Linear Permutations and their Compositional Inverses over $\mathbb{F}_{q^n}$

DOI10.1142/S0219498822502206arXiv2005.14349MaRDI QIDQ6341660

Publication date: 28 May 2020

Abstract: The use of permutation polynomials has appeared, along to their compositional inverses, as a good choice in the implementation of cryptographic systems. Hence, there has been a demand for constructions of these polynomials which coefficients belong to a finite field. As a particular case of permutation polynomial, involution is highly desired since its compositional inverse is itself. In this work, we present an effective way of how to construct several linear permutation polynomials over

m a t h b b F_{q^{n}}

as well as their compositional inverses using a decomposition of

d i s p l a y s t y l e f r a c m a t h b b F_{q} [x] l e f t l a n g l e x^{n} - 1 i g h t a n g l e

based on its primitive idempotents. As a consequence, an immediate construction of involutions is presented.

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Polynomials over finite fields (11T06) Arithmetic theory of polynomial rings over finite fields (11T55)

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