素数元旋转对称弹性布尔函数的构造与计数

通过对素数元旋转对称弹性布尔函数特征矩阵的研究,给出了其特征矩阵的若干性质,得到了素数元旋转对称布尔函数为弹性函数的一个充要条件,由此完全决定了旋转对称弹性函数的构造以及这类函数的精确计数公式,最后还给出了所有的三元、五元、七元旋转对称弹性布尔函数的构造方案与精确计数。     

GF(p)上q元旋转对称弹性函数的一个等价刻画

基于旋转对称弹性函数l值支撑矩阵的性质,给出了GF(p)上q变元旋转对称弹性函数的一个等价刻画,证明了GF(p)上q变元旋转对称一阶弹性函数的构造问题等价于一个方程组的求解问题,并且利用方程组的所有解给出这类函数计数结果的一个表示。     

基于拉丁方的GF(p)上q元旋转对称弹性函数的新构造

在特征为p的有限域上,基于弹性函数与正交表大集间的等价关系,借助于一个具有最大圈结构的拉丁方,给出了一个构造q元旋转对称弹性函数的新方法.此外,通过一个具体的实例说明了本文的方法能够构造出已有方法不能构造的GF（p）上的q元旋转对称弹性函数.     

高非线性度多输出布尔函数的构造

本文主要讨论了构造具有高非线性度多输出布尔函数的方法.对于输入变量个数少于输出变量个数的多输出布尔函数,我们给出了存在非零非线性度的充分必要条件及具体的构造方法.我们还利用一类特殊的多输出bent函数构造出具有非常高非线性度的无偏多输出函数.     

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。     

Constructions of rotation symmetric 2-resilient functions with 4t-1 number of variables

Some properties of rotation symmetric orbits were proposed in n dimensional vector space over finite field of characteristic 2,a matrix on the distributions of number pairs such as 00,01 and 11 was defined,and a new characterization of 2-resilient rotation symmetric functions was introduced.Constructions of rotation symmetric 2-resilient Boolean functions with 4t-1 number of variables were presented by modifying the support of the linear rotation symmetric functions,such as f₀(x)=x₁+x₂+…+x_n,where n=4t-1.At last,an example was demonstrated to introduce the spirit of the proposed method to construct 2-resilient rotation symmetric functions with 4t-1 number of variables.     

Some results on the algebraic immunity of Boolean functions

From the motivation of algebraic attacks on stream and block ciphers,the concept of algebraic immunity(AI) of a Boolean function was introduced and studied extensively.High algebraic immunity is a necessary condition for resisting algebraic attacks.In this paper,we give some lower bounds on the algebraic immunity of Boolean functions.The results are applied to give lower bounds on the AI of symmetric Boolean functions and rotation symmetric Boolean functions.Some balanced rotation symmetric Boolean functions with their AI near the maximum possible value「n/2」are constructed.     

均衡弹性函数的结构与弹性阶

弹性函数是相关免疫布尔函数的自然推广。本文讨论均衡弹性函数,得到以下结果:给出了均衡弹性函数的一种结构,并因此得到了由均衡(n,m,2t)弹性函数构造均衡(n+1,m,2t+1)弹性函数的非线性方法;证明了均衡线性函数的弹性阶等于对应线性分组码的码字最小重最减1,且弹性阶上确界常常能由非线性函数所达到。     

多输出Plateaued函数的密码学性质

该文对多输出Plateaued函数的一些密码学性质进行了研究,以多输出函数的特征函数为工具,建立了多输出Plateaued函数的差分转移概率与其Walsh谱及阶数之间的关系。给出了多输出Plateaued函数的Walsh谱值在一定条件下的分布情形,指出多输出Plateaued函数的在其输出分量函数的任意非零线性组合函数均为非平衡函数时,其输入变量个数、输出变量个数与其阶数之间的关系满足。     

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     

多输出前馈函数的一种相关分析方法

本文提出了分析多输出前馈网络的一种方法,该方法的基本思想是收集输入信息在多个输出端上的信息泄漏,从而达到更充分地利用所有泄漏的信息的目的。作为应用,利用文中给出的方法分析了一类重要的多输出前馈网络一多输出Bent函数,并用一个具体实例说明了这种方法的全过程。     

Algebraic immunity for cryptographically significant Boolean functions: analysis and construction

Recently, algebraic attacks have received a lot of attention in the cryptographic literature. It has been observed that a Boolean function f used as a cryptographic primitive, and interpreted as a multivariate polynomial over F/sub 2/, should not have low degree multiples obtained by multiplication with low degree nonzero functions. In this paper, we show that a Boolean function having low nonlinearity is (also) weak against algebraic attacks, and we extend this result to higher order nonlinearities. Next, we present enumeration results on linearly independent annihilators. We also study certain classes of highly nonlinear resilient Boolean functions for their algebraic immunity. We identify that functions having low-degree subfunctions are weak in terms of algebraic immunity, and we analyze some existing constructions from this viewpoint. Further, we present a construction method to generate Boolean functions on n variables with highest possible algebraic immunity /spl lceil/n/2/spl rceil/ (this construction, first presented at the 2005 Workshop on Fast Software Encryption (FSE 2005), has been the first one producing such functions). These functions are obtained through a doubly indexed recursive relation. We calculate their Hamming weights and deduce their nonlinearities; we show that they have very high algebraic degrees. We express them as the sums of two functions which can be obtained from simple symmetric functions by a transformation which can be implemented with an algorithm whose complexity is linear in the number of variables. We deduce a very fast way of computing the output to these functions, given their input.     

构造具有良好密码学性质的旋转对称布尔函数

该文提出构造具有良好密码学性质的2m元旋转对称布尔函数的新方法。该类函数是平衡的,具有最大代数免疫度、最优代数次数和高非线性度,是一类能够同时满足多种密码学指标的优良函数。     

(n+1,m,2t)均衡弹性函数的非线性构造方法

基于GF(2)n上(n,m,2t-1)均衡弹性函数,运用其对偶分布性质和各分量函数弹性阶的相关特性,得到了(n 1,m,2t)均衡弹性函数的非线性构造方法。这些方法使得自变量的维数与弹性阶同步增长,且函数的代数次数也相应增加,从而避免了线性构造的缺陷。     

次数最大的平衡相关免疫函数的构造

Maitra和Sarkar于1999年提出了一种递归构造n元平衡相关免疫布尔函数的方法。该文给出了一种新的递归构造方法,构造出非线性度很高的n元m阶n- m-1次的平衡相关免疫函数。与原构造方法相比,该文构造方法得到的函数性质相同,数量更大。     

High output impedance current-mode universal biquadratic filters with five inputs using multi-output CCIIs

Three current-mode universal biquadratic filters each with five input terminals and one output terminal are presented. The first proposed circuit uses three multi-output second-generation current conveyors, two grounded capacitors and three resistors. This circuit offers the following advantageous features: orthogonal controllability of resonance angular frequency and quality factor, high output impedance, the versatility to synthesize all standard filter types without component matching condition and using grounded capacitors. The second proposed circuit uses three multi-output second-generation current conveyors, two grounded capacitors and two resistors. This circuit offers the following advantageous features: using minimum passive components, high output impedance, the versatility to synthesize all standard filter types without component matching condition and using grounded capacitors. The third proposed circuit uses three multi-output second-generation current conveyors, two grounded capacitors and three grounded resistors. This circuit offers the following advantageous features: the versatility to synthesize all standard filter types, high output impedance and using only grounded passive components. Each of the proposed circuits can get five kinds of filter functions by using only one current input signal.     

多输出布尔函数的相关免疫性

本文讨论多输出布尔函数的相关免疫性,证明了多输出相关免疫函数的一个性质,并给出了多输出相关免疫函数的一种构造方法.     

An infinite class of counterexamples to a conjecture concerning nonlinear resilient functions

The main construction for resilient functions uses linear errorcorrecting codes; a resilient function constructed in this way is said to be linear. It has been conjectured that if a resilient function exists, then a linear function with the same parameters exists. In this note we construct infinite classes of nonlinear resilient functions from the Kerdock and Preparata codes. We also show that linear resilient functions having the same parameters as the functions that we construct from the Kerdock codes do not exist. Thus, the aforementioned conjecture is disproved.kResearch supported by NSF Grant CCR-9121051.     

具有最大代数免疫度函数的研究

代数免疫度是私钥密码学中的重要概念。具有高代数免疫度的函数能抵抗新型攻击——代数攻击。CARLET Claude和FENG Keqin构造了具有最大代数免疫度的平衡函数及其线性等价函数,根据CARLET和FENG的构造,首先证明这类最大代数免疫度函数的数目,然后给出曹浩等人给出的定理6的简化证明,最后说明没有矩阵满足曹浩等人给出的定理7的条件（即不能用曹浩等人的方法构造具有最大代数免疫度的1阶弹性函数）．     

MIMO systems properties preservation under SPR substitutions

The preservation of some control-oriented positive real properties (passivity, positivity, bounded realness, as well as input-output behavior) in multi-input multi-output transfer functions is studied, when performing substitutions (of the complex Laplace variable s) by a particular class of rational strictly positive real (SPR) functions, the so-called SPR functions of zero relative degree (SPR0 functions). We also consider here the preservation of stability properties of a class of unforced linear time-invariant systems with memoryless (possibly time-varying nonlinear) input depending on the system output.