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Gauss periods: orders and cryptographical applications |
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| Authors: | Shuhong Gao Joachim von zur Gathen Daniel Panario |
| Institution: | Department of Mathematical Sciences Clemson University Clemson, SC 29634-1907, USA ; Fachbereich Mathematik-Informatik Universität-GH Paderborn D-33095 Paderborn, Germany ; Department of Computer Science University of Toronto Toronto, Ontario M5S 1A4, Canada |
| 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. |
| Keywords: | Finite fields primitive elements normal bases cryptography pseudorandom bit generators |
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