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Journal of Mathematical Cryptology

Managing Editor: Magliveras, Spyros S. / Steinwandt, Rainer / Trung, Tran

Editorial Board: Blackburn, Simon R. / Blundo, Carlo / Burmester, Mike / Cramer, Ronald / Dawson, Ed / Gilman, Robert / Gonzalez Vasco, Maria Isabel / Grosek, Otokar / Helleseth, Tor / Kim, Kwangjo / Koblitz, Neal / Kurosawa, Kaoru / Lauter, Kristin / Lange, Tanja / Menezes, Alfred / Nguyen, Phong Q. / Pieprzyk, Josef / Rötteler, Martin / Safavi-Naini, Rei / Shparlinski, Igor E. / Stinson, Doug / Takagi, Tsuyoshi / Williams, Hugh C. / Yung, Moti

4 Issues per year

CiteScore 2017: 1.43

SCImago Journal Rank (SJR) 2017: 0.293
Source Normalized Impact per Paper (SNIP) 2017: 1.117

Mathematical Citation Quotient (MCQ) 2017: 0.51

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Volume 8, Issue 1


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

Joppe W. Bos / Alina Dudeanu / Dimitar Jetchev
Published Online: 2014-01-16 | DOI: https://doi.org/10.1515/jmc-2012-0032


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(|𝐆|) by a factor of log|𝐆| and are based on mixing time estimates for random walks on finite abelian groups due to Dou and Hildebrand.

Keywords: Pollard rho; additive walk; collision bound; random walk; mixing times

MSC: 94A60; 05C81

About the article

Received: 2012-12-14

Revised: 2013-08-02

Accepted: 2013-12-23

Published Online: 2014-01-16

Published in Print: 2014-02-01

Funding Source: Swiss National Science Foundation

Award identifier / Grant number: 200020-132160

Citation Information: Journal of Mathematical Cryptology, Volume 8, Issue 1, Pages 71–92, ISSN (Online) 1862-2984, ISSN (Print) 1862-2976, DOI: https://doi.org/10.1515/jmc-2012-0032.

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