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

  • Alfred J. Menezes
  • Scott A. Vanstone
Article

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 logarithms Genus 0 curves General linear group Elliptic curves 

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Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Alfred J. Menezes
    • 1
  • Scott A. Vanstone
    • 1
  1. 1.Department of Combinatorics and OptimizationUniversity of WaterlooWaterlooCanada

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