Analysis of the fruitless cycle of Pollard's rho method based attack for solving ECDLP over Barreto-Naehrig curves
Hiromasa Miura, Ken Ikuta, Sho Joichi, Takuya Kusaka, Yasuyuki Nogami · 2019 34th International Technical Conference on Circuits/Systems, Computers and Communications (ITC-CSCC) · 2019
This paper focuses on the computational security of elliptic curve discrete logarithm (ECDLP), which can evaluate by an actual attack. The authors apply Pollard's rho method to a Barreto-Naehrig curve with minimum parameters for solving an ECDLP. An analysis of the structure for all combinations of a select of seed and starting points are given. Then, we propose the method for selecting a set of efficient seed points for a random walk for the rho method.