Bent functions linear on elements of some classical spreads and presemifields spreads

Kanat Abdukhalikov, Sihem Mesnager

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

Abstract

Bent functions are maximally nonlinear Boolean functions with an even number of variables. They have attracted a lot of research for four decades because of their own sake as interesting combinatorial objects, and also because of their relations to coding theory, sequences and their applications in cryptography and other domains such as design theory. In this paper we investigate explicit constructions of bent functions which are linear on elements of spreads. After presenting an overview on this topic, we study bent functions which are linear on elements of presemifield spreads and give explicit descriptions of such functions for known commutative presemifields. A direct connection between bent functions which are linear on elements of the Desarguesian spread and oval polynomials over finite fields was proved by Carlet and the second author. Very recently, further nice extensions have been made by Carlet in another context. We introduce oval polynomials for semifields which are dual to symplectic semifields. In particular, it is shown that from a linear oval polynomial for a semifield one can get an oval polynomial for transposed semifield.

Original languageEnglish
Pages (from-to)3-21
Number of pages19
JournalCryptography and Communications
Volume9
Issue number1
DOIs
Publication statusPublished - Jan 1 2017

Keywords

  • Bent functions
  • Boolean functions
  • Oval polynomials
  • Quasifields
  • Semifields
  • Spreads
  • Symplectic semifields
  • Walsh Hadamard transform

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Computational Theory and Mathematics
  • Applied Mathematics

Fingerprint

Dive into the research topics of 'Bent functions linear on elements of some classical spreads and presemifields spreads'. Together they form a unique fingerprint.

Cite this