Non-Boolean almost perfect nonlinear functions on non-Abelian groups

Laurent Poinsot (1) , Alexander Pott (2)

1 LIPN - Laboratoire d'Informatique de Paris-Nord
2 IAG - Institut für Algebra und Geometrie

The purpose of this paper is to present the extended definitions and characterizations of the classical notions of APN and maximum nonlinear Boolean functions to deal with the case of mappings from a finite group K to another one N with the possibility that one or both groups are non-Abelian.

Mots clés: APN functions; bent functions; group algebra; representation theory; Fourier transform

Domaines: Cryptographie et sécurité [cs.CR]

Laurent Poinsot, Alexander Pott. Non-Boolean almost perfect nonlinear functions on non-Abelian groups. International Journal of Foundations of Computer Science, 2011, 22 (6), pp.1351-1367. ⟨10.1142/S0129054111008751⟩. ⟨hal-00575007⟩