It is believed that the ECDHP, the ECDLP, and the BPI are hard problems for proper parameter setting.
Given a valid released [c.sub.i][R.sub.v] and another point [??], one cannot derive the value [c.sub.i][??] as long as the ECDHP is hard.
* Elliptic Curve Diffie-Hellman Problem (ECDHP
): Given three points P, r*P, s*P belonging to [E.sub.p](a, b) for r, s [member of] [F.sup.*.sub.p], this problem asks to find the point r*s*P over [E.sub.p](a,b).