自对偶布尔函数的若干密码学性质研究

计算机工程与应用 ›› 2012, Vol. 48 ›› Issue (9): 63-66.

自对偶布尔函数的若干密码学性质研究

刘杨1，2，冯有前1，李瑞虎1

1.空军工程大学理学院，西安 710051
2.空军第一航空学院，河南信阳 464000

收稿日期:1900-01-01 修回日期:1900-01-01 出版日期:2012-03-21 发布日期:2012-04-11

Research on some cryptographical properties of self-dual Boolean function

LIU Yang1，2, FENG Youqian1, LI Ruihu1

1.College of Science, Air Force Engineering University, Xi’an 710051, China
2.The First Aeronautical College of Air Force, Xinyang, Henan 464000, China

Received:1900-01-01 Revised:1900-01-01 Online:2012-03-21 Published:2012-04-11

摘要/Abstract

摘要： 通过分析布尔函数的特征，建立了[n]元自对偶布尔函数和[n-1]元布尔函数之间的关系，根据此关系讨论了[n]元自对偶布尔函数的代数免疫度及其非线性度，得出自对偶布尔函数的非零次单项式个数为奇数，给出了[n]元[n-1]次自对偶布尔函数的个数和代数正规型表示的特征及其密码学性质，对其代数次数为[t]的单项式个数提出了猜想，对其中两种特殊情况进行了证明。

关键词: 自对偶布尔函数, 线性结构, 代数免疫度, 代数次数, 单项式个数

Abstract: By analyzing character of Boolean function, the connection between [n]-variables self-dual Boolean function and [n-1]-variables Boolean function is set up, and according to this connection the algebraic immunity and nonlinearity of [n]-variables self-dual Boolean function are discussed. It is also obtained that terms of monomials with algebraic degree nonzero are odd. The number, algebraic norm formation and cryptographical property of [n]-variables self-dual function with algebraic degree [n-1] are presented. A conjecture about terms of monomials with algebraic degree [t] is proposed, and two special cases are proved out.

Key words: self-dual Boolean function, linear structure, algebraic immunity, algebraic degree, terms of monomials

刘杨1，2，冯有前1，李瑞虎1. 自对偶布尔函数的若干密码学性质研究[J]. 计算机工程与应用, 2012, 48(9): 63-66.

LIU Yang1，2, FENG Youqian1, LI Ruihu1. Research on some cryptographical properties of self-dual Boolean function[J]. Computer Engineering and Applications, 2012, 48(9): 63-66.

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