Kangaroos, Monopoly and Discrete Logarithms

Abstract.

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.