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一类三次Bent函数的二阶非线性度 被引量：2

On second order nonlinearity of cubic Bent functions
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摘要 研究了形如yTr(x5)+Tr(x3)的三次Bent函数,通过研究其导数的非线性度的下界,得到了该函数的二阶非线性度的下界,将所得结果与Carlet的结果进行了比较,结果表明,该函数的二阶非线性度大于Carlet给出的下界。 This paper studied a cubic Bent Boolean function of the form yTr（x5）＋Tr（x3）.By studying the lower bound of the nonlinearity of the derivative of this function,derived the lower bound on the second order nonlinearity of this form.The results demonstrate that the lower bound of the second order nonlinearity of the function of this form is larger than the general lower bounds obtained by Carlet.
作者 徐媛 崇金凤 卓泽朋
机构地区 淮北师范大学数学科学学院 西安电子科技大学综合业务网国家重点实验室
出处 《计算机应用研究》 CSCD 北大核心 2011年第7期2687-2689,2718,共4页 Application Research of Computers
基金 国家自然科学基金资助项目(60773121) 安徽省高等学校自然科学基金资助项目(KJ2008B124 KJ2011B146)
关键词 布尔函数 BENT函数 二阶非线性度 导数 Boolean function bent function second order nonlinearity derivative
分类号 TN918.1 [电子电信—通信与信息系统]
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参考文献10

  • 1CARLET 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.
  • 2CARLET C. Recursive lower bounds on the nonlinearity profile of Boolean functions and their applications[ J]. IEEE 3-rans Information Theory,2008,54(3 ) : 1262-1272.
  • 3SUN G, WU C. 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.
  • 4GANGOPADHYAY 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.
  • 5IWATA T, KUROSAWA K. Probabilistic higher order differential attack and higher order bent functions [ C ]//Advances in Cryptology ASIACRYPT. London : Springer-Verlag, 1999 : 62-74.
  • 6CHARPIN P, PASALIC E, TAVERNIER C. On bent and semi-bent quadratic Boolean functions[ J ]. I EEE Yrans Information Theory,2005,51 (12): 4286-4298.
  • 7LEANDER G, McGUIRE G. Construction of bent functions from nearbent functions [ J ]. Journal of Combinatorial Theory, 2009,116 (4) : 960-970.
  • 8CANTEAUT A,CHARPIN P, KYUREGHYAN G M. A new class of monomial bent functions [ J]. Finite Fields and their Applications, 2008,14( 1 ) : 221-241.
  • 9CARLET C. On the higher order nonlinearities of algebra/c immune functions[ C ]//Advances in Cryptology CRYPTO. Berlin : SpringerVerlag,2006:584-601.
  • 10CARLET C, DALAI D, GUPTA K, et al. Algebraic immunity for cryptographically significant Boolean functions: analysis and construction [J]. IEEE Trans on Information Theory,2006,52(7) : 3105-3121.

同被引文献16

  • 1Carlet 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.
  • 2Dumer 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.
  • 3Fourquet 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.
  • 4Carlet C. Recursive lower bounds on the nonlinearity profile of Boolean functions and their applications[J]. IEEE Transactions Information Theory, 2008,54 (3) : 1262-1272.
  • 5Sun 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.
  • 6Gangopadhyay 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.
  • 7Iwata 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.
  • 8Charpin P, Pasalic E ,Tavernier C. On bent and semibent quadratic Boolean Junctions[J]. IEEE Transactions Information Theory, 2005,51 (12) : 4286-4298.
  • 9Khoo K, Gong G, Stinson D R. A new family of Gold-like sequences[C]/ / Proceedings of the IEEE International Symposium on Information Theory, Lausanne: IEEE, 2002:181.
  • 10Canteaut A, Charpin P,Kyureghyan G M. A new class of monomial bent functions [J]. Finite Fields and Their Applications, 2008,14 : 221-241.

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计算机应用研究
2011年 第7期

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