Malaysian Journal of Mathematical Sciences, June 2015, Vol. 9(S)
Special Issue: The 4th International Cryptology and Information Security Conference 2014 (Cryptology 2014)

Harmonic Analysis and a Bentness-Like Notion in Certain Finite Abelian Groups Over Some Finite Fields

Laurent Poinsot and Nadia El Mrabet

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It is well-known that degree two finite field extensions can be equipped with a Hermitian-like structure similar to the extension of the complex field over the reals. In this contribution, using this structure, we develop a modular character theory and the appropriate Fourier transform for some particular kind of finite Abelian groups. Moreover we introduce the notion of bent functions for finite field valued functions rather than usual complex-valued functions, and we study several of their properties.

Keywords: Hermitian-like structure, modular character theory, Fourier transform, Abelian groups



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