Method to Eliminate Fruitless Cycles for Pollard's Rho Method with Splitting Table

This research focuses on attacks against a type of curve suitable for pairing, called Barreto-Naehring curves. The accelerated attack will evaluate the level of security with respect to the elliptic curve discrete logarithm problem (ECDLP). Then the rho method is known to efficiently solve ECDLPs, the random walk path sometimes induces unsolvable cycles, called fruitless cycles, and the random walk must be restarted from yet another starting point. The authors confirm the effectiveness of a method for eliminating fruitless cycles in a random walk path with parallel Pollard's rho method using skewed Frobenius maps of curves. In this paper, the authors proposed a parallel rho method using skew Frobenius mapping and several tables with novel approach. The results show that the proposed method can effectively eliminate fruitless cycles.