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Cryptography and Communications

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10-05-2018

On Boolean functions with several flat spectra

Authors: Gaofei Wu, Matthew Geoffrey Parker

Published in: Cryptography and Communications | Issue 5/2019

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Abstract

In this paper, two constructions of Boolean functions which have at least two flat spectra with respect to {H, N}ⁿ are proposed. Some known results about bent-negabent functions can be seen as special cases of our results. Furthermore, some lower bounds on the numbers of flat spectra of Boolean functions with respect to {H, N}ⁿ or {I, N}ⁿ are given. In particular, we show that any Maiorana-McFarland bent function of n (n even) variables has at least \(\frac {n}{2}+ 2^{\frac {n}{2}} \) flat spectra with respect to {H, N}ⁿ. Finally, following the work by Riera, Petrides, and Parker, we develop recursive formulae for the numbers of flat spectra of some structural quadratics, including star function, star-line function, and star-line-star function.

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Title: On Boolean functions with several flat spectra
Authors: Gaofei Wu
Matthew Geoffrey Parker
Publication date: 10-05-2018
Publisher: Springer US
Published in: Cryptography and Communications / Issue 5/2019
Print ISSN: 1936-2447
Electronic ISSN: 1936-2455
DOI: https://doi.org/10.1007/s12095-018-0309-2

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