| 三次单项布尔函数的二阶非线性度下界 |
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| 引用本文： | 李雪莲,胡予濮,高军涛,方益奇.三次单项布尔函数的二阶非线性度下界[J].北京工业大学学报,2010,36(5). |
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| 作者姓名： | 李雪莲 胡予濮 高军涛 方益奇 |
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| 作者单位： | 西安电子科技大学,应用数学系,西安,710071;西安电子科技大学,计算机网络与信息安全教育部重点实验室,西安,710071;西安电子工程研究所,总体七部,西安,710100 |
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| 基金项目： | 国家"九七三"重点发展计划基金资助，国家自然科学基金资助，广西信息与通讯技术重点实验室资助 |
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| 摘 要： | 本文研究了形如fμ(x)=Tr(μxd)的n元单项布尔函数,其中d=2i+2j+1,μ∈GF(2n)*,i,j均为正整数,且nij.已有结论表明:当n2i时,fμ(x)具有良好的二阶非线性度下界.在此基础上本文研究了n≤2i时fμ(x)所有导数的非线性度下界,并给出n≤2i时fμ(x)的二阶非线性度下界.结果表明n≤2i时fμ(x)的二阶非线性度下界比n2i时fμ(x)的二阶非线性度下界更紧.因此,fμ(x)无论在n2i还是n≤2i时都可以抵抗二次函数逼近和仿射逼近攻击.
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| 关 键 词： | 密码学 布尔函数 Walsh变换 非线性度 |
The Nonlinearity Lower Bounds on the Second Order of Cubic Monomial Boolean Functions |
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| LI Xue-lian,HU Yu-pu,GAO Jun-tao,FANG Yi-qi.The Nonlinearity Lower Bounds on the Second Order of Cubic Monomial Boolean Functions[J].Journal of Beijing Polytechnic University,2010,36(5). |
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| Authors: | LI Xue-lian HU Yu-pu GAO Jun-tao FANG Yi-qi |
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| Affiliation: | LI Xue-lian1,HU Yu-pu2,GAO Jun-tao2,FANG Yi-qi3 (1.Department of Applied Mathematics,Xidian University,Xi' an,710071,China,2.Key Laboratory of Computer networks & Information Security,3.Xi'an Electronic Engineering Institute,710100,China) |
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| Abstract: | This paper investigates cubic monomial Boolean functions fμ(x)=Tr(μxd) with n variables,where d=2i+2j+1,μ∈GF(2n)*,and n>i>j.The known results show that the Boolean functions fμ(x) has good lower bounds on the second nonlinearity for n>2i.This paper firstly studies all lower bounds on the nonlinearity of the derivatives of fμ(x),then the lower bounds on the second order nonlinearity of fμ(x) for n≤2i are given.The results show that the lower bounds on the second order nonlinearity of fμ(x) for n≤2i are tighter than that of fμ(x) for n>2i.Therefore,whether n>2i or n≤2i,the Boolean functions fμ(x) can resist quadratic or linear approximation attacks. |
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| Keywords: | cryptography boolean function walsh transforms nonlinearity |
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