共查询到18条相似文献,搜索用时 78 毫秒
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对称布尔函数的代数免疫性 总被引:2,自引:0,他引:2
在流密码和分组密码的加密体制中,需要构作具有各种密码学性质的布尔函数,用来作为密钥,以抵抗已有的各种有效攻击方法。近年来,人们提出了代数攻击方法,为了抵抗这种攻击方式,构作代数免疫度很大的布尔函数,成为近五年来信息安全领域一个研究热点。本文综述布尔函数代数免疫性方面的重要问题和主要进展,其中包括中国学者在对称布尔函数代数免疫性的研究成果。 相似文献
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本文对多输出布尔函数的第二类非线性度进行研究,该定义是衡量抵抗最佳多输出仿射逼近攻击性能的一项重要准则.利用多输出布尔函数的Walsh变换,我们给出第二类非线性度的一种表达式,并在此基础上得到第二类非线性度的一个上界.进一步地,我们给出了当第一类非线性度达到最优时,其第二类非线性度的一个界.此外,本文还给出任意多输出布尔函数与所有多输出线性函数之间距离的均值. 相似文献
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相关免疫布尔函数的一种构造方法 总被引:3,自引:0,他引:3
本文证明了布尔函数的谱分解定理,定义了布尔函数的谱(分解)特征向量,给出相应的充要条件,将全部N元相关免疫布尔函数的构造问题转化为线性方程组的求解问题,为相关免疫布尔函数的构造提供了新的方法。)满足,可求得符合要求的用上述方法我们通过人工计算确定出86个符合要求的谱特征向量,注意到向量中各分量地位的对称性,并注意到定理4,我们得知全部4无相关免疫的非平凡布尔函数共2×324=648个N=4,m=2时,定理6中条件即从后面11个方程可求得联系(Ⅱ)中的第5~14个方和即知在(Ⅲ4)下b1、b2、b3、b4全为1(全为0平凡情况),在(Ⅲ4)下b1、b2、b3、b4中有3个取1、1个取0,由此可得全部4元至少2阶相关免疫的非平凡布尔函数所对应的谱特征向量如下:它们所对应的的布尔函数依次是(此结论与[1]p155上结论相符),因而4元1阶相关免疫的布尔函数共有648-10=638个。一般情况下,在我们的方法里构造全部N元相关免疫布尔函数实质上是在定理6中“约束条件”(1)下去求2N-1个变元、N个方程的方程组(Ⅱ)所有解,构造全部N元至少m(≥2)附相关免疫布尔函数实质上是在定理6中“约束条件,(1)下去解2N- 相似文献
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定义了布尔函数的类差分和类差分平衡函数,研究了类差分平衡函数的密码学性质以及构造方法。作为类差分平衡函数的应用, 给出了Z24上逻辑函数是完全非线性函数的充要条件,并在首先分析得到所有四元类差分平衡函数的基础上,编程搜索出Z24上所有的完全非线性函数。 相似文献
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Ziran Tu Dabin Zheng Xiangyong Zeng Lei Hu 《Applicable Algebra in Engineering, Communication and Computing》2011,22(5-6):359-366
Are there other Boolean functions having two distinct Walsh coefficients except affine Boolean functions and maximal nonlinear (i.e. bent) Boolean functions? This paper proves that all Boolean functions with exactly two distinct Walsh coefficients are just the two known classes of affine and bent Boolean functions and the Boolean functions obtained by modifying the value of affine or bent Boolean functions at x?=?0. 相似文献
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M. A. Alekhina 《Measurement Techniques》2006,49(3):217-221
The task is considered of realizing Boolean functions asymptotically the best as regards reliability by circuits with constant
faults of the same type only at the outputs or only at the inputs of the gates. The complexity of the circuits made of unreliable
components that are asymptotically the best on reliability is of the same order as the complexity of circuits constructed
only from reliable components.
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Translated from Izmeritel’naya Tekhnika, No. 3, pp. 12–15, March, 2006. 相似文献
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The basic Boolean primitive in quantum cellular automata (QCA) is the majority gate. In this paper, a method for reducing the number of majority gates required for computing three-variable Boolean functions is developed to facilitate the conversion of sum-of-products expression into QCA majority logic. Thirteen standard functions are introduced to represent all three-variable Boolean functions and the simplified majority expressions corresponding to these standard functions are presented. We describe a novel method for using these standard functions to convert the sum-of-products expression to majority logic. By applying this method, the hardware requirements for a QCA design can be reduced. As an example, a 1-bit QCA adder is constructed with only three majority gates and two inverters. The adder is designed and simulated using QCADesigner, a design and simulation tool for QCA. We will show that the proposed method is very efficient and fast in deriving the simplified majority expressions in QCA design. 相似文献
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Meera Sitharam Timothy Straney 《Applicable Algebra in Engineering, Communication and Computing》2000,11(2):89-109
We obtain efficient sampling methods for recovering or compressing functions over finite Abelian groups with few Fourier
coefficients, i.e., functions that are (approximable by) linear combinations of few, possibly unknown Fourier basis functions or characters. Furthermore, our emphasis is on efficiently and deterministically finding small, uniform sample sets, which can be used for sampling all functions in natural approximation classes of Boolean functions. Due to this requirement, even the simplest versions of this
problem (say, when the set of approximating characters is known) require somewhat different techniques from the character
theory of finite Abelian groups that are commonly used in other discrete Fourier transform applications. We briefly discuss
applications of our efficient, uniform sampling methods in computational learning theory, efficient generation of pseudorandom
strings, and testing linearity; we also state highly related open problems that are not only applicable in these contexts,
but are also of independent mathematical interest.
Received: December 14, 1998; revised version: October 20, 1999 相似文献
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Cell signalling plays a vital role in development, sustaining, differentiation, and reproduction of cells. Pathways involved in signalling networks are quite interwoven and complex. Complexity encountered in understanding these pathways is often reduced with the help of Boolean circuit representation. In this study, the authors provide communication aspect of the signalling pathways that have two input Boolean logic AND/OR implemented at the rear effector protein. Communication is assumed to be taking place in extracellular and intracellular environment. The two environments are connected using a receptor protein acting as relay between a molecular source and effector protein. Each relay detects molecules from outside environment and stimulates the production of signals in the intracellular space. These signals/molecules further activate the effector protein which acts as a Boolean switch driven by AND/OR logic. Assuming Poisson reception at the relay as well as at the receiver, the authors provide probability of error of the AND and OR Boolean logic communication systems. Furthermore, reliability and some capacity bounds are deduced for the given Boolean communication system.Inspec keywords: cellular biophysics, integrated circuit modelling, stochastic processes, probability, cellular transport, proteins, molecular biophysics, Boolean functions, biochemistryOther keywords: cell signalling, communication perspective, signalling networks, Boolean circuit representation, communication aspect, signalling pathways, input Boolean logic, rear effector protein, extracellular environment, intracellular environment, receptor protein, relay, stimulates, signals/molecules, Boolean switch, Boolean logic communication systems, given Boolean communication system 相似文献
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Because of the advances made in optical technology, an extension can be made from the well-known stack filter to a new kind of gray-scale filter by using arbitrary Boolean functions instead of positive Boolean functions in the second step of a three-step process. Applications of these threshold-decomposed Boolean-based gray-scale filters in image processing include image smoothing and feature detection. A general optical implementation approach of nonlinear threshold-decomposed Boolean-based gray-scale filters is also described that utilizes area coding, gray scale correlation and lookup table thresholding techniques. Some experimental results are demonstrated. 相似文献