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b0ab12e6 | 1 | /* -*-c-*- |
2 | * | |
b0ab12e6 | 3 | * Elliptic curves over prime fields |
4 | * | |
5 | * (c) 2001 Straylight/Edgeware | |
6 | */ | |
7 | ||
45c0fd36 | 8 | /*----- Licensing notice --------------------------------------------------* |
b0ab12e6 | 9 | * |
10 | * This file is part of Catacomb. | |
11 | * | |
12 | * Catacomb is free software; you can redistribute it and/or modify | |
13 | * it under the terms of the GNU Library General Public License as | |
14 | * published by the Free Software Foundation; either version 2 of the | |
15 | * License, or (at your option) any later version. | |
45c0fd36 | 16 | * |
b0ab12e6 | 17 | * Catacomb is distributed in the hope that it will be useful, |
18 | * but WITHOUT ANY WARRANTY; without even the implied warranty of | |
19 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the | |
20 | * GNU Library General Public License for more details. | |
45c0fd36 | 21 | * |
b0ab12e6 | 22 | * You should have received a copy of the GNU Library General Public |
23 | * License along with Catacomb; if not, write to the Free | |
24 | * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, | |
25 | * MA 02111-1307, USA. | |
26 | */ | |
27 | ||
b0ab12e6 | 28 | /*----- Header files ------------------------------------------------------*/ |
29 | ||
41cb1beb | 30 | #include <mLib/sub.h> |
31 | ||
b0ab12e6 | 32 | #include "ec.h" |
33 | ||
dbfee00a | 34 | /*----- Simple prime curves -----------------------------------------------*/ |
b0ab12e6 | 35 | |
8823192f | 36 | static const ec_ops ec_primeops, ec_primeprojops, ec_primeprojxops; |
41cb1beb | 37 | |
38 | static ec *ecneg(ec_curve *c, ec *d, const ec *p) | |
b085fd91 | 39 | { |
40 | EC_COPY(d, p); | |
ceb3f0c0 | 41 | if (d->y) |
42 | d->y = F_NEG(c->f, d->y, d->y); | |
b085fd91 | 43 | return (d); |
44 | } | |
45 | ||
8823192f | 46 | static ec *ecfind(ec_curve *c, ec *d, mp *x) |
47 | { | |
48 | mp *p, *q; | |
8823192f | 49 | field *f = c->f; |
50 | ||
51 | q = F_SQR(f, MP_NEW, x); | |
52 | p = F_MUL(f, MP_NEW, x, q); | |
432c4e18 | 53 | q = F_MUL(f, q, x, c->a); |
8823192f | 54 | p = F_ADD(f, p, p, q); |
432c4e18 | 55 | p = F_ADD(f, p, p, c->b); |
8823192f | 56 | MP_DROP(q); |
57 | p = F_SQRT(f, p, p); | |
58 | if (!p) | |
59 | return (0); | |
60 | EC_DESTROY(d); | |
61 | d->x = MP_COPY(x); | |
62 | d->y = p; | |
63 | d->z = MP_COPY(f->one); | |
b085fd91 | 64 | return (d); |
65 | } | |
66 | ||
67 | static ec *ecdbl(ec_curve *c, ec *d, const ec *a) | |
b0ab12e6 | 68 | { |
1ccdb13a | 69 | if (EC_ATINF(a) || F_ZEROP(c->f, a->y)) |
b085fd91 | 70 | EC_SETINF(d); |
b085fd91 | 71 | else { |
72 | field *f = c->f; | |
b085fd91 | 73 | mp *lambda; |
74 | mp *dy, *dx; | |
75 | ||
8823192f | 76 | dx = F_SQR(f, MP_NEW, a->x); /* %$x^2$% */ |
77 | dy = F_DBL(f, MP_NEW, a->y); /* %$2 y$% */ | |
78 | dx = F_TPL(f, dx, dx); /* %$3 x^2$% */ | |
432c4e18 | 79 | dx = F_ADD(f, dx, dx, c->a); /* %$3 x^2 + A$% */ |
8823192f | 80 | dy = F_INV(f, dy, dy); /* %$(2 y)^{-1}$% */ |
81 | lambda = F_MUL(f, MP_NEW, dx, dy); /* %$\lambda = (3 x^2 + A)/(2 y)$% */ | |
b085fd91 | 82 | |
8823192f | 83 | dx = F_SQR(f, dx, lambda); /* %$\lambda^2$% */ |
84 | dy = F_DBL(f, dy, a->x); /* %$2 x$% */ | |
85 | dx = F_SUB(f, dx, dx, dy); /* %$x' = \lambda^2 - 2 x */ | |
86 | dy = F_SUB(f, dy, a->x, dx); /* %$x - x'$% */ | |
87 | dy = F_MUL(f, dy, lambda, dy); /* %$\lambda (x - x')$% */ | |
88 | dy = F_SUB(f, dy, dy, a->y); /* %$y' = \lambda (x - x') - y$% */ | |
b0ab12e6 | 89 | |
b085fd91 | 90 | EC_DESTROY(d); |
91 | d->x = dx; | |
92 | d->y = dy; | |
93 | d->z = 0; | |
94 | MP_DROP(lambda); | |
95 | } | |
96 | return (d); | |
97 | } | |
98 | ||
8823192f | 99 | static ec *ecprojdbl(ec_curve *c, ec *d, const ec *a) |
100 | { | |
1ccdb13a | 101 | if (EC_ATINF(a) || F_ZEROP(c->f, a->y)) |
8823192f | 102 | EC_SETINF(d); |
8823192f | 103 | else { |
104 | field *f = c->f; | |
8823192f | 105 | mp *p, *q, *m, *s, *dx, *dy, *dz; |
106 | ||
f69ab683 MW |
107 | q = F_ADD(f, MP_NEW, a->y, a->z); /* %$y + z$% */ |
108 | dz = F_SQR(f, MP_NEW, q); /* %$(y + z)^2 = y^2 + 2 y z + z^2$% */ | |
8823192f | 109 | p = F_SQR(f, MP_NEW, a->z); /* %$z^2$% */ |
f69ab683 MW |
110 | dz = F_SUB(f, dz, dz, p); /* %$y^2 + 2 y z$% */ |
111 | q = F_SQR(f, q, p); /* %$z^4$% */ | |
432c4e18 | 112 | p = F_MUL(f, p, q, c->a); /* %$A z^4$% */ |
8823192f | 113 | m = F_SQR(f, MP_NEW, a->x); /* %$x^2$% */ |
114 | m = F_TPL(f, m, m); /* %$3 x^2$% */ | |
115 | m = F_ADD(f, m, m, p); /* %$m = 3 x^2 + A z^4$% */ | |
116 | ||
f69ab683 MW |
117 | p = F_SQR(f, p, a->y); /* %$y^2$% */ |
118 | dz = F_SUB(f, dz, dz, p); /* %$z' = 2 y z$% */ | |
8823192f | 119 | |
f69ab683 | 120 | p = F_QDL(f, p, p); /* %$4 y^2$% */ |
8823192f | 121 | s = F_MUL(f, MP_NEW, p, a->x); /* %$s = 4 x y^2$% */ |
122 | q = F_SQR(f, q, p); /* %$16 y^4$% */ | |
123 | q = F_HLV(f, q, q); /* %$t = 8 y^4$% */ | |
124 | ||
125 | p = F_DBL(f, p, s); /* %$2 s$% */ | |
126 | dx = F_SQR(f, MP_NEW, m); /* %$m^2$% */ | |
127 | dx = F_SUB(f, dx, dx, p); /* %$x' = m^2 - 2 s$% */ | |
128 | ||
129 | s = F_SUB(f, s, s, dx); /* %$s - x'$% */ | |
130 | dy = F_MUL(f, p, m, s); /* %$m (s - x')$% */ | |
131 | dy = F_SUB(f, dy, dy, q); /* %$y' = m (s - x') - t$% */ | |
132 | ||
133 | EC_DESTROY(d); | |
134 | d->x = dx; | |
135 | d->y = dy; | |
136 | d->z = dz; | |
137 | MP_DROP(m); | |
138 | MP_DROP(q); | |
139 | MP_DROP(s); | |
140 | } | |
141 | return (d); | |
142 | } | |
143 | ||
f69ab683 MW |
144 | /* #define USE_SQUARE */ |
145 | ||
8823192f | 146 | static ec *ecprojxdbl(ec_curve *c, ec *d, const ec *a) |
147 | { | |
1ccdb13a | 148 | if (EC_ATINF(a) || F_ZEROP(c->f, a->y)) |
8823192f | 149 | EC_SETINF(d); |
8823192f | 150 | else { |
151 | field *f = c->f; | |
152 | mp *p, *q, *m, *s, *dx, *dy, *dz; | |
153 | ||
f69ab683 MW |
154 | #ifdef USE_SQUARE |
155 | q = F_ADD(f, MP_NEW, a->y, a->z); /* %$y + z$% */ | |
156 | dz = F_SQR(f, MP_NEW, q); /* %$(y + z)^2 = y^2 + 2 y z + z^2$% */ | |
157 | #else | |
158 | q = MP_NEW; | |
159 | #endif | |
8823192f | 160 | m = F_SQR(f, MP_NEW, a->z); /* %$z^2$% */ |
f69ab683 MW |
161 | #ifdef USE_SQUARE |
162 | dz = F_SUB(f, dz, dz, m); /* %$y^2 + 2 y z$% */ | |
163 | #endif | |
8823192f | 164 | p = F_SUB(f, MP_NEW, a->x, m); /* %$x - z^2$% */ |
f69ab683 | 165 | q = F_ADD(f, q, a->x, m); /* %$x + z^2$% */ |
8823192f | 166 | m = F_MUL(f, m, p, q); /* %$x^2 - z^4$% */ |
167 | m = F_TPL(f, m, m); /* %$m = 3 x^2 - 3 z^4$% */ | |
168 | ||
f69ab683 MW |
169 | #ifdef USE_SQUARE |
170 | p = F_SQR(f, p, a->y); /* %$y^2$% */ | |
171 | dz = F_SUB(f, dz, dz, p); /* %$z' = 2 y z$% */ | |
172 | p = F_QDL(f, p, p); /* %$4 y^2$% */ | |
173 | #else | |
174 | q = F_DBL(f, q, a->y); /* %$2 y% */ | |
175 | dz = F_MUL(f, MP_NEW, a->z, q); /* %$z' = 2 y z$% */ | |
176 | p = F_SQR(f, p, q); /* %$4 y^2% */ | |
177 | #endif | |
8823192f | 178 | |
8823192f | 179 | s = F_MUL(f, MP_NEW, p, a->x); /* %$s = 4 x y^2$% */ |
180 | q = F_SQR(f, q, p); /* %$16 y^4$% */ | |
181 | q = F_HLV(f, q, q); /* %$t = 8 y^4$% */ | |
182 | ||
183 | p = F_DBL(f, p, s); /* %$2 s$% */ | |
184 | dx = F_SQR(f, MP_NEW, m); /* %$m^2$% */ | |
185 | dx = F_SUB(f, dx, dx, p); /* %$x' = m^2 - 2 s$% */ | |
186 | ||
187 | s = F_SUB(f, s, s, dx); /* %$s - x'$% */ | |
188 | dy = F_MUL(f, p, m, s); /* %$m (s - x')$% */ | |
189 | dy = F_SUB(f, dy, dy, q); /* %$y' = m (s - x') - t$% */ | |
190 | ||
191 | EC_DESTROY(d); | |
192 | d->x = dx; | |
193 | d->y = dy; | |
194 | d->z = dz; | |
195 | MP_DROP(m); | |
196 | MP_DROP(q); | |
197 | MP_DROP(s); | |
198 | } | |
199 | return (d); | |
200 | } | |
201 | ||
b085fd91 | 202 | static ec *ecadd(ec_curve *c, ec *d, const ec *a, const ec *b) |
203 | { | |
b0ab12e6 | 204 | if (a == b) |
205 | ecdbl(c, d, a); | |
206 | else if (EC_ATINF(a)) | |
207 | EC_COPY(d, b); | |
208 | else if (EC_ATINF(b)) | |
209 | EC_COPY(d, a); | |
b085fd91 | 210 | else { |
211 | field *f = c->f; | |
212 | mp *lambda; | |
213 | mp *dy, *dx; | |
214 | ||
215 | if (!MP_EQ(a->x, b->x)) { | |
8823192f | 216 | dy = F_SUB(f, MP_NEW, a->y, b->y); /* %$y_0 - y_1$% */ |
217 | dx = F_SUB(f, MP_NEW, a->x, b->x); /* %$x_0 - x_1$% */ | |
218 | dx = F_INV(f, dx, dx); /* %$(x_0 - x_1)^{-1}$% */ | |
b085fd91 | 219 | lambda = F_MUL(f, MP_NEW, dy, dx); |
8823192f | 220 | /* %$\lambda = (y_0 - y1)/(x_0 - x_1)$% */ |
221 | } else if (F_ZEROP(c->f, a->y) || !MP_EQ(a->y, b->y)) { | |
b0ab12e6 | 222 | EC_SETINF(d); |
b085fd91 | 223 | return (d); |
224 | } else { | |
8823192f | 225 | dx = F_SQR(f, MP_NEW, a->x); /* %$x_0^2$% */ |
226 | dx = F_TPL(f, dx, dx); /* %$3 x_0^2$% */ | |
432c4e18 | 227 | dx = F_ADD(f, dx, dx, c->a); /* %$3 x_0^2 + A$% */ |
8823192f | 228 | dy = F_DBL(f, MP_NEW, a->y); /* %$2 y_0$% */ |
229 | dy = F_INV(f, dy, dy); /* %$(2 y_0)^{-1}$% */ | |
41cb1beb | 230 | lambda = F_MUL(f, MP_NEW, dx, dy); |
8823192f | 231 | /* %$\lambda = (3 x_0^2 + A)/(2 y_0)$% */ |
b085fd91 | 232 | } |
233 | ||
8823192f | 234 | dx = F_SQR(f, dx, lambda); /* %$\lambda^2$% */ |
235 | dx = F_SUB(f, dx, dx, a->x); /* %$\lambda^2 - x_0$% */ | |
236 | dx = F_SUB(f, dx, dx, b->x); /* %$x' = \lambda^2 - x_0 - x_1$% */ | |
237 | dy = F_SUB(f, dy, b->x, dx); /* %$x_1 - x'$% */ | |
238 | dy = F_MUL(f, dy, lambda, dy); /* %$\lambda (x_1 - x')$% */ | |
ceb3f0c0 | 239 | dy = F_SUB(f, dy, dy, b->y); /* %$y' = \lambda (x_1 - x') - y_1$% */ |
b0ab12e6 | 240 | |
b085fd91 | 241 | EC_DESTROY(d); |
242 | d->x = dx; | |
243 | d->y = dy; | |
244 | d->z = 0; | |
245 | MP_DROP(lambda); | |
b0ab12e6 | 246 | } |
b085fd91 | 247 | return (d); |
b0ab12e6 | 248 | } |
249 | ||
8823192f | 250 | static ec *ecprojadd(ec_curve *c, ec *d, const ec *a, const ec *b) |
251 | { | |
252 | if (a == b) | |
253 | c->ops->dbl(c, d, a); | |
254 | else if (EC_ATINF(a)) | |
255 | EC_COPY(d, b); | |
256 | else if (EC_ATINF(b)) | |
257 | EC_COPY(d, a); | |
258 | else { | |
259 | field *f = c->f; | |
391faf42 | 260 | mp *p, *q, *r, *w, *u, *uu, *s, *ss, *dx, *dy, *dz; |
8823192f | 261 | |
262 | q = F_SQR(f, MP_NEW, a->z); /* %$z_0^2$% */ | |
263 | u = F_MUL(f, MP_NEW, q, b->x); /* %$u = x_1 z_0^2$% */ | |
264 | p = F_MUL(f, MP_NEW, q, b->y); /* %$y_1 z_0^2$% */ | |
265 | s = F_MUL(f, q, p, a->z); /* %$s = y_1 z_0^3$% */ | |
266 | ||
391faf42 | 267 | q = F_SQR(f, MP_NEW, b->z); /* %$z_1^2$% */ |
268 | uu = F_MUL(f, MP_NEW, q, a->x); /* %$uu = x_0 z_1^2$%*/ | |
269 | p = F_MUL(f, p, q, a->y); /* %$y_0 z_1^2$% */ | |
270 | ss = F_MUL(f, q, p, b->z); /* %$ss = y_0 z_1^3$% */ | |
271 | ||
272 | w = F_SUB(f, p, uu, u); /* %$w = uu - u$% */ | |
273 | r = F_SUB(f, MP_NEW, ss, s); /* %$r = ss - s$% */ | |
8823192f | 274 | if (F_ZEROP(f, w)) { |
ceb3f0c0 | 275 | MP_DROP(w); |
276 | MP_DROP(u); | |
277 | MP_DROP(s); | |
391faf42 | 278 | MP_DROP(uu); |
279 | MP_DROP(ss); | |
8823192f | 280 | if (F_ZEROP(f, r)) { |
8823192f | 281 | MP_DROP(r); |
8823192f | 282 | return (c->ops->dbl(c, d, a)); |
283 | } else { | |
8823192f | 284 | MP_DROP(r); |
8823192f | 285 | EC_SETINF(d); |
286 | return (d); | |
287 | } | |
288 | } | |
391faf42 | 289 | u = F_ADD(f, u, u, uu); /* %$t = uu + u$% */ |
3f19a2c1 | 290 | s = F_ADD(f, s, s, ss); /* %$m = ss + s$% */ |
8823192f | 291 | |
391faf42 | 292 | uu = F_MUL(f, uu, a->z, w); /* %$z_0 w$% */ |
293 | dz = F_MUL(f, ss, uu, b->z); /* %$z' = z_0 z_1 w$% */ | |
8823192f | 294 | |
391faf42 | 295 | p = F_SQR(f, uu, w); /* %$w^2$% */ |
8823192f | 296 | q = F_MUL(f, MP_NEW, p, u); /* %$t w^2$% */ |
297 | u = F_MUL(f, u, p, w); /* %$w^3$% */ | |
298 | p = F_MUL(f, p, u, s); /* %$m w^3$% */ | |
45c0fd36 | 299 | |
8823192f | 300 | dx = F_SQR(f, u, r); /* %$r^2$% */ |
301 | dx = F_SUB(f, dx, dx, q); /* %$x' = r^2 - t w^2$% */ | |
302 | ||
303 | s = F_DBL(f, s, dx); /* %$2 x'$% */ | |
304 | q = F_SUB(f, q, q, s); /* %$v = t w^2 - 2 x'$% */ | |
305 | dy = F_MUL(f, s, q, r); /* %$v r$% */ | |
306 | dy = F_SUB(f, dy, dy, p); /* %$v r - m w^3$% */ | |
307 | dy = F_HLV(f, dy, dy); /* %$y' = (v r - m w^3)/2$% */ | |
308 | ||
309 | EC_DESTROY(d); | |
310 | d->x = dx; | |
311 | d->y = dy; | |
312 | d->z = dz; | |
313 | MP_DROP(p); | |
314 | MP_DROP(q); | |
315 | MP_DROP(r); | |
316 | MP_DROP(w); | |
317 | } | |
318 | return (d); | |
319 | } | |
320 | ||
321 | static int eccheck(ec_curve *c, const ec *p) | |
322 | { | |
8823192f | 323 | field *f = c->f; |
34e4f738 | 324 | mp *l, *x, *r; |
8823192f | 325 | int rc; |
34e4f738 | 326 | if (EC_ATINF(p)) return (0); |
327 | l = F_SQR(f, MP_NEW, p->y); | |
328 | x = F_SQR(f, MP_NEW, p->x); | |
329 | r = F_MUL(f, MP_NEW, x, p->x); | |
432c4e18 | 330 | x = F_MUL(f, x, c->a, p->x); |
8823192f | 331 | r = F_ADD(f, r, r, x); |
432c4e18 | 332 | r = F_ADD(f, r, r, c->b); |
8823192f | 333 | rc = MP_EQ(l, r) ? 0 : -1; |
334 | mp_drop(l); | |
335 | mp_drop(x); | |
336 | mp_drop(r); | |
337 | return (rc); | |
338 | } | |
339 | ||
340 | static int ecprojcheck(ec_curve *c, const ec *p) | |
341 | { | |
342 | ec t = EC_INIT; | |
343 | int rc; | |
45c0fd36 | 344 | |
8823192f | 345 | c->ops->fix(c, &t, p); |
346 | rc = eccheck(c, &t); | |
347 | EC_DESTROY(&t); | |
348 | return (rc); | |
349 | } | |
350 | ||
41cb1beb | 351 | static void ecdestroy(ec_curve *c) |
352 | { | |
432c4e18 | 353 | MP_DROP(c->a); |
354 | MP_DROP(c->b); | |
355 | DESTROY(c); | |
41cb1beb | 356 | } |
357 | ||
358 | /* --- @ec_prime@, @ec_primeproj@ --- * | |
359 | * | |
dbfee00a | 360 | * Arguments: @field *f@ = the underlying field for this elliptic curve |
41cb1beb | 361 | * @mp *a, *b@ = the coefficients for this curve |
362 | * | |
02d7884d | 363 | * Returns: A pointer to the curve, or null. |
41cb1beb | 364 | * |
365 | * Use: Creates a curve structure for an elliptic curve defined over | |
366 | * a prime field. The @primeproj@ variant uses projective | |
367 | * coordinates, which can be a win. | |
368 | */ | |
369 | ||
370 | extern ec_curve *ec_prime(field *f, mp *a, mp *b) | |
371 | { | |
432c4e18 | 372 | ec_curve *c = CREATE(ec_curve); |
373 | c->ops = &ec_primeops; | |
374 | c->f = f; | |
375 | c->a = F_IN(f, MP_NEW, a); | |
376 | c->b = F_IN(f, MP_NEW, b); | |
377 | return (c); | |
41cb1beb | 378 | } |
379 | ||
8823192f | 380 | extern ec_curve *ec_primeproj(field *f, mp *a, mp *b) |
381 | { | |
432c4e18 | 382 | ec_curve *c = CREATE(ec_curve); |
8823192f | 383 | mp *ax; |
384 | ||
385 | ax = mp_add(MP_NEW, a, MP_THREE); | |
386 | ax = F_IN(f, ax, ax); | |
387 | if (F_ZEROP(f, ax)) | |
432c4e18 | 388 | c->ops = &ec_primeprojxops; |
8823192f | 389 | else |
432c4e18 | 390 | c->ops = &ec_primeprojops; |
8823192f | 391 | MP_DROP(ax); |
432c4e18 | 392 | c->f = f; |
393 | c->a = F_IN(f, MP_NEW, a); | |
394 | c->b = F_IN(f, MP_NEW, b); | |
395 | return (c); | |
41cb1beb | 396 | } |
397 | ||
398 | static const ec_ops ec_primeops = { | |
f94b972d | 399 | "prime", |
34e4f738 | 400 | ecdestroy, ec_stdsamep, ec_idin, ec_idout, ec_idfix, |
bc985cef | 401 | ecfind, ecneg, ecadd, ec_stdsub, ecdbl, eccheck |
8823192f | 402 | }; |
403 | ||
404 | static const ec_ops ec_primeprojops = { | |
f94b972d | 405 | "primeproj", |
34e4f738 | 406 | ecdestroy, ec_stdsamep, ec_projin, ec_projout, ec_projfix, |
bc985cef | 407 | ecfind, ecneg, ecprojadd, ec_stdsub, ecprojdbl, ecprojcheck |
8823192f | 408 | }; |
409 | ||
410 | static const ec_ops ec_primeprojxops = { | |
f94b972d | 411 | "primeproj", |
34e4f738 | 412 | ecdestroy, ec_stdsamep, ec_projin, ec_projout, ec_projfix, |
bc985cef | 413 | ecfind, ecneg, ecprojadd, ec_stdsub, ecprojxdbl, ecprojcheck |
41cb1beb | 414 | }; |
415 | ||
416 | /*----- Test rig ----------------------------------------------------------*/ | |
417 | ||
418 | #ifdef TEST_RIG | |
419 | ||
420 | #define MP(x) mp_readstring(MP_NEW, #x, 0, 0) | |
421 | ||
ceb3f0c0 | 422 | int main(int argc, char *argv[]) |
41cb1beb | 423 | { |
424 | field *f; | |
425 | ec_curve *c; | |
426 | ec g = EC_INIT, d = EC_INIT; | |
427 | mp *p, *a, *b, *r; | |
ceb3f0c0 | 428 | int i, n = argc == 1 ? 1 : atoi(argv[1]); |
41cb1beb | 429 | |
dbfee00a | 430 | printf("ec-prime: "); |
431 | fflush(stdout); | |
41cb1beb | 432 | a = MP(-3); |
432c4e18 | 433 | b = MP(0xb3312fa7e23ee7e4988e056be3f82d19181d9c6efe8141120314088f5013875ac656398d8a2ed19d2a85c8edd3ec2aef); |
434 | p = MP(39402006196394479212279040100143613805079739270465446667948293404245721771496870329047266088258938001861606973112319); | |
435 | r = MP(39402006196394479212279040100143613805079739270465446667946905279627659399113263569398956308152294913554433653942642); | |
41cb1beb | 436 | |
f46efa79 | 437 | f = field_niceprime(p); |
ceb3f0c0 | 438 | c = ec_primeproj(f, a, b); |
45c0fd36 | 439 | |
432c4e18 | 440 | g.x = MP(0xaa87ca22be8b05378eb1c71ef320ad746e1d3b628ba79b9859f741e082542a385502f25dbf55296c3a545e3872760ab7); |
441 | g.y = MP(0x3617de4a96262c6f5d9e98bf9292dc29f8f41dbd289a147ce9da3113b5f0b8c00a60b1ce1d7e819d7a431d7c90ea0e5f); | |
41cb1beb | 442 | |
45c0fd36 | 443 | for (i = 0; i < n; i++) { |
ceb3f0c0 | 444 | ec_mul(c, &d, &g, r); |
445 | if (EC_ATINF(&d)) { | |
446 | fprintf(stderr, "zero too early\n"); | |
447 | return (1); | |
448 | } | |
449 | ec_add(c, &d, &d, &g); | |
450 | if (!EC_ATINF(&d)) { | |
451 | fprintf(stderr, "didn't reach zero\n"); | |
452 | MP_EPRINT("d.x", d.x); | |
453 | MP_EPRINT("d.y", d.y); | |
454 | return (1); | |
455 | } | |
456 | ec_destroy(&d); | |
dbfee00a | 457 | } |
41cb1beb | 458 | ec_destroy(&g); |
459 | ec_destroycurve(c); | |
460 | F_DESTROY(f); | |
dbfee00a | 461 | MP_DROP(p); MP_DROP(a); MP_DROP(b); MP_DROP(r); |
462 | assert(!mparena_count(&mparena_global)); | |
463 | printf("ok\n"); | |
41cb1beb | 464 | return (0); |
465 | } | |
466 | ||
467 | #endif | |
468 | ||
b0ab12e6 | 469 | /*----- That's all, folks -------------------------------------------------*/ |