Computer Engineering and Applications ›› 2010, Vol. 46 ›› Issue (33): 9-12.DOI: 10.3778/j.issn.1002-8331.2010.33.003

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Structure of Boolean functions with two order algebraic immunity

DU Jiao1,2,WANG Shou-yin1   

  1. 1.Department of Mathematics,Xinxiang University,Xinxiang,Henan 453003,China
    2.State Key Lab of Networking & Switching Technology,Beijing University of Posts & Telecommunications,Beijing 100876,China
  • Received:2010-08-31 Revised:2010-10-29 Online:2010-11-21 Published:2010-11-21
  • Contact: DU Jiao


杜 蛟1,2,王守印1   

  1. 1.新乡学院 数学系,河南 新乡 453003
    2.北京邮电大学 网络与交换技术国家重点实验室,北京 100876
  • 通讯作者: 杜 蛟

Abstract: The construction of one order algebraic immunity Boolean functions is given.Based on the research,the constructions of Boolean functions are studied with two order algebraic immunity,and some necessary and sufficient conditions are attained on how to concatenate two n variables Boolean functions with one order algebraic immunity to a Boolean function with two order algebraic immunity.Especially the constructions of them are given,and some criteria on how to judge a Boolean function with two order algebraic immunity are given.

摘要: 对一阶代数免疫函数的结构进行了刻画,在此基础上讨论了一类二阶代数免疫布尔函数的构造问题,给出了两个[n]元一阶代数免疫函数通过级联得到[n]+1元二阶代数免疫函数的充分条件,并且给出了它们的若干结构和几个判断二阶代数免疫函数的判别准则。

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