多输出Plateaued函数的构造方法

Plateaued函数具有很高的非线性度,可以满足相关免疫性、平衡性,在密码函数领域具有重要作用。为此,基于Carlet等提出的单输出Plateaued函数构造方法(FSE’03会议论文集),利用m序列的状态转移矩阵,构造一类多输出Plateaued函数,并参考Johansson方法中的引理5(IEEE Transactions on Information Theory, 2003, No.2),提出另一种多输出Plateaued函数的构造方法,由此得到的2种函数适用于S盒、滤波(组合)函数、杂凑函数等的设计。     

Plateaued函数的对偶性

研究了Plateaued函数的对偶性;基于Plateaued函数对偶性的定义及函数限制的理论,得到了Plateaued函数与其对偶函数在子空间上的限制及正规性上的对应关系;利用Plateaued的对偶这一工具,得到了两个Plateaued函数的互相关平方和指标的界。     

半Bent函数和多输出布尔函数的构造

半bent函数是一类非线性度几乎最优且平衡的布尔函数,它弥补了bent函数的一些不足,如变元个数可以是奇数,具有平衡性.半bent函数可用于对称密码系统的设计和CDMA系统中的正交可变扩频码的构造.本文利用不相交线性码构造了一类新的半bent函数,设输入维度为n,当n=2k+1时,将F2^n划分为2^k+1个[n,k]线性码和1个[n,k+1]线性码,通过从该码集中选取合适线性码作支撑集来构造新的半bent函数.另一方面,多输出布尔函数(向量值函数)在应用中的效率更高,因此其使用场景更为广泛.本文同时利用不相交线性码构造了(n,n-k)平衡的多输出布尔函数,其中n/3相似文献   

奇数变元plateaued函数代数免疫性质研究

Plateaued函数是包含Bent函数和部分Bent函数的更大函数类,具有许多优良的密码学性质。基于布尔函数非线性度与代数免疫阶之间的关系,利用Walsh谱等工具,讨论奇数变元的plateaued函数的代数免疫性质,得到其存在低次零化子的一个充分条件,并进一步刻画变元个数n与plateaued函数的阶r之间的具体关系,利用此关系可确定函数代数免疫阶的上界。     

n元Bent函数的级联构造

结合级联构造方法,通过k元Bent函数级联构造n元Bent函数,分析构造出的n元Bent函数的各种密码学性质,给出一种不同于直接构造和二次构造的新型构造方法.推导并验证n元布尔函数为Bent函数的充要条件,基于n元Bent函数的线性不变性,进一步构造出一个Bent函数集.     

一种混合核函数的支持向量机

为了提高支持向量机分类效果、学习能力和外推能力,分析了两种支持向量机的核函数:K型核函数和logistic核函数,构造出一种新的混合核函数的支持向量机,并且对其性能进行了理论分析。把构造出的混合核函数支持向量机与常用核函数构造的向量机应用到二维数据分类与图片分类中进行实验对比。二维数据点和图片分类的实验结果表明,混合核函数的支持向量机的分类效果、学习能力和外推能力,明显优于常用核函数构造的支持向量机。     

关于多变量开关函数化简的问题

本文提出n维立方体及顶点编号方法的模型,应用它可以解决多变量开关函数化简问题。该模型能全面准确地揭示出n维空间中2~n个多变量开关函数每个最小项之间相邻的数学关系,相邻单元的组合关系,并给出合并最小项的差值合并定理及系统化简方法,方法简单直观,可获得最简表达式。这对大规模集成电路设计和计算机辅助开关电路设计具有十分重要的意义。     

使用超椭球参数化坐标的支持向量机

基于n维超椭球面坐标变换公式,构造一类核函数--n维超椭球坐标变换核.由于是同维映射,且增大了类间距离,这类核函数在一定程度上改善了支持向量机的性能.与其他核函数(如高斯核)相比,将所构造的核函数用于支持向量机,仅产生了很少的支持向量,因而大大加快了学习速度,改善了泛化性能.数值实验结果表明了所构造的核函数的有效性和正确性.     

基于深度置信网络的多变量时间序列分类方法

针对当前多变量时间序列分类方法未考虑降维处理多变量时间序列,导致多变量时间序列分类精度较低,分类时间较长的问题,提出了基于深度置信网络的多变量时间序列分类方法.通过构建深度置信网络模型结构,基于受限玻尔兹曼机,提取可见单元与隐藏单元特征信息,采用Isomap算法,在深度置信网络内进行优先特征提取操作,通过附加约束构造半正定矩阵,降维处理多变量时间序列.在低维特征空间内,利用支持向量机中分线性分类函数,计算得到拉格朗日乘子,根据正则化参数特性,通过高斯核函数,计算得到最优核函数,完成多变量时间序列分类.实验结果表明,提出方法的泛化误差较小,能够有效提高多变量时间序列分类精度,缩短多变量时间序列分类时间.     

利用MATLAB实现二维窗函数

在科学研究和工程实践中,往往要进行大量的科学计算。这些运算一般来说难以手工精确和快捷地进行。利用MATLAB则可大大减少从算法到程序转化的工作量,而且简便易学,深受大家的欢迎。笔者在进行图像处理的算法研究中,积累了一些MATLAB的使用经验,在本文中与大家交流,以期抛砖引玉,共同进步。 1.二维窗函数简介 二维窗函数设计法是二维FIR滤波器的最早的设计技术之一,这是一维窗函数法的直接推广。设要设计的二维FIR滤波器的单位冲激响应为:h(n_1,n_2)=w(n_1,n_1)i(n_1,n_2) (1)其中,i(n_1,n_2)是无限区域(支持域)冲激响应序列;w(n_1,n_2)是二维窗函数(或称窗序列)。对无限区域冲激     

On the value distributions of Walsh spectrums of quadratic Plateaued functions

Plateaued functions have many cryptographically desirable properties, and have been used in cryptography and coding theory. However the properties of Plateaued functions have not been completely determined yet. Since many cryptographic properties can be estimated or evaluated by the value distribution of Walsh spectrum, it is essential to determine the value distribution of Walsh spectrum of a given Plateaued function.Based on the properties of trace functions and quadratic forms, this paper investigates the value distributions of Walsh spectrums of quadratic Plateaued functions of the form Tr(R(x)) with n variables. Firstly, we give all possible value distributions of Walsh spectrums of the functions. Furthermore, we proceed to determine the value distributions of Walsh spectrums of the functions on condition that the coefficients of R(x) belong to some given sets. Our results can be used to estimate the nonlinearities of these functions and their resiliency orders.     

Construction of highly nonlinear resilient Boolean functions satisfying strict avalanche criterion

Boolean functions with high nonlinearity, high resiliency and strict avalanche criterion （SAC） play an important role in the designs of conventional cryptographic systems. In this paper, a method is proposed to construct resilient Boolean functions on n variables （n even） satisfying SAC with nonlinearity 〉 2n-1 -2n/2. A large class of cryptographic Boolean functions that were not known earlier were obtained.     

Controller Design Using Walsh‐Basis‐Function Neural Networks

ABSTRACT This paper investigates the function approximation problem by using Walsh functions to establish a Walsh‐basis‐function neural network (WBFNN). The proposed novel system avoids the possible heavy computation problem of a controller usually encountered in adaptive neural controller design. With the developed adaptation scheme combined with the sliding mode control strategy for a class of nonlinear systems, the proposed WBFNN‐based controller can guarantee global stability of the closed‐loop system in the Lyapunov sense. The output tracking error then converges to zero asymptotically, and boundedness of all the signals in the whole system is ensured. Simulation validation for a nonlinear unstable system was performed to verify the effectiveness of the proposed controller design.     

Stabilization of Nonlinear Systems with Filtered Lyapunov Functions and Feedback Passivation

In this paper a generalized class of filtered Lyapunov functions is introduced, which are Lyapunov functions with time‐varying parameters satisfying certain differential equations. Filtered Lyapunov functions have the same stability properties as Lyapunov functions. Tools are given for designing composite filtered Lyapunov functions for cascaded systems. These functions are used to design globally stabilizing dynamic feedback laws for block‐feedforward systems with stabilizable linear approximation.     

On the computation of convex robust control invariant sets for nonlinear systems

In this paper we provide a method to compute robust control invariant sets for nonlinear discrete-time systems. A simple criterion to evaluate if a convex set in state space is a robust control invariant set for a nonlinear uncertain system is presented. The criterion is employed to design an algorithm for computing a polytopic robust control invariant set. The method is based on the properties of DC functions, i.e. functions which can be expressed as the difference of two convex functions. Since the elements of a wide class of nonlinear functions have DC representation or, at least, admit an arbitrarily close approximation, the method is quite general. The algorithm requires relatively low computational resources.     

A certain class of starlike functions

This paper presents a new class of functions analytic in the open unit disc, and closely related to the class of starlike functions. Besides being an introduction to this field, it provides an interesting connections defined class with well known classes. The paper deals with several ideas and techniques used in geometric function theory. The order of starlikeness in the class of convex functions of negative order is also considered here.     

New approaches to relaxed stabilization conditions and H-infinity control designs for T-S fuzzy systems

This paper focuses on the problem of fuzzy control for a class of continuous-time T-S fuzzy systems.New methods of stabilization design and H infinity control are derived based on a relaxed approach in...