扩散准则与相关免疫  

Propagation criteria and correlation immunity

作　　者：戚文峰[1] 何德峰[1] 

机构地区：[1]郑州信息工程大学信息工程学院应用数学系,河南郑州450002

出　　处：《通信学报》2004年第6期40-49,共10页Journal on Communications

基　　金：全国优秀博士学位论文专项基金资助项目(200060);国家自然科学基金资助项目(60373092)

摘　　要：对于布尔函数f(x),设不满足扩散准则的元素之集为Rf,不满足相关免疫的元素之集为zf ,即Rf={ai|(ai)0,0≤i≤2n-1},zf={ai|<x,ila>0,0≤i≤2n-1}。本文首先讨论了集合zf中元素的相关性, 并讨论了|zf|=1,2,3,4时函数的结构和性质。其次讨论了Rf构成线性子空间时,Rf和线性结构之集Lf之间的关系,其中Lf={ai||(ai)|=2n, 0≤I≤2n-1},给出Rf构成线性子空间时,Rf中的元素全部是线性结构的充要条件。还给出一种2阶扩散准则函数的构造方法。For a boolean function f(x), let Rf be the set of vectors which do not satisfy the propagation criteria and zf be the set of vectors which do not satisfy the correlation immunity, i.e Rf={ai|(ai)0,0≤i≤2n-1},zf={ai|<x,ila>0, 0≤i≤2n-1}. In this paper, firstly the correlation of the vectors contained in zf is discussed , and the structure and properties of f(x) are discussed when |zf|=1,2,3,4. Secondly when Rf is a linear subspace, the relationships between Rf and Lf are discussed , where Lf={ai||(ai)|=2n, 0≤i≤2n-1}, and the condition that the vectors of Rf are all linear structures is presented. The construction of functions which satisfy propagation criteria of degree 2 is given.

关 键 词：布尔函数 扩散准则 相关免疫 线性结构 

分 类 号：TN911.2[电子电信—通信与信息系统]