A Twin for Euler’s φ Function in \(\mathbb{F}_2[X]\)

  • R. Durán Díaz
  • J. Muñoz Masqué
  • A. Peinado Domínguez
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4547)


In this paper, we present a function in \(\mathbb{F}_2[X]\) and prove that several of its properties closely resemble those of Euler’s φ function. Additionally, we conjecture another property for this function that can be used as a simple primality test in \(\mathbb{F}_2[X]\), and we provide numerical evidence to support this conjecture. Finally, we further apply the previous results to design a simple primality test for trinomials.

Mathematics Subject Classification 2000: Primary 13P05; Secondary 11T06, 12E05, 15A04.


Characteristic-2 field Euler φ function polynomial factorization 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • R. Durán Díaz
    • 1
  • J. Muñoz Masqué
    • 2
  • A. Peinado Domínguez
    • 3
  1. 1.Departamento de Automática, Universidad de Alcalá de Henares, Carretera de Madrid-Barcelona, km. 33.6, 28871-Alcalá de HenaresSpain
  2. 2.CSIC, Instituto de Física Aplicada, C/ Serrano 144, 28006-MadridSpain
  3. 3.Departamento de Ingeniería de Comunicaciones, E.T.S. de Ingenieros de Telecomunicación, Universidad de Málaga, Campus de Teatinos, 29071-MálagaSpain

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