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Cryptography and Communications

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19-09-2023 | Research

Some classes of permutation binomials and trinomials of index \(q-1\) over \({\mathbb {F}_{q^n}}\)

Authors: Rohit Gupta, Luciane Quoos, Qiang Wang

Published in: Cryptography and Communications | Issue 2/2024

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Abstract

In this paper, using the classification of degree 7 permutations over \(\mathbb {F}_q\), we classify certain sparse PPs of the form \(P(x)=x^rf(x^{\frac{q^n-1}{q-1}})\) of \(\mathbb {F}_{q^n}\) for \(n=2\) and 3. In particular, we give necessary and sufficient conditions for the polynomial \(f_{a,b}(x):=x(x^{2(q^2+q+1)}+ax^{q^2+q+1}+b)\) in \(\mathbb {F}_{q^3}[x]\) to be a permutation polynomial over \(\mathbb {F}_{q^3}\), where \(q >409\) is a prime power.

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Title: Some classes of permutation binomials and trinomials of index over
Authors: Rohit Gupta
Luciane Quoos
Qiang Wang
Publication date: 19-09-2023
Publisher: Springer US
Published in: Cryptography and Communications / Issue 2/2024
Print ISSN: 1936-2447
Electronic ISSN: 1936-2455
DOI: https://doi.org/10.1007/s12095-023-00674-y

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