Plateaued函数的构造方法研究

Plateaued函数在密码学及编码等领域有着极其重要的应用,该文提出一种Plateaued函数的直接构造方法,研究了由该方法构造的Plateaued函数的密码学性质,证明了现有的直接构造方法可归约到本构造方法。     

Enumerating Boolean functions of cryptographic significance

In this paper we describe applications of functions from GF(2) ^m onto GF(2) ⁿ in the design of encryption algorithms. If such a function is to be useful it must satisfy a set of criteria, the actual definition of which depends on the type of encryption technique involved. This in turn means that it is important to ensure that the selected criteria do not restrict the choice of function too severely, i.e., the set of functions must be enumerated. We discuss some of the possible sets of criteria and then give partial results on the corresponding enumeration problems. Many open problems remain, some of them corresponding to well-known hard enumeration questions.     

Further enumerating boolean functions of cryptographic significance

Open problems about enumerating Boolean functions of cryptographic significance are (partially) solved in this paper.Project supported by Trans-Century Training Programme Foundation for the Talents by the State Education Commission.     

bent函数和半bent函数的二阶非线性度下界

该文研究了形如f(x,y)的n+1变元bent函数和半bent函数的二阶非线性度,其中xGF(2n), yGF(2)。首先给出了f(x,y)的2n-1个导数非线性度的精确值;然后推导出了函数f(x,y)的其余2n个导数的非线性度紧下界。进而给出了f(x,y)的二阶非线性度的紧下界。通过比较可知所得下界要优于现有的一般结论。结果表明f(x,y)具有较高的二阶非线性度,可以抵抗二次函数逼近和仿射逼近攻击。     

几类密码函数的线性结构研究

线性结构是度量密码函数安全性的一个重要指标。本文基于线性分组码理论，分析了文献[1～4]所构造的密码函数的线性结构，并指出这些函数均具有线性结构，且其线性结构集和构造这些函数所运用的线性分组码的对偶码有关。这就说明了文献[1～4]的密码函数本质上是密码学意义下的弱函数。     

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.     

Plateaued函数的正规性

Plateaued函数作为Bent函数和部分Bent函数的扩展,是一类能实现多个密码学准则折中的性质优良的密码函数。该文基于布尔函数与其分解函数的Walsh谱之间的关系研究了Plateaued函数的复杂性度量指标之一的正规性,根据其正规性质给出了判定给定Plateaued函数是否正规的一个较为简单的算法,并分析了已知Plateaued函数类的正规性。     

一类密码函数的构造与分析

利用t+1个n元布尔函数(称为基函数)级联构造了一类n+t元布尔函数G(x,y),并给出了G(x,y)的Walsh循环谱和自相关系数。通过Krawtchouk多项式与Krawtchouk矩阵对G(x,y)和基函数的关系进行了研究。分析了G(x,y)的密码学性质:相关免疫性、扩散性和代数免疫性。特别地,当t=2时,分析了G(x,y)与基函数的具体关系。另外,一般化该构造方法构造了一类多输出布尔函数,给出了该类多输出布尔函数的广义Walsh循环谱,进而分析了该类多输出布尔函数的相关免疫性和代数免疫性。     

密码学中布尔函数的零化子

布尔函数的零化子与代数攻击息息相关,但是如何构造一个给定函数的低次零化子仍然是一个悬而未决的问题.本文对此问题进行了研究,研究结果表明,如果布尔函数的零点集有一个k维子空间,那么,函数就会有代数次数为n-k的零化子.然而如何找到函数的具有最低代数次数的零化子仍然是一个亟待解决的难题.     

Hamming重量为k的布尔函数的全局特征和非线性度

该文给出了布尔函数的自相关系数和互相关系数的一些性质,得到n元布尔函数f (x)满足t 阶扩散准则时,n,t 和Hamming重量wt(f)的制约关系,给出了任意Hamming重量为k的布尔函数的平方和指标下界表达式,推出了仅由布尔函数Hamming重量所确定的非线性度的上界表达式。这些结论推广了已有结果。     

The structured design of cryptographically good s-boxes

We describe a design procedure for the s-boxes of private key cryptosystems constructed as substitution-permutation networks (DES-like cryptosystems). Our procedure is proven to construct s-boxes which are bijective, are highly nonlinear, possess the strict avalanche criterion, and have output bits which act (vitually) independently when any single input bit is complemented. Furthermore, our procedure is very efficient: we have generated approximately 60 such 4 × 4 s-boxes in a few seconds of CPU time on a SUN workstation.This work was partially supported by a grant from the Natural Sciences and Engineering Research Council of Canada.     

Z_q~n上函数的非线性度研究

本文对Z_q~n上函数的非线性度进行了研究,证明了函数非线性度的一些性质     

多输出plateaued函数的性质和构造

该文用仿射变换、级联、单射集及m序列的状态转移矩阵等方法构造了多输出plateaued函数,并明确了构造中阶数的变换情况,给出了由上述方法所构造的多输出plateaued函数的广义一阶Walsh循环谱值.另外,还给出了单射集的构造方法.由此,可以构造出一系列不同阶数、新的多输出plateaued函数.     

一种计算旋转对称布尔函数的汉明重量和非线性度的新方法

旋转对称布尔函数是一类重要的密码学函数,研究其重量和非线性度等密码学性质具有很好的理论价值。区别于已有的计算方法,该文利用特定的正规基把这些布尔函数的问题转化为有限域上的指数和问题,得到了4 ?? n和n=2s 时一些二次旋转对称布尔函数的重量和非线性度的新结果。使用所提的方法,可以计算几乎全部的二次旋转对称布尔函数的重量和非线性度。所提的新方法对于研究一般的旋转对称布尔函数具有一定的参考意义。     

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.     

γ-型线性结构函数的性质

本文讨论了r型线性结构函数的谱特征,证明了具有r型线性结构函数的有关性质,给出了两个判别r型线性结构的充要条件。     

两类Plateaued函数的Walsh谱值分布

Based on the properties of trace functions and quadratic forms, this paper presents value distributions of Walsh spectrum of the Plateaued functions of the form Tr(R(x)) with n=3r or 4r variables, where r > 1 is an odd integer. Our results can be used to determine the numbers of non-zero Walsh spectrum values and the nonlinearities of these functions, and estimate their resiliency orders. Especially, the value distributions can be used to deduce the tight lower bounds of the second order nonlinearity of two classes of Boolean functions. It is demonstrated that our bounds are better than the previously obtained bounds.     

IMPROVEMENT OF THE ALGORITHM PRINCIPLES FOR MINIMIZATION OF MULTI-OUTPUT FUNCTIONS

In this paper,the application of extraction principle for logic function minimiza-tion to multi-output case is studied.A defect in original algorithm in dealing with multi-outputextrema is made up,and on this base,three kinds of less-than terms in different conditions aredefined.In addition,three kinds of generalized definition of less-than terms are given,so as to findout more efficiently the covers with minimal number of terms and irredundant function outputs.This work makes the multi-output extraction principle closer to perfection.An algorithm basedon the work is presented.     

旋转对称布尔函数线性结构的2个公开问题

证明了代数次数为 的偶变元平衡旋转对称布尔函数不存在非零线性结构这个公开问题,给出了代数次数为 的奇变元旋转对称布尔函数不存在非零线性结构这个公开问题成立的充分条件和不成立的必要条件。