Cryptographically significant mappings over $mathbb{F}_2^n$.

In the first part of the talk, we give basic definitions and properties of some cryptographically significant mappings, including (vectorial) bent functions, s-plateaued function, APN and AB functions as well as the notion of duals of bent and s-plateaued functions.

In the second part of the talk (joint work with Enes Pasalic and Samir Hodžić) we present some results and current research topics: Characterization of semi-bentness (bentness) of the component functions (duals of component functions) of the Gold AB function in spectral domain; Generic construction of vectorial bent functions motivated by the constructions of Zheng et al. (construction of vectorial bent functions) and Tang et al. (construction of bent functions).

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