基于混沌系统与多方向扩散的图像加密算法

目的为了避免只从单一方向来扩散图像像素,并提高加密密文的安全性,设计了混沌系统与多方向连续扩散的图像加密算法。方法综合Tent,sine映射,联合改进的Logistic映射,设计混合混沌机制,将Logistic模型的输出值作为触发器,获取一组随机性较强的混沌序列,对初始明文进行交叉置乱,高度混淆其像素位置,有效降低置乱周期性;构建量化机制对混沌序列进行处理,获取密钥流,从而设计多方向连续扩散机制,从4个不同的方向,利用不同的扩散模型来改变像素值,显著降低扩散周期性。结果实验结果显示,与当前混沌加密机制相比,所提算法具有更高的安全性与敏感性。结论所提加密算法能够确保图像在网络中安全传输,在包装信息防伪等领域具有较好的应用价值。     

混沌时间序列的自适应非线性滤波预测

本文基于混沌动力系统相空间的延迟坐标重构，根据混沌序列产生的确定性和非线性机制及混沌序列高阶奇异谱特征，提出了混沌时间序列的二阶Volterra和高阶非线性HONFIR两种模型，引入Sigmoid函数后又提出了一种少数参数非线性自适应滤波预测模型，并对它们的自适应算法作了介绍。     

基于动态可变参数的复合混沌系统的语音加密算法研究

利用混沌理论,基于Hénon映射和Logistic映射设计了一个复合混沌系统,并证明了其具有更好的初值敏感性。对产生的混沌二值序列进行美国国家标准与技术研究所(National Institute of Standard and Technology,NIST)随机数测试,分析得出该序列具有较好的随机性,可用于加密。依此设计了一个语音加密算法,实现了语音信号的加/解密功能。仿真分析表明,该混沌语音加密算法具有较高的安全性,能产生足够的密钥空间,有较强的保密性能。     

基于奇异值分解和混沌映射的脆弱认证水印

提出一种基于奇异值分解和混沌映射的图像脆弱认证水印算法,将混沌映射的初值敏感性应用到图像的篡改检测中.对图像子块进行奇异值分解,同时利用Logistic混沌映射产生认证水印;然后利用Logistic混沌映射设计了一个子块与子块之间的映射函数,将认证水印序列嵌入在相应映射块的LSB上.实验结果表明,算法不仅对篡改非常敏感,而且能够有效地抵抗拼贴攻击和区分篡改图像内容与篡改水印.     

改进相空间重构方法在混沌识别中的应用研究

讨论了传统非线性时间序列相空间重构方法的特点。提出了一种改进的相空间重构方法．为了揭示非线性时间序列中的非线性相关性。采用了一种基于关联积分的统计量，并研究了不同参数对它的影响．研究了延迟时间和嵌入维数之间的关系，并采用时间窗口描述这2个参数的变化规律．同时，应用改进方法计算了混沌时间序列的重构参数。重构了混沌信号的吸引子．研究结果表明。该方法能够从时间序列有效地重构原系统的相空间，为混沌信号识别提供了新的途径．     

非线性函数全局最优化的一种混沌优化混合算法

混沌优化方法是近年出现的利用混沌的遍历性、随机性作为全局优化机制的一种优化技术。已有的混沌优化方法都是利用Logistic映射作为混沌序列发生器,而由Logistic映射产生的混沌序列的概率密度函数服从两头多、中间少的切比雪夫型分布,这种分布特性会严重影响混沌优化全局搜索能力和效率。利用Logistic映射的特点,在混沌搜索时预先筛选掉劣质点,建立改进的混沌BFGS混合优化算法。复杂非线性测试函数计算结果表明,与文献中不加改进的混沌混合算法相比,本算法以同样的混沌搜索次数找到全局最优解的概率提高了10-30%,而以概率1获得全局最优解的最大混沌搜索次数减少了8-10倍。另外,还将细搜索策略引入到改进的混沌BFGS混合算法中,对具有较大边界约束范围的非线性函数进行了优化计算。     

基于一类离散混沌系统的加密技术研究

针对一维离散混沌加密系统密钥空间小、安全性能差等缺点,提出了一种基于连续混沌系统通过最小二乘法构造离散混沌系统的方法,改进了加(解)密实数混沌序列映射为加(解)密因子序列的位序列方法.实验研究表明,本文提出的离散混沌系统加密技术既保留了一维离散混沌系统加密、解密效率高的特点又进一步提高了加密系统抗破译的能力.     

一种有限区间内无限折叠的混沌映射

提出了一种在有限区间内具有无限折叠的一维混沌映射。理论分析和仿真检验证实，该映射具有远较传统的有限折叠混沌映射复杂的动力学行为和理想的分布特性，且易于分析和实现，是构造混沌扩谱通信方案和混沌密码体制的理想候选。     

Henon映射的图像加密新算法

从混沌动力学的角度出发,运用非线形控制系统的原理来研究混沌序列.以Henon映射为基础,在控制系统设置控制参数以形成混沌序列.同时也证明了模加减运算是成立的,并给出了相应定理的证明.在图像加密新算法中,运用了异或运算和模加减运算相结合的方式.实验结果证明,该算法生成的混沌序列对图像加密具有比较好的效果.     

基于3D-CS混沌系统的双DNA编码图像加密算法

目的为解决加密算法中明文与混沌系统密钥关联小,且置乱扩散不能同步进行造成的安全性低的问题。在结合Chebyshev和Sine映射的基础上,新建三维Chebyshev-Sine混沌映射系统(3D-CS),提出一种基于3D-CS混沌系统的双DNA编码图像加密算法。方法设定二进制与四进制双重DNA编码,利用约瑟夫环变换对经过二进制DNA编码的图像RGB各层进行位置索引,同时完成置乱和扩散,然后将混沌系统产生的序列值经过处理后进行四进制DNA编码,最后将2种DNA序列进行加法运算后解码得到密文。结果仿真实验表明,索引序列和混沌序列通过了随机性检验,密文各层NPCR值分别为99.63%,99.61%,99.59%,UACI值分别为33.43%,33.44%,33.40%,信息熵分别为7.9992,7.9991,7.9993。结论所设计的混沌序列相较于其他混沌序列有一定优势,针对提出的问题有效提高了加密算法的安全性,密文能有效地抵御各种统计攻击与差分攻击。     

Weak quantifier elimination for the full linear theory of the integers

We describe a weak quantifier elimination procedure for the full linear theory of the integers. This theory is a generalization of Presburger arithmetic, where the coefficients are arbitrary polynomials in non-quantified variables. The notion of weak quantifier elimination refers to the fact that the result possibly contains bounded quantifiers. For fixed choices of parameters these bounded quantifiers can be expanded into disjunctions or conjunctions. We furthermore give a corresponding extended quantifier elimination procedure, which delivers besides quantifier-free equivalents also sample values for quantified variables. Our methods are efficiently implemented within the computer logic system redlog, which is part of reduce. Various examples demonstrate the applicability of our methods. These examples include problems currently discussed in practical computer science.     

Asymptotic behaviour of monotone multi-valued dynamical systems

We introduce the concept of a monotone multi-valued semi-flow as an order-preserving map. This definition is motivated by the applications in the theory of differential equations without uniqueness of solutions. For an order-preserving multi-valued semi-flow we prove several results on the structure of the global attractor. Some applications to models governed by ordinary differential equations and delay equations with continuous right-hand side are presented. In particular, the abstract results are applied to a biochemical control circuit.     

Semilinear Motion Planning in REDLOG

We study a new type of motion planning problem in dimension 2 and 3 via linear and quadratic quantifier elimination. The object to be moved and the free space are both semilinear sets with no convexity assumptions. The admissible motions are finite continuous sequences of translations along prescribed directions. When the number of translations is bounded in advance, then the corresponding path finding problem can be modelled and solved as a linear quantifier elimination problem. Moreover the problem to find a shortest or almost shortest admissible path can be modelled as a special quadratic quantifier elimination problem. We give upper complexity bounds on these problems, report experimental results using the elimination facilities of the REDLOG package of REDUCE, and indicate a possible application. Received: September 27, 1999; revised version: August 23, 2001     

Quantifier Elimination for Real Algebra — the Quadratic Case and Beyond

 We present a new, “elementary” quantifier elimination method for various special cases of the general quantifier elimination problem for the first-order theory of real numbers. These include the elimination of one existential quantifier ∃x in front of quantifier-free formulas restricted by a non-trivial quadratic equation in x (the case considered also in [7]), and more generally in front of arbitrary quantifier-free formulas involving only polynomials that are quadratic in x. The method generalizes the linear quantifier elimination method by virtual substitution of test terms in [9]. It yields a quantifier elimination method for an arbitrary number of quantifiers in certain formulas involving only linear and quadratic occurrences of the quantified variables. Moreover, for existential formulas ϕ of this kind it yields sample answers to the query represented by ϕ. The method is implemented in REDUCE as part of the REDLOG package (see [4, 5]). Experiments show that the method is applicable to a range of benchmark examples, where it runs in most cases significantly faster than the QEPCAD package of Collins and Hong. An extension of the method to higher degree polynomials using Thom’s lemma is sketched. Received June 27, 1994; revised version April 11, 1996     

Quantifier elimination supported proofs in the numerical treatment of fluid flows

During the analysis of numerical methods for fluid flows some properties of numerical methods as stability or monotonicity can be stated as quantified problems and proved by quantifier elimination. A case study demonstrating such proofs is presented. The study shows that the stability region of the central scheme for advection-diffusion equation with Runge–Kutta time discretization is much bigger than classical stability region.     

A statistical method for verifying mesh convergence in Monte Carlo simulations with application to fragmentation

A novel method is presented for assessing the convergence of a sequence of statistical distributions generated by direct Monte Carlo sampling. The primary application is to assess the mesh or grid convergence, and possibly divergence, of stochastic outputs from non‐linear continuum systems. Example systems include those from fluid or solid mechanics, particularly those with instabilities and sensitive dependence on initial conditions or system parameters. The convergence assessment is based on demonstrating empirically that a sequence of cumulative distribution functions converges in the L_infty norm. The effect of finite sample sizes is quantified using confidence levels from the Kolmogorov–Smirnov statistic. The statistical method is independent of the underlying distributions. The statistical method is demonstrated using two examples: (1) the logistic map in the chaotic regime, and (2) a fragmenting ductile ring modeled with an explicit‐dynamics finite element code. In the fragmenting ring example the convergence of the distribution describing neck spacing is investigated. The initial yield strength is treated as a random field. Two different random fields are considered, one with spatial correlation and the other without. Both cases converged, albeit to different distributions. The case with spatial correlation exhibited a significantly higher convergence rate compared with the one without spatial correlation. Copyright © 2011 John Wiley & Sons, Ltd.     

Cryptographic pseudo-random sequences from the chaotic Hénon map

A scheme for pseudo-random binary sequence generation based on the two-dimensional discrete-time Hénon map is proposed. Properties of the proposed sequences pertaining to linear complexity, linear complexity profile, correlation and auto-correlation are investigated. All these properties of the sequences suggest a strong resemblance to random sequences. Results of statistical testing of the sequences are found encouraging. An estimate of the keyspace size is presented.     

自由空间法测量复合材料复电磁参数

自由空间法可以方便地改变入射电磁波的角度和极化方向, 适用于测量复合材料的电磁参数。对自由空间法测量复合材料电磁参数进行了初步研究, 探讨了测量结果在计算过程中产生的多值问题, 并通过理论分析给出了一些有效的解决方案。用自由空间法测量了4种聚合物复合材料样品在X波段(8.2~12.4GHz)的复电磁参数, 并用波导测量法进行了验证。研究结果表明自由空间法测量复合材料电磁参数具有较高的精确度。      

Effect of variation of input banwidth on the response of hardening Duffing oscillators

The response of hardening Duffing oscillators to coloured noise excitation is considered. It is shown that for certain combinations of excitation intensity and bandwidth the system realises multi-valued response states. Theoretical predictions of bounds in the parameter space which define regions of multiple statistical moments are supported by numerical simulation results. The effect of the occurrence and persistence of multi-level responses on the probability distribution of the peaks is also considered.     

单种子和多种子对正态随机序列质量的影响

通常一个正态随机序列是由同一个种子生成的,然而实际上序列中的每一个随机数还可用不同的种子来产生。提出了多种子的产生方法以及连续调用随机数发生器时防止产生相同序列的措施,利用统计模拟和假设检验理论,采用四个不同的统计量从正态性、均值、方差、随机性这四个方面对单、多种子法在不同时间段生成的大量随机序列的质量进行了对比研究,结果表明,多种子法生成的随机序列在正态性和方差质量方面有明显的优势,而在均值和随机性方面,这两种方法的效果基本一致,故总的说来多种子法要优于单种子法。