Paper 2012/325

A note on generalized bent criteria for Boolean functions

Sugata Gangopadhyay, Enes Pasalic, and Pantelimon Stanica


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].

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Secret-key cryptography
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Published elsewhere. Unknown where it was published
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gsugata @ gmail com
2012-07-02: last of 2 revisions
2012-06-12: received
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      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{}},
      url = {}
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