Session 7A

Algorithms and Computations

Volume 1004 of the series Lecture Notes in Computer Science pp 208-215

Date:

Orders of Gauss periods in finite fields

  • Joachim von zur GathenAffiliated withFB Mathematik-Informatik, Universität-GH PaderbornSchool of MPCE, Macquarie University
  • , Igor ShparlinskiAffiliated withFB Mathematik-Informatik, Universität-GH PaderbornSchool of MPCE, Macquarie University

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Abstract

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