基于强度统计算法的混沌序列复杂度分析

为了分析混沌序列的复杂度,文中采用强度统计复杂度算法分别对离散混沌系统(TD-ERCS)和连续混沌系统(简化Lorenz系统)进行复杂度分析,计算了混沌序列随参数变化的复杂度,分析了连续混沌系统产生的伪随机序列分别进行m序列和混沌伪随机序列扰动后的复杂度.研究表明,强度统计复杂度算法是一种有效的复杂度分析方法,离散混沌序列复杂度大于连续混沌序列复杂度,但对连续混沌系统的伪随机序列进行m序列和混沌伪随机序列扰动后可大大增加复杂度,为混沌序列在信息加密中的应用提供了理论依据. 关键词： 强度统计复杂度算法 TD-ERCS系统 简化Lorenz系统 序列扰动     

TD-ERCS离散混沌伪随机序列的复杂性分析

采用相空间直接观察法和行为复杂性算法,系统地分析了新型TD-ERCS离散混沌系统产生的伪随机序列的复杂性,得出了其复杂性变化规律.在Kolmogorov复杂性基础上,应用经典的Limpel-Ziv算法,ApEn算法和PE算法,从一维时间序列到多维相空间重构两方面计算了TD-ERCS离散混沌伪随机序列的复杂度大小.计算结果表明,TD-ERCS系统的行为复杂性高,而且该系统的复杂性大小随系统参数改变的变化范围小,是一个复杂性非常稳定的全域性离散混沌系统,其产生的混沌伪随机序列适合于信息加密或扩频通信. 关键词： 混沌 混沌伪随机序列 TD-ERCS系统 复杂度     

混沌伪随机序列的谱熵复杂性分析

为了准确分析混沌伪随机序列的结构复杂性,采用谱熵算法对Logistic映射、Gaussian映射和TD-ERCS系统产生的混沌伪随机序列复杂度进行了分析.谱熵算法具有参数少、对序列长度N(惟一参数)和伪随机进制数K鲁棒性好的特点.采用窗口滑动法分析了混沌伪随机序列的复杂度演变特性,计算了离散混沌系统不同初值和不同系统参数条件下的复杂度.研究表明,谱熵算法能有效地分析混沌伪随机序列的结构复杂度;在这三个混沌系统中,TD-ERCS系统为广域高复杂度混沌系统,复杂度性能最好;不同窗口和不同初值条件下的混沌系统复杂度在较小范围内波动.为混沌序列在信息安全中的应用提供了理论和实验依据.     

基于切延迟椭圆反射腔映射系统的单向Hash函数构造

提出了一种基于切延迟椭圆反射腔映射系统(TD-ERCS)的单向Hash函数算法.该算法只需将明文信息线性变换为系统的参数序列，然后让TD-ERCS依次迭代，再依照一定的规则提取Hash值，勿需要增加任何冗余计算.该算法的密钥在［2⁶⁴,2¹⁶⁰］内任意取值，输出Hash值长160bit.基础的安全性测试表明，这种Hash函数具有很好的单向性、弱碰撞性、初值敏感性，较其他混沌系统构造的Hash函数具有更强的安全性，且实现简单，运行速度快，是传统Hash函数的一种理想的替代算法.还导出了评估碰撞性的一个客观标准. 关键词： 混沌 Hash函数 TD-ERCS     

混沌伪随机序列的复杂度的稳定性研究

增强统计复杂度能反映混沌伪随机序列的随机本质,在此基础上提出了k错增强统计复杂度的定义,用来衡量混沌伪随机序列复杂度的稳定性,并证明了其两个基本特性.以Logistic,Henon,Cubic,Chebyshev和Tent映射产生的混沌伪随机序列为例,说明了该方法的应用.仿真结果表明,该方法能区分不同混沌伪随机序列的稳定性,是一种衡量混沌序列稳定性的有效方法. 关键词： 稳定性 k错增强统计复杂度')" href="#">k错增强统计复杂度 混沌 伪随机序列     

空间混沌序列的加密特性研究

提出一个基于空间混沌系统的伪随机序列发生器,对空间混沌产生的伪随机位序列进行了FIPS140-1统计性检验和相关性分析,并应用空间混沌产生的各态历经矩阵实现图像的加密解密,实验的结果表明这种基于空间混沌系统的伪随机序列产生器具有优良的随机性,巨大的密钥空间和敏感性. 关键词： 伪随机序列 空间混沌系统 图像加密     

一种混沌伪随机序列复杂度分析法

分析了已有的序列线性复杂度分析方法，提出了用近似熵算法计算混沌运动的测度熵，作为衡量混沌伪随机序列复杂度的标准.理论研究表明，利用较短的观察序列，该方法能够准确地反映混沌系统和混沌伪随机序列复杂度的大小，可以作为判断利用混沌系统产生的伪随机序列的复杂度准则.实验结果表明该方法的有效性和理论结果的正确性. 关键词： 混沌 伪随机序列 熵     

混沌伪随机序列复杂度分析的符号动力学方法

通过将混沌伪随机序列看成一个符号序列，提出了用符号动力学的 方法来分析混沌伪随机序列的复杂度.以Logistic映射和耦合映射格子系统产生的混沌伪随 机序列为例，说明了该方法的应用，并将计算结果与近似熵ApEn法的计算结果作了比较.结 果表明，该方法可以有效地判断出不同的混沌伪随机序列的复杂程度，而且比近似熵法更为 优越. 关键词： 混沌 伪随机序列 符号动力学 熵     

一种新型的混沌伪随机数发生器

针对z-logistic这类特殊的混沌映射，实现了有限位计算精度下其真实演化轨道的精确计算.将该生成轨道的二值粗粒化输出用作伪随机序列，很大程度上保留了定义在实数域上混沌随机数发生器作为理想信息源的统计特性和随机特性，使得这种伪随机数发生器优良的统计分布和密码学性能得到理论上的强力支持.此外，该伪随机数发生器的周期长度可准确预测，采用简单算法可有效排除产生短周期的弱密钥，克服了传统混沌伪随机数发生器存在弱密钥且无法简单排除的重大缺陷.理论分析和数值实验验证了这种新型混沌伪随机数发生器在周期长度、统计分布和 关键词： 混沌 伪随机数发生器 信息源     

基于切延迟的椭圆反射腔离散混沌系统及其性能研究

根据椭圆反射腔物理模型， 提出了一种改变系统演化轨道的切延迟操作方法，导出了基于该方法的一类离散混沌映射系 统.实验表明，这类离散混沌系统最大Lyapunov指数恒大于零,状态变量等概率分布且与参 数和初值无关,全域零相关性，切延迟1单位时存在一个稳定不变的方形吸引子，切延迟大于 1单位时走向各态遍历.这类离散混沌系统可以产生两个独立的伪随机序列，其特殊性质和 复杂的动力学行为极具密码学应用价值. 关键词： 混沌 切延迟 Lyapunov指数 TD-ERCS 吸引子     

Two-Dimensional Cellular Automata for Pseudo-Random Pattern Generators and for Highly Secure Stream Ciphers

Pseudo-random properties of a class of two-dimensional (2-D) 5-neighborhood cellular automata (CA), built around nonlinear (OR, AND) and linear (XOR) Boolean functions are studied. The site values at each step of the 2-D CA evolution are taken in parallel and form pseudo-random sequences, which satisfy the criteria established for pseudo random number generator (PRNG): long period, excellent random qualities, single bit error propagation (avalanche criteria), easy and fast generation of the random bits. A block-scheme for secure Stream Cipher based on 2-D CA is proposed. The 2-D CA based PRNG algorithm has simple structure, use space-invariant and local interconnections and can be easily realized in very large scale integration or parallel optoelectronic architectures.     

FPGA implementation and image encryption application of a new PRNG based on a memristive Hopfield neural network with a special activation gradient

A memristive Hopfield neural network(MHNN)with a special activation gradient is proposed by adding a suitable memristor to the Hopfield neural network(HNN)with a special activation gradient.The MHNN is simulated and dynamically analyzed,and implemented on FPGA.Then,a new pseudo-random number generator(PRNG)based on MHNN is proposed.The post-processing unit of the PRNG is composed of nonlinear post-processor and XOR calculator,which effectively ensures the randomness of PRNG.The experiments in this paper comply with the IEEE 754-1985 high precision32-bit floating point standard and are done on the Vivado design tool using a Xilinx XC7 Z020 CLG400-2 FPGA chip and the Verilog-HDL hardware programming language.The random sequence generated by the PRNG proposed in this paper has passed the NIST SP800-22 test suite and security analysis,proving its randomness and high performance.Finally,an image encryption system based on PRNG is proposed and implemented on FPGA,which proves the value of the image encryption system in the field of data encryption connected to the Internet of Things(Io T).     

Statistical tests and chaotic synchronization based pseudorandom number generator for string bit sequences with application to image encryption

Recently, a stream encryption scheme using d-bit segment sequences has been proposed. This scheme may generate key avalanche effect. The randomness tests of d-bit segment pseudorandom number generator will be important for implementing such a scheme. Firstly this paper extends Beker and Piper’s binary pseudorandom sequence statistical test suite to d-bit segment sequences case. Secondly, a novel 3-dimensional polynomial discrete chaotic map (3DPDCM) is proposed. The calculated Lyapunov exponents of the 3DPCDM are 0.213, 0.125 and ? 3.228. Using the 3DPDCM constructs a 6-dimensional generalized synchronization chaotic system. Based on this system, a 8-bit segment chaotic pseudorandom number generator (CPRNG) is introduced. Using the generalized test suite tests 100 key streams generated via the 8-bit PRNG with different initial conditions and perturbed system parameters. The tested results are similar to those of the key streams generated via RC4 PRNG. As an application, using the key streams generated via the CPRNG and the RC4 PRNG encrypts an RGB image Landscape. The results have shown that the encrypted RGB images have significant avalanche effects. This research suggests that the requirements for PRNGs are not as strict as those under the traditional avalanche criteria. Suitable designed chaos-based d-bit string PRNGs may be qualified candidates for the stream encryption scheme with avalanche effect.     

Digital chaotic sequence generator based on coupled chaotic systems

Chaotic systems perform well as a new rich source of cryptography and pseudo-random coding. Unfortunately their digital dynamical properties would degrade due to the finite computing precision. Proposed in this paper is a modified digital chaotic sequence generator based on chaotic logistic systems with a coupling structure where one chaotic subsystem generates perturbation signals to disturb the control parameter of the other one. The numerical simulations show that the length of chaotic orbits, the output distribution of chaotic system, and the security of chaotic sequences have been greatly improved. Moreover the chaotic sequence period can be extended at least by one order of magnitude longer than that of the uncoupled logistic system and the difficulty in decrypting increases 2¹²⁸*2¹²⁸ times indicating that the dynamical degradation of digital chaos is effectively improved. A field programmable gate array (FPGA) implementation of an algorithm is given and the corresponding experiment shows that the output speed of the generated chaotic sequences can reach 571.4~Mbps indicating that the designed generator can be applied to the real-time video image encryption.     

Pseudo-random number generation for Brownian Dynamics and Dissipative Particle Dynamics simulations on GPU devices

Brownian Dynamics (BD), also known as Langevin Dynamics, and Dissipative Particle Dynamics (DPD) are implicit solvent methods commonly used in models of soft matter and biomolecular systems. The interaction of the numerous solvent particles with larger particles is coarse-grained as a Langevin thermostat is applied to individual particles or to particle pairs. The Langevin thermostat requires a pseudo-random number generator (PRNG) to generate the stochastic force applied to each particle or pair of neighboring particles during each time step in the integration of Newton’s equations of motion. In a Single-Instruction-Multiple-Thread (SIMT) GPU parallel computing environment, small batches of random numbers must be generated over thousands of threads and millions of kernel calls. In this communication we introduce a one-PRNG-per-kernel-call-per-thread scheme, in which a micro-stream of pseudorandom numbers is generated in each thread and kernel call. These high quality, statistically robust micro-streams require no global memory for state storage, are more computationally efficient than other PRNG schemes in memory-bound kernels, and uniquely enable the DPD simulation method without requiring communication between threads.     

Are random walks random?

Random walks have been created using the pseudo-random generators in different computer language compilers (BASIC, PASCAL, FORTRAN, C++) using a Pentium processor. All the obtained paths have apparently a random behavior for short walks (2¹⁴ steps). From long random walks (2³³ steps) different periods have been found, the shortest being 2¹⁸ for PASCAL and the longest 2³¹ for FORTRAN and C++, while BASIC had a 2²⁴ steps period. The BASIC, PASCAL and FORTRAN long walks had even (2 or 4) symmetries. The C++ walk systematically roams away from the origin. Using deviations from the mean-distance rule for random walks, d² ∝ N, a more severe criterion is found, e.g. random walks generated by a PASCAL compiler fulfills this criterion to N < 10 000.     

Characterizing pattern dependence in transmitters and receivers for modeling optical communication systems

We study the pattern dependences in 10 Gbit/s return-to-zero (RZ) transmitters and receivers. We describe a procedure to characterize and separate out the individual contributions from the transmitter and receiver to the pattern dependences in a 10 Gbit/s RZ system, and we validate the procedure experimentally using a transmitted pseudo-random bit string of length 2⁷ − 1.