Connections between quaternary and Boolean bent functions

Authors

  • Natalia Tokareva Sobolev Institute of Mathematics
  • Alexander Shaporenko Novosibirsk State University
  • Patrick Sole Aix-Marseille University

Keywords:

Boolean functions, generalized Boolean functions, quaternary functions, bent functions, semi bent functions, nonlinearity, linear cryptanalysis, Gray map, $\ZZ_4$-linear codes.

Abstract

Boolean bent functions were introduced by Rothaus (1976) as combinatorial objects related to difference sets, and have since \linebreak enjoyed a great popularity in symmetric cryptography and low correlation sequence design. In this paper connections between classical Boolean bent functions, generalized Boolean bent functions and quaternary bent functions are studied. We also study Gray images of bent functions and notions of generalized nonlinearity for functions that are relevant to generalized linear cryptanalysis.

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Published

2021-05-26

Issue

Vol. 18 No. 1 (2021)

Section

Discrete mathematics and mathematical cybernetics