Securing Elliptic Curve based El-Gamal against Pollard Rho attack using Elliptic Curve based Diffie-Hellman Key Exchange

Elliptic Curve based El-Gamal (ECEG) cryptosystem is one of many widely used public key cryptosystems that makes use the elliptic curve discrete logarithm problem (ECDLP). For breaking ECDLP, Pollard Rho is currently the fastest attack. In this study a hybrid of Elliptic Curve based Diffie-Hellman Key Exchange (ECDHKE) and ECEG, is modified as an attempt to make harder for an attacker to reveal ECEG´s private key by executing Pollard Rho attack using information from the public key gained by eavesdropping. This study examine the modified ECEG strength increase and the feasibility for implementing the modified ECEG.