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

  • Alfred J. Menezes
  • Scott A. Vanstone

DOI: 10.1007/BF01189025

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


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.


Discrete logarithmsGenus 0 curvesGeneral linear groupElliptic curves

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