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.
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Notes
An algorithm is quasi-linear time in \(n\) if it has complexity \(O(n\log ^kn)\) for a constant \(k\).
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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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Communicated by G. Mullen.
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Doliskani, J., Schost, É. Computing in degree \(2^k\)-extensions of finite fields of odd characteristic. Des. Codes Cryptogr. 74, 559–569 (2015). https://doi.org/10.1007/s10623-013-9875-7
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DOI: https://doi.org/10.1007/s10623-013-9875-7