Applications of the Hasse–Weil bound to permutation polynomials

Hou, Xiang‐dong

doi:10.1016/j.ffa.2018.08.005

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Cited by 17 publications

(2 citation statements)

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“…One of the main approaches to show that P (x) is not a permutation uses the theory of curves and their number of rational points, for instance see [1,2]. The approach can be summarized as follows.…”

Section: Introductionmentioning

confidence: 99%

Curves over Finite Fields and Permutations of the Form x k

Anbar¹

2019

Turk J Math

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Section: Introductionmentioning

confidence: 99%

Curves over Finite Fields and Permutations of the Form x k

Anbar¹

2019

Turk J Math

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“…Recently, some classes of PPs are found; see for example [10,13,23,24,26] for PPs of the form x r h(x q−1 ) of F q 2 , [16,27] for PPs of the form (x q − x + c) s + L(x) of F q 2 , [9,25,31] for PPs of the form (ax q + bx + c) r φ((ax q + bx + c) s ) + ux q + vx of F q 2 , and [1,4,7] for PPs studied by using the Hasse-Weil bound and Hermite's criterion.…”

Section: Introductionmentioning

confidence: 99%

On Inverses of Permutation Polynomials of Small Degree Over Finite Fields

Zheng

Wang

Wei

2020

IEEE Trans. Inform. Theory

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Complete characterization of a class of permutation trinomials in characteristic five

Grassl,

Özbudak,

Özkaya

et al. 2024

Cryptogr. Commun.

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In this paper, we address an open problem posed by Bai and Xia in [2]. We study polynomials of the form $$f(x)=x^{4q+1}+\lambda _1x^{5q}+\lambda _2x^{q+4}$$ f ( x ) = x 4 q + 1 + λ 1 x 5 q + λ 2 x q + 4 over the finite field $${\mathbb F}_{5^{k}}$$ F 5 k , which are not quasi-multiplicative equivalent to any of the known permutation polynomials in the literature. We find necessary and sufficient conditions on $$\lambda _1, \lambda _2 \in {\mathbb F}_{5^{k}}$$ λ 1 , λ 2 ∈ F 5 k so that f(x) is a permutation monomial, binomial, or trinomial of $${\mathbb F}_{5^{2k}}$$ F 5 2 k .

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Applications of the Hasse–Weil bound to permutation polynomials

Cited by 17 publications

References 21 publications

Curves over Finite Fields and Permutations of the Form x k

Curves over Finite Fields and Permutations of the Form x k

On Inverses of Permutation Polynomials of Small Degree Over Finite Fields

Complete characterization of a class of permutation trinomials in characteristic five

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