Designs, Codes and Cryptography

, Volume 39, Issue 2, pp 275-280

First online:

Efficient Computation of Roots in Finite Fields

  • Paulo S. L. M. BarretoAffiliated withLaboratório de Arquitetura e Redes de Computadores (LARC), Escola Politécnica, Universidade de São Paulo
  • , José Felipe VolochAffiliated withDepartment of Mathematics, University of Texas Email author 

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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 m 3 log3 q) steps.


finite fields root computation efficient algorithms

AMS Classification

11Y16 12Y05