On Constructing Bent Functions From Cyclotomic Mappings

We propose to study the construction of Boolean bent functions from cyclotomic mappings. By considering Dillon functions, Niho functions and Kasami functions as different branch functions respectively, we obtain three generic constructions from this new perspective. As a result, several infinite classes of bent functions belonging to the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\mathcal {PS}}_{ap}$ </tex-math></inline-formula> class, class <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {H}$ </tex-math></inline-formula> and the completed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {MM}$ </tex-math></inline-formula> class are derived, thereby providing simple representations of known classes of bent functions through cyclotomic mappings. In addition, computer experiments show that examples of bent functions outside these three well-known classes can also be obtained by selecting other branch functions.