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Cryptography and Communications

Erschienen in:

11.07.2019

Multiple characters transforms and generalized Boolean functions

verfasst von: Sihem Mesnager, Constanza Riera, Pantelimon Stănică

Erschienen in: Cryptography and Communications | Ausgabe 6/2019

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Abstract

In this paper we investigate generalized Boolean functions whose spectrum is flat with respect to a set of Walsh-Hadamard transforms defined using various complex primitive roots of 1. We also study some differential properties of the generalized Boolean functions in even dimension defined in terms of these different characters. We show that those functions have similar properties to the vectorial bent functions. We next clarify the case of gbent functions in odd dimension. As a by-product of our proofs, more generally, we also provide several results about plateaued functions. Furthermore, we find characterizations of plateaued functions with respect to different characters in terms of second derivatives and fourth moments.

Vorheriger Artikel Generalized bent functions into from the partial spread and the Maiorana-McFarland class

Nächster Artikel Several new classes of self-dual bent functions derived from involutions

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Titel: Multiple characters transforms and generalized Boolean functions
verfasst von: Sihem Mesnager
Constanza Riera
Pantelimon Stănică
Publikationsdatum: 11.07.2019
Verlag: Springer US
Erschienen in: Cryptography and Communications / Ausgabe 6/2019
Print ISSN: 1936-2447
Elektronische ISSN: 1936-2455
DOI: https://doi.org/10.1007/s12095-019-00383-5

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