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Constructing bent functions outside the Maiorana-McFarland class using a general form of RothausZhang, Fengrong ...In the mid 1960s, Rothaus proposed the so-called "most general form" of constructing new bent functions by using three (initial) bent functions whose sum is again bent. In this paper, we utilize a ... special case of Rothaus construction when two of these three bent functions differ by a suitably chosen characteristic function of an ▫$n/2$▫-dimensional subspace. This simplification allows us to treat the induced bent conditions more easily, also implying the possibility to specify the initial functions in the partial spread class and most notably to identify several instances of the so-called non-normal bent functions. Affine inequivalent bent functions within this class are then identified using a suitable selection of initial bent functions within the partial spread class (stemming from the complete Desarguesian spread). It is also shown that when the initial bent functions belong to the class ▫$\mathcal{D}$▫, then, under certain conditions, the constructed functions provably do not belong to the completed Maiorana-McFarland class. We conjecture that our method potentially generates an infinite class of non-normal bent functions (all tested ten-variable functions are non-normal but unfortunately they are weakly normal) though there are no efficient computational tools for confirming this.Vir: IEEE transactions on information theory. - ISSN 0018-9448 (Vol. 63, no. 8, 2017, str. 5336-5349)Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasleLeto - 2017Jezik - angleškiCOBISS.SI-ID - 18073433
Avtor
Zhang, Fengrong |
Pašalić, Enes |
Wei, Yongzhuang |
Cepak, Nastja
Teme
Rothaus konstrukcija |
ukrivljene funkcije |
razred Maiorana McFarland |
nenormalne ukrivljene funkcije |
šibko normalne ukrivljene funkcije |
Rothaus construction |
bent functions |
Maiorana-McFarland class |
partial spread |
non-normal bent functions |
weakly normal bent functions
vir: IEEE transactions on information theory. - ISSN 0018-9448 (Vol. 63, no. 8, 2017, str. 5336-5349)
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Zhang, Fengrong | |
Pašalić, Enes | 27777 |
Wei, Yongzhuang | |
Cepak, Nastja | 37552 |
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