New Cryptographic Bent Functions from Permutations and Linear Translator in Cyber Security

Cryptographic bent functions are maximally nonlinear Boolean functions with an even number of variables. They are not only closely related to some interesting combinatorial objects, but also have important applications in coding, sequence design, cryptography and cyber security. In this paper, we firstly investigate the Walsh transform of two families of functions via Maiorana-MacFarland's class. Secondly, we present new infinite families of permutations. We show that those families have nice property that one can select three elements among them which can be used to construct bent functions. Finally, by using two linear translators, we construct bent functions from the class of Maiorana-MacFarland.