A variant of Pollard’S rho Attack on Elliptic Curve Cryptosystems

Elliptic Curve cryptosystems appear to be more secure and efficient when requiring small key size to implement than other public key cryptosystems. Its security is based upon the difficulty of solving Elliptic Curve Discrete Logarithm Problem (ECDLP). This study proposes a variant of generic algorithm Pollard’s Rho for finding ECDLP using cycle detection with stack and a mixture of cycle detection and random walks. The Pollard’s Rho using cycle detection with stack requires less iterations than Pollard’s Rho original in reaching collision. Random walks allow the iteration function to act randomly than the original iteration function, thus, the Pollard rho method performs more efficiently. In practice, the experiment results show that the proposed methods decreases the number of iterations and speed up the computation of discrete logarithm problem on elliptic curves.