On Bent and Semi-Bent Quadratic Boolean Functions

Charpin, Pascale; Pašalić, Enes; Tavernier, Cédric

doi:10.1109/tit.2005.858929

Cited by 111 publications

(72 citation statements)

References 9 publications

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“…is called quadratic, its algebraic degree is two, see [4,6]. Every quadratic function from F p n to F p is s-plateaued, where s is the dimension of the kernel of the linear transformation on F p n defined by…”

Section: Quadratic Functionsmentioning

confidence: 99%

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A construction of bent functions from plateaued functions

Çeşmelioğlu

Meidl

2012

Des. Codes Cryptogr.

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Abstract. In this presentation a technique for constructing bent functions from plateaued functions is introduced. This generalizes earlier techniques for constructing bent from near-bent functions. Analysing the Fourier spectrum of quadratic functions we then can construct weakly regular as well as non-weakly regular bent functions both in even and odd dimension. This type of functions yield the first known infinite classes of non-weakly regular bent functions. Weakly regular bent functions with certain additional properties can be used to construct partial difference sets and strongly regular graphs. We show how to obtain appropriate bent functions using our construction.

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Section: Quadratic Functionsmentioning

confidence: 99%

“…The case s = 0 corresponds to bent functions by definition. For 1-plateaued functions the term near-bent function is common (see [3,7]), binary 1-plateaued and 2-plateaued functions are referred to as semi-bent functions in [4].…”

Section: Introductionmentioning

confidence: 99%

A construction of bent functions from plateaued functions

Çeşmelioğlu

Meidl

2012

Des. Codes Cryptogr.

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“…2 Theorem 1. Let the functions f λ (and λ itself ) be defined by (8) Note that u belongs to F * 2 r while β i for i = 0 does not. Thus T 3r r (λy) = uT 3r r (λβ i ), which implies that (10) can be rewritten…”

Section: Proposition 2 Let Us Definementioning

confidence: 99%

A new class of monomial bent functions

Canteaut

Charpin

Kyureghyan

2006

2006 IEEE International Symposium on Information Theory

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We study the Boolean functions f λ : F 2 n → F 2 , n = 6r, of the form f (x) = Tr(λx d ) with d = 2 2r + 2 r + 1 and λ ∈ F 2 n . Our main result is the characterization of those λ for which f λ are bent. We show also that the set of these cubic bent functions contains a subset, which with the constantly zero function forms a vector space of dimension 2r over F 2 . Further we determine the Walsh spectra of some related quadratic functions, the derivatives of the functions f λ .

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“…Primary and secondary constructions of bent functions are the two kinds of construction of bent functions. In the primary construction, there is no use of previously existing bent functions to construct new ones, while in secondary construction some previously known bent functions are used to construct new bent functions, see [13,14,15,16]. Several constructions of bent functions are discussed in [17,18].…”

Section: Introductionmentioning

confidence: 99%

Construction of a New Class of Bent and Semi-bent Functions

Sharma¹,

Dhiman²

2017

IJCA

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Bent functions play an important role in the designing of Sboxes. These functions also have significant applications in coding theory, graph theory and sequence design. In the literature of bent functions their complete classification and characterization is still elusive, so the constructions and characterizations of bent functions are challenging problems. Many constructions methods and characterizations of bent functions are discussed in the literature. In this paper we obtain a new infinite class of bent and semi-bent functions using few Walsh transform values.

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On Bent and Semi-Bent Quadratic Boolean Functions

Cited by 111 publications

References 9 publications

A construction of bent functions from plateaued functions

A construction of bent functions from plateaued functions

A new class of monomial bent functions

Construction of a New Class of Bent and Semi-bent Functions

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