An approach to enhancement in security using elliptic curve cryptography over RSA

Due to the huge amount of data transmitted along with securing data content is becoming more important concern. Data encryption is widely used to ensure security in open networks such as the Internet. Development of cryptography research and enhancement of computer technology, the capabilities of cryptosystems such as RSA and Diffie-Hellman are inadequate due to the requirement of large number of data. The cryptosystem based on Elliptic Curve Cryptography is recently gained a popularity in industry. ECC Encryption and decryption methods can only encrypt and decrypt a point on the curve and not messages. The Encoding (converting message to a point) and Decoding (converting a point to a message) are important functions in encryption and decryption in ECC. This paper investigates the improvement of performance in security of text, images, audio based application using Elliptic Curve Cryptography (ECC) algorithm and evaluate the effectiveness of ECC over RSA algorithm. For the similar level of security for currently known attacks, elliptic curve based systems can be implemented with smaller parameters, leading to significant performance advantages. In the present study the performance advantages of elliptic curve systems are highlighted by comparing their performance with RSA based systems. The elliptic curves considered in the study are defined over Zp, called the prime curves and all the mathematical operations of ECC is defined over the elliptic curve y2 = x3 + Ax + B, where 4A3 + 27B2 ≠ 0. ‘A’ and ‘B’ are called curve parameters and different values of these parameters define different elliptic curve. The public key is a point (x, y) lying on the curve and the private key is a random number. The public key is obtained by multiplying the private key with the generator point G in the curve. The generator point G, the curve parameters ‘A’ and ‘B’, together with few more constants constitutes the domain parameter of ECC. One main advantage of ECC is its small key size. A 160-bit key used in ECC is considered to be as secured as 1024-bit key in RSA.