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Bent functions on a finite nonabelian group. (English) Zbl 1105.43002
A bent function on a finite nonabelian group is introduced in this paper; it is a natural generalization of a bent function on a finite abelian group introduced by O. A. Logachev, A. A. Salnikov and V. V. Yashchenko [Discrete Math. Appl. 7, 547–564 (1997; Zbl 0982.94012)]. Using the theory of linear representations and noncommutative harmonic analysis of finite groups, several properties of such functions similar to the corresponding properties of traditional abelian bent functions are given.

MSC:
43A32 Other transforms and operators of Fourier type
94A60 Cryptography
33E99 Other special functions
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