Abstract
This paper concerns an exhaustive search for normal bases with minimum complexity in finite fields \(\mathbb {F}_{2^n}\) over \(\mathbb {F}_2\) for \(n \le 46\). This is a followup paper to [11], which appeared one decade ago in 2008 and completed the cases \(n \le 39\). We extend the results in [11] by taking advantage of a combination of algorithmic improvements, more efficient implementations and massive parallelism.
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We would like to thank the three reviewers for their helpful suggestions, which greatly improved the presentation of this paper.
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Moura, L., Panario, D., Thomson, D. (2018). Normal Basis Exhaustive Search: 10 Years Later. In: Budaghyan, L., Rodríguez-Henríquez, F. (eds) Arithmetic of Finite Fields. WAIFI 2018. Lecture Notes in Computer Science(), vol 11321. Springer, Cham. https://doi.org/10.1007/978-3-030-05153-2_10
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DOI: https://doi.org/10.1007/978-3-030-05153-2_10
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