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Mathematics of Computation

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



Computing special powers in finite fields

Authors: Joachim von zur Gathen and Michael Nöcker
Journal: Math. Comp. 73 (2004), 1499-1523
MSC (2000): Primary 68Q40; Secondary 11Y16
Published electronically: September 26, 2003
MathSciNet review: 2047098
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Abstract: We study exponentiation in nonprime finite fields with very special exponents such as they occur, for example, in inversion, primitivity tests, and polynomial factorization. Our algorithmic approach improves the corresponding exponentiation problem from about quadratic to about linear time.

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Additional Information

Joachim von zur Gathen
Affiliation: Fakultät für Elektrotechnik, Informatik, Mathematik, Universität Paderborn, D-33095 Paderborn, Germany

Michael Nöcker
Affiliation: Bückeburger Str. 12, D-59174 Kamen, Germany

Received by editor(s): July 28, 2002
Received by editor(s) in revised form: December 9, 2002
Published electronically: September 26, 2003
Article copyright: © Copyright 2003 American Mathematical Society