/* -*-c-*-
*
- * $Id: ec.c,v 1.4.4.1 2003/06/10 13:43:53 mdw Exp $
+ * $Id: ec.c,v 1.6 2004/03/23 15:19:32 mdw Exp $
*
* Elliptic curve definitions
*
/*----- Revision history --------------------------------------------------*
*
* $Log: ec.c,v $
+ * Revision 1.6 2004/03/23 15:19:32 mdw
+ * Test elliptic curves more thoroughly.
+ *
+ * Revision 1.5 2004/03/21 22:52:06 mdw
+ * Merge and close elliptic curve branch.
+ *
+ * Revision 1.4.4.2 2004/03/20 00:13:31 mdw
+ * Projective coordinates for prime curves
+ *
* Revision 1.4.4.1 2003/06/10 13:43:53 mdw
* Simple (non-projective) curves over prime fields now seem to work.
*
ec *ec_copy(ec *d, const ec *p) { EC_COPY(d, p); return (d); }
+/* --- @ec_eq@ --- *
+ *
+ * Arguments: @const ec *p, *q@ = two points
+ *
+ * Returns: Nonzero if the points are equal. Compares external-format
+ * points.
+ */
+
+int ec_eq(const ec *p, const ec *q) { return (EC_EQ(p, q)); }
+
/*----- Standard curve operations -----------------------------------------*/
-/* --- @ec_idin@, @ec_idout@ --- *
+/* --- @ec_idin@, @ec_idout@, @ec_idfix@ --- *
*
* Arguments: @ec_curve *c@ = pointer to an elliptic curve
* @ec *d@ = pointer to the destination
return (d);
}
+ec *ec_idfix(ec_curve *c, ec *d, const ec *p)
+{
+ EC_COPY(d, p);
+ return (d);
+}
+
/* --- @ec_projin@, @ec_projout@ --- *
*
* Arguments: @ec_curve *c@ = pointer to an elliptic curve
if (EC_ATINF(p))
EC_SETINF(d);
else {
- mp *x, *y, *z;
+ mp *x, *y, *z, *zz;
field *f = c->f;
z = F_INV(f, MP_NEW, p->z);
- x = F_MUL(f, d->x, p->x, z);
+ zz = F_SQR(f, MP_NEW, z);
+ z = F_MUL(f, z, zz, z);
+ x = F_MUL(f, d->x, p->x, zz);
y = F_MUL(f, d->y, p->y, z);
mp_drop(z);
+ mp_drop(zz);
mp_drop(d->z);
d->x = F_OUT(f, x, x);
d->y = F_OUT(f, y, y);
return (d);
}
+ec *ec_projfix(ec_curve *c, ec *d, const ec *p)
+{
+ if (EC_ATINF(p))
+ EC_SETINF(d);
+ else if (d->z == c->f->one)
+ EC_COPY(d, p);
+ else {
+ mp *z, *zz;
+ field *f = c->f;
+ z = F_INV(f, MP_NEW, p->z);
+ zz = F_SQR(f, MP_NEW, z);
+ z = F_MUL(f, z, zz, z);
+ d->x = F_MUL(f, d->x, p->x, zz);
+ d->y = F_MUL(f, d->y, p->y, z);
+ mp_drop(z);
+ mp_drop(zz);
+ mp_drop(d->z);
+ d->z = MP_COPY(f->one);
+ }
+ return (d);
+}
+
/* --- @ec_stdsub@ --- *
*
* Arguments: @ec_curve *c@ = pointer to an elliptic curve
{
ec t = EC_INIT;
EC_NEG(c, &t, q);
+ EC_FIX(c, &t, &t);
EC_ADD(c, d, p, &t);
EC_DESTROY(&t);
return (d);
x = F_IN(c->f, MP_NEW, x);
if ((d = EC_FIND(c, d, x)) != 0)
EC_OUT(c, d, d);
- mp_drop(x);
+ MP_DROP(x);
return (d);
}
ec pp, qq;
EC_IN(c, &pp, p);
EC_IN(c, &qq, q);
- EC_SUB(c, d, &qq, &qq);
+ EC_SUB(c, d, &pp, &qq);
EC_OUT(c, d, d);
EC_DESTROY(&pp);
EC_DESTROY(&qq);
return (EC_OUT(c, d, d));
}
+/* --- @ec_check@ --- *
+ *
+ * Arguments: @ec_curve *c@ = pointer to an elliptic curve
+ * @const ec *p@ = pointer to the point
+ *
+ * Returns: Zero if OK, nonzero if this is an invalid point.
+ *
+ * Use: Checks that a point is actually on an elliptic curve.
+ */
+
+int ec_check(ec_curve *c, const ec *p)
+{
+ ec t = EC_INIT;
+ int rc;
+
+ if (EC_ATINF(p))
+ return (0);
+ EC_IN(c, &t, p);
+ rc = EC_CHECK(c, &t);
+ EC_DESTROY(&t);
+ return (rc);
+}
+
+/* --- @ec_rand@ --- *
+ *
+ * Arguments: @ec_curve *c@ = pointer to an elliptic curve
+ * @ec *d@ = pointer to the destination point
+ * @grand *r@ = random number source
+ *
+ * Returns: The destination @d@.
+ *
+ * Use: Finds a random point on the given curve.
+ */
+
+ec *ec_rand(ec_curve *c, ec *d, grand *r)
+{
+ mp *x = MP_NEW;
+ do x = F_RAND(c->f, x, r); while (!EC_FIND(c, d, x));
+ mp_drop(x);
+ if (grand_range(r, 2)) EC_NEG(c, d, d);
+ return (EC_OUT(c, d, d));
+}
+
/* --- @ec_imul@, @ec_mul@ --- *
*
* Arguments: @ec_curve *c@ = pointer to an elliptic curve
EC_SETINF(d);
if (MP_LEN(n) == 0)
;
- else if (MP_LEN(n) < EXP_THRESH)
- EXP_SIMPLE(*d, t, n);
- else
- EXP_WINDOW(*d, t, n);
+ else {
+ if (n->f & MP_NEG)
+ EC_NEG(c, &t, &t);
+ if (MP_LEN(n) < EXP_THRESH)
+ EXP_SIMPLE(*d, t, n);
+ else
+ EXP_WINDOW(*d, t, n);
+ }
EC_DESTROY(&t);
return (d);
}