Computer Engineering and Applications ›› 2019, Vol. 55 ›› Issue (11): 40-45.DOI: 10.3778/j.issn.1002-8331.1809-0074

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Constructions of Triples of  Boolean Permutations

LIU Shishi1,2, ZHANG Fengrong1,2, XIA Shixiong1, ZHOU Yong1   

  1. 1.Mine Digitization Engineering Research Center of the Ministry of Education, School of Computer Science and Technology, China University of Mining and Technology, Xuzhou, Jiangsu 221116, China
    2.Guangxi Key Laboratory of Cryptography and Information Security, Guilin University of Electronic Technology, Guilin, Guangxi 541004, China
  • Online:2019-06-01 Published:2019-05-30


刘师师1,2,张凤荣1,2,夏士雄1,周  勇1   

  1. 1.中国矿业大学 计算机科学与技术学院 矿山数字化教育部工程研究中心,江苏 徐州 221116
    2.桂林电子科技大学 广西密码学与信息安全重点实验室,广西 桂林 541004

Abstract: Boolean permutations and bent functions play an important role in cryptography. From a generalized method of constructing triples of Boolean permutations(these permutations can be used to construct bent functions) provided by Coulter and Mesnager, an equivalent method and an algorithm for constructing triples of Boolean permutation are presented. Furthermore, the interrelationships among three permutations are further studied. A necessary and sufficient condition for constructing triples of Boolean permutations is proposed, and a new algorithm for constructing Boolean permutation is provided. Finally, the properties of the bent functions which are constructed by using these triples of permutations are analyzed.

Key words: Boolean function, bent function, Boolean permutation, nonlinearity

摘要: 布尔置换和bent函数在密码学中起着非常重要的作用。在Coulter和Mesnager所提出的三元组布尔置换广义构造方法(该三元组布尔置换可以用来构造bent函数)的基础上,给出了一个等价的构造三元组布尔置换的具体方法。利用此具体方法,提供了一个构造三元组布尔置换的算法。对三个置换之间的依赖关系做了进一步研究,提出了一个三元组置换成立的充要条件,并给出了一个构造三元组布尔置换的新算法。分析了利用三元组布尔置换所得bent函数的性质。

关键词: 布尔函数, bent函数, 布尔置换, 非线性度