### A note on generalized bent criteria for Boolean functions

Sugata Gangopadhyay, Enes Pasalic, and Pantelimon Stanica

##### Abstract

In this paper, we consider the spectra of Boolean functions with respect to the action of unitary transforms obtained by taking tensor products of the Hadamard, denoted by $H$, and the nega--Hadamard, denoted by $N$, kernels. The set of all such transforms is denoted by $\{H, N\}^n$. A Boolean function is said to be bent$_4$ if its spectrum with respect to at least one unitary transform in $\{H, N\}^n$ is flat. We prove that the maximum possible algebraic degree of a bent$_4$ function on $n$ variables is $\lceil \frac{n}{2} \rceil$, and hence solve an open problem posed by Riera and Parker [cf. IEEE-IT: 52(2)(2006) 4142--4159]. We obtain a relationship between bent and bent$_4$ functions which is a generalization of the relationship between bent and negabent Boolean functions proved by Parker and Pott [cf. LNCS: 4893(2007) 9--23].

Available format(s)
Category
Secret-key cryptography
Publication info
Published elsewhere. Unknown where it was published
Contact author(s)
gsugata @ gmail com
History
2012-07-02: last of 2 revisions
See all versions
Short URL
https://ia.cr/2012/325

CC BY

BibTeX

@misc{cryptoeprint:2012/325,
author = {Sugata Gangopadhyay and Enes Pasalic and Pantelimon Stanica},
title = {A note on generalized bent criteria for Boolean functions},
howpublished = {Cryptology ePrint Archive, Paper 2012/325},
year = {2012},
note = {\url{https://eprint.iacr.org/2012/325}},
url = {https://eprint.iacr.org/2012/325}
}

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