Abstract:

Hyper-bent functions are special bent functions which have many useful applications in cryptography and communications. Using the properties of permutations, we find the sufficient and necessary condition for one Boolean function is hyper-bent function and the relation between hyper-bent functions and PS class bent functions. We also provide one generalized method to construct multi-output hyper-bent functions and use this method to construct balanced multi-output functions with high nonlinearity.

Key words: Bent functions, hyper-bent functions, balanced functions, nonlinearity.