A Twin for Euler's φ Function in $\mathbb{F}_2[X]$

Authors:
R. Durán Díaz;J. Muñoz Masqué;A. Peinado Domínguez
Affiliations:
Departamento de Automática, Universidad de Alcalá de Henares, Carretera de Madrid-Barcelona, km. 33.6, 28871-Alcalá de Henares, Spain;CSIC, Instituto de Física Aplicada, C/ Serrano 144, 28006-Madrid, Spain;Departamento de Ingeniería de Comunicaciones, E.T.S. de Ingenieros de Telecomunicación, Universidad de Málaga, Campus de Teatinos, 29071-Málaga, Spain
Venue:
WAIFI '07 Proceedings of the 1st international workshop on Arithmetic of Finite Fields
Year:
2007

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Abstract

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 茂戮驴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.