部分Bent函数的扩散特性  

Special Propagation Characteristics of Partially-Bent Functions

作　　者：段明[1] 戚文峰[1] 

机构地区：[1]信息工程大学信息工程学院,河南郑州450002

出　　处：《信息工程大学学报》2005年第1期15-18,共4页Journal of Information Engineering University

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

摘　　要：文章研究了部分Bent函数满足扩散准则的元素之集Rc和Walsh循环谱值为零的元素之集ζc的大小,证明了若Rc(ζc)非空,则2n-1≤|Rc|<2n(2n-1≤|ζc|<2n),并给出了非退化线性变换下部分Bent函数满足严格雪崩准则和1阶相关免疫的充分必要条件。本文还指出若部分Bent函数{0}∪Rc中所含极大线性子空间的维数为λ,则|Rc|=2n-1+2n-2+…+2n-λ。最后,在|Rc|>2的条件下,给出了部分Bent函数满足扩散准则次数的上界。In this paper, the set Rc of the vectors satisfying the propagation criteria and ζc of the vectors whose Walsh spectrums euqal to zero of patially-bent functions is discussed. If Rc (ζc) is a non-empty set, then 2n-1≤|Rc|<2n(2n-1≤|ζc|<2n). Under the condition of nondegenerate linear transformation, a patially-bent function f(x) on Vn satisfies the SAC if and only if there exists a vector α∈Vn such that △f(α)=0 and satisfies the CI(1) if and only if there exists a vector α∈Vn such that S(f)(α)=0. If the maximum dimention of the linear subspaces contained in {0} ∪ Rc, denote by λ, then|Rc|= 2n-1+2n-2+…+2n-λ. Finally under the condition of|R|>2, we present an upper bound of the degree of partially-bent functions that satisfy the propagation criteria.

关 键 词：部分BENT函数 扩散准则 线性子空间 线性变换 相关免疫 

分 类 号：O157[理学—数学]