<Emphasis Type="Italic">t</Emphasis>-resilient functions and the partial exposure problem

The Wire-Tap Channel II introduced by L. H. Ozarow, A.D. Wyner was the first instance of a Partial Exposure Problem. General Exposure-Resilient Functions (ℓ-ERF) are known to be appropriate to provide a solution to the Partial Exposure Problem as long as random secret chains are to be protected. It is known that a perfect ℓ-ERF is nothing but a t-resilient function for t = n − ℓ, where n is the length of the exposed symbol-chain and t the largest number of symbols that an adversary is able to observe. We here manage to adapt the use of t-resilient functions for protecting messages against partial exposure. A solution to that problem had been given by the perfect local pseudo-random generator introduced by Maurer and Massey which is based upon a t-resilient function, but its use needs a secret key shared by the sender and the receiver. We are able to provide solutions to protect messages against Partial Exposure without using secret keys, for various ranges of parameters. Moreover low complexity algorithms are devised to that end.     

关于等重码的对偶距离

本文借助于对偶距离和相关免疫阶的关系，证明了等重码的对偶距离为１或２。     

一阶相关免疫布尔函数的计数

本文研究线性结构布尔函数的相关免疫性,得到了一大类满足一阶相关免疫的线性结构函数,并大大改进了一阶相关免疫函数的计数结果,得到了目前为止的最好下界.     

一阶相关免疫函数的计数

通过研究布尔函数的线性结构,得到了一类满足一阶相关免疫的不具有线性结构的函数,由此给出了一阶相关免疫函数个数的一个新下界。     

Rijndael算法字节代替变换的扩散和相关免疫性能研究

该文深入研究了Rijndael算法字节代替变换的扩散性能和相关免疫性能。     

Construction and Count of 1-Resilient Rotation Symmetric Boolean Functions on pr Variables

Construction and count of 1-resilient Rotation symmetric Boolean functions （RSBFs） on pr variables are demonstrated. It is proved that constructions of 1-resilient RSBFs on pr variables are equivalent to solving an equation system. An accurate enumeration formula of all 1-resilient RSBFs on pr variables is also proposed. Some examples are given, and the exact numbers of 1-resilient RSBFs on 8 and 9 variables are obtained respectively.     

非退化相关免疫函数的构造与计数

本文给出了非退化一阶相关免疫函数的一个构造方法，得到了这类函数的一个新的下界，并且给出了阶数大于１的相关免疫函数非退化的一个充分条件及实例。     

多值逻辑函数与其变元的几种无关性的谱分析

多值逻辑函数与它们的变元之间有许多种特殊关系,单从它们的表达式是较难判断的。本文给出了多值逻辑函数与其变元无关和统计无关的一些充分必要条件;给出了多值逻辑函数与其某些变元代数无关(也称为退化)的一些条件和最大程度地退化一个函数的方法;指出了这些结果在实际中的应用。所有这些结果都是Chrestenson谱方法来研究的。     

相关免疫函数的稳定性

本文讨论了相关免疫函数的稳定性,证明了相关免疫性是不稳定的,但广义相关免疫却具有较好的稳定性。     

ENUMERATING CORRELATION-IMMUNE BOOLEAN FUNCTIONS OF ORDER ONE

A large class of linear structural functions(LSF) satisfying the condition of correlational immunity of order one are constructed by studying the linear structural Boolean functions. With these new founded functions, the known enumeration bounds of correlation-immune functions of order one are greatly improved. In fact, the best, up to now, lower bound is found.