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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Gauss periods: orders
and cryptographical applications


Authors: Shuhong Gao, Joachim von zur Gathen and Daniel Panario
Journal: Math. Comp. 67 (1998), 343-352
MSC (1991): Primary 11T30, 94A60; Secondary 11Y16, 12Y05, 68Q25
Supplement: Additional information related to this article.
MathSciNet review: 1458221
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Abstract | References | Similar Articles | Additional Information

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
Email: sgao@math.clemson.edu

Joachim von zur Gathen
Affiliation: Fachbereich Mathematik-Informatik\ Universität-GH Paderborn\ D-33095 Paderborn, Germany
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

DOI: http://dx.doi.org/10.1090/S0025-5718-98-00935-1
PII: S 0025-5718(98)00935-1
Keywords: Finite fields, primitive elements, normal bases, cryptography, pseudorandom bit generators
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.
Article copyright: © Copyright 1998 American Mathematical Society