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.

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.

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.

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.

A Novel Triangular Chaotic Map (TCM) with Full Intensive Chaotic Population Based on Logistic Map

Chaos theory attempts to explain the result of a system that is sensitive to initial conditions, complex, and shows an unpredictable behaviour. Chaotic systems are sensitive to any change or changes in the initial condition(s) and are unpredictable in the long term. Chaos theory are implementing today in many different fields of studies. In this research, we propose a new one-dimensional Triangular Chaotic Map (TCM) with full intensive chaotic population. TCM chaotic map is a one-way function that prevents the finding of a relationship between the successive output values and increases the randomness of output results. The tests and analysis results of the proposed triangular chaotic map show a great sensitivity to initial conditions, have unpredictability, are uniformly distributed and random-like and have an infinite range of intensive chaotic population with large positive Lyapunov exponent values. Moreover, TCM characteristics are very promising for possible utilization in many different study fields.

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。

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。

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.

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。

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.

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。

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..

A class of two-dimensional rational maps with self-excited and hidden attractors

This paper studies a new class of two-dimensional rational maps exhibiting self-excited and hidden attractors. The mathematical model of these maps is firstly formulated by introducing a rational term. The analysis of existence and stability of the fixed points in these maps suggests that there are four types of fixed points, i.e., no fixed point, one single fixed point, two fixed points and a line of fixed points. To investigate the complex dynamics of these rational maps with different types of fixed points, numerical analysis tools, such as time histories, phase portraits, basins of attraction, Lyapunov exponent spectrum, Lyapunov(Kaplan–Yorke) dimension and bifurcation diagrams, are employed. Our extensive numerical simulations identify both self-excited and hidden attractors, which were rarely reported in the literature. Therefore, the multi-stability of these maps, especially the hidden one, is further explored in the present work.

Logistic混沌映射性能分析与改进

混沌系统是基于混沌的数据加密领域的一个重要研究对象,Logistic混沌映射是最简单和有效的混沌系统,被广泛应用在大多数混沌加密算法中,Logistic映射的安全性成为研究的热点。针对Logistic序列存在的吸引子与空白区问题,该文提出一种基于初始值和分形控制参数之间关系的Logistic映射改进方法。利用两者之间关系对映射自变量区间进行合理分段,扩大了混沌控制参数区域,将满射范围扩大到整个控制参数区间,使产生的序列分布更均匀,解决了"稳定窗"与空白区等问题。通过将改进Logistic与其它分段Logistic映射进行仿真对比,实验结果表明改进后的映射产生的序列混沌特性得到显著加强,分布更均匀,具有更好的随机性能测试指标。另外,改进Logistic映射计算复杂度低,实现简单,在扩频通信与混沌密码等领域有广阔的应用前景。

改进分段Logistic混沌映射的方法及其性能分析

Logistic混沌映射和Tent映射是两种广泛应用于通信安全领域的混沌映射,Tent映射具有分段特性,由此联想到将Logistic混沌映射推广为分段映射.提出一种三分段相切的Logistic混沌序列的方法,不仅规避了Tent映射需施加随机扰动的过程,并改善了Logistic混沌映射的随机性能,增加了系统的复杂度和抗攻击能力.实验证明在相同的区间上,三分段相切的Logistic混沌映射更早地进入混沌状态,且在3.57≤μ≤4时运动轨迹愈发地不稳定,Lyapunov指数为逐渐增大的正数,更复杂的非线性方程提高了系统的安全性.在相同的分叉判定阈值下,三分段相切Logistic混沌映射进入混沌状态时需要的迭代次数明显减小.因此,三分段相切的Logistic混沌序列具有更加良好的随机性和不可预测性.经过研究表明,该三分段相切的Logistic混沌映射具有良好的初值敏感性,广泛地适用于信息安全领域.

基于Logistic映射的加密算法的安全性分析与改进

分析Logistic混沌映射所产生的序列用于加密时存在的安全问题,针对这些安全问题提出相应的改进算法.算法通过增大分支参数的值解决Logistic混沌映射所存在的"稳定窗"、空白窗口和序列分布不均匀等问题,通过取模运算解决产生的序列超界的问题,突破了分支控制参数不能大于4的限制.实验表明,改进算法所产生序列的伪随机性好,计算复杂度低,同时密钥空间有大幅度提高,非常适合于多媒体等数据的加密.

Logistic映射数字混沌产生器

对用于保密通信系统的连续流混沌产生器的原理及可实现性进行分析．在对Ｌｏｇｉｓｔｉｃ映射的区间特性分析的基础上，首次研究并实现了一种Ｌｏｇｉｓｔｉｃ映射数字混沌产生器．实验结果表明，输出混沌信号与ｌｏｇｉｓｔｉｃ映射的分析结果一致，这说明了数字混沌产生器的有效性．

基于Logistic映射的图像保密通信

将Logistic映射产生的混沌序列作为载波 ,利用序列具有的良好相关特性 ,提出了一种图像保密通信方案。计算机仿真结果表明 ,只要收发双方使用相同的初值条件 ,即使在有一定噪声的情况下也能正确地进行图像传输 ,而初值的微小差异将导致通信失败 ,表明混沌序列用于保密通信具有很高的安全性能 ,同时方案具有很强的抗干扰能力。对图像恢复质量进行了评估 。

改进型Logistic混沌映射及其在图像加密与隐藏中的应用

鉴于原Logistic映射的映射范围有限、混沌参数范围小、分布不均匀等缺陷,该文提出一个新的改进型Logistic混沌映射。该映射有μ和α两个参数,x_(n-1)和_(n-1)两个初值,参数和初值选取范围可扩展到任意实数,其混沌映射均为满映射,且映射范围可任意调控。将该映射应用到图像加密,其算法采用像素值异或(XOR)加密、像素位置置乱处理。之后再把密文数据隐藏在与密文无关的载图之中。对密文图像做了一系列的分析,包括图像的相邻像素点相关性,直方图分析和密钥敏感性测试。分析结果表明,所提加密算法具有很好的安全性和加密效果。