Collision bounds for the additive Pollard rho algorithm for solving discrete logarithms

Journal of mathematical cryptology

article

Joppe W. Bos¹  Alina Dudeanu²  Dimitar Jetchev² 

[1] Microsoft Research;Laboratory for Cryptologic Algorithms

关键词: Pollard rho;    additive walk;    collision bound;    random walk;    mixing times;   

DOI  :  10.1515/jmc-2012-0032

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

Abstract. We prove collision bounds for the Pollard rho algorithm to solve the discrete logarithm problem in a general cyclic group ?$\mathbf {G}$. 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 ?(|?|)$\mathcal {O}(\sqrt{\vert \mathbf {G}\vert })$ by a factor of log|?|$\sqrt{\log {\vert \mathbf {G}\vert }}$ and are based on mixing time estimates for random walks on finite abelian groups due to Dou and Hildebrand.

【 授权许可】

CC BY|CC BY-NC-ND