布尔随机向量联合分布的分解及其应用

本文首先给出了一般概率空间上ｎ维尔随机向量的联合分布的“分解式”，然后将之应用于与布尔函数相应的布尔随机变量的有关联合分布的分解，揭示了关于布尔函数，布尔向量函数相关免疫性的若干等价条件的概率内在联系。     

基于相关向量机的高光谱影像混合像元分解

 提出了一种利用相关向量机后验概率进行高光谱影像混合像元分解的方法.基于支持向量机后验概率输出的高光谱影像混合像元分解方法中,类别后验概率需要通过带参数的S形函数近似,而且模型需要通过交叉验证获取较好的规则化系数.相关向量机是在贝叶斯框架下提出的更加稀疏的学习机器,它没有规则化系数,核函数不需要满足Mercer条件.本文从分析支持向量机用于高光谱影像混合像元分解存在的不足出发,介绍了稀疏贝叶斯分类模型和模型参数推断,采用了快速序列稀疏贝叶斯学习算法.通过PHI影像的混合像元分解实验分析,表明了基于相关向量机的高光谱影像混合像元分解方法的优势.     

一类二阶相关免疫布尔函数

本文给出了一种称为完全组的向量组，利用它构造了一类二阶相关免疫布尔函数，并对这类函数结构间的关系进行了论述。     

布尔函数的代数厚度

基于布尔函数的代数次数和代数厚度,给出了布尔函数和其分解函数的代数厚度的关系,利用递归和反证法导出了n元布尔函数代数厚度的上界是2* *(n-1),这个上界回答了"是否存在代数厚度大于2* *(n-1)的n元布尔函数"这个公开问题.在此基础上改进了n元k(2≤k≤(n-1)/2)次基本对称布尔函数的代数厚度的上界,同时也得到了布尔函数的代数厚度的一些性质.     

一种新的两参数改进威布尔分布的图像特征

针对Almalki S J和Yuan J提出的具有单调、单峰和浴盆形失效率函数的五参数改进威布尔分布,首先,通过增加一个形状参数得到六参数改进威布尔分布;其次,对其参数进行简化得到两参数改进威布尔分布;最后,研究了该分布的基本性质,从理论上证明了该分布的密度函数、失效率函数和平均失效率函数的图像特征,以及k阶矩的存在性。     

相关免疫的m值逻辑函数的几种构造

本文从ｍ（ｍ〉２为正整数）值逻辑函数相关免疫性的定义出发，以谱和概率方法为工具，给出了与相关免疫布尔函数的构造相对应的相关免疫ｍ值逻辑函数的几种典型的构造方法。     

平衡H布尔函数的相关免疫性研究

引入布尔函数的E-导数,并结合导数一起作为工具讨论关系密码系统安全性能的平衡H布尔函数的相关免疫性。通过E-导数和导数深入揭示了平衡H布尔函数0和1值的分布结构,得出判定H布尔函数是否相关免疫的重要结果。并得以采用区分不同结构的计算方法来简化计算,解决了平衡H布尔函数相关免疫最高阶数这一问题。     

立方攻击成功率分析

在一般随机布尔函数及布尔函数的代数次数或代数标准型项数受限情况下,从理论上分析了立方攻击的成功概率,对立方攻击密码分析方法提供了理论支持。理论结果与对流密码算法Trivium及Grain v1的实验结果是相吻合的。     

布尔函数的线性结构的特征

本文首先利用布尔函数的特征集合对布尔函数的线性结构进行了刻划，给出了寻找布尔函数的线性结构的一种方法，其次引入了布尔函数的ｒ型线性结构的概念，并对其进行了研究，同时还指出了布尔函数的ｒ型线性结构的密码学意义。     

线性结构与非线性度之间的关系

本文分析了布尔函数的非线性度与线性结构之间的关系。结果表明布尔函数的非线性度和线性结构有一定的制约关系,并解决了非线性度小于２＾ｎ－２的平衡布尔函数的线性结构集和反子对偶点集的维数分布问题。     

环Zm上随机变量联合分布的一种分解式及其应用

本文给出了ｍ值随机变量联合分布的分解式,考察了一类ｍ值（ｍ为正整数,ｍ≥２）逻辑函数Ｃｈｒｅｓｔｅｎｓｏｎ谱的“分解式”,并据此分解式给出了相关免疫ｍ值逻辑函数的一些新的构造法。     

对序列密码统计测试的新方法

对密钥流的统计分析是序列密码算法设计与分析中的重要内容。文中从随机布尔函数和随机向量值函数的Walsh谱的分布特性出发,对同步序列密码提出了两种新的选择IV统计分析方法。并利用这些新方法对入选eSTREAM计划的Grainv0、Grainv1和Trivium算法进行了统计测试。结果表明,Grainv0和Grainv1的伪随机性没有达到最好。     

On the construction of odd-variable boolean functions with optimal algebraic immunity

Algebraic immunity is an important cryptographic property of Boolean functions. In this paper, odd-variable balanced Boolean functions with optimal algebraic immunity are obtained by m-sequence and consequently, we get bases with special constructions of vector space. Furthermore, through swapping some vectors of these two bases, we establish all kinds of odd-variable balanced Boolean functions with optimal algebraic immunity.     

An iterative algorithm for testing two-asummability of boolean functions

An iterative algorithm for testing two-asummability of any given Boolean function is described in this letter. The method is based on the decomposition of Boolean functions in terms of reduced functions, and it is suitable for machine computation.     

Constructions of vector output Boolean functions with high generalized nonlinearity

Carlet et al. recently introduced generalized nonlinearity to measure the ability to resist the improved correlation attack of a vector output Boolean function. This article presents a construction of vector output Boolean fimctions with high generalized nonlinearity using the e-biased sample space. The relation between the resilient order and generalized nonlinearity is also discussed.     

Ternary Walsh Transform and Its Operations for Completely and Incompletely Specified Boolean Functions

The new ternary Walsh transform is considered in this paper. Such a ternary Walsh transform can be used in a similar manner as the standard Walsh transform for binary logic functions as shown here. It is based on the Kronecker product as well as the Galois field and new ternary operations. The same hardware implementation can be used for both forward and inverse ternary Walsh transforms based on its fast algorithms and properties. The ternary Walsh transform is suitable for processing both completely and incompletely specified Boolean functions. Its properties for the decomposition and symmetry detections of the Boolean functions are shown.     

Maximum Correlation Analysis of Nonlinear Combining Functions in Stream Ciphers

The maximum correlation of a Boolean function to all Boolean functions of a subset of its input variables is investigated. A relationship is derived between the maximum correlation and the mutual information between the output of a balanced Boolean function and a subset of its random input variables. For bent functions (which are never balanced), both the mutual information and the maximum correlation are bounded and shown to be small in a strong sense. Received 14 February 1996 and revised 15 January 2000 Online publication 19 May 2000     

多输出相关免疫逻辑函数的等价刻划及其应用

该文对多输出逻辑函数相关免疫性的两种刻划进行了讨论,在利用Walsh变换理论导出二元随机向量概率分布分解式的基础上,证明了两种刻划的等价性,并利用多输出相关免疫逻辑函数构造了一类不具有输入输出线性组合符合优势的密钥流生成器。     

Realization of Boolean Functions via CNN: Mathematical Theory, LSBF and Template Design

As a paradigm for nonlinear spatial-temporal processing, cellular nonlinear networks (CNN) are biologically inspired systems where computation emerges from a collection of simple locally coupled nonlinear cells. Our investigation is an exploration of an important and difficult aspect of implementing arbitrary Boolean functions by using CNN. A typical class of basic key Boolean functions is the class of linearly separable ones. In this paper, we focus on establishing a complete set of mathematical theories for the linearly separable Boolean functions (LSBF) that are identical to a class of uncoupled CNN. First, we obtain an essential relationship between the template and the offset levels as well as the basis of the binary input vector set in the uncoupled CNN. More precisely, we construct a neat binary input–output truth table and some interesting properties of the offset levels of the uncoupled CNN, and develop a practical design formula for the class of CNN template. Especially, we found a criterion for LSBF, which depends only on symbolic relations between a Boolean function's outputs. Furthermore, we develop a method for representing any linearly nonseparable Boolean function into a logic operation of a sequence of linearly separable ones for a small number of inputs.