Applicable Algebra in Engineering, Communication and Computing

, Volume 3, Issue 1, pp 67–74

A note on cyclic groups, finite fields, and the discrete logarithm problem

Authors

  • Alfred J. Menezes
    • Department of Combinatorics and OptimizationUniversity of Waterloo
  • Scott A. Vanstone
    • Department of Combinatorics and OptimizationUniversity of Waterloo
Article

DOI: 10.1007/BF01189025

Cite this article as:
Menezes, A.J. & Vanstone, S.A. AAECC (1992) 3: 67. doi:10.1007/BF01189025

Abstract

We show how the discrete logarithm problem in some finite cyclic groups can easily be reduced to the discrete logarithm problem in a finite field. The cyclic groups that we consider are the set of points on a singular elliptic curve over a finite field, the set of points on a genus 0 curve over a finite field given by the Pell equation, and certain subgroups of the general linear group.

Keywords

Discrete logarithmsGenus 0 curvesGeneral linear groupElliptic curves
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Copyright information

© Springer-Verlag 1992