Designs, Codes and Cryptography

, Volume 39, Issue 2, pp 275–280

Efficient Computation of Roots in Finite Fields


DOI: 10.1007/s10623-005-4017-5

Cite this article as:
Barreto, P.S.L.M. & Voloch, J.F. Des Codes Crypt (2006) 39: 275. doi:10.1007/s10623-005-4017-5


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(rm3 log3q) steps.


finite fieldsroot computationefficient algorithms

AMS Classification


Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • Paulo S. L. M. Barreto
    • 1
  • José Felipe Voloch
    • 2
  1. 1.Laboratório de Arquitetura e Redes de Computadores (LARC), Escola PolitécnicaUniversidade de São PauloBrazil
  2. 2.Department of MathematicsUniversity of TexasAustinUSA