Elliptic Curves as Tool for Public Key Cryptography

- Cryptography is the technique of transforming an intelligible message into unintelligible format so that the message can’t be read or understood by an unauthorized person during its transmission over the public networks. A number of cryptographic techniques have been developed over the centuries. With technological advancement, new techniques have been evolved significantly. Public key cryptography offers a great security for transmitting data over the public networks such as Internet. The popular public key cryptosystems like RSA and Diffie- Hellman are becoming slowly disappearing because of requirement of large number of bits in the encryption and decryption keys. Elliptic Curve Cryptograph (ECC) is emerging as an alternative to the existing public key cryptosystems. This paper describes the idea of Elliptic Curve Cryptography (ECC) and its implementation through two dimensional (2D) geometry for data encryption and decryption. This paper discusses the implementation of ECC over prime field. Much attention has been given on the mathematics of elliptic curves starting from their derivations.