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

Bos, Joppe W. ; Dudeanu, Alina ; Jetchev, Dimitar

In: Journal of Mathematical Cryptology, 2014, vol. 8, no. 1, p. 71-92

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    Titre
    • Collision bounds for the additive Pollard rho algorithm for solving discrete logarithms
    Auteur
    • Bos, Joppe W.. Microsoft Research, One Microsoft Way, Redmond, WA 98052, USA
    • Dudeanu, Alina. Laboratory for Cryptologic Algorithms, EPFL, Lausanne, Switzerland
    • Jetchev, Dimitar. Laboratory for Cryptologic Algorithms, EPFL, Lausanne, Switzerland
    Type de document
    • Postprint
    Langue
    • Anglais
    Publié dans
    • Journal of Mathematical Cryptology, 2014, vol. 8, no. 1, p. 71-92. Walter de Gruyter GmbH
    Autre version électronique
    Identifiant OAI-PMH
    • oai:doc.rero.ch:304952
    Summary
    We prove collision bounds for the Pollard rho algorithm to solve the discrete logarithm problem in a general cyclic group 𝐆$\mathbf {G}$ . 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 𝒪(|𝐆|)$\mathcal {O}(\sqrt{\vert \mathbf {G}\vert })$ by a factor of log|𝐆|$\sqrt{\log {\vert \mathbf {G}\vert }}$ and are based on mixing time estimates for random walks on finite abelian groups due to Dou and Hildebrand