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bent函数和半bent函数的二阶非线性度下界 被引量：3

The Lower Bounds on the Second Order Nonlinearity of Bent Functions and Semi-bent Functions
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摘要 该文研究了形如f(x,y)的n+1变元bent函数和半bent函数的二阶非线性度,其中x∈GF(2n),y∈GF(2)。首先给出了f(x,y)的2n-1个导数非线性度的精确值;然后推导出了函数f(x,y)的其余2n个导数的非线性度紧下界。进而给出了f(x,y)的二阶非线性度的紧下界。通过比较可知所得下界要优于现有的一般结论。结果表明f(x,y)具有较高的二阶非线性度,可以抵抗二次函数逼近和仿射逼近攻击。 This paper studies the lower bounds on the second order nonlinearity of bent functions and semi-bent functions f（x,y ）with n ＋ 1variables,where x ∈ GF（2n ）,y ∈ GF（2）.Firstly,the values of the nonlinearity of the 2n-1 derivatives of the Boolean function f（x,y ）are given.Then,the tight lower bounds on the other 2n derivatives of f（x,y ） are deduced.Furthermore,the tight lower bounds on the second order nonlinearity of f（x,y ） are presented.The derived bounds are better than the existing general ones.The results show that these functions f（x,y ） have higher second order nonlinearity,and can resist the quardratic and affine approximation attacks.
作者 李雪莲 胡予濮 高军涛
机构地区 西安电子科技大学应用数学系 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
出处 《电子与信息学报》 EI CSCD 北大核心 2010年第10期2521-2525,共5页 Journal of Electronics & Information Technology
基金 国家973计划项目(2007CB311201) 国家自然科学基金项目(60833008 60803149) 广西信息与通讯技术重点实验室基金(20902)资助课题
关键词 密码学 布尔函数 WALSH变换 非线性度 Cryptography Boolean functions Walsh transforms Nonlinearity
分类号 TN918.1 [电子电信—通信与信息系统]
  • 相关文献

参考文献10

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同被引文献21

  • 1Carlet C.On the Degree,Nonlinearity,Algebraic Thickness and Nonnormality of Boolean Functions,with Developments on Symmetric Functions[J].IEEE Transactions on Information Theory,2004,50(9):2178-2185.
  • 2Williams F J,Sloane N J.The Theory of Error-correcting Codes[M].Amsterdam,the Netherlands:[s.n.] ,1997.
  • 3Gangopadhyay S,Sarkar S,Telang R.On the Lower Bounds of the Second Order Nonlinearities of Some Boolean Functions[J].Information Sciences,2010,180(2):266-273.
  • 4Carlet C, Mesnager S. Improving the upper bounds on the covering radii of binary Reed-Muller codes [J]. IEEE Transactions Information Theory, 2007,53 ( 1 ) : 162-173.
  • 5Dumer I, Kabatiansky G, Tavernier C. List decoding of second order Reed-Muller codes up to the Johnson bound with almost linear complexity[C]//Proceedings of the IEEE International Symposium on Information Theory 2006, Seattle: WA, 2006:38-142.
  • 6Fourquet R, Tavernier C. List decoding of second or der Reed-Muller codes and its covering radius implica tions[C]//Proceedings of the WCC 2007, Versailles WA,2007:147-156.
  • 7Carlet C. Recursive lower bounds on the nonlinearity profile of Boolean functions and their applications[J]. IEEE Transactions Information Theory, 2008,54 (3) : 1262-1272.
  • 8Sun Guanghong,Wu Chuankun. The lower bounds on the second order nonlinearity of three classes of Boolean functions with high nonlinearity[J]. Information Sciences, 2009,179(3) : 267-278.
  • 9Gangopadhyay S, Sarkar S, Telang R. On the lower bounds of the second order nonlinearities of some Boolean functions[J]. Information Sciences, 2010,180 (2) : 266-273.
  • 10Iwata T, Kurosawa K. Probabilistic higher order differential attack and higher order bent functions[C]// Proceedings of the ASIACRYPT, LNCS. Berlin: Springer Verlag, 1999 = 62-74.

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电子与信息学报
2010年 第10期

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