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Vectorial bent functions in odd characteristic and their components

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Abstract

Bent functions in odd characteristic can be either (weakly) regular or non-weakly regular. Furthermore one can distinguish between dual-bent functions, which are bent functions for which the dual is bent as well, and non-dual bent functions. Whereas a weakly regular bent function always has a bent dual, a non-weakly regular bent function can be either dual-bent or non-dual-bent. The classical constructions (like quadratic bent functions, Maiorana-McFarland or partial spread) yield weakly regular bent functions, but meanwhile one knows constructions of infinite classes of non-weakly regular bent functions of both types, dual-bent and non-dual-bent. In this article we focus on vectorial bent functions in odd characteristic. We first show that most p-ary bent monomials and binomials are actually vectorial constructions. In the second part we give a positive answer to the question if non-weakly regular bent functions can be components of a vectorial bent function. We present the first construction of vectorial bent functions of which the components are non-weakly regular but dual-bent, and the first construction of vectorial bent functions with non-dual-bent components.

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Acknowledgement

W.M. is supported by the FWF Project P 30966.

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Correspondence to Ayça Çeşmelioğlu.

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This article belongs to the Topical Collection: Boolean Functions and Their Applications IV

Guest Editors: Lilya Budaghyan and Tor Helleseth

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Çeşmelioğlu, A., Meidl, W. & Pott, A. Vectorial bent functions in odd characteristic and their components. Cryptogr. Commun. 12, 899–912 (2020). https://doi.org/10.1007/s12095-020-00444-0

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  • DOI: https://doi.org/10.1007/s12095-020-00444-0

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