On the linear structures of Balanced functions and quadratic APN\n functions

2019/09/25 by Augustine Musukwa, Massimiliano Sala, Musukwa, Augustine +1
Biochemistry, Genetics and Molecular Biology · Computer Science · #06E30 #14G50 #94A60 #Coding theory and cryptography #Cryptography and Security (cs.CR) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #Quantum-Dot Cellular Automata #Receptor Mechanisms and Signaling

paper · pdf · doi:10.48550/arxiv.1909.11465

openalex publication_date 2019/09/25 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28

Abstract

The set of linear structures of most known balanced Boolean functions is\nnontrivial. In this paper, some balanced Boolean functions whose set of linear\nstructures is trivial are constructed. We show that any APN function in even\ndimension must have a component whose set of linear structures is trivial. We\ndetermine a general form for the number of bent components in quadratic APN\nfunctions in even dimension and some bounds on the number are produced. We also\ncount bent components in any quadratic power functions.\n

Related

• A lower bound on the number of bent squares
• New construction of APN quaratic
• On Some Properties of Quadratic APN Functions of a Special Form
• Millions of inequivalent quadratic APN functions in eight variables
• Generalised Bent Criteria for Boolean Functions (II)