Journal of Cryptology

, Volume 13, Issue 4, pp 437–447

Kangaroos, Monopoly and Discrete Logarithms

  • J. M. Pollard

DOI: 10.1007/s001450010010

Cite this article as:
Pollard, J. J. Cryptology (2000) 13: 437. doi:10.1007/s001450010010


The kangaroo method computes a discrete logarithm in an arbitrary cyclic group, given that the value is known to lie in a certain interval. A parallel version has been given by van Oorschot and Wiener with ``linear speed-up''. We improve the analysis of the running time, both for serial and parallel computers. We explore the variation of the running time with the set of ``jumps'' of the kangaroos, and confirm that powers of two are a good choice (we do not claim they are the best choice). We illustrate the theory with some calculations of interest to Monopoly players, and the method itself with a card trick due to Kruskal.

Key words. Discrete logarithms, Kangaroo method.

Copyright information

© International Association for Criptologic Rese 2000

Authors and Affiliations

  • J. M. Pollard
    • 1
  1. 1.Tidmarsh Cottage, Manor Farm Lane, Tidmarsh, Reading RG8 8EX, England jmptidcott@hotmail.comUK