Collision Bounds for the Additive Pollard Rho Algorithm for Solving Discrete Logarithms

Joppe W.  Bos; Alina Dudeanu; Dimitar Jetchev

Paper 2012/087 Original: eprint.iacr.org/2012/087 ↗

Collision Bounds for the Additive Pollard Rho Algorithm for Solving Discrete Logarithms

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.

Metadata

Available format(s): PDF
Publication info: Preprint.
History: 2012-02-23: last updated; 2012-02-23: published
Short URL: https://ia.cr/2012/087
License: https://creativecommons.org/licenses/by/4.0/

BibTeX

@misc{cryptoeprint:2012/087,
      author = {Joppe W.  Bos and Alina Dudeanu and Dimitar Jetchev},
      title = {Collision Bounds for the Additive Pollard Rho Algorithm for Solving Discrete Logarithms},
      howpublished = {Cryptology {ePrint} Archive, Paper 2012/087},
      year = {2012},
      url = {https://eprint.iacr.org/2012/087}
}