Linear Permutations and their Compositional Inverses over \mathbbF_qⁿ

2020/05/29 by Bastos, Gustavo Terra
#Commutative Algebra (math.AC) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2005.14349

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 \mathbbF_qⁿ as well as their compositional inverses using a decomposition of \frac\mathbbF_q[x]⟨ xⁿ -1 ⟩ based on its primitive idempotents. As a consequence, an immediate construction of involutions is presented.

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