/* -*-c-*-
*
- * $Id: ec-prime.c,v 1.3.4.2 2004/03/20 00:13:31 mdw Exp $
+ * $Id: ec-prime.c,v 1.6 2004/03/23 15:19:32 mdw Exp $
*
* Elliptic curves over prime fields
*
/*----- Revision history --------------------------------------------------*
*
* $Log: ec-prime.c,v $
+ * Revision 1.6 2004/03/23 15:19:32 mdw
+ * Test elliptic curves more thoroughly.
+ *
+ * Revision 1.5 2004/03/22 02:19:10 mdw
+ * Rationalise the sliding-window threshold. Drop guarantee that right
+ * arguments to EC @add@ are canonical, and fix up projective implementations
+ * to cope.
+ *
+ * Revision 1.4 2004/03/21 22:52:06 mdw
+ * Merge and close elliptic curve branch.
+ *
+ * Revision 1.3.4.3 2004/03/21 22:39:46 mdw
+ * Elliptic curves on binary fields work.
+ *
* Revision 1.3.4.2 2004/03/20 00:13:31 mdw
* Projective coordinates for prime curves
*
static ec *ecneg(ec_curve *c, ec *d, const ec *p)
{
EC_COPY(d, p);
- d->y = F_NEG(c->f, d->y, d->y);
+ if (d->y)
+ d->y = F_NEG(c->f, d->y, d->y);
return (d);
}
dx = F_SUB(f, dx, dx, b->x); /* %$x' = \lambda^2 - x_0 - x_1$% */
dy = F_SUB(f, dy, b->x, dx); /* %$x_1 - x'$% */
dy = F_MUL(f, dy, lambda, dy); /* %$\lambda (x_1 - x')$% */
- dy = F_SUB(f, dy, dy, b->y);
- /* %$y' = \lambda (x_1 - x') - y_1$% */
+ dy = F_SUB(f, dy, dy, b->y); /* %$y' = \lambda (x_1 - x') - y_1$% */
EC_DESTROY(d);
d->x = dx;
EC_COPY(d, a);
else {
field *f = c->f;
- mp *p, *q, *r, *w, *u, *s, *dx, *dy, *dz;
+ mp *p, *q, *r, *w, *u, *uu, *s, *ss, *dx, *dy, *dz;
q = F_SQR(f, MP_NEW, a->z); /* %$z_0^2$% */
u = F_MUL(f, MP_NEW, q, b->x); /* %$u = x_1 z_0^2$% */
p = F_MUL(f, MP_NEW, q, b->y); /* %$y_1 z_0^2$% */
s = F_MUL(f, q, p, a->z); /* %$s = y_1 z_0^3$% */
- w = F_SUB(f, p, a->x, u); /* %$w = x_0 - u$% */
- r = F_SUB(f, MP_NEW, a->y, s); /* %$r = y_0 - s$% */
+ q = F_SQR(f, MP_NEW, b->z); /* %$z_1^2$% */
+ uu = F_MUL(f, MP_NEW, q, a->x); /* %$uu = x_0 z_1^2$%*/
+ p = F_MUL(f, p, q, a->y); /* %$y_0 z_1^2$% */
+ ss = F_MUL(f, q, p, b->z); /* %$ss = y_0 z_1^3$% */
+
+ w = F_SUB(f, p, uu, u); /* %$w = uu - u$% */
+ r = F_SUB(f, MP_NEW, ss, s); /* %$r = ss - s$% */
if (F_ZEROP(f, w)) {
+ MP_DROP(w);
+ MP_DROP(u);
+ MP_DROP(s);
+ MP_DROP(uu);
+ MP_DROP(ss);
if (F_ZEROP(f, r)) {
- MP_DROP(w);
MP_DROP(r);
- MP_DROP(u);
- MP_DROP(s);
return (c->ops->dbl(c, d, a));
} else {
- MP_DROP(w);
MP_DROP(r);
- MP_DROP(u);
- MP_DROP(s);
EC_SETINF(d);
return (d);
}
}
- u = F_ADD(f, u, u, a->x); /* %$t = x_0 + u$% */
- s = F_ADD(f, s, s, a->y); /* %$m = y_0 + r$% */
+ u = F_ADD(f, u, u, uu); /* %$t = uu + u$% */
+ s = F_ADD(f, s, s, ss); /* %$m = ss + r$% */
- dz = F_MUL(f, MP_NEW, a->z, w); /* %$z' = z_0 w$% */
+ uu = F_MUL(f, uu, a->z, w); /* %$z_0 w$% */
+ dz = F_MUL(f, ss, uu, b->z); /* %$z' = z_0 z_1 w$% */
- p = F_SQR(f, MP_NEW, w); /* %$w^2$% */
+ p = F_SQR(f, uu, w); /* %$w^2$% */
q = F_MUL(f, MP_NEW, p, u); /* %$t w^2$% */
u = F_MUL(f, u, p, w); /* %$w^3$% */
p = F_MUL(f, p, u, s); /* %$m w^3$% */
static const ec_ops ec_primeops = {
ecdestroy, ec_idin, ec_idout, ec_idfix,
- 0, ecneg, ecadd, ec_stdsub, ecdbl, eccheck
+ ecfind, ecneg, ecadd, ec_stdsub, ecdbl, eccheck
};
static const ec_ops ec_primeprojops = {
ecdestroy, ec_projin, ec_projout, ec_projfix,
- 0, ecneg, ecprojadd, ec_stdsub, ecprojdbl, ecprojcheck
+ ecfind, ecneg, ecprojadd, ec_stdsub, ecprojdbl, ecprojcheck
};
static const ec_ops ec_primeprojxops = {
ecdestroy, ec_projin, ec_projout, ec_projfix,
- 0, ecneg, ecprojadd, ec_stdsub, ecprojxdbl, ecprojcheck
+ ecfind, ecneg, ecprojadd, ec_stdsub, ecprojxdbl, ecprojcheck
};
/*----- Test rig ----------------------------------------------------------*/
#define MP(x) mp_readstring(MP_NEW, #x, 0, 0)
-int main(void)
+int main(int argc, char *argv[])
{
field *f;
ec_curve *c;
ec g = EC_INIT, d = EC_INIT;
mp *p, *a, *b, *r;
+ int i, n = argc == 1 ? 1 : atoi(argv[1]);
printf("ec-prime: ");
fflush(stdout);
r = MP(6277101735386680763835789423176059013767194773182842284080);
f = field_prime(p);
- c = ec_prime(f, a, b);
+ c = ec_primeproj(f, a, b);
g.x = MP(0x188da80eb03090f67cbf20eb43a18800f4ff0afd82ff1012);
g.y = MP(0x07192b95ffc8da78631011ed6b24cdd573f977a11e794811);
- ec_mul(c, &d, &g, r);
- if (EC_ATINF(&d)) {
- fprintf(stderr, "zero too early\n");
- return (1);
- }
- ec_add(c, &d, &d, &g);
- if (!EC_ATINF(&d)) {
- fprintf(stderr, "didn't reach zero\n");
- MP_EPRINT("d.x", d.x);
- MP_EPRINT("d.y", d.y);
- return (1);
+ for (i = 0; i < n; i++) {
+ ec_mul(c, &d, &g, r);
+ if (EC_ATINF(&d)) {
+ fprintf(stderr, "zero too early\n");
+ return (1);
+ }
+ ec_add(c, &d, &d, &g);
+ if (!EC_ATINF(&d)) {
+ fprintf(stderr, "didn't reach zero\n");
+ MP_EPRINT("d.x", d.x);
+ MP_EPRINT("d.y", d.y);
+ return (1);
+ }
+ ec_destroy(&d);
}
-
- ec_destroy(&d);
ec_destroy(&g);
ec_destroycurve(c);
F_DESTROY(f);
projects / u / mdw / catacomb / blobdiff