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