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 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.
Supported by Ministerio de Educación y Ciencia of Spain under grant number MTM2005–00173 and Consejería de Educación y Cultura de la Junta de Castilla y León under grant number SA110A06.
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Díaz, R.D., Masqué, J.M., Domínguez, A.P. (2007). A Twin for Euler’s φ Function in \(\mathbb{F}_2[X]\) . In: Carlet, C., Sunar, B. (eds) Arithmetic of Finite Fields. WAIFI 2007. Lecture Notes in Computer Science, vol 4547. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73074-3_25
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DOI: https://doi.org/10.1007/978-3-540-73074-3_25
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