Enhanced Chaos-based Pseudo Random Numbers Generator

An improved image encryption algorithm with finite computing precision

A number of methods have been proposed for synchronizing chaotic systems. The most widely used methods are continuous synchronization schemes. In a continuous synchronization scheme, chaotic systems are coupled to each other continuously such that synchronization errors converge to zero. In this paper, chaos synchronization in coupled discrete-time dynamical systems is presented. Simulation results finally demonstrate the effectiveness of the method. Experimental results show that chaotic and hyperchaotic systems can be synchronized by impulses sampled from one or two state variables. The impulsive synchronization can be applied to almost all chaotic and hyperchaotic systems even in the case when continuous synchronization systems fail to work. In this paper the concept of chaotic communication is based on digital chaotic systems where dual receivers are used for evaluation of information. The main advantage of digital chaotic systems is simple reproduction of devices, simple parameter setting and parameter stability. The dual receiver is used for improved function and error detection.

A general hybrid model for chaos robust synchronization and degradation reduction

A highly robust chaotic synchronization scheme is proposed in this paper. Different from most synchronization scheme, the two continuous chaotic systems is not driven by each other, but the separated standard digital chaotic systems. Since the digital chaotic systems are not affected by the internal noise and external noise, our synchronization scheme is much more robust than other synchronization schemes. Based on this synchronization scheme, a chaos-based secure communication system is designed. We use return-map and spectrum to analyze the security of our system. Simulation results shows that our system is highly security.

The dynamical degradation of digital chaotic systems (DCSs) often has serious negative influences on some digital chaos-based systems and then becomes one of the bottleneck problems stopping chaos from some applications. In this paper, we first restrict the Devaney’s chaos definition to finite state sets to describe the chaotic motion of digital systems. Then, we propose a novel control method for DCSs based on the differential mean value theorem and state feedback technology. Simulation results show the effectiveness, robustness, and superiority of the proposed method. Finally, we construct a new pseudorandom number generator (PRNG) and evaluate its randomness via NIST SP800-22 and TestU01 test suites. Statistical test results show that the proposed PRNG has high reliability of randomness, thus it can be used for cryptography and other potential applications.

When chaotic systems are implemented on finite precision machines, it will lead to the problem of dynamical degradation. Aiming at this problem, most previous related works have been proposed to improve the dynamical degradation of low-dimensional chaotic maps. This paper presents a novel method to construct high-dimensional digital chaotic systems in the domain of finite computing precision. The model is proposed by coupling a high-dimensional digital system with a continuous chaotic system. A rigorous proof is given that the controlled digital system is chaotic in the sense of Devaney’s definition of chaos. Numerical experimental results for different high-dimensional digital systems indicate that the proposed method can overcome the degradation problem and construct high-dimensional digital chaos with complicated dynamical properties. Based on the construction method, a kind of pseudorandom number generator (PRNG) is also proposed as an application.

The current work presents a novel digital chaotic communication system with antipodal chaotic shift keying modulation, implemented in a field-programmable gate array (FPGA). Such systems provide high security on the physical communication level and can be used in wireless sensor network systems. A modified Chua circuit chaos generator and error linear feedback chaotic synchronization are implemented in FPGA and used to develop a chaotic communication system with digital transmitter and receiver an analog in-between signal transmission. Additionally, a validated mathematical model of the communication system prototype is created in the Simulink environment, which is used to compare the performance of the prototype and its nodes with the simulation and simplify its development. The performance is evaluated using simulation with the additive white Gaussian noise channel and analyzing the bit error ratio.

Digital chaotic systems used in various applications such as signal processing, artificial intelligence, and communications often suffer from the issue of dynamical degradation. This paper proposes a solution to address this problem in the digital tent map. Our proposed method includes a simple and optimized hardware architecture, along with a hardware-efficient perturbation method, to create a high-performance computing system that retains its chaotic properties. We implemented our proposed architecture using an FPGA (Field-Programmable Gate Array) and the 1’s complement fixed-point format. Our results demonstrate that the implemented digital circuit reduces logical resource consumption compared to state-of-the-art references and exhibits pseudo-random nature, as confirmed by various statistical tests. We validated our proposed pseudo-random number generator in a hardware architecture for particle swarm optimization, demonstrating its effectiveness.

The new image encryption algorithm based on Logistic chaotic map is designed. First, after two initial values of Logistic chaotic map are pretreated, two of the modified initial values are obtained based on which two chaotic sequences are generated. Next, taking the first n-gray value of the original image in turn, pixel gray value (n is odd and even) is respectively encrypted by the chaotic sequence generated by two key. Results and analysis of experiment show that the proposed scheme has higher security.

Chaotic sequences and chaotic dynamical systems are attractive candidates for use in signal synthesis and analysis as well as in communications applications. In previous works, various methods for the estimation of chaotic sequences under noise were developed. However, although the methods were different, their qualitative performance was the same: for high signal-to-noise ratio (SNR) the performance was good, but below some threshold SNR, a sharp degradation in performance occurred. We prove and quantify the existence of this threshold effect and derive lower bounds on the value of the threshold SNR. Using information-theoretic tools, we prove that for any ergodic chaotic system, there is a certain threshold SNR level below which the ratio between the mean-square error obtained by any estimator of the system's initial state at the output of additive white Gaussian noise (AWGN) channel and the Cramer-Rao bound increases exponentially fast as the number of observations N grows without bound. We explain the connection between the existence of a threshold effect in the estimation of chaotic sequences and the converse to the joint source-channel coding theorem. We derive lower bounds on SNR/sub th/, the value of the threshold SNR, as a function of the system's Lyapunov exponent. Our bounds have two versions, one for a finite number of observations, and one for the asymptotic regime as N/spl rarr//spl infin/. For the asymptotic regime, the bound we develop on the threshold SNR incorporates the key parameters of chaotic systems, the Lyapunov exponent, and the chaotic sequence power spectrum into a simple formula. We demonstrate our results on the chaotic system governed by the r-diadic map.

A novel universal approach for design and implementation of chaotic digital communication system based on IEEE-754 standard and field programmable gate array technology (FPGA) is proposed, combing chaos encryption with traditional cipher realization. By using the Euler algorithm and appropriate discrete processing, the continuous chaotic system is converted to a discrete chaotic system. Using FPGA hardware design system, digital chaotic sequence is generated as the key. Scrambling and expansion encryption algorithm is realized and analyzed. Driven and response of secure communication system is designed by constructing a loop including the signal and achieving chaotic synchronization between sender and receiver. Taking grid Chua chaotic system as an example, the secure communication system using FPGA hardware platform is implemented. The technical development process, algorithm flow chart, hardware design and realization result are also given.

Properties of logistic chaotic map is studied, and it is pointed out that phase space is not ergodic when parameters of the chaotic system change. Based on these analysis, a piecewise logistic chaotic map is constructed. The bifurcation diagram and Lyapunov exponent of logistic and piecewise logistic map are studied, and the properties of randomicity, correlation coefficient and power spectrum etc. of the sequences generated by these two maps are analyzed experimentally. A new performance evaluation index for chaotic system, the bifurcation iteration time, is defined. Simulation results show that the defined piecewise logistic map is not only ergodic in phase space, and its corresponding chaotic performance evaluation indices are also better.

Communication is essential to every society, and securely exchanging data are critical in the age of digital data. The image has been the center of interest for security; chaotic maps image encryption become widely used in recent years. In our study, authors assessed the pixel rearrangement (permutation) and pixel dissemination (diffusion) stage used in cipher image established on designed scheme Pseudo-random number Generators (PRNGs) and Logistic chaotic map. Logistic maps used to generate seed value for PRNG and two-permutation stage and PRNGs used in diffusion operation. The proposed design through experimental tests demonstrate decent Statistical output, and high security for our image encryption schema, Our PRNGs passed NIST SP 800-22, and TestU01 practical randomness test suggests PRNGs have suitable statistical property.

In stream cipher systems, random key sequence generation is the primary task. The concept of chaotic systems can be considered in generating a random key sequence due to its inherent randomness property. Though the chaotic real sequences are random, the randomness will be lost after converting them to binary sequences. In this context, the authors propose a technique which uses a non‐linear feedback system to enhance the randomness of the binary sequences. In this work, three binary chaotic sequences using a logistic map are generated with three different initial conditions and each real value of the chaotic sequence is converted to ‘k’ bit binary value using a thresholding function. Some of the resulting sequences are not random. Hence, in this article a non‐linear structure is used to make the resulting sequence random. Here, a non‐linear function similar to the structure of the Simplified Data Encryption Standard is used to generate a sequence using two non‐random chaotic binary sequences. The resulting sequence is XORed with another non‐random chaotic binary sequence to get a random sequence. Sequences obtained from this nonlinear system are subjected to randomness tests and the results indicate that the sequences pass all the randomness tests. Hence, the sequences qualify as random key sequences, which can be used in a stream cipher based system to encrypt the data samples like audio, image, video, and so forth.

Chaotic systems provide a simple means of generating deterministic signals that resemble white noise. It is this noise-like property that provides the potential for applying chaotic systems in communications. In this work, we report a detailed study of the logistic map for use as direct-sequence spread-spectrum (DS/SS) codes. The advantages of the chaotic DS/SS codes are the almost unlimited number of distinct sequences of arbitrary lengths, the ease of generating these sequences, and the increased privacy afforded by the noise-like appearance of these sequences. Some design criteria are provided from the correlation properties of these sequences, and bit-error rate (BER) results are generated by Monte Carlo simulations.