */ |
8823192f |
266 | dy = F_DBL(f, MP_NEW, a->y); /* %$2 y_0$% */ |
267 | dy = F_INV(f, dy, dy); /* %$(2 y_0)^{-1}$% */ |
41cb1beb |
268 | lambda = F_MUL(f, MP_NEW, dx, dy); |
8823192f |
269 | /* %$\lambda = (3 x_0^2 + A)/(2 y_0)$% */ |
b085fd91 |
270 | } |
271 | |
8823192f |
272 | dx = F_SQR(f, dx, lambda); /* %$\lambda^2$% */ |
273 | dx = F_SUB(f, dx, dx, a->x); /* %$\lambda^2 - x_0$% */ |
274 | dx = F_SUB(f, dx, dx, b->x); /* %$x' = \lambda^2 - x_0 - x_1$% */ |
275 | dy = F_SUB(f, dy, b->x, dx); /* %$x_1 - x'$% */ |
276 | dy = F_MUL(f, dy, lambda, dy); /* %$\lambda (x_1 - x')$% */ |
ceb3f0c0 |
277 | dy = F_SUB(f, dy, dy, b->y); /* %$y' = \lambda (x_1 - x') - y_1$% */ |
b0ab12e6 |
278 | |
b085fd91 |
279 | EC_DESTROY(d); |
280 | d->x = dx; |
281 | d->y = dy; |
282 | d->z = 0; |
283 | MP_DROP(lambda); |
b0ab12e6 |
284 | } |
b085fd91 |
285 | return (d); |
b0ab12e6 |
286 | } |
287 | |
8823192f |
288 | static ec *ecprojadd(ec_curve *c, ec *d, const ec *a, const ec *b) |
289 | { |
290 | if (a == b) |
291 | c->ops->dbl(c, d, a); |
292 | else if (EC_ATINF(a)) |
293 | EC_COPY(d, b); |
294 | else if (EC_ATINF(b)) |
295 | EC_COPY(d, a); |
296 | else { |
297 | field *f = c->f; |
391faf42 |
298 | mp *p, *q, *r, *w, *u, *uu, *s, *ss, *dx, *dy, *dz; |
8823192f |
299 | |
300 | q = F_SQR(f, MP_NEW, a->z); /* %$z_0^2$% */ |
301 | u = F_MUL(f, MP_NEW, q, b->x); /* %$u = x_1 z_0^2$% */ |
302 | p = F_MUL(f, MP_NEW, q, b->y); /* %$y_1 z_0^2$% */ |
303 | s = F_MUL(f, q, p, a->z); /* %$s = y_1 z_0^3$% */ |
304 | |
391faf42 |
305 | q = F_SQR(f, MP_NEW, b->z); /* %$z_1^2$% */ |
306 | uu = F_MUL(f, MP_NEW, q, a->x); /* %$uu = x_0 z_1^2$%*/ |
307 | p = F_MUL(f, p, q, a->y); /* %$y_0 z_1^2$% */ |
308 | ss = F_MUL(f, q, p, b->z); /* %$ss = y_0 z_1^3$% */ |
309 | |
310 | w = F_SUB(f, p, uu, u); /* %$w = uu - u$% */ |
311 | r = F_SUB(f, MP_NEW, ss, s); /* %$r = ss - s$% */ |
8823192f |
312 | if (F_ZEROP(f, w)) { |
ceb3f0c0 |
313 | MP_DROP(w); |
314 | MP_DROP(u); |
315 | MP_DROP(s); |
391faf42 |
316 | MP_DROP(uu); |
317 | MP_DROP(ss); |
8823192f |
318 | if (F_ZEROP(f, r)) { |
8823192f |
319 | MP_DROP(r); |
8823192f |
320 | return (c->ops->dbl(c, d, a)); |
321 | } else { |
8823192f |
322 | MP_DROP(r); |
8823192f |
323 | EC_SETINF(d); |
324 | return (d); |
325 | } |
326 | } |
391faf42 |
327 | u = F_ADD(f, u, u, uu); /* %$t = uu + u$% */ |
328 | s = F_ADD(f, s, s, ss); /* %$m = ss + r$% */ |
8823192f |
329 | |
391faf42 |
330 | uu = F_MUL(f, uu, a->z, w); /* %$z_0 w$% */ |
331 | dz = F_MUL(f, ss, uu, b->z); /* %$z' = z_0 z_1 w$% */ |
8823192f |
332 | |
391faf42 |
333 | p = F_SQR(f, uu, w); /* %$w^2$% */ |
8823192f |
334 | q = F_MUL(f, MP_NEW, p, u); /* %$t w^2$% */ |
335 | u = F_MUL(f, u, p, w); /* %$w^3$% */ |
336 | p = F_MUL(f, p, u, s); /* %$m w^3$% */ |
337 | |
338 | dx = F_SQR(f, u, r); /* %$r^2$% */ |
339 | dx = F_SUB(f, dx, dx, q); /* %$x' = r^2 - t w^2$% */ |
340 | |
341 | s = F_DBL(f, s, dx); /* %$2 x'$% */ |
342 | q = F_SUB(f, q, q, s); /* %$v = t w^2 - 2 x'$% */ |
343 | dy = F_MUL(f, s, q, r); /* %$v r$% */ |
344 | dy = F_SUB(f, dy, dy, p); /* %$v r - m w^3$% */ |
345 | dy = F_HLV(f, dy, dy); /* %$y' = (v r - m w^3)/2$% */ |
346 | |
347 | EC_DESTROY(d); |
348 | d->x = dx; |
349 | d->y = dy; |
350 | d->z = dz; |
351 | MP_DROP(p); |
352 | MP_DROP(q); |
353 | MP_DROP(r); |
354 | MP_DROP(w); |
355 | } |
356 | return (d); |
357 | } |
358 | |
359 | static int eccheck(ec_curve *c, const ec *p) |
360 | { |
8823192f |
361 | field *f = c->f; |
34e4f738 |
362 | mp *l, *x, *r; |
8823192f |
363 | int rc; |
34e4f738 |
364 | if (EC_ATINF(p)) return (0); |
365 | l = F_SQR(f, MP_NEW, p->y); |
366 | x = F_SQR(f, MP_NEW, p->x); |
367 | r = F_MUL(f, MP_NEW, x, p->x); |
432c4e18 |
368 | x = F_MUL(f, x, c->a, p->x); |
8823192f |
369 | r = F_ADD(f, r, r, x); |
432c4e18 |
370 | r = F_ADD(f, r, r, c->b); |
8823192f |
371 | rc = MP_EQ(l, r) ? 0 : -1; |
372 | mp_drop(l); |
373 | mp_drop(x); |
374 | mp_drop(r); |
375 | return (rc); |
376 | } |
377 | |
378 | static int ecprojcheck(ec_curve *c, const ec *p) |
379 | { |
380 | ec t = EC_INIT; |
381 | int rc; |
382 | |
383 | c->ops->fix(c, &t, p); |
384 | rc = eccheck(c, &t); |
385 | EC_DESTROY(&t); |
386 | return (rc); |
387 | } |
388 | |
41cb1beb |
389 | static void ecdestroy(ec_curve *c) |
390 | { |
432c4e18 |
391 | MP_DROP(c->a); |
392 | MP_DROP(c->b); |
393 | DESTROY(c); |
41cb1beb |
394 | } |
395 | |
396 | /* --- @ec_prime@, @ec_primeproj@ --- * |
397 | * |
dbfee00a |
398 | * Arguments: @field *f@ = the underlying field for this elliptic curve |
41cb1beb |
399 | * @mp *a, *b@ = the coefficients for this curve |
400 | * |
02d7884d |
401 | * Returns: A pointer to the curve, or null. |
41cb1beb |
402 | * |
403 | * Use: Creates a curve structure for an elliptic curve defined over |
404 | * a prime field. The @primeproj@ variant uses projective |
405 | * coordinates, which can be a win. |
406 | */ |
407 | |
408 | extern ec_curve *ec_prime(field *f, mp *a, mp *b) |
409 | { |
432c4e18 |
410 | ec_curve *c = CREATE(ec_curve); |
411 | c->ops = &ec_primeops; |
412 | c->f = f; |
413 | c->a = F_IN(f, MP_NEW, a); |
414 | c->b = F_IN(f, MP_NEW, b); |
415 | return (c); |
41cb1beb |
416 | } |
417 | |
8823192f |
418 | extern ec_curve *ec_primeproj(field *f, mp *a, mp *b) |
419 | { |
432c4e18 |
420 | ec_curve *c = CREATE(ec_curve); |
8823192f |
421 | mp *ax; |
422 | |
423 | ax = mp_add(MP_NEW, a, MP_THREE); |
424 | ax = F_IN(f, ax, ax); |
425 | if (F_ZEROP(f, ax)) |
432c4e18 |
426 | c->ops = &ec_primeprojxops; |
8823192f |
427 | else |
432c4e18 |
428 | c->ops = &ec_primeprojops; |
8823192f |
429 | MP_DROP(ax); |
432c4e18 |
430 | c->f = f; |
431 | c->a = F_IN(f, MP_NEW, a); |
432 | c->b = F_IN(f, MP_NEW, b); |
433 | return (c); |
41cb1beb |
434 | } |
435 | |
436 | static const ec_ops ec_primeops = { |
34e4f738 |
437 | ecdestroy, ec_stdsamep, ec_idin, ec_idout, ec_idfix, |
bc985cef |
438 | ecfind, ecneg, ecadd, ec_stdsub, ecdbl, eccheck |
8823192f |
439 | }; |
440 | |
441 | static const ec_ops ec_primeprojops = { |
34e4f738 |
442 | ecdestroy, ec_stdsamep, ec_projin, ec_projout, ec_projfix, |
bc985cef |
443 | ecfind, ecneg, ecprojadd, ec_stdsub, ecprojdbl, ecprojcheck |
8823192f |
444 | }; |
445 | |
446 | static const ec_ops ec_primeprojxops = { |
34e4f738 |
447 | ecdestroy, ec_stdsamep, ec_projin, ec_projout, ec_projfix, |
bc985cef |
448 | ecfind, ecneg, ecprojadd, ec_stdsub, ecprojxdbl, ecprojcheck |
41cb1beb |
449 | }; |
450 | |
451 | /*----- Test rig ----------------------------------------------------------*/ |
452 | |
453 | #ifdef TEST_RIG |
454 | |
455 | #define MP(x) mp_readstring(MP_NEW, #x, 0, 0) |
456 | |
ceb3f0c0 |
457 | int main(int argc, char *argv[]) |
41cb1beb |
458 | { |
459 | field *f; |
460 | ec_curve *c; |
461 | ec g = EC_INIT, d = EC_INIT; |
462 | mp *p, *a, *b, *r; |
ceb3f0c0 |
463 | int i, n = argc == 1 ? 1 : atoi(argv[1]); |
41cb1beb |
464 | |
dbfee00a |
465 | printf("ec-prime: "); |
466 | fflush(stdout); |
41cb1beb |
467 | a = MP(-3); |
432c4e18 |
468 | b = MP(0xb3312fa7e23ee7e4988e056be3f82d19181d9c6efe8141120314088f5013875ac656398d8a2ed19d2a85c8edd3ec2aef); |
469 | p = MP(39402006196394479212279040100143613805079739270465446667948293404245721771496870329047266088258938001861606973112319); |
470 | r = MP(39402006196394479212279040100143613805079739270465446667946905279627659399113263569398956308152294913554433653942642); |
41cb1beb |
471 | |
f46efa79 |
472 | f = field_niceprime(p); |
ceb3f0c0 |
473 | c = ec_primeproj(f, a, b); |
41cb1beb |
474 | |
432c4e18 |
475 | g.x = MP(0xaa87ca22be8b05378eb1c71ef320ad746e1d3b628ba79b9859f741e082542a385502f25dbf55296c3a545e3872760ab7); |
476 | g.y = MP(0x3617de4a96262c6f5d9e98bf9292dc29f8f41dbd289a147ce9da3113b5f0b8c00a60b1ce1d7e819d7a431d7c90ea0e5f); |
41cb1beb |
477 | |
ceb3f0c0 |
478 | for (i = 0; i < n; i++) { |
479 | ec_mul(c, &d, &g, r); |
480 | if (EC_ATINF(&d)) { |
481 | fprintf(stderr, "zero too early\n"); |
482 | return (1); |
483 | } |
484 | ec_add(c, &d, &d, &g); |
485 | if (!EC_ATINF(&d)) { |
486 | fprintf(stderr, "didn't reach zero\n"); |
487 | MP_EPRINT("d.x", d.x); |
488 | MP_EPRINT("d.y", d.y); |
489 | return (1); |
490 | } |
491 | ec_destroy(&d); |
dbfee00a |
492 | } |
41cb1beb |
493 | ec_destroy(&g); |
494 | ec_destroycurve(c); |
495 | F_DESTROY(f); |
dbfee00a |
496 | MP_DROP(p); MP_DROP(a); MP_DROP(b); MP_DROP(r); |
497 | assert(!mparena_count(&mparena_global)); |
498 | printf("ok\n"); |
41cb1beb |
499 | return (0); |
500 | } |
501 | |
502 | #endif |
503 | |
b0ab12e6 |
504 | /*----- That's all, folks -------------------------------------------------*/ |