Implementation of Pollard Rho attack on elliptic curve cryptography over binary fields

Abstract

Elliptic Curve Cryptography (ECC) is a public key cryptosystem with a security level determined by discrete logarithm problem called Elliptic Curve Discrete Logarithm Problem (ECDLP). John M. Pollard proposed an algorithm for discrete logarithm problem based on Monte Carlo method and known as Pollard Rho algorithm. The best current brute-force attack for ECC is Pollard Rho algorithm. In this research we implement modified Pollard Rho algorithm on ECC over GF (241). As the result, the runtime of Pollard Rho algorithm increases exponentially with the increase of the ECC key length. This work also presents the estimated runtime of Pollard Rho attack on ECC over longer bits.