In the earlier cryptography articles, we have seen classical cryptosystems, various public-key cryptosystems and many primality tests. In this article we shall see how elliptic curves are used in cryptography. When public-key cryptography was introduced to the research community by Diffe and Hellman in 1976 [4], it represented an exciting innovation in cryptography and a surprising applications of number theory. Strictly speaking, number theory provides many trapdoor one way functions (definition of such a function has been already introduced in the earlier article).