Cubic Maiorana–McFarland bent functions with no affine derivative. Issue 1 (2nd January 2017)

• Record Type: Journal Article
• Authors: Mandal, Bimal; Gangopadhyay, Sugata; Stănică, Pantelimon
• Is Part Of: International journal of computer mathematics. Volume 2:Issue 1(2017)
• Page Start: 14
• Page End: 27
• Publication Date: 2017-01-02
• Subjects: Boolean functions -- bent functions -- differentials -- vector spaces -- counting; Computer systems -- Periodicals; Computer systems; Periodicals; 004
• DOI: 10.1080/23799927.2017.1304453
• Languages: English
• ISSNs: 2379-9927

Abstract

ABSTRACT: A class of cubic Maiorana–McFarland ( ) bent functions having no affine derivative was constructed by Canteaut and Charpin [ Decomposing bent functions, IEEE Trans. Inform. Theory 49(8) (2003), pp. 2004–2019], thereby solving an open problem posed by Hou [ Cubic bent functions, Discrete Math. 189 (1998), pp. 149–161]. The goal of the paper is twofold: we construct two classes of cubic bent functions with no affine derivative and show their mutual affine inequivalence.