Advertisement

Orders of Gauss Periods in Finite Fields

  • Joachim von zur Gathen
  • Igor Shparlinski

Abstract

It is shown that Gauss periods of a special type give an explicit polynomial-time computation of elements of exponentially large multiplicative order in some finite fields. This can be considered as a step towards solving the celebrated problem of finding primitive roots in finite fields in polynomial time.

Key words Finite fields, Algorithms, Primitive roots, Normal bases, Artin's conjecture 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Joachim von zur Gathen
    • 1
  • Igor Shparlinski
    • 2
  1. 1.FB Mathematik-Informatik, Universität-GH Paderborn, D-33095 Paderborn, Germany (e-mail: gathen@uni-paderborn.de)DE
  2. 2.School of MPCE Macquarie University Sydney, NSW 2109, Australia (e-mail: igor@mpce.mq.edu.au)AU

Personalised recommendations