Welcome to the resource topic for 2012/325
Title:
A note on generalized bent criteria for Boolean functions
Authors: Sugata Gangopadhyay, Enes Pasalic, 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].
ePrint: https://eprint.iacr.org/2012/325
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