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Efficient Computation of Roots in Finite Fields

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Abstract

We present an algorithm to compute rth roots in \(\mathbb{F}_{q^m}\) with complexity Õ[(log m + r log q) m log q] if (m,q) = 1 and either (q(q−1),r) = 1 or r|(q−1) and ((q−1)/r,r) = 1. This compares well to previously known algorithms, which need O(r m3 log3 q) steps.

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Correspondence to José Felipe Voloch.

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Communicated by: S. Gao

Paulo S. L. M. Barreto: Supported by Scopus Tecnologia S. A.

José Felipe Voloch: Supported by NSA grant MDA904-03-1-0117.

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Barreto, P.S.L.M., Voloch, J.F. Efficient Computation of Roots in Finite Fields. Des Codes Crypt 39, 275–280 (2006). https://doi.org/10.1007/s10623-005-4017-5

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  • DOI: https://doi.org/10.1007/s10623-005-4017-5

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