Open AccessHighly nonlinear plateaued functions
Author(s) -
Cusick Thomas W.
Publication year - 2017
Publication title -
iet information security
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.308
H-Index - 34
eISSN - 1751-8717
pISSN - 1751-8709
DOI - 10.1049/iet-ifs.2016.0131
Subject(s) - boolean function , mathematics , quadratic equation , nonlinear system , cryptography , discrete mathematics , bent function , quadratic function , degree (music) , function (biology) , combinatorics , pure mathematics , algorithm , physics , quantum mechanics , geometry , evolutionary biology , acoustics , biology
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.