A New Public Key Cryptosystem based on Weil Pairing

In 1987 Koblitz and Miller first proposed public key cryptosystems using the group of points of an elliptic curve over a finite field. The security of these cryptosystems was based upon the presumed intractability of the problem of computing logarithm in the elliptic curve group. Now we propose a new cryptosystem over elliptic curves whose security is based on expressing a torsion point in terms of the basis points. Since latter is more complicated than solving ECDLP. Consequently our cryptosystem is more secure than all cryptosystems based on ECDLP.