New characterizations and construction methods of bent and hyper-bent Boolean functions

Sihem Mesnager; Bimal Mandal; Chunming Tang

doi:10.1016/j.disc.2020.112081

New characterizations and construction methods of bent and hyper-bent Boolean functions

Sihem Mesnager, Bimal Mandal, Chunming Tang

Research output: Contribution to journal › Journal Article › peer-review

4 Citations (Scopus)

Abstract

In this paper, we first derive a necessary and sufficient condition for a bent Boolean function by analyzing their support set. Next, using this condition and the Pless power moment identities, we propose a construction method of bent functions of 2k variables by a suitable choice of 2k-dimension subspace of F₂^{2^2k−1−2^k−1}. Further, we extend our results to the so-called hyper-bent functions.

Original language	English
Article number	112081
Journal	Discrete Mathematics
Volume	343
Issue number	11
DOIs	https://doi.org/10.1016/j.disc.2020.112081
Publication status	Published - Nov 2020
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2020 Elsevier B.V.

Keywords

Bent function
Boolean function
Hyper-bent function
Pless power moment identity
Walsh–Hadamard transform

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10.1016/j.disc.2020.112081

Cite this

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abstract = "In this paper, we first derive a necessary and sufficient condition for a bent Boolean function by analyzing their support set. Next, using this condition and the Pless power moment identities, we propose a construction method of bent functions of 2k variables by a suitable choice of 2k-dimension subspace of F222k−1−2k−1. Further, we extend our results to the so-called hyper-bent functions.",

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AU - Mandal, Bimal

AU - Tang, Chunming

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N2 - In this paper, we first derive a necessary and sufficient condition for a bent Boolean function by analyzing their support set. Next, using this condition and the Pless power moment identities, we propose a construction method of bent functions of 2k variables by a suitable choice of 2k-dimension subspace of F222k−1−2k−1. Further, we extend our results to the so-called hyper-bent functions.

AB - In this paper, we first derive a necessary and sufficient condition for a bent Boolean function by analyzing their support set. Next, using this condition and the Pless power moment identities, we propose a construction method of bent functions of 2k variables by a suitable choice of 2k-dimension subspace of F222k−1−2k−1. Further, we extend our results to the so-called hyper-bent functions.

KW - Bent function

KW - Boolean function

KW - Hyper-bent function

KW - Pless power moment identity

KW - Walsh–Hadamard transform

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UR - https://openalex.org/W3062244034

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JO - Discrete Mathematics

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IS - 11

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ER -

New characterizations and construction methods of bent and hyper-bent Boolean functions

Abstract

Bibliographical note

Keywords

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