A new approach to Elliptic Curve Cryptography

There are lots of cryptosystem which provides high security but they all come with a price that is large key size which requires high computing power device. Researchers have come up with an alternative for this that provides high security with smaller key size. This alternative is the Elliptic Curve Cryptosystem. This paper deals with the mathematics involve in the cryptosystem and an approach to work with smaller key size when the elliptic curve equation and the generator are kept secret between the users.