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Designs, Codes and Cryptography

, Volume 74, Issue 3, pp 559–569 | Cite as

Computing in degree \(2^k\)-extensions of finite fields of odd characteristic

  • Javad Doliskani
  • Éric Schost
Article

Abstract

We show how to perform basic operations (arithmetic, square roots, computing isomorphisms) over finite fields of the form \(\mathbb F _{q^{2^k}}\) in essentially linear time.

Keywords

Finite field Algebraic closure Complexity Square root 

Mathematics Subject Classification

11Y16 12Y05 68W30 

Notes

Acknowledgments

The authors are supported by NSERC and the Canada Research Chairs program. We wish to thank the reviewers for their helpful remarks and suggestions.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Western UniversityLondonUSA

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