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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Gauss periods: orders and cryptographical applications
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by Shuhong Gao, Joachim von zur Gathen and Daniel Panario PDF
Math. Comp. 67 (1998), 343-352 Request permission

Abstract:

Experimental results on the multiplicative orders of Gauss periods in finite fields are presented. These results indicate that Gauss periods have high order and are often primitive (self-dual) normal elements in finite fields. It is shown that Gauss periods can be exponentiated in quadratic time. An application is an efficient pseudorandom bit generator.
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Additional Information
  • Shuhong Gao
  • Affiliation: Department of Mathematical Sciences Clemson University Clemson, SC 29634-1907, USA
  • MR Author ID: 291308
  • Email: sgao@math.clemson.edu
  • Joachim von zur Gathen
  • Affiliation: Fachbereich Mathematik-Informatik Universität-GH Paderborn D-33095 Paderborn, Germany
  • MR Author ID: 71800
  • Email: gathen@uni-paderborn.de
  • Daniel Panario
  • Affiliation: Department of Computer Science University of Toronto Toronto, Ontario M5S 1A4, Canada
  • Email: daniel@cs.toronto.edu
  • Received by editor(s): February 16, 1996
  • Additional Notes: This paper is in final form, no version of it will be submitted for publication elsewhere.
  • © Copyright 1998 American Mathematical Society
  • Journal: Math. Comp. 67 (1998), 343-352
  • MSC (1991): Primary 11T30, 94A60; Secondary 11Y16, 12Y05, 68Q25
  • DOI: https://doi.org/10.1090/S0025-5718-98-00935-1
  • MathSciNet review: 1458221