Journal of Cryptology

, Volume 12, Issue 3, pp 193–196

The Discrete Logarithm Problem on Elliptic Curves of Trace One

  • N. P. Smart

DOI: 10.1007/s001459900052

Cite this article as:
Smart, N. J. Cryptology (1999) 12: 193. doi:10.1007/s001459900052


In this short note we describe an elementary technique which leads to a linear algorithm for solving the discrete logarithm problem on elliptic curves of trace one. In practice the method described means that when choosing elliptic curves to use in cryptography one has to eliminate all curves whose group orders are equal to the order of the finite field.

Key words. 2pt

Copyright information

© International Association for Criptologic Research 1999

Authors and Affiliations

  • N. P. Smart
    • 1
  1. 1.Hewlett-Packard LaboratoriesBristolEngland