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Erschienen in:
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2014 | OriginalPaper | Buchkapitel

On Semi-bent Functions and Related Plateaued Functions Over the Galois Field \(\mathbb{F}_{2^{n}}\)

verfasst von : Sihem Mesnager

Erschienen in: Open Problems in Mathematics and Computational Science

Verlag: Springer International Publishing

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Abstract

Plateaued functions were introduced in 1999 by Zheng and Zhang as good candidates for designing cryptographic functions since they possess desirable various cryptographic characteristics. They are defined in terms of the Walsh–Hadamard spectrum. Plateaued functions bring together various nonlinear characteristics and include two important classes of Boolean functions defined in even dimension: the well-known bent functions and the semi-bent functions. Bent functions (including their constructions) have been extensively investigated for more than 35 years. Very recently, the study of semi-bent functions has attracted the attention of several researchers. Much progress in the design of such functions has been made. The chapter is devoted to certain plateaued functions. The focus is particularly on semi-bent functions defined over the Galois field \(\mathbb{F}_{2^{n}}\) (n even). We review what is known in this framework and investigate constructions.

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Vorheriges Kapitel Open Problems on Binary Bent Functions
Nächstes Kapitel True Random Number Generators
Fußnoten
1
A Boolean function f is said to be homogeneous of degree r if \(f(x) =\sum _{ i=0}^{2^{n}-1 }a_{i}x^{i}\) where a i  = 0 for wt(i) ≠ r, where wt(i) is the Hamming weight of i.
 
2
We say a point p = (x 0, …, x n ) is on a line L[y 0, …, y n ] if and only if \(x_{0}y_{0} + x_{1}y_{1} + \cdots x_{n}y_{n} = 0\).
 
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Metadaten
Titel
On Semi-bent Functions and Related Plateaued Functions Over the Galois Field
verfasst von
Sihem Mesnager
Copyright-Jahr
2014
Buch
Open Problems in Mathematics and Computational Science

Print ISBN: 978-3-319-10682-3

Electronic ISBN: 978-3-319-10683-0

Copyright-Jahr: 2014

DOI
https://doi.org/10.1007/978-3-319-10683-0_11