Implementation of Pollard Rho over binary fields using Brent Cycle Detection Algorithm

Abstract

The security of Elliptic Curve Cryptography depends on how to solve the Elliptic Curve Cryptography Discrete Logarithm Problem (ECDLP). In this paper we propose the use of modified Pollard Rho Algorithm by using Brent Cycle Detection Algorithm to solve the ECDLP. We give performance comparison on time and the number of iterations between Pollard Rho with Brent Cycle Detection and Pollard Rho with Negation map. In particular, for Koblitz curve, we also give comparison between Pollard Rho with Brent Cycle Detection and Pollard Rho with Negation and Frobenius maps.