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  • A complete characterization of ▫$\cD_0 \cap \cM^\#$▫ and a general framework for specifying bent functions in ▫$\cC$▫ outside ▫$\cM^\#$▫
    Kudin, Sadmir ; Pašalić, Enes
    In this paper we characterize the intersection of the completed Maiorana-McFarland class of bent functions ▫$\cM^{\#}$▫ and Carlet's ▫$\cD_0$▫ class of bent functions. As a consequence of this ... characterization, we prove that when the degree of a permutation ▫$\pi$▫ is greater than ▫$2$▫ the Boolean function ▫$f(x,y)=x \cdot \pi(y) + \delta_0(x)$▫, with ▫$ f:\F_2^n \times \F_2^n \to \F_2$▫, is always outside ▫$\cM^{\#}$▫ class. This also refines the sufficient condition of Carlet, which claims that if ▫$\pi$▫ is not affine on some hyperplane then ▫$f \not \in \cM^\#$▫. More precisely, this condition is also necessary when ▫$\deg(\pi)=2$▫, but it is not needed in the case ▫$\deg(\pi)>2$▫. We also specify a rather general framework for specifying bent functions in Carlet's ▫$\cC$▫ class which are provably outside the class ▫$\cM^{\#}$▫. Finally, using ranks of bent functions, we investigate the intersection of the class ▫$\cC$▫ and the subclass of the partial spread class ▫$\mathcal{PS}_{ap}$▫ and prove that the probability that an ▫$n$▫ variable function in ▫$\mathcal{PS}_{ap}$▫ is also in ▫$\cC$▫ approaches zero as ▫$n$▫ increases.
    Vir: Designs, codes and cryptography. - ISSN 0925-1022 (Vol. 90, iss. 8, 2022, str. 1783-1796)
    Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
    Leto - 2022
    Jezik - angleški
    COBISS.SI-ID - 118828035

    Povezava(-e):

    https://doi.org/10.1007/s10623-022-01079-3
    https://link.springer.com/article/10.1007/s10623-022-01079-3
    DOI

vir: Designs, codes and cryptography. - ISSN 0925-1022 (Vol. 90, iss. 8, 2022, str. 1783-1796)

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