Lower bounds of second-order nonlinearity of Boolean functions

被引：0

作者：

Li X.-L. ^{[1
]}

Hu Y.-P. ^{[2
]}

Gao J.-T. ^{[2
]}

机构：

[1] Department of Applied Mathematics, Xidian University, Xi' an 710071, Shaanxi

[2] School of Telecommunications Engineering, Xidian University, Xi' an 710071, Shaanxi

来源：

Huanan Ligong Daxue Xuebao/Journal of South China University of Technology (Natural Science) | 2010年 / 38卷 / 06期

关键词：

Boolean functions; Cryptography; Derivatives; Nonlinearities; Walsh transforms;

D O I：

10.3969/j.issn.1000-565X.2010.06.018

中图分类号：

学科分类号：

摘要：

This paper deals with the second-order nonlinearities of the Boolean functions f(x)=tr(∑(i, j=1)⌊(n-1)/2⌋ bijxd) with n variables, where d=2i+2j+1, bij∈GF(2) and 1≤i<j≤ ⌊(n-1)/2⌋. The derivatives with the maximal nonlinearity of f(x) are determined for odd n, and, for even n, the derivatives which are semi-Bent functions are obtained. Based on these derivatives with high nonlinearity, the tight lower bounds of the second-order nonlinearity of f(x) are given. The results show that f(x) with high second-order nonlinearity, can resist the quadratic and affine approximation attacks.

引用

页码：95 / 99

页数：4

共 9 条

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