On some permutation polynomials over $\mathbb {F}_q$ of the form $x^r h(x^{(q-1)/d})$

Zieve, Michael E.

doi:10.1090/s0002-9939-08-09767-0

Cited by 141 publications

(74 citation statements)

References 31 publications

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“…The following lemma, which will be used to prove our main results, was proved by Park The polynomials of the form x r h(x) s have been widely studied, see [1,19,20,22,25,26] for example.…”

Section: Preliminariesmentioning

confidence: 96%

Several classes of permutation trinomials from Niho exponents

Helleseth

2016

Cryptogr. Commun.

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Motivated by recent results on the constructions of permutation polynomials with few terms over the finite field F2n , where n is a positive even integer, we focus on the construction of permutation trinomials over F2n from Niho exponents. As a consequence, several new classes of permutation trinomials over F2n are constructed from Niho exponents based on some subtle manipulation of solving equations with low degrees over finite fields.

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“…The following lemma, which will be used to prove our main results, was proved by Park The polynomials of the form x r h(x) s have been widely studied, see [1,19,20,22,25,26] for example.…”

Section: Preliminariesmentioning

confidence: 96%

Several classes of permutation trinomials from Niho exponents

Helleseth

2016

Cryptogr. Commun.

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“…Finding new PPs and CPPs of finite fields is a difficult problem and there are rare classes of CPPs known. For more study of PPs and CPPs can be found in [1][2][3][4]6,9,10,15,17,19,20].…”

Section: Introductionmentioning

confidence: 99%

Complete permutation polynomials over finite fields of odd characteristic

Cao

2015

Finite Fields and Their Applications

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“…The subset of such bijective mappings was characterized by Zieve in [13]. Lemma 1 is the binary version of [13, Lemma 2.1].…”

Section: On Differential Spectrum Of a Class Of Permutationsmentioning

confidence: 99%

“…In Section 3 we show that the differential spectrum of a class of permutations described by Zieve [13] is determined by a small number of derivatives (Theorem 6). Finally we focus on binomials and give some numerical results.…”

Section: Introductionmentioning

confidence: 99%

On sets determining the differential spectrum of mappings

Charpin

Kyureghyan

2017

IJICOT

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The differential uniformity of a mapping F : F 2 n → F 2 n is defined as the maximum number of solutions x for equations F (x+a)+F (x) = b when a ̸ = 0 and b run over F 2 n . In this paper we study the question whether it is possible to determine the differential uniformity of a mapping by considering not all elements a ̸ = 0, but only those from a special proper subset of F 2 n \ {0}.We show that the answer is "yes", when F has differential uniformity 2, that is if F is APN. In this case it is enough to take a ̸ = 0 on a hyperplane in F 2 n . Further we show that also for a large family of mappings F of a special shape, it is enough to consider a from a suitable multiplicative subgroup of F 2 n .

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On some permutation polynomials over $\mathbb {F}_q$ of the form $x^r h(x^{(q-1)/d})$

Abstract: Abstract. Several recent papers have given criteria for certain polynomials to permute F q , in terms of the periods of certain generalized Lucas sequences. We show that these results follow from a more general criterion which does not involve such sequences.

Cited by 141 publications

References 31 publications

Several classes of permutation trinomials from Niho exponents

Several classes of permutation trinomials from Niho exponents

Complete permutation polynomials over finite fields of odd characteristic

On sets determining the differential spectrum of mappings

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