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Data encryption is widely used to ensure security in open networks such as the internet. With the fast development of cryptography research and computer technology, the capabilities of cryptosystems such as of RSA and Diffie-Hellman are inadequate due the requirement of large number of bits. The cryptosystem based on elliptic curve cryptography (ECC) is becoming the recent trend of public key cryptography. This paper presents the implementation of ECC by first transforming the message into an affine point on the elliptic curve (EC), over the finite field GF(p). In ECC we normally start with an affine point called Pm(x,y) which lies on the elliptic curve. In this paper we illustrate the process of encryption/decryption of a text message . It is almost infeasible to attempt a brute force attack to break the cryptosystem using ECC.