Highly nonlinear plateaued functions. (1st March 2017)

• Record Type: Journal Article
• Authors: Cusick, Thomas W.
• Is Part Of: IET information security. Volume 11:Number 2(2017)
• Page Start: 78
• Page End: 81
• Publication Date: 2017-03-01
• Subjects: cryptography -- Boolean functions -- nonlinear functions; highly nonlinear plateaued functions -- Boolean functions -- quadratic function -- cryptographic properties; Computer security -- Periodicals; Cryptography -- Periodicals; Computer networks -- Security measures -- Periodicals; Database security -- Periodicals; 005.8
• DOI: 10.1049/iet-ifs.2016.0131
• Languages: English
• ISSNs: 1751-8709

Abstract

Abstract : The authors describe a method for producing Boolean functions of degree d ≥ 3 in n = 2 dk − 1 ( k = 1, 2, …) variables, such that the functions are plateaued and balanced, have high nonlinearity and have no linear structures. The nonlinearity is 2 n −1 − 2 ( n −1)/2, which is the same as the largest possible nonlinearity for a quadratic function in n (odd) variables (the so‐called 'quadratic bound'). Their theorem uses some new ideas to generalise a theorem, which gave the case d = 3, in a 2009 paper by Fengrong Zhang et al . They discuss the cryptographic properties and applications for the functions.