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The Discrete Logarithm Problem

  • Chapter
Applications of Finite Fields

Part of the book series: The Springer International Series in Engineering and Computer Science ((SECS,volume 199))

Abstract

Let G be a finite cyclic group, and let a be a generator for G. Then

$$G = \{ {\alpha ^i}|0 \leqslant i\# G\} $$

, where #G is the order of G. The discrete logarithm (logarithm) of an element β to the base α in G is an integer x such that α x = β. If x is restricted to the interval 0 ≤ x < #G then the discrete logarithm of β to the base α is unique. We typically write x = log α β.

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Author information

Authors and Affiliations

  1. University of Waterloo, Canada

    Ian F. Blake, XuHong Gao, Ronald C. Mullin, Scott A. Vanstone & Tomik Yaghoobian

Authors
  1. Ian F. Blake
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  2. XuHong Gao
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  3. Ronald C. Mullin
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  4. Scott A. Vanstone
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  5. Tomik Yaghoobian
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Editor information

Alfred J. Menezes

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© 1993 Springer Science+Business Media New York

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Blake, I.F., Gao, X., Mullin, R.C., Vanstone, S.A., Yaghoobian, T. (1993). The Discrete Logarithm Problem. In: Menezes, A.J. (eds) Applications of Finite Fields. The Springer International Series in Engineering and Computer Science, vol 199. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-2226-0_6

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  • DOI: https://doi.org/10.1007/978-1-4757-2226-0_6

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4419-5130-4

  • Online ISBN: 978-1-4757-2226-0

  • eBook Packages: Springer Book Archive

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