Experimental evaluation of the efficiency of associative rational points for random walks on ECDLP

Pollard´s Rho method is well-known as a method for solving Elliptic Curve Discrete Logarithm Problem (ECDLP). It is based on an efficient random walk of rational points on elliptic curve. This research accelerates the random walk with associative rational points. Since associative rational points are generated with a small additional cost and thus the random walk becomes more efficient. In order to solve an ECDLP over Barreto-Naehrig curve, for an example, this paper applies associative rational points and then evaluates the efficiency by some experiments.