Bent and Semi-bent Functions via Linear Translators

Koçak, Neşe; Mesnager, Sihem; Özbudak, Ferruh

doi:10.1007/978-3-319-27239-9_13

Cited by 9 publications

(2 citation statements)

References 19 publications

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“…The following result can be derived from [19]. For making the paper self-contained, we include its proof.…”

Section: Constructions Of 2-to-1 Mappings From Linear Translatorsmentioning

confidence: 99%

On Two-to-One Mappings Over Finite Fields

Mesnager

2019

IEEE Trans. Inform. Theory

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Two-to-one (2-to-1) mappings over finite fields play an important role in symmetric cryptography. In particular they allow to design APN functions, bent functions and semi-bent functions. In this paper we provide a systematic study of two-to-one mappings that are defined over finite fields. We characterize such mappings by means of the Walsh transforms. We also present several constructions, including an AGWlike criterion, constructions with the form of x r h(x (q−1)/d ), those from permutation polynomials, from linear translators and from APN functions. Then we present 2-to-1 polynomial mappings in classical classes of polynomials: linearized polynomials and monomials, low degree polynomials, Dickson polynomials and Muller-Cohen-Matthews polynomials, etc. Lastly, we show applications of 2-to-1 mappings over finite fields for constructions of bent Boolean and vectorial bent functions, semi-bent functions, planar functions and permutation polynomials. In all those respects, we shall review what is known and provide several new results.

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“…The following result can be derived from [19]. For making the paper self-contained, we include its proof.…”

Section: Constructions Of 2-to-1 Mappings From Linear Translatorsmentioning

confidence: 99%

On Two-to-One Mappings Over Finite Fields

Mesnager

2019

IEEE Trans. Inform. Theory

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“…These constructions divides into two categories: the primary constructions-giving bent functions from scratch, and the secondary ones-building new bent functions from one or several given bent functions. For an non-exhaustive list of references dealing with these two kinds of constructions, see [13][14][15][16][17][18][19][20][21][22][23][24]. On the other hand, every bent function has a dual function, which is a bent function as well.…”

Section: Introductionmentioning

confidence: 99%

Three new infinite families of bent functions

Wang

Liu

et al. 2017

Sci. China Inf. Sci.

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Bent functions are maximally nonlinear Boolean functions with an even number of variables. They are closely related to some interesting combinatorial objects and also have important applications in coding, cryptography and sequence design. In this paper, we firstly give a necessary and sufficient condition for a type of Boolean functions, which obtained by adding the product of finitely many linear functions to given bent functions, to be bent. In the case that these known bent functions are chosen to be Kasami functions, Gold-like functions and functions with Niho exponents, respectively, three new explicit infinite families of bent functions are obtained. Computer experiments show that the proposed familes also contain such bent functions attaining optimal algebraic degree.

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Plateaued Functions: Generalities and Characterizations

Mesnager

2016

Bent Functions

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Bent and Semi-bent Functions via Linear Translators

Cited by 9 publications

References 19 publications

On Two-to-One Mappings Over Finite Fields

On Two-to-One Mappings Over Finite Fields

Three new infinite families of bent functions

Plateaued Functions: Generalities and Characterizations

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