Efficient Computation of Roots in Finite Fields

Authors:
Paulo S. Barreto;José Felipe Voloch
Affiliations:
Laboratório de Arquitetura e Redes de Computadores (LARC), Escola Politécnica, Universidade de São Paulo, Brazil;Department of Mathematics, University of Texas, Austin, USA 78712
Venue:
Designs, Codes and Cryptography
Year:
2006

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Abstract

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