Computer Engineering and Applications ›› 2010, Vol. 46 ›› Issue (27): 85-87.DOI: 10.3778/j.issn.1002-8331.2010.27.023

• 网络、通信、安全 • Previous Articles     Next Articles

Construction of Boolean functions with optimal algebraic immunity

DONG Xin-feng,ZHANG Wen-zheng,QIAO Tong-xu,ZHAO Wei   

  1. State Key Laboratory for Modern Communications,Chengdu 610041,China
  • Received:2009-11-20 Revised:2010-03-18 Online:2010-09-21 Published:2010-09-21
  • Contact: DONG Xin-feng

具有最优代数免疫阶的一类新布尔函数的构造

董新锋,张文政,谯通旭,赵 伟   

  1. 现代通信国家重点实验室,成都 610041
  • 通讯作者: 董新锋

Abstract: A class of Boolean functions f with suboptimal(or optimal) algebraic immunity is presented,by means of the second construction methods,a new class of Boolean functions h with optimal immunity is gotten.The h is different from what have been constructed before.The number of the functions f is given,the nonlinearity of the function h is discussed in the case of even number variables.Finally,the nonlinearity is discussed and that the nonlinearity of the function h constructed by means of the majority function Fn can make the Lobanov bound tight is found.

摘要: 构造了一类至少具有次优代数免疫阶的布尔函数f,并利用级联的方法构造了一类具有最优代数免疫阶的布尔函数h。这类函数h不同于以前相关文献中所提出的最优代数免疫的布尔函数,给出了f的数目,并进一步讨论了h(偶数个变元的情况下)的非线性度,发现利用择多函数Fn构造的一类函数h非线性度达到Lobanov界。

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