Secondary constructions of highly nonlinear Boolean functions and disjoint spectra plateaued functions

被引：28

作者：

Zhang, Feng-rong ^{[1
]}

Carlet, Claude ^{[2
]}

Hu, Yu-pu ^{[3
]}

Cao, Tian-jie ^{[1
]}

机构：

[1] China Univ Min & Technol, Sch Comp Sci & Technol, Xuzhou 221116, Jiangsu, Peoples R China

[2] Univ Paris 08, CNRS, LAGA, UMR 7539, F-93526 St Denis 02, France

[3] Xidian Univ, State Key Lab Integrated Serv Networks, Xian 710071, Peoples R China

来源：

INFORMATION SCIENCES | 2014年 / 283卷

基金：

美国国家科学基金会;

关键词：

Boolean function; Resilient function; Bent function; High nonlinearity; REED-MULLER CODE; COVERING RADIUS; CORRELATION-IMMUNE; RESILIENT; BENT; NUMBER;

D O I：

10.1016/j.ins.2014.06.024

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In this paper, we modify a generalized indirect sum construction to construct functions with high nonlinearity. By utilizing the modified construction, highly nonlinear functions in (n + m) variables can be obtained from known bent functions in n variables and highly nonlinear functions in m variables. It is possible to obtain new (n + 15)-variable functions with nonlinearity 2(n+15-1) - 2((n+15-1)/2) + 20 x 2(n/2) and new 12-variable 2-resilient functions with nonlinearity 2000 and algebraic degree 8, which achieve optimal algebraic immunity. Moreover, the modified construction can also be used as an iterative construction of a quadruple of disjoint spectra plateaued functions. In addition, we present sufficient conditions for a quadruple of disjoint spectra plateaued functions to have no nonzero linear structure. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：94 / 106

页数：13

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