Non Abelian bent functions

作者：Poinsot Laurent^*

来源：Cryptography and Communications, 2012, 4(1): 1-23.

DOI：10.1007/s12095-011-0058-y

• Bent functions
• Perfect nonlinearity
• Finite non Abelian groups
• Fourier transform
• Linear representations

Perfect nonlinear functions from a finite group G to another one H are those functions f : G -%26gt; H such that for all nonzero alpha epsilon G, the derivative d alpha f : x bar right arrow f (alpha x) f (x)(-1) is balanced. In the case where both G and H are Abelian groups, f : G -%26gt; H is perfect nonlinear if, and only if, f is bent, i.e., for all nonprincipal character chi of H, the (discrete) Fourier transform of chi circle f has a constant magnitude equals to vertical bar G vertical bar. In this paper, using the theory of linear representations, we exhibit similar bentness-like characterizations in the cases where G and/or H are (finite) non Abelian groups. Thus we extend the concept of bent functions to the framework of non Abelian groups.

• 出版日期2012-3