Two-dimensional-lag complex logistic map with complex parameters and its encryption application

With the rapid development of internet technology,security protection of information has become more and more prominent,especially information encryption.Considering the great advantages of chaotic encryption,we propose a 2D-lag complex logistic map with complex parameters(2D-LCLMCP)and corresponding encryption schemes.Firstly,we present the model of the 2D-LCLMCP and analyze its chaotic properties and system stability through fixed points,Lyapunov exponent,bifurcation diagram,phase diagram,etc.Secondly,a block cipher algorithm based on the 2D-LCLMCP is proposed,the plaintext data is preprocessed using a pseudorandom sequence generated by the 2D-LCLMCP.Based on the generalized Feistel cipher structure,a round function F is constructed using dynamic S-box and DNA encoding rules as the core of the block cipher algorithm.The generalized Feistel cipher structure consists of two F functions,four XOR operations,and one permutation operation per round.The symmetric dynamic round keys that change with the plaintext are generated by the 2D-LCLMCP.Finally,experimental simulation and performance analysis tests are conducted.The results show that the block cipher algorithm has low complexit,good diffusion and a large key space.When the block length is 64 bits,only six rounds of encryption are required to provide sufficient security and robustness against cryptographic attacks.

Logistic混沌映射与差分进化改进人工蜂群优化水下定位

水下节点定位时通常采用距离估算法,在节点之间利用点到点的距离来估计或基于角度估计来完成节点定位。然而,这种算法存在较大的定位误差。为了提升定位的精确度,引入了人工蜂群(ABC)优化算法,该算法通过将节点定位结果优化问题转化为对节点目标函数的优化问题,有效地提高了水下节点的定位精度。尽管如此,ABC算法在迭代过程中仍存在收敛速度慢、易陷入局部最优的问题。针对这些问题,提出了一种通过Logistic混沌映射与差分进化改进的人工蜂群优化水下定位算法(improved artificial bee colony optimization underwater localization algorithm by Logistic chaos mapping and differential evolution,LDIABC)。首先,在算法种群初始化阶段,引入了Logistic混沌映射,利用该映射函数产生的混沌序列代替随机数生成器,从而使种群在初始化分布时蜜源位置更均匀,并从理论上证明了Logistic混沌序列的互异性,从而避免由于种群分布过于密集导致算法在迭代过程中陷入局部最优;其次,提出了适应度方差这一标准来验证在算法迭代过程中未陷入局部最优,进一步证明其有效性;然后,在引领蜂搜索阶段,基于差分进化的变异策略,提出了权重因子改进引领蜂邻域搜索方式,提高了引领蜂的全局搜索效率,加快了算法的收敛速度。仿真实验表明,LDIABC算法能够有效避免传统ABC算法收敛速度慢和易陷入局部最优的问题。相较于Tent-IABC算法、ELOABC算法、CODEGWO算法以及SAPSO算法,LDIABC算法在收敛速度和节点定位成功率上均有显著提升,并且优化定位精度分别提升了6.36%、13.33%、14.16%和16.88%。这些结果证明LDIABC算法能够有效提升水下节点定位精度,具有良好的优化效果。

改进型Logistic-Map混沌序列分析

为了进一步提高Logistic-Map混沌序列的互相关性与自相关性,提出了一种改进型的Logistic-Map混沌序列的构造方法。通过Matlab仿真出扩频通信系统,并对改进型Logistic-Map混沌序列的相关性特性进行了分析,并与传统的Logistic-Map混沌序列做了比较。仿真结果表明,改进型Logistic-Map混沌序列与白噪声的统计特性一致,并且该混沌序列具有更为理想的互相关和自相关特性,更加适合作为扩频通信地址码。

基于Logistic-Map的数字混沌调制方法

离散混沌动力系统Ｌｏｇｉｓｔｉｃ－Ｍａｐ产生的混沌离散序列具有良好的统计特性和对初值非常敏感的特性，利用这些特性，提出一种基于Ｌｏｇｉｓｔｉｃ－Ｍａｐ数字混沌调制方法并构造相应的保密通信系统，且进行了计算机仿真。在此基础上提出了调制系数宽范围变化的数字混沌调制方法。

基于Logistic-map的长周期混沌序列发生器

利用无周期的混沌映射生成长周期伪随机序列具有巨大的优越性,但有限字长效应会使混沌序列出现动力学特征退化,从而出现短周期现象,导致混沌序列安全性显著降低。分析了采用整数类型实现Logistic型混沌序列对周期特性的影响,指出整数型Logitstic-map序列不具备长周期特性,提出了一种利用m序列加扰Logistic-map的长周期混沌序列发生器的实现方案,并对输出序列特性进行了仿真分析。该方案易于实现,降低了长周期对整数位数的要求,输出序列的周期得到明显扩展,随机性、相关性和线性复杂度良好。

基于Logistic映射的社交网络敏感信息加密算法

为保护多种社交网络敏感信息安全,研究基于Logistic映射的社交网络敏感信息加密算法.此算法采用基于经验模态分解的社交网络信息预处理方法,以经验模态分解的方式,对复杂的社交网络信息去冗后,通过基于演化超网络的社交网络敏感信息挖掘方法,提取去冗后社交网络信息中敏感信息;由基于Logistic映射分组加密算法,生成敏感信息二进制随机序列,将其分为两部分明文,一部分明文执行置乱处理,另一部分明文执行异或运算,构建社交网络敏感信息的密文,完成社交网络敏感信息加密.实验结果表明,所提算法加密性能良好,可以有效改变文本类、图像类社交网络敏感信息,原始敏感信息特征完全改变,可保护多种社交网络敏感信息安全.

并行组合扩频通信中Logistic-Map序列的优选研究

直接序列扩频通信通常选择m序列和gold码作为地址码,但对于并行组合扩频系统其地址码数量少。在分析并行组合扩频系统基础上,研究Logistic-Map混沌扩频序列优选准则。Logistic-Map混沌扩频序列应用在并行组合扩频系统中,仿真结果表明,Logistic-Map混沌扩频序列可以提供数量众多的适于并行组合扩频通信系统的扩频序列族。

基于SHA-256和Arnold映射的量子Logistic映射图像加密算法

在AI和5G时代,各种应用层出不穷,带宽增加和算力提升为众多信息系统的高密集交互提供了基础保障,但同时安全问题日益突显.图像在多媒体通信中有重要作用,且许多图片涉及个人隐私或国家机密,因此图像保护尤为重要.为了解决上述问题,提出基于SHA-256和Arnold映射的量子Logistic映射图像加密算法.实验结果表明:该文算法的解密图像与明文图像基本一致;该文算法具有较强的密钥敏感性;相对于其他算法,该文算法具有更强的抵抗统计攻击能力.因此,该文算法具有较强的加密性能.

Logistic Map三维耦合格子模型模拟环带球晶

应用Logistic map三维耦合格子模型对环带球晶进行了模拟.利用数值计算的方法预测了与实验中环带球晶形貌一致的图案.对于本体体系,环带球晶形貌的带宽随Logistic map中可调参量μ的增大而变窄,随耦合模型中的扩散项系数ε的增大而变宽;对薄膜体系,环带球晶形貌的带宽随格子厚度的增加而变宽,模拟结果与实验结果一致.同时,还给出了螺旋状环带结构在三维空间中的形貌.

Logistic混沌映射最低数字位5的特性研究

Logistic混沌映射在真实轨道中迭代真值在最低数字位是5的时候,迭代真值高数字位部分表现出随机特性,迭代真值低数字位表现出线性递增的公共数字位.实验分析显示,在绝对精度条件下,混沌真实轨道保持随机性和公共部分稳定的结构特征,在有限精度条件下,迭代值随机性受计算精度影响很大,公共部分只能通过低位迭代法获取.

Modified Logistic Maps for Cryptographic Application

In this paper, definition and properties of logistic map along with orbit and bifurcation diagrams, Lyapunov exponent, and its histogram are considered. In order to expand chaotic region of Logistic map and make it suitable for cryptography, two modified versions of Logistic map are proposed. In the First Modification of Logistic map (FML), vertical symmetry and transformation to the right are used. In the Second Modification of Logistic (SML) map, vertical and horizontal symmetry and transformation to the right are used. Sensitivity of FML to initial condition is less and sensitivity of SML map to initial condition is more than the others. The total chaotic range of SML is more than others. Histograms of Logistic map and SML map are identical. Chaotic range of SML map is fivefold of chaotic range of Logistic map. This property gave more key space for cryptographic purposes.

属性Logistic混沌映射下的物联网隐私数据安全共享

为加强物联网隐私数据保护,提高用户信任度与满意度,提出属性Logistic混沌映射下的物联网隐私数据安全共享。构建基于主从式结构的三层物联网隐私数据安全共享模型并设计数据访问机制,在此基础上,基于量子细胞神经网络和Logistic映射得到矩阵A,对其分解后,得到矩阵B和序列C,由B矩阵构造混沌序列池,对C序列元素作映射处理,生成索引序列,并确定Logistic映射初始值,再对索引作Logistic映射后,从混沌序列池检索出CP-ABE加密算法的公钥、主密钥后,利用其与用户属性集合生成用户私钥,基于数据访问结构实现物联网隐私数据的加密。实验结果表明,该方法生成的密钥能够通过随机性验证,实现物联网隐私数据加密,且操作数量少,加密强度高。

Analysis and confirmation of fixed points in logistic mapping digital-flow chaos

The fixed points in logistic mapping digital-flow chaos strange attractor arestudied in detail. When k=n in logistic equation, there exist no more than 2n fixed points, whichare deduced and proved theoretically. Three corollaries about the fixed points of logistic mappingare proposed and proved respectively. These theorem and corollaries provide a theoretical basis forchoosing parameter of chaotic sequences in chaotic secure communication and chaotic digitalwatermarking. And they are testified by simulation.

Logistic-Map混沌序列的单片机实现

混沌序列的产生是混沌理论应用于保密通信领域的一个重要问题。通过对Logistic映射进行变换处理,利用整数运算代替小数运算,使程序便于在MCS-51系列单片机平台上运行,由此产生Logistic-Map混沌序列。

A novel class of two-dimensional chaotic maps with infinitely many coexisting attractors

We study a novel class of two-dimensional maps with infinitely many coexisting attractors.Firstly,the mathematical model of these maps is formulated by introducing a sinusoidal function.The existence and the stability of the fixed points in the model are studied indicating that they are infinitely many and all unstable.In particular,a computer searching program is employed to explore the chaotic attractors in these maps,and a simple map is exemplified to show their complex dynamics.Interestingly,this map contains infinitely many coexisting attractors which has been rarely reported in the literature.Further studies on these coexisting attractors are carried out by investigating their time histories,phase trajectories,basins of attraction,Lyapunov exponents spectrum,and Lyapunov(Kaplan–Yorke)dimension.Bifurcation analysis reveals that the map has periodic and chaotic solutions,and more importantly,exhibits extreme multi-stability.

基于logistic回归模型的生态系统服务簇变化驱动力分析——以关天经济区为例

生态系统服务簇(ESB)是多种生态系统服务在特定空间上形成的不同组合,探索影响其变化的驱动因素有助于理解ESB的功能变化特征,为国土空间优化提供理论支撑。以2000-2020年关中-天水经济区为例,在量化土壤保持、NPP、游憩服务、生境质量和粮食生产5种生态系统服务的基础上,利用自组织映射网络识别ESB,并探讨了影响不同ESB变化的驱动因素。结果表明,1)土壤保持、NPP、生境质量和游憩服务4种生态系统服务呈现出中西部低、南北山系高的空间分布格局,而粮食生产则恰好相反。2)研究区被划分为4种ESB,其中ESB1和ESB2主要分布在秦岭地区,ESB1的土壤保持服务显著高于ESB2;ESB3主要位于关中平原城市建成区和天水市,簇中5种生态系统服务水平均较低;ESB4则集中分布在关中平原地区,以粮食生产服务为主。3)ESB间的转换主要表现为6种类型,且其主要驱动因素存在一定差异。即:土地利用对4种ESB的转换均有重要驱动作用,其中以耕地和建筑用地的影响最显著;同时,ESB1、ESB4还受到降水等自然因素的影响,ESB2、ESB3、ESB4则多受GDP等社会经济因素的影响。该研究为关中-天水经济区的生态保护和可持续发展提供了新视角和科学依据。

Hybrid Image Compression-Encryption Scheme Based on Multilayer Stacked Autoencoder and Logistic Map

Secure transmission of images over a communication channel, with limited data transfer capacity, possesses compression and encryption schemes. A deep learning based hybrid image compression-encryption scheme is proposed by combining stacked auto-encoder with the logistic map. The proposed structure of stacked autoencoder has seven multiple layers, and back propagation algorithm is intended to extend vector portrayal of information into lower vector space. The randomly generated key is used to set initial conditions and control parameters of logistic map. Subsequently, compressed image is encrypted by substituting and scrambling of pixel sequences using key stream sequences generated from logistic map.The proposed algorithms are experimentally tested over five standard grayscale images. Compression and encryption efficiency of proposed algorithms are evaluated and analyzed based on peak signal to noise ratio(PSNR), mean square error(MSE), structural similarity index metrics(SSIM) and statistical,differential, entropy analysis respectively. Simulation results show that proposed algorithms provide high quality reconstructed images with excellent levels of security during transmission..

Image encryption technique based on new two-dimensional fractional-order discrete chaotic map and Menezes–Vanstone elliptic curve cryptosystem

We propose a new fractional two-dimensional triangle function combination discrete chaotic map(2D-TFCDM)with the discrete fractional difference.Moreover,the chaos behaviors of the proposed map are observed and the bifurcation diagrams,the largest Lyapunov exponent plot,and the phase portraits are derived,respectively.Finally,with the secret keys generated by Menezes-Vanstone elliptic curve cryptosystem,we apply the discrete fractional map into color image encryption.After that,the image encryption algorithm is analyzed in four aspects and the result indicates that the proposed algorithm is more superior than the other algorithms.

基于logistic map的未来几年成都市人口数量预测

针对近几年成都市人口的迅速增长,运用线性回归分析和数据拟合等构建了logistic map模型,确定了较准确的变化参数r,以预测未来几年成都市的人口数量。综合运用MATLAB和Excel等软件求解,研究认为变化参数r与其所在的年限呈正相关,可以结合近10年来成都市的人口数量推测出未来几年成都市的人口数量。

Asymmetric image encryption algorithm based on a new three-dimensional improved logistic chaotic map

Based on some analyses of existing chaotic image encryption frameworks and a new designed three-dimensional improved logistic chaotic map(3D-ILM),an asymmetric image encryption algorithm using public-key Rivest–Shamir–Adleman(RSA)is presented in this paper.In the first stage,a new 3D-ILM is proposed to enhance the chaotic behavior considering analysis of time sequence,Lyapunov exponent,and Shannon entropy.In the second stage,combined with the public key RSA algorithm,a new key acquisition mathematical model(MKA)is constructed to obtain the initial keys for the 3D-ILM.Consequently,the key stream can be produced depending on the plain image for a higher security.Moreover,a novel process model(NPM)for the input of the 3D-ILM is built,which is built to improve the distribution uniformity of the chaotic sequence.In the third stage,to encrypt the plain image,a pre-process by exclusive OR(XOR)operation with a random matrix is applied.Then,the pre-processed image is performed by a permutation for rows,a downward modulo function for adjacent pixels,a permutation for columns,a forward direction XOR addition-modulo diffusion,and a backward direction XOR addition-modulo diffusion to achieve the final cipher image.Moreover,experiments show that the the proposed algorithm has a better performance.Especially,the number of pixels change rate(NPCR)is close to ideal case 99.6094%,with the unified average changing intensity(UACI)close to 33.4634%,and the information entropy(IE)close to 8.