Connections between Quaternary and Binary Bent Functions

Boolean bent functions were introduced by Rothaus (1976) as combinatorial objects related to difference sets, and have since enjoyed a great popularity in symmetric cryptography and low correlation sequence design. In this paper direct links between Boolean bent functions, generalized Boolean bent functions (Schmidt, 2006) and quaternary bent functions (Kumar, Scholtz, Welch, 1985) are explored. We also study Gray images of bent functions and notions of generalized nonlinearity for functions that are relevant to generalized linear cryptanalysis.