ANALYSIS OF NEW COLLISION POLLARD RHO METHOD IN SOLVING ELLIPTIC CURVE DISCRETE LOGARITHM PROBLEM - Made Sukrawan, I
The security level of elliptic curve cryptography is largely determined by the complexity of elliptic curve discrete logarithm problem. Various approaches have been used to speed up calculations in finding solutions to discrete logarithms. At present, the most efficient method known is the Pollard Rho method. The efficiency of the Pollard Rho method is determined by the speed at which collisions are detected and techniques for creating collisions themselves. Several algorithms have been developed to detect collisions such as the Floyd’s Cycle-Finding, Brent, Stack, and Distinguished Point algorithms. In 2015, Neamah proposed a new technique to create collisions (new collisions) so as to improve the efficiency of Floyd’s Cycle- Finding algorithm in detecting collisions. In this study, an analysis of the Pollard Rho new collision method was conducted and it was found that the proposed technique was less effective in creating collisions, but was very efficient and could significantly improve the performance of the Pollard Rho method. Then several developments were made to improve the performance of the Pollard Rho new collision method. In addition, analysis was also carried out on the computational security and performance of elliptic curve cryptographic parameters recommended by Certicom.