Ankita Soni, Nisheeth Saxena
Abstract: The paper describes the basic idea of Elliptic Curve Cryptography (ECC) and the use of Elliptic curves in Elliptic curve cryptography. This paper gives an introduction to elliptic curves and the basic operations of elliptic curves. Elliptic Curve Diffie Hellman (ECDH) key exchange protocol of ECC is described. The paper illustrates the procedure of Encryption and Decryption of message by first transforming the message into an affine point on the Elliptic Curve (EC), over the finite field GF (p). In ECC we normally starts with an affine point called Pm (x, y) which lies on the elliptic curve. And further the process of encryption and decryption of a text message is implemented. A comparison is performed between the encrypted text messages using different key sizes, to calculate the time consumed by each. The security strength of ECC lies in the unfeasibility of solving the ECDLP (Elliptic Curve Discrete Logarithmic Problem) .
Keywords: Elliptic curve cryptography ECC, Elliptic Curve EC, Discrete Logarithm Problem DLP, Elliptic Curve Diffie Hellman ECDH