Journal of Cryptology

, Volume 13, Issue 4, pp 473–492

Computing Discrete Logarithms in Quadratic Orders


  • Michael J. Jacobson
    • Centre for Applied Cryptographic Research, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1

DOI: 10.1007/s001450010013

Cite this article as:
Jacobson, M. J. Cryptology (2000) 13: 473. doi:10.1007/s001450010013


We present efficient algorithms for computing discrete logarithms in the class group of a quadratic order and for principality testing in a real quadratic order, based on the work of Düllmann and Abel. We show how the idea of generating relations with sieving can be applied to improve the performance of these algorithms. Computational results are presented which demonstrate that our new techniques yield a significant increase in the sizes of discriminants for which these discrete logarithm problems can be solved.

Key words. Discrete logarithm, Principal ideal testing, Quadratic order, Class group, Computational number theory.

Copyright information

© International Association for Criptologic Rese 2000