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



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.


Finite field Algebraic closure Complexity Square root 

Mathematics Subject Classification

11Y16 12Y05 68W30 


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Western UniversityLondonUSA

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