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28. Design methods for semi-bent functionsEnes Pašalić, Sugata Gangopadhyay, WeiGuo Zhang, Samed Bajrić, 2019, original scientific article Abstract: Semi-bent functions play an important role in the construction of orthogonal variable spreading factor codes used in code-division multiple-access (CDMA) systems as well as in certain cryptographic applications. In this article we provide several infinite classes of semi-bent functions, where each class is characterized by either a different decomposition of such a function with respect to the Walsh spectra of its subfunctions, or by the method used for its derivation. In particular, we also give the exact number of possibilities of decomposing bent functions, in a subclass of the Maiorana-McFarland class.
Keywords: cryptography, Boolean functions, bent functions, semi-bent functions, derivatives
Published in RUP: 19.12.2018; Views: 3269; Downloads: 171
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29. On derivatives of planar mappings and their connections to complete mappingsAmela Muratović-Ribić, Enes Pašalić, 2018, original scientific article Abstract: Given are necessary conditions for a permutation polynomial to be the derivative of a planar mapping. These conditions are not sufficient and there might exist permutation polynomials which are not derivatives of some planar mapping satisfying these conditions. For the first time we show that there is a close connection between two seemingly unrelated structures, namely planar and complete mappings. It is shown that any planar mapping induces a sequence of complete mappings having some additional interesting properties. Furthermore, a class of almost planar mappings over extension fields is introduced having the property that its derivatives are permutations in most of the cases. This class of functions then induces many infinite classes of complete mappings (permutations) as well.
Keywords: planar mapping, derivatives, complete mappings, permutation polynomials
Published in RUP: 19.12.2018; Views: 2202; Downloads: 243
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