Random Walks Revisited: Extensions of Pollard’s Rho Algorithm for Computing Multiple Discrete Logarithms

  • Fabian Kuhn
  • René Struik
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2259)


This paper extends the analysis of Pollard’s rho algorithm for solving a single instance of the discrete logarithm problem in a finite cyclic group G to the case of solving more than one instance of the discrete logarithm problem in the same group G. We analyze Pollard’s rho algorithm when used to iteratively solve all the instances. We also analyze the situation when the goal is to solve any one of the multiple instances using any DLP algorithm.


Group Operation Elliptic Curve Cyclic Group Distinguished Point Group Element 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Fabian Kuhn
    • 1
  • René Struik
    • 2
  1. 1.Departement InformatikETH ZentrumZürichSwitzerland
  2. 2.Certicom ResearchOntarioCanada

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