1. Rotation-symmetric bent functions outside the completed Maiorana-McFarland classAlexandr Polujan, Sadmir Kudin, Enes Pašalić, 2026, original scientific article Abstract: Rotation-symmetric (RS) bent functions, which are invariant under the action of the cyclic group, have attracted significant attention over the past three decades due to their importance in cryptographic applications. For the last three decades of research on these objects, most known RS bent func- tions have been obtained by applying extended-affine equivalence to specific Maiorana-McFarland bent functions, in a way that ensures the resulting function retains invariance under the cyclic group action. Due to the intrinsic difficulty of characterizing RS bent functions that do not belong to the completed Maiorana- McFarland class M#, there has been no evidence for the existence of such functions until now. In this paper, we provide, for the first time, a solution to this problem. First, we perform a computational classification of RS cubic bent functions in ten variables under extended-affine equivalence and demonstrate that one of the resulting classes is outside the M# class. Next, we prove that an infinite family of RS bent functions on Fn 2 of maximum algebraic degree n/2 (Su, Adv. Math. Commun. 13(2): 253–265, 2019) does not belong to M#, for all n ≥ 8. Finally, we show that a family of quartic RS bent functions on Fn 2 (Carlet, Gao, and Liu, J. Comb. Theory Ser. A 127: 161–175, 2014), does not belong to the M# class for infinitely many n.
Keywords: bent function, rotation-symmetry, Maiorana-McFarland class
Published in RUP: 19.08.2026; Views: 17; Downloads: 2
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2. Vectorial negabent concepts : similarities, differences, and generalizationsNurdagül Anbar, Sadmir Kudin, Wilfried Meidl, Enes Pašalić, Alexandr Polujan, 2025, original scientific article Abstract: In Pasalic et al. (IEEE Trans Inf Theory 69:2702–2712, 2023), and in Anbar and Meidl (Cryptogr Commun 10:235–249, 2018), two different vectorial negabent and vectorial bent- negabent concepts are introduced, which leads to seemingly contradictory results. One of the main motivations for this article is to clarify the differences and similarities between these two concepts. Moreover, the negabent concept is extended to generalized Boolean functions from Fn 2 to the cyclic group Z2k . It is shown how to obtain nega-Z2k -bent functions from Z2k -bent functions, or equivalently, corresponding non-splitting relative difference sets from the splitting relative difference sets. This generalizes the shifting results for Boolean bent and negabent functions. We finally point to constructions of Z8 -bent functions employing per- mutations with the (Am ) property, and more generally we show that the inverse permutation gives rise to Z2k -bent functions.
Keywords: bent function, Maiorana-McFarland class, negabent functions
Published in RUP: 12.09.2025; Views: 1040; Downloads: 38
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3. The algebraic characterization of M-subspaces of bent concatenations and its applicationSadmir Kudin, Enes Pašalić, Alexandr Polujan, Fengrong Zhang, 2025, original scientific article Abstract: Every Boolean bent function f can be written either as a concatenation f = f1|| f2 of two complementary semi-bent functions f1, f2; or as a concatenation f = f1|| f2|| f3|| f4 of four Boolean functions f1, f2, f3, f4, all of which are simultaneously bent, semi-bent, or 5-valued spectra-functions. In this context, it is essential to specify conditions for these bent concatenations so that f does (not) belong to the completed Maiorana-McFarland class M#. In this article, we resolve this question completely by providing the algebraic characterization of M-subspaces for the concatenation of the form f = f1|| f2 and f = f1|| f2|| f3|| f4, which allows us to estimate ind( f ), the linearity index of f, and consequently to establish the necessary and sufficient conditions so that f is outside M#. Based on these conditions, we propose several explicit and generic design methods of specifying bent functions outside M# in the special case when f = g||h||g||(h+1), where g and h are bent functions. Moreover, we show that it is possible to even decrease the linearity index of f = g||h||g||(h+1), compared to ind(g) and ind(h), if the largest dimension of a common M-subspace of g and h is small enough (less than min{ind(g), ind(h)} − 1). This also induces iterative methods of constructing bent functions outside M# with (controllable) low linearity index. Finally, we derive a lower bound on the 2-rank of f and show that this concatenation method can generate bent functions that are provably outside M# ∪ PS# ap. In difference to the approach of Weng et al. (2007) that uses the direct sum and a bent function g outside M#, our method employs g, h ∈ M# for the same purpose.
Keywords: bent function, Maiorana-McFarland class, M-subspaces
Published in RUP: 04.08.2025; Views: 1200; Downloads: 10
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4. Konstrukcije novih superrazredov ukrivljenih funkcij in nadaljnje konstrukcije kriptografsko pomembnih preslikav izven M# : doktorska disertacijaAmar Bapić, 2022, doctoral dissertation Keywords: vecotorial bent function, class inclusion, complete Maiorana-McFaralnd class, MNBC functions, secondary constructions, weakly/almost strongly/strongly outside M#, 4-decomposition, SC and CD class, direct and indirect sum
Published in RUP: 12.12.2022; Views: 4615; Downloads: 44
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6. Full characterization of generalized bent functions as (semi)-bent spaces, their dual, and the Gray imageSamir Hodžić, Wilfried Meidl, Enes Pašalić, 2018, original scientific article Keywords: generalized bent functions, Zq-bent functions, Gray maps, dual of generalized bent function, relative difference sets
Published in RUP: 08.06.2018; Views: 4175; Downloads: 106
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