Journal of South China University of Technology(Natural Science) >

2010 , Vol. 38 >Issue 6: 95 - 99

DOI: https://doi.org/10.3969/j.issn.1000-565X.2010.06.018

Computer Science & Technology

Lower Bounds of Second-Order Nonlinearity of Boolean Functions

Expand
  • 1.Department of Applied Mathematics,Xidian University,Xi＇ an 710071,Shannxi,China;2.School of Telecommunications Engineering,Xidian University,Xi＇ an 710071,Shannxi,China
李雪莲（1979-），女，讲师，博士生，主要从事密码函数、流密码研究．

Received date: 2009-08-11

  Revised date: 2010-01-22

  Online published: 2010-06-25

Supported by

国家“973”计划项目（2007CB311201）; 国家自然科学基金资助项目（60833008 60803149）; 广西信息与通讯技术重点实验室资助项目（20902）

Fold

Abstract

This paper deals with the second-order nonlinearities of the Boolean functions f（x）=tr（∑（n-1）/2」i,j=1bijxd） with n variables,where d=2i＋2j＋1,bij GF（2） and 1≤ij≤L（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 nonlinerity,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.

Key words： Boolean functions; cryptography; nonlinearities; Walsh transforms; derivatives

Cite this article

Li Xue-lian Hu Yu-pu Gao Jun-tao . Lower Bounds of Second-Order Nonlinearity of Boolean Functions[J]. Journal of South China University of Technology(Natural Science), 2010 , 38(6) : 95 -99 . DOI: 10.3969/j.issn.1000-565X.2010.06.018

Options
Outlines

/

〈 〉