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Cryptography and Communications

Erschienen in:

23.03.2020

Shifted plateaued functions and their differential properties

verfasst von: Nurdagül Anbar, Canan Kaşıkçı, Wilfried Meidl, Alev Topuzoğlu

Erschienen in: Cryptography and Communications | Ausgabe 6/2020

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Abstract

A bent₄ function is a Boolean function with a flat spectrum with respect to a certain unitary transform \(\mathcal {T}\). It was shown previously that a Boolean function f in an even number of variables is bent₄ if and only if f + σ is bent, where σ is a certain quadratic function depending on \(\mathcal {T}\). Hence bent₄ functions are also called shifted bent functions. Similarly, a Boolean function f in an odd number of variables is bent₄ if and only if f + σ is a semibent function satisfying some additional properties. In this article, for the first time, we analyse in detail the effect of the shifts on plateaued functions, on partially bent functions and on the linear structures of Boolean functions. We also discuss constructions of bent and bent₄ functions from partially bent functions and study the differential properties of partially bent₄ functions, unifying the previous work on partially bent functions.

Vorheriger Artikel Regular (k, R, 1)-packings with and their locally repairable codes

Nächster Artikel Correcting mistakes in the paper “A mass formula for negacyclic codes of length 2k and some good negacyclic codes over ” [Cryptogr. Commun. (2017) 9: 241–272]

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Titel: Shifted plateaued functions and their differential properties
verfasst von: Nurdagül Anbar
Canan Kaşıkçı
Wilfried Meidl
Alev Topuzoğlu
Publikationsdatum: 23.03.2020
Verlag: Springer US
Erschienen in: Cryptography and Communications / Ausgabe 6/2020
Print ISSN: 1936-2447
Elektronische ISSN: 1936-2455
DOI: https://doi.org/10.1007/s12095-020-00426-2

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