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Mathematics of Computation

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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: 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

Joachim von zur Gathen
Affiliation: Fachbereich Mathematik-Informatik Universität-GH Paderborn D-33095 Paderborn, Germany
MR Author ID: 71800

Daniel Panario
Affiliation: Department of Computer Science University of Toronto Toronto, Ontario M5S 1A4, Canada

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