A note on two classes of Boolean functions with optimal algebraic immunity

Tu and Deng proposed a class of bent functions which are of optimal algebraic immunity under the assumption of a combinatorial conjecture.In this paper,the authors compute the dual of the Tu-Deng functions and then show that they are still of optimal algebraic immunity under the assumption of the same conjecture.For another class of Boolean functions constructed by Tang,et al.which are of optimal algebraic immunity with similar forms to Tu-Deng functions,the authors show that they are not bent functions by using some basic properties of binary complete Kloosterman sums.     

A Construction of 1-Resilient Boolean Functions with Good Cryptographic Properties

This paper proposes a general method to construct 1-resilient Boolean functions by modifying the Tu-Deng and Tang-Carlet-Tang functions. Cryptographic properties such as algebraic degree, nonlinearity and algebraic immunity are also considered. A sufficient condition of the modified functions with optimal algebraic degree in terms of the Siegenthaler bound is proposed. The authors obtain a lower bound on the nonlinearity of the Tang-Carlet-Tang functions, which is slightly better than the known result. If the authors do not break the “continuity” of the support and zero sets, the functions constructed in this paper have suboptimal algebraic immunity. Finally, four specific classes of 1-resilient Boolean functions constructed from this construction and with the mentioned good cryptographic properties are proposed. Experimental results show that there are many 1-resilient Boolean functions have higher nonlinearities than known 1-resilient functions modified by Tu-Deng and Tang-Carlet-Tang functions.     

A characteristic set method for solving boolean equations and applications in cryptanalysis of stream ciphers*

This paper presents a characteristic more efficient and has better properties than the set method for solving Boolean equations, which is general characteristic set method. In particular, the authors give a disjoint and monic zero decomposition algorithm for the zero set of a Boolean equation system and an explicit formula for the number of solutions of a Boolean equation system. The authors also prove that a characteristic set can be computed with a polynomial number of multiplications of Boolean polynomials in terms of the number of variables. As experiments, the proposed method is used to solve equations from cryptanalysis of a class of stream ciphers based on nonlinear filter generators. Extensive experiments show that the method is quite effective.     

基于二元关系和布尔推理的分级决策模型

分级决策问题是将备选方案分类到预先定义的具有偏好顺序的决策类中.其中每个方案是由一个有限属性集合来描述的,该属性集合包括名义属性、连续型属性和有序属性.为了建立分级决策模型.提出了一种基于粗集理论和二元关系、布尔推理相结合的方法.首先在名义属性、连续型属性和有序属性上分别定义了不可分辨关系、相似关系和优势关系.然后提出了分辨-相似-支配矩阵的概念来建立相应的布尔函数.通过计算布尔函数的主蕴含,得到了"IF…THEN…"分级决策规则集作为偏好模型.最后利用一个算例说明了该方法的有用性.     

数字多路选择器网络设计的一种代数方法

多路选择器是一种重要的多功能通用逻辑元件。利用布尔代数运算 ,导出了求布尔函数的简化的不相交SOP形式的一种代数方法 ,提出了基于这种SOP形式的数字多路选择器网络设计的一种代数方法。这种方法可以使待设计的数字多路选择器网络简化到最小树形网络。给出的设计实例说明这种方法是有效而易行的     

A Combinatorial Condition and Boolean Functions with Optimal Algebraic Immunity

This paper first proposes an infinite class of 2k-variable Boolean functions with high nonlinearity and high algebraic degree. Then an infinite class of balanced Boolean functions are proposed by modifying the above Boolean functions. This class of balanced Boolean functions have optimal algebraic degree and high nonlinearity. Both classes have optimal algebraic immunity based on a general combinatorial conjecture.     

基于VMD和特征融合的辐射源信号识别

在日趋复杂的电子对抗中,如何提高雷达辐射源信号(radar emitter signal, RES)识别率和抗噪性能是亟待解决的问题。为此提出了一种变分模态分解(variational mode decomposition, VMD)和特征融合相结合的RES识别方法。首先利用VMD算法对各雷达信号进行分解得到3个本征模态函数(intrinsic mode function, IMF);然后,对这3个IMF分量提取排列熵(permutation entropy, PE)和样本熵(sample entropy, SE)特征进行特征融合，构成六维特征向量；最后利用支持向量机对辐射源信号进行识别。利用6种不同的辐射源信号对该方法进行了验证,仿真实验结果表明,该方法在低信噪比(signal to noise ratio, SNR)下能取得较好的识别率,当SNR不低于0 dB时,六维特征向量的识别率达到100%,具有较强的抗噪性能。     

Analyzing Boolean Functions via Solving Parametric Polynomial Systems

Journal of Systems Science and Complexity - In this paper, a new method to analyze Boolean functions is proposed. By this method, one can analyze the balancedness, the nonlinearity, and the...     

基于全方位优化算法的改进马田系统分类方法

针对马田系统的若干不足, 提出一种改进的马田系统优化模型, 其核心思想是 根据分类问题的目的和特点提出若干优化目标, 采用优化模型替代正交表和信噪比筛选关键变量. 针对模型的特点, 采用了一种全方位优化算法进行求解. 通过对4个 UCI数据集的算例分析表明, 该方法不仅有较好的分类精度, 且能筛选关键变量, 降维效果明显. 最后对一个实际生产案例 进行了研究, 结果表明该方法在保持高分类效率的情况下, 能够显著减少质量检测变量, 降低成本, 提高生产效率.     

An Adaptive Collocation Method with Weighted Extended PHT-Splines

This paper presents an adaptive collocation method with weighted extended PHT-splines.The authors modify the classification rules for basis functions based on the relation between the basis vertices and the computational domain. The Gaussian points are chosen to be collocation points since PHT-splines are C1 continuous. The authors also provide relocation techniques to resolve the mismatch problem between the number of basis functions and the number of interpolation conditions. Compared to the traditional Greville collocation method, the new approach has improved accuracy with fewer oscillations. Several numerical examples are also provided to test our the proposed approach.     

On the observability of free Boolean networks via the semi-tensor product method

This paper investigates the observabihty of free Boolean networks by using the semi-tensor product method,and presents some new results.First,the concept of observability for free Boolean networks is proposed,based on which and the algebraic form of Boolean networks,a kind of observabihty matrix is constructed.Second,by the observability matrix,a new necessary and sufficient condition is given for the observability of Boolean networks.Third,the concept of observabihty index for observable Boolean networks is defined,and an algorithm is established to calculate the observability index.Finally,a practical example of D.Melanogaster segmentation polarity gene networks is studied to support our new results.The study of the illustrative example shows that the new results obtained in this paper are very effective in investigating the observability of free Boolean networks.     

Recent Results on Constructing Boolean Functions with (Potentially) Optimal Algebraic Immunity Based on Decompositions of Finite Fields

Boolean functions with optimal algebraic immunity (OAI functions) are important cryptographic primitives in the design of stream ciphers. During the past decade, a lot of work has been done on constructing such functions, among which mathematics, especially finite fields, play an important role. Notably, the approach based on decompositions of additive or multiplicative groups of finite fields turns out to be a very successful one in constructing OAI functions, where some original ideas are contributed by Tu and Deng (2012), Tang, et al. (2017), and Lou, et al. (2015). Motivated by their pioneering work, the authors and their collaborators have done a series of work, obtaining some more general constructions of OAI functions based on decompositions of finite fields. In this survey article, the authors review our work in this field in the past few years, illustrating the ideas for the step-by-step generalizations of previous constructions and recalling several new observations on a combinatorial conjecture on binary strings known as the Tu-Deng conjecture. In fact, the authors have obtained some variants or more general forms of Tu-Deng conjecture, and the optimal algebraic immunity of certain classes of functions we constructed is based on these conjectures.

     

Dynamic weighted voting for multiple classifier fusion:a generalized rough set method

1 .INTRODUCTIONMultiple classifier fusion or combination has prov-enitself a powerful tool for achieving high classifi-cation accuracy with moderately discri minatingclassifiers .If only output class labels are availablethe voting fusion[1]is often used as a decisionlevelfusion. However ,the main drawback of the votingfusion is that all classifiers are considered equallyreliable and this maylead to a confident decisiontobe changed by a less reliable classifier . A possibleway of overcomin…     

矿井通风网络最小独立路集不交化可靠度的计算

运用可靠性工程理论及不交型积之和定律 ,在大型网络系统可靠度计算的基础上 ,提出了矿井通风网络系统最大线性无关最小独立路集予以真子集涤除的不交化可靠度计算的实现方法 .根据不交化可靠度计算法 ,当最小独立路集按所含网络分支的多少进行升序排列时 ,还可进一步减少中间过程的计算量 ,从而达到最佳不交化简化计算的效果 .实例分析表明 :采用升序排列的最小独立路集并按不交型积之和定理予以真子集涤除的不交化处理后 ,不仅计算值等同于一般网络分析中用全概率公式计算的矿井通风网络系统可靠度 ,而且 ,计算工作量大为简化 .     

基于完备循环差集的type-Ⅱ QC-LDPC码的构造

针对当前type-Ⅱ的准循环低密度奇偶校验(quasi-cyclic low-density parity check, QC-LDPC)码中仅含有权重为2的循环置换矩阵而引入短环,导致迭代译码性能下降的问题,基于完备循环差集给出了近似双对角结构的type-Ⅱ QC-LDPC码的设计方法,该方法构造的奇偶校验矩阵由零矩阵,权重为1的循环单位阵和权重为2的循环矩阵组成,不但围长至少为8,而且还保留了type-Ⅱ QC-LDPC码具有更高最小距离上界的优点,从而使译码时可快速收敛。仿真结果表明:构造的type-Ⅱ QC-LDPC码在加性高斯白噪声(additive white Gauss noise, AWGN)信道下,采用和积(sum-product algorithm, SPA)译码时,码字无明显的错误平层且具有良好的纠错性能。     

POLSAR多视复图像的特征提取和分类方法

Pauli分解和Krogager分解通常用于对极化合成孔径雷达(POLSAR)单视复图像中的相干复散射矩阵进行分解.基于Pauli分解和Krogager分解提出一种改进的极化特征分解方法,用于POLSAR多视复图像极化特征提取.首先利用Pauli分解分离出多视复图像数据的对称部分和非对称部分,然后利用Krogager分解提取出对称部分的极化特征,最后利用AdaBoost算法对所提取的极化特征进行分类.使用SIR-C的数据验证了方法的有效性.     

Radar Target Recognition Algorithm Based on RCS Observation Sequence——Set-Valued Identification Method

This paper studies the problem of radar target recognition based on radar cross section (RCS) observation sequence. First, the authors compute the discrete wavelet transform of RCS observation sequence and extract a valid statistical feature vector containing five components. These five components represent five different features of the radar target. Second, the authors establish a set-valued model to represent the relation between the feature vector and the authenticity of the radar target. By set-valued identification method, the authors can estimate the system parameter, based on which the recognition criteria is given. In order to illustrate the efficiency of the proposed recognition method, extensive simulations are given finally assuming that the true target is a cone frustum and the RCS of the false target is normally distributed. The results show that the set-valued identification method has a higher recognition rate than the traditional fuzzy classification method and evidential reasoning method.     

基于线谱频率点的一种频域盲分离方法

研究了卷积混合信号的频率域盲分离问题,为解决不同频率点分离输出信号的次序与幅度模糊性对信号分离造成的不利影响,利用高阶累积量谱线增强技术确定特殊频率点,提出了一种基于少数线谱频率点的频域盲分离方法,并提出多频率点间盲分离信号强相似的次序调整准则和幅度规范化。该方法既能有效分离独立源信号,又能节省运算时间,有利于实时信号分离恢复。使用语音信号和实录舰船辐射水声信号对算法进行了仿真检验,结果表明该方法分离效果较好。     

极化SAR数据的细节保持分割

提出一种保持场景局部细节的极化合成孔径雷达数据非监督分割方法.该方法将传统的基于极化目标分解的极化SAR分类方法与基于马尔可夫随机场的分类方法相结合,利用迭代条件模型方法得到分割结果.为保持细节特征,同时又能对各向同性区域进行平滑,利用总功率(span)图像的场景均匀性对分类结果进行修正.实验结果表明,与已有方法相比,该方法在细节保持方面有一定改进.     

基于广义模糊CMAC的强化学习算法

针对传统的小脑模型,提出了一种广义模糊小脑模型神经网络(GFCMAC)。它采用模糊隶属度函数作为接收域函数,可以获得较常规CMAC连续性强且有解析微分的复杂函数近似,具有计算量少,学习效率高等优点。研究了GFCMAC接收域函数的映射方法、隶属度函数及其参数的选取规律和学习算法。结合强化学习,提出了一种基于GFCAMC的强化学习算法,讨论了其实现过程。应用于船舶航向控制的仿真结果表明,在有各种风浪干扰下,船舶航向跟踪快且操舵动作合理,适合船舶转向控制要求。