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Title:
Collision Bounds for the Additive Pollard Rho Algorithm for Solving Discrete Logarithms
Authors: Joppe W. Bos, Alina Dudeanu, Dimitar Jetchev
Abstract:We prove collision bounds for the Pollard rho algorithm to solve the discrete logarithm problem in a general cyclic group G. Unlike the setting studied by Kim et al. we consider additive walks: the setting used in practice to solve the elliptic curve discrete logarithm problem. Our bounds differ from the birthday bound O(\sqrt{|G|}) by a factor of \sqrt{\log{|G|}} and are based on mixing time estimates for random walks on finite abelian groups due to Hildebrand.
ePrint: https://eprint.iacr.org/2012/087
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