Knapsack Based ECC Encryption and Decryption

Elliptic Curve Cryptography provides a secure means of exchanging keys among communicating hosts using the Diffie Hellman Key Exchange algorithm. Encryption and Decryption of texts and messages have also been attempted. This paper presents the implementation of ECC by first transforming the message into an affine point on the EC, and then applying the knapsack algorithm on ECC encrypted message over the finite field GF(p). In ECC we normally start with an affine point called Pm(x,y). This point lies on the elliptic curve. In this paper we have illustrated encryption/decryption involving the ASCII value of the characters constituting the message, and then subjecting it to the knapsack algorithm. We compare our proposed algorithm with RSA algorithm and show that our algorithm is better due to the high degree of sophistication and complexity involved. It is almost infeasible to attempt a brute force attack. Moreover only one parameter, namely the Knapsack vector ai alone needs to be kept secret. On the contrary in RSA, three parameters such as the modulus n, its factors p and q need to be kept secret.