NDLI: Non Abelian bent functions

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Non Abelian bent functions

Content Provider	Springer Nature Link
Author	Poinsot, Laurent
Copyright Year	2011
Abstract	Perfect nonlinear functions from a finite group G to another one H are those functions f: G →H such that for all nonzero α ∈ G, the derivative $d_{\alpha}f: x \mapsto f(\alpha x) f(x)^{-1}$ is balanced. In the case where both G and H are Abelian groups, f: G →H is perfect nonlinear if, and only if, f is bent, i.e., for all nonprincipal character χ of H, the (discrete) Fourier transform of χ ∘ f has a constant magnitude equals to \|G\|. 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.
Starting Page	1
Ending Page	23
Page Count	23
File Format	PDF
ISSN	19362447
Journal	Cryptography and Communications
Volume Number	4
Issue Number	1
e-ISSN	19362455
Language	English
Publisher	Springer US
Publisher Date	2011-11-15
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Bent functions Perfect nonlinearity Finite non Abelian groups Fourier transform Linear representations Algebraic coding theory; cryptography General theory for finite groups Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc. Mathematics of Computing Information and Communication, Circuits Communications Engineering, Networks Coding and Information Theory Data Structures, Cryptology and Information Theory
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computer Networks and Communications Computational Theory and Mathematics

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