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Discrete logarithms for finite groups

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Abstract

We present group-theoretic and cryptographic properties of a generalization of the traditional discrete logarithm problem from cyclic to arbitrary finite groups. Questions related to properties which contribute to cryptographic security are investigated, such as distributional, coverage and complexity properties. We show that the distribution of elements in a certain multiset tends to uniform. In particular we consider the family of finite non-abelian groups \({PSL_2(\mathbb{F}_p)}\) , p a prime, as possible candidates in the design of new cryptographic primitives, based on our new discrete logarithm.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Florida Atlantic University, 777 Glades Road, Boca Raton, FL, 33431, USA

    Lee C. Klingler, Spyros S. Magliveras & Fred Richman

  2. Department of Computer Science, University of Calgary, 2500 University Drive NW, Calgary, AB, T2N 1N4, Canada

    Michal Sramka

Authors
  1. Lee C. Klingler
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  2. Spyros S. Magliveras
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  3. Fred Richman
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  4. Michal Sramka
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Correspondence to Spyros S. Magliveras.

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Klingler, L.C., Magliveras, S.S., Richman, F. et al. Discrete logarithms for finite groups. Computing 85, 3–19 (2009). https://doi.org/10.1007/s00607-009-0032-0

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