Abstract

PEREZ ROBLE, Alberto; PEREZ LOPEZ, Beatriz; CUELLAR JUSTIZ, Oristela  and  MADARRO CAPO, Evaristo J.. Aritmetic on Tower over Finite Field of characteristic two, applied to primitive polynomials generation. Rev cuba cienc informat [online]. 2021, vol.15, n.4, suppl.1, pp. 17-32.  Epub Dec 01, 2021. ISSN 2227-1899.

With the advancement of cryptography and the new tools made available, the security of cryptographic al- gorithms is based mainly on the use of finite fields of big dimensions what makes difficult the arithmetic on them, besides the symmetrical systems that use primitive polynomials on these fields, also present great difficulties for the determination of the same. In this work we analyze the towers of finite fields as a tool for efficient arithmetic, examples of these are also given, through the representation of the elements, belonging to fields of characteristic two on normal bases, emphasizing in exponentiation operation. Finally, is analyzed a proposal that employs towers with representation on normal bases in the algorithm of generation of primitive polynomials exposed by E. Madarro in 2017.

Keywords : Tower finite field; normal bases; primitive polynomials.

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