Cryptology ePrint Archive: Report 2012/325

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].

Category / Keywords: secret-key cryptography /

Date: received 8 Jun 2012, last revised 2 Jul 2012

Contact author: gsugata at gmail com

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Version: 20120702:124756 (All versions of this report)

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