Use Of Chaotic Signals Research Articles

Introduction to the statistical theory of differential communication based on chaotic signals

The purpose of this paper is to analyse the statistical characteristics of a Direct Chaotic Differentially Coherent communication scheme based on chaotic radio pulses in a communication channel with additive white Gaussian noise, where the chaotic signal is given by different instantaneous distributions. Methods. To achieve this goal, numerical modelling of the noise immunity of Direct Chaotic Differentially Coherent communication is conducted and compared with the results of analytical research. Results. The regularities associated with the use of chaotic signals with various statistical distributions of instantaneous values were studied. The minimum values of energy per bit to white Gaussian noise power spectral density ratio were obtained, providing the required error probabilities. Conclusion. It is shown that the proposed system works efficiently at high values of processing gain, and as the processing gain increases, the dependence of noise immunity on the specific statistical distribution of the chaotic signal is levelled out.

Internet of Medical Things Application in Encryption of Medical Images Based on Synchronization of Multi-state Chaotic Systems

Introduction: Studies on the security and interoperability of Internet of medical things (IoMT)in health are still scarce. The most important effects of the IoMT on health care are the ability to exchange information and reduce hospitalization and health care costs. The main challenges of the IoMT in healthcare are security and protection of privacy, among which encryption of images is very important in the field of communication and security. The main purpose of this study was to design a secure channel for encrypting and sending medical data. Methods: This study presents a new method for encrypting medical images to preserve patient information by synchronizing two chaotic systems. The use of chaotic signals as carriers of medical images greatly enhances security and greatly reduces the possibility of detection. The idea of synchronization of chaotic systems was presented in multi states with fixed time delay. In this idea, with the help of Lyapunov’s theory of stability, a controller was designed to establish the stability of the closed-loop system. Then, according to the synchronization idea and its error, a chaotic masking method was proposed to encrypt patient images. The simulation and accuracy of the results of the presented method were investigated in MATLAB software version 2020.Results: The simulations were performed on medical color images and CT, MRI, and X-ray images. Encrypted and recovered images were obtained by the proposed system. To evaluate the performance of the proposed method, various criteria including image histogram, signal-to-noise rate, correlation, and entropy of information were evaluated. The results showed the excellent image encrypting efficiency of the proposed method.Conclusion: Using the proposed method, medical images were encrypted based on a secure protocol, and then with satisfactory quality, images were recovered after transmission.

Оценка криптостойкости к деструктивному воздействию «просмотр передаваемых данных» в случае использования квантовых компьютеров

In this paper, we evaluate the crypto resistance of known cryptographic methods and methods based on the use of noise-like signals, similar in properties to "limited" white noise and used to spread spectrum of transmitted messages, to the destructive effect of "viewing transmitted data" (decipher), based on the search of code structures (brute force), in the case of quantum computers. It’s established that the required value of the number of code structures (key space), taking into account the constantly improving and developing computing power of quantum computers, for the next few years should be considered a value of 1032 of the number of code structures (key space) and higher, providing crypto resistance for a minimum of 3 years. It’s shown that the Grover algorithm is similar to the destructive effect of "viewing transmitted data" (decipher), based on a complete search of all code structures (brute force) using modern super- computers. It’s established that well-known symmetric cryptographic methods can potentially be used in the post-quantum era and methods based on noise-like signals potentially, provided they are detected and aware of the methods underlying them (without knowledge of the key), cannot be applied in the post-quantum era. According to the authors, a promising approach in the post-quantum era for information security issues is the use of chaotic signals.

АНАЛИЗ ИСПОЛЬЗОВАНИЯ ОТФИЛЬТРОВАННЫХ С ПОМОЩЬЮ ПОЛОСОВОГО ФИЛЬТРА ХАОТИЧЕСКИХ СИГНАЛОВ ДЛЯ ПЕРЕДАЧИ ДАННЫХ В СИСТЕМАХ РАДИОСВЯЗИ

The analysis of the use of chaotic signals filtered through a broadband bandpass filter to ensure stealth and reliability of data transmission operations in radio communication systems is carried out. Time realizations of chaotic signals generated by the well-known Chua and Rikitake generators are obtained. They were filtered using a broadband bandpass filter, and the data obtained was studied using BDS-statistic and crest factor. As a result of the studies, it was found that under certain research conditions, time realizations of Chua generator and Rikitake generator, obtained by broadband filtering, are suitable. Other considered time realizations are not suitable for radio communication systems, since either they have low stealth from the outside observer, or they have an unacceptable crest factor value for radio communication systems. From this we can conclude that filtering chaotic signals using a broadband bandpass filter as a whole is a promising approach to ensure the stealth and reliability of data transmission in radio communication systems. The authors, basing on the conducted research and conclusions from well-known works, consider it appropriate to use broadband filtering to ensure the stealth and reliability of data transmission in radio communication systems when using chaotic signals, along with widely used methods.

Modeling of information channel by using of pseudorandom signals of nonlinear dynamical system

Pseudorandom signals of nonlinear dynamical systems are studied and the possibility of their application in information systems analyzed. Continuous and discrete dynamical systems are considered: Lorenz System, Bernoulli and Henon maps. Since the parameters of dynamical systems (DS) are included in the equations linearly, the principal possibility of the state linear control of a nonlinear DS is shown. The correlation properties comparative analysis of these DSs signals is carried out.. Analysis of correlation characteristics has shown that the use of chaotic signals in communication and radar systems can significantly increase their resolution over the range and taking into account the specific properties of chaotic signals, it allows them to be hidden. The representation of nonlinear dynamical systems equations in the form of stochastic differential equations allowed us to obtain an expression for the likelihood functional, with the help of which many problems of optimal signal reception are solved. It is shown that the main step in processing the received message, which provides the maximum likelihood functionals, is to calculate the correlation integrals between the components and the systems under consideration. This made it possible to base the detection algorithm on the correlation reception between signal components. A correlation detection receiver was synthesized and the operating characteristics of the receiver were found.

Adaptation of dynamical properties of time series data and its applications in deep brain stimulation

The chaotic nature of the brain can be observed by electroencephalogram signals. This chaotic behavior can be affected by the progressive nature of neurodegenerative disorders like Parkinson disease. The gradual changes in dynamical behavior of brain can be tracked to facilitate effective and timely treatment. Deep brain stimulation (DBS) is used in therapy when the medication stops working. We investigate the use of chaotic signal as stimulus in DBS. We stimulate a simulated model of isolated neuron with different types of stimuli to see if periodicity in neuronal spiking can be disrupted and show that neuron, when stimulated with chaotic signal, does fire up in non-periodic/chaotic manner. Furthermore, as a step toward the development of our system for estimation of chaotic behavior of brain, we investigate the use of recurrent neural networks to adapt the chaotic characteristics of a chaotic time series in this research work. We explore two different setups of long short-term memory (LSTM). In first setup, we define three unique topologies of LSTM network and analyze those for chaotic parameter estimation in seven different test cases for shallow and deep networks. We show that the deep LSTM networks are capable of modeling the chaotic behavior of a wide range of parameters and that the network performs the best when the architecture is driven by chaotic attributes of the time series data. In second setup, we use LSTM network in a traditional configuration to predict the chaotic time series data and demonstrate that the LSTM network can make prediction over a range of chaotic parameters with adequate accuracy. This provides the basis for the generation of chaotic stimulation signals when required.

Modeling and Analysis of Chaos-based Spread Spectrum Scheme using Irregular LDPC Code and Non-Coherent 16-DCSK under Fading and Jamming

In chaos-based spread spectrum systems, the use of spreading code and chaotic binary sequence expands the bandwidth of the information-bearing signal but this expansion results in SNR degradation under the constraint of constant channel capacity according to Hartley-Shannon law. To compensate for this drawback, our proposed model employs an irregular low-density parity-check (LDPC) code with its iterative decoding algorithm. Coupled with this forward error correction (FEC) coding, we used non-coherent (NC) 16-ary differential chaos shift keying (16-DCSK) that additionally provides the ability of data encryption due to its use of chaotic signals compared with the conventional modulation schemes. Analytical expressions of bit error probability (BEP) are derived under the assumption of the three-ray model along with partial band noise jamming (PBNJ) over a Rayleigh fading channel. Simulation results assert that the proposed system can mitigate the effect of PBNJ via lowering BEP by coding gain and processing gain under identical transmission power. It is also confirmed that a higher level of security can be provided by the use of proposed two iteration functions of Duffing Map-based chaotic binary sequence than the security level of one iteration function of Logistic Map, based on the balance and autocorrelation analysis.

Chaotic Spreading Sequence for Linear Frequency Modulation

In the presented article the use of chaotic signals as spreading sequences for linear-frequency modulation is proposed. An example of a simplified block diagram for a chaotic signal generator constructed on the basis of linear and switching elements is given, as well as equations describing the operation of the circuit. The results of calculation and simulation of processes with specific specified parameters of the circuit are shown. The calculation of differential equations is carried out by a numerical method of Runge-Kutt of the fourth order of accuracy. It is shown that carrier frequency varies linearly, according to the scanning voltage. To maintain the full range of changes the beginning of each linear variable voltage function can be shifted for certain time interval. It is shown that when forming a range of frequency changes, it is necessary to take into account the presence of a "dead zone". The dependence of the transition from one frequency to another is random and depends on the values of correlation coefficient. A bifurcation diagram and display functions for processes with two and three attraction points are presented, The first zone of chaotic oscillations corresponds to the value of the coefficient, which is approximately in the range from 15 to 19. The second zone of chaotic oscillations correspond to the coefficient values from 40 to 59. The third zone of chaotic oscillations correspond to the coefficient values from 117 to 173. Between these zones regular oscillations are presented in the system. With an increase of correlation coefficient the number of attraction points and the corresponding display points can increase or decrease. The formulas for the calculation and the graph of the change in the correlation coefficient are given. It is shown that the correlation function is close to zero, some of its periodicity and the difference from zero is probably due to the existence of repeating areas of transient process. An example of an integer sequence for a process with two attraction points is given. For a process with two attraction points an example of integer sequences is given, which it is proposed to use to identify the type of chaotic process. The feature of generated chaotic sequences is shown – the sequence of integer function periods, which are enclosed between two attraction points is chaotic and unique. With using the deterministic equations with switching functions, a chaotic spreading sequence of linear frequency modulation is build, for identification of which it is proposed to use integer sequences of the number of periods that are enclosed between the points of generated frequencies.Ref. 7, fig. 4, table 1.

1 Gb/s chaotic encoded W-band wireless transmission for physical layer data confidentiality in radio-over-fiber systems

Physical layer encryption methods are emerging as effective, low-latency approaches to ensure data confidentiality in wireless networks. The use of chaotic signals for data masking is a potential solution to prevent a possible eavesdropper to distinguish between noise and sensitive data. In this work, we experimentally demonstrate the W-band wireless transmission of a 1 Gb/s chaotic signal over 2 m in a radio-over-fiber architecture. The chaos encoding scheme is based on the transition between different states of a Duffing oscillator system, digitally implemented. The bit error rate achieved in all cases was below the forward error correction limit for 7 % overhead. The presented results validate the proposed chaos-based physical layer encoding solution for gigabit data transmissions in hybrid millimeter-wave/photonic networks.

Chaos time‐domain reflectometry for distributed diagnosis of complex topology wired networks

A new reflectometry-based wire diagnosis method using chaotic signals is presented. It shows excellent potential for the diagnosis of live wires (i.e. during their operational usage) and complex topology networks. The use of chaotic signals for distributed diagnosis and the detection of defects in wires is investigated. Chaos time-domain Reflectometry (CTDR) using low auto-correlation sidelobes signals, shows high performances in very noisy environment: the detection and location of hard defects are possible, even if several reflectometers inject their signals concurrently with the diagnosis and the normal operation of the cable. This enables using CTDR for distributed diagnosis of complex topology networks.

Study on Digital Image Scrambling Algorithm

Encryption algorithm of traditional cryptology has strong safety, but the effect of encrypting images is not good. Digital image scrambling means that a digital image is transformed into a chaotic image which has no evident significance, but the operator can reconstruct the chaotic image into the original image by using the specific algorithm. Image scrambling encryption technology based on chaos theory makes use of chaotic signal to encrypt image data flow, which has the advantages of high safety, rapid encryption speed, large key space and good scrambling effect. The paper studies invalid-key and quasi invalid-key existed in chaotic sequence which is generated by Logistic map, and proposes image scrambling encryption algorithm based on mixed and chaotic sequence. The algorithm has a good robustness for the JPEG compression with the fixed coefficient, and a good fragileness for the illegal manipulation.

A New and Secure Cryptosystem for Image Encryption and Decryption

Illegal data access has become prevalent in wireless and general communication networks. Recently, the use of chaotic signals for secure data transmission has shown significant growth in developing chaotic encryption and decryption algorithms. The application of the Brahmagupta–Bhãskara (BB) equation for encryption is reported in a very recent article. However, a number of chaos-based algorithms are proved to be insecure in the literature. It is also shown in the literature that the BB equation based algorithm can be broken by a low complexity known plaintext attack. Hence, in this paper, a new secure cryptosystem based on the BB equation and chaos is proposed for image encryption and decryption. Cryptanalysis of the proposed cryptosystem is also provided. The efficacy of the proposed cryptosystem is illustrated through implementation results on two images.

EXPLOITING CHAOTIC DYNAMICS FOR A-D CONVERTER TESTING

In this paper we discuss the possible use of chaotic signals for testing Analog-to-Digital Converters (ADCs), with particular reference to the well-known Code Density Test (CDT, also called Histogram Test). In detail, we discuss the implementation of a chaos-based discrete-time noise generator circuit, providing the theoretical analysis of its statistical characterization. The implementation of the chaos-based device is discussed with reference to a generic hardware architecture, taking into account the nonidealities introduced by the presence of noise and the variability of the circuit parameters. Based on this device, we propose a method for generating noisy samples that are distributed, over a target subinterval of the circuit output range, according to a probability density function (pdf) that can be made arbitrarily close to the ideal uniform pdf, in exchange for an acceptable reduction of the uniform-distributed samples generation rate. Theoretical results, also supported by two experiments, confirm the reliability of the proposed solution, showing that chaotic systems can represent an alternative with respect to traditional methods for the generation of signals to be used in the Code Density Test of ADCs.

High-capacity and security packet switching using the nonlinear effects in micro ring resonators

We propose a new design of secured packet switching generated by using nonlinear behaviors of light in a micro ring resonator. The use of chaotic signals generated by the micro ring resonator to form the filtering and packet switching characteristics is described, where the high-capacity and security switching using such form is presented. The key advantage is that the high capacity of communication data can be secured in the transmission link, where the nonlinear penalty of light traveling in the device is beneficial. For instance, the required information can be transmitted and retrieved by using the proposed packet switching scheme. In principle, the chaotic signals are generated by a Kerr effects nonlinear type of light in a micro ring resonator, where the control input power can be specified by the required output filtering signals. The ring radii used range between 10 and 20 μm, κ=0.0225, α=0.5 dB and n 2=2.2×10 −15 m 2/W. Simulation results obtained have been described based on the practical device parameters. Three forms of the applications have been simulated, the potential of using for the tunable band pass and band stop filters, in which high-capacity packet switching data can be performed, and the fs switching time is plausible.

Optimizing chaos-based signals for complex radar targets

There has been interest in the use of chaotic signals for radar, but most researchers consider only a few chaotic systems and how these signals perform for the detection of point targets. The range of possible chaotic signals is far greater than what most of these researchers consider, so to demonstrate this, I use a chaotic map whose parameters may be adjusted by a numerical optimization routine, producing different chaotic signals that are modulated onto a carrier and optimized for different situations. It is also suggested that any advantage for these chaos-based signals may come in the detection of complex targets, not point targets, and I compare the performance of chaos-based signals to a standard radar signal, the linear frequency modulated chirp. I find that I can optimize a chaos-based signal to increase the cross-correlation with the reflection from one complex target compared to the cross-correlation with the reflection from a different target, thus allowing the identification of a complex target. I am also able to increase the cross-correlation of the reflection from a complex target compared with the cross-correlation with the reflection from spatially extended clutter. I show that a larger output signal-to-noise ratio is possible if I cross-correlate with a reference signal that is different from the transmitted signal, and I justify my results by showing how the ambiguity diagram for a chaos-based signal can be different than the ambiguity diagram for a noise signal.

An investigation of the use of chaotic signals in active sonar

Many natural effects are now known to be chaotic rather than random, i.e., are generated by simple non-linear systems. The paper reports the outcome of a theoretical and experimental study to assess whether signals based on chaotic time series offer advantages in active sonar. It is noted that for conventional detection, the detailed structure of the signal is unimportant. Any advantage will come from novel effects due to interactions with the target or the environment. An overview is given of apparently novel behavior in echoes from a resonant target which were first noted in simulations and then observed in laboratory ultrasonic measurements. An explanation in terms of linear systems theory is outlined. The limitations which inhibit the use of advanced non-linear techniques for detection will be discussed and illustrated with reference to the results of analyzing data measured in an outdoor acoustic test facility.

Blind Multiuser Receivers for Chaos Based Communications

Recently, there has been a good deal of interest in the use of chaotic signals for direct sequence code division multiple access (DS-CDMA) communication systems. The capacity of DS-CDMA systems is interference-limited, and can therefore be increased by techniques that suppress interference. This letter is devoted to the evaluation of the impact of blind multiuser detection techniques on chaos based DS-CDMA systems. Blind receivers can suppress multiple access interference and do not require knowledge of the code sequences and propagation channels of the interference. We demonstrate that, for chaotic sequence-based communications, blind multiuser receivers significantly improve the BER with respect to single-user receivers, and that their use is practically essential with a high number of users.

Chaotic sequences for multiple access

The use of chaotic signals as generators of binary and multilevel sequences suitable for code division multiple access (CDMA) is proposed. The number of obtained sequences is found to be greater than the number of m-sequences of the same length. These new chaotic sequences are used as spreading codes in a CDMA system. Simulation results are presented and compared with those obtained for m-sequences in terms of BER performance.

An IC chip of Chua's circuit

Reports a working microelectronic chip implementation of Chua's circuit. This chip has been designed and fabricated by using a 2 mu m CMOS technology, with the circuit itself occupying a silicon area of 2.5mm*2.8mm. The chip needs to be powered with a single 9V battery, is autonomous, and generates chaotic signals from the three state variables of Chua's circuit. The proper operation of this chip has been confirmed by experimental reproduction of bifurcation and chaotic phenomena. This microelectronic design of Chua's circuit can be employed as a basic component in the VLSI synthesis of complex circuits making use of chaotic signals, including a class of cellular neural networks and secure communication systems.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Chaotic Circuits Applied to Secure Communications

In this paper, we discuss the use of chaotic signals in cryptography. A comparative analysis of three different analogue chaotic communication systems is presented. The paper concludes with a discussion of some possible measures that could improve the security of these systems.