Chaotic Adaptive Synchronization Control and Application in Chaotic Secure Communication for Industrial Internet of Things

본 논문에서는 카오스 신호를 이용하여 음성신호의 보안전송을 위한 아날로그 비화통신 시스템을 제안하고 통신성능을 분석하였다. 기존의 카오스 동기화 및 카오스 변조통신 알고리즘을 개선하여 통신환경에서 발생하는 다양한 조건들을 적용하여 음성신호의 복원능력을 모의실험 하였다. 일반적인 PC(Pecora ＆ Carroll) 제어기법과 제안한 SFB(Self-FeedBack) 마스킹 기법을 사용하여 송신단에서 음성신호를 카오스 신호로 마스킹하여 변조하고, 통신채널에 잡음신호를 추가하여 전송하였다. 수신단에서는 카오스 응답시스템을 이용하여 음성신호를 복조하고, 복원성능을 계산하기 위하여 아날로그 복원 에러 신호의 평균전력을 제안하여 계산하였다. 실험결과 마스킹 정도, 파라미터들의 민감성, 채널잡음 등에 대하여 PC 제어기법보다 피드백 제어기법의 복원성능이 우수함을 정량적인 데이터로 확인할 수 있었다. 또한 로렌쯔 카오스 비화통신시스템에 사용할 경우 파라미터들의 조합으로 암호키를 구성해야 하므로 파라미터 변화율에 대응하는 복원에러율의 관계를 모의실험 값으로 구하였다. This paper presents analog secure communication system about safe speech transmission using chaotic signals. We applied various conditions that happen in actuality communication environment modifying chaotic synchronization and chaotic communication schemes and analyzed restoration performance of speech signal to computer simulation. In transmitter, we made the chaotic masking signal which is added voice signal to chaotic signal using PC(Pecora ＆ Carroll) and SFB(self-feedback) control techniques and transmitted encryption signal to noisy communication channel And in order to calculate the degree of restoration performance, we proposed the definition of analog average power of recovered error signals in receiver chaotic system. The simulation results show that feedback control techniques can certify that restoration performance is superior to quantitative data than PC method about masking degree, susceptibility of parameters and channel noise. We experimentally computed the table of relation of parameter fluxion to restoration error rate which is applied the encryption key values to the chaotic secure communication.

Chaotic optical communication at high bit rates has attracted great attention because of its potential application in secure communications. In a chaotic optical communication system, a message can participate in the dynamics of the nonlinear system and further affect the characteristics of the chaotic carrier waveform. Message encoding can also change the synchronization quality if an encoding scheme breaks the symmetry between a transmitter and a receiver. In this presentation, we experimentally investigate the influence of message encoding on the characteristics of chaotic dynamics, chaos synchronization, and chaotic communication, using three encoding schemes, namely chaos shift keying, chaos masking, and chaos modulation, with the setup of a chaotic optical communication system with optoelectronic feedback. The chaos shift keying and chaos modulation schemes are found to be able to increase the complexity of the chaotic carrier waveform due to the random nature of the encoded message. Meanwhile, the chaos shift keying and chaos masking schemes are found to deteriorate the synchronization quality when the amplitude of the message is increased. Consequently, only the chaos modulation scheme has the desired feature in increasing the complexity of the chaotic carrier waveform while maintaining the quality of chaos synchronization, which is an important feature in secure communication.

The signal detection in chaotic background has gradually become one of the research focuses in recent years. Previous research showed that the measured signals were often unavoidable to be contaminated by the chaotic noise, such as the radar signal detection from sea clutter wave,signal source extraction from chaotic secure communication and ECG/EEG abnormal signal detection,etc.At present,there are two methods to detect the target signal from the chaotic background.One is to detect the target signals by using the difference in geometric structure between the chaotic signal and the target signal,and the other is to regard the chaotic signal as the noise,and the target signal is extracted from the chaotic background by the time frequency analysis method,such as wavelet transform and empirical mode decomposition. The first kind of method can detect the target signal well,but it needs to characterize the chaotic system and reconstruct the phase space,which is difficult in the practical applications.The second kind of method does not need to reconstruct the chaotic phase space and can effectively extract the target signal from the chaotic background.However,the wavelet transform lacks adaption and how to select the optimal wavelet basis and decomposition layers is a difficult problem.In the empirical mode decomposition there exists the mode mixing that is very sensitive to the noise.The synchrosqueezed wavelet transform (SST) effectively improves the mixing of mode by compressing the continuous wavelet coefficients in the frequency direction,but also it has good robustness to noise.Therefore,the SST can extract the harmonic signal well from the chaotic background.In the present algorithm of abstracting harmonic signal from chaotic background by SST,the harmonic signals are extracted by using single accumulation frequency range SST (SAFR-SST) based on wavelet ridge detection.If the target signal is stable harmonic signal,whose frequency does not change with time,the SAFR-SST method can have a high abstraction precision.But if the target signal is the non-stable harmonic signal whose frequency changes with time,the SAFR-SST method is not enough nor can obtain high abstraction precision.In order to overcome the shortcomings of the SST in extracting the non-stationary harmonic signal from the chaotic background, an improved SST extracting method is proposed which is based on the adaptive optimal cumulative frequency range. Firstly,the formulas of calculating the adaptive cumulative frequency range in SST extraction are deduced according to the relationship between the wavelet coefficient of non-stationary harmonic and the interval of supporting wavelet bases.Then,the optimal values of the parameters in the adaptive cumulative frequency range formula are calculated by the minimum energy error criterion according to the integrity and orthogonality of the intrinsic mode types function.Finally,the SST adaptive extraction of the non-stationary harmonic signal is realized according to the SST inverse transform.In experiment,the different types of non-stationary harmonics are extracted from the Lorenz and Duffing chaotic background.The experimental results show that the proposed method can effectively extract the non-stationary harmonic from the noisy chaotic background.Compared with the classical SST method with single cumulative frequency range,the proposed method has good performance in both mean square error and correlation coefficient.And when the chaotic background contains different-intenity Gauss white noises,the proposed method can also effectively abstract the non-stationary harmonic from the chaos and noise interference.So,the proposed method has a good practice value.

Alternant-channel chaotic laser secure communication system and its chaos alternant coding (CAC) are presented and deeply studied via two coupled lasers synchronizing or desynchronizing with another single laser. The coupled lasers are used as two chaotic transmitters and transmit two chaotic carriers to mask two information signals, respectively. One conventional encoding scheme is that the single laser is used as a receiver and obtain synchronization with one of two chaotic transmitters for chaos decoding. And another CAC scheme as a non-conventional coding is presented and its coding principle is defined for secure communication. CAC coding and scheme is that one laser of chaotic transmitters transmits a chaotic carrier to mask an information signal, where the carrier is modulated by an information signal, while the decoding of CAC is performed via synchronization or de-synchronization between another laser of two chaotic transmitters and a receiver. A physical model of the synchronous system is presented using a drive-feedback technique while a chaotic synchronization is obtained between a chaotic transmitter and a receiver. And alternant-channel chaotic secure communication and CAC are successfully implemented while a novel CAC technique is validated. The system has the characteristics of high dimension, many degrees of freedom in phase-space, a high degree of nonlinearity, a nonconventional CAC, and many secret keys. So it has high security and can transmit securely two chaotic carries masking two information signals, respectively.

In this study, we propose a novel Deeply Optimized Adaptive chaotic synchronization algorithm system (DOA), which adopts the ideas of genetic algorithm, Deep Image Prior (DIP) network, Deep Convolutional Generative Adversarial Network (DCGAN) network, and slide mode control algorithm. Traditional Deep Learning (DL)-based methods perform well in complex multi-parameter operations, but training on large datasets is typically a complicated, time-consuming, and high-cost process. Such methods are also difficult to adapt to dynamic parameter changes. The algorithmic network model in the proposed DOA reduces reliance on large datasets by learning the deep mining methods of the data characteristics in DIP, and can adjust system parameters adaptively, accurately, and quickly, providing high synchronization efficiency and excellent stability over various chaotic signals. By applying Lyapunov stability theory, the robustness and global stability of the model in dynamic systems are proven. This paper also uses an advanced Recurrent Neural Network (RNN)-based chaotic synchronization system as a benchmark. The simulation results show that, when compared to the Recurrent Neural Network based synchronization system, the DOA architecture has significant advantages in robustness, convergence, and training over noisy channels. Experiments show that under strong noise (AWGN variance = 2) and parameter mismatch (±20 percent drift), the synchronization error of DOA (<0.3) is significantly lower than that of the RNN benchmark system (>1.5), and the training data volume is reduced by more than 30%. Simulation results show that, the DOA architecture has significant advantages in robustness, convergence, and training over noisy channels. The proposed DOA scheme improves the effect of chaotic synchronization and paves the way for the development of a new class of modulator schemes that meet the robustness, convergence, and training requirements for encrypted communication.

Chaotic spread spectrum communication systems are sought after for their high levels of security, derived from the apparent randomness of the underlying chaotic spreading signal. Traditionally this "randomness" is quantified by the use of Lyupanov exponent(s) that give rates of chaotic state divergence, for continuous-time chaotic circuits. The downside of such continuous-time analog chaotic systems is that they are difficult to synchronize, leading to reduced channel capacity via re-synchronization overhead or compromises in security. These chaotic signals also possess colored spectra, leading to detection and channel utilization disadvantages. Discrete-time and -amplitude systems are simpler to implement, yet more difficult to quantify their "chaotic-ness;" the rate of state divergence is dependent on both computational precision and sampling intervals in sequence generation. Moreover, the existence of a well-defined chaotic attractor is evidence of a failure to meet the desired maximal entropy signal characteristic required for maximum channel capacity throughput. This paper presents comparative simulation measures quantifying the underlying randomness and computational sensitivities for a collection of digital chaotic mappings, qualifying their suitability for use in secure communication systems. Under most measures, the tent map and the logistic map fail to meet the needed performance. The skew tent mapping is found to be better, yet techniques for closed field calculations are found to be superior, without a significant increase in computational resources.

In this paper, we mainly propose a chaotic secure communication scheme which is based on the synchronization of double-layered and multiple complex dynamical networks. Compared with the previous chaotic secure communication schemes, in which only two chaotic systems or just a single-layer network composed of multiple chaotic systems is used, the introduction of a double-layered and multiple complex networks model composed of many encryption/encryption units can not only reflect the complex characteristics of different nodes, but also can improve the complexity and security of information encryption. By using a clustering method, nodes with the same characteristics belong to the same subnet, while the nodes with different characteristics belong to different ones. The subnets in the transmitter and receiver are one-to-one correspondence and form a pair of matching subnets, but the node size of each subnet can be inconsistent. Each subnet is only responsible for encrypting a certain part of information, and thus, the synchronization between each pair of matching subnets plays a crucial role on the correct recovery of information. Multiple encryption/decryption units operating in parallel way can speed up the encryption of information, and the key space can grow with the number of nodes in the transmitter. The proposed scheme utilizes the chaotic signals generated by many chaotic systems as the key sequences and adopts the one-time-one-cipher encryption method. Moreover, this scheme is not subject to the constraint that the amplitude of the encrypted signal should be much smaller than that of the chaotic signal, and it is particularly suitable for the big data encryption. Both theoretical analysis and numerical simulation demonstrate the feasibility and effectiveness of the proposed scheme.

The chaotic system is widely used in chaotic cryptosystem and chaotic secure communication. In this paper, a universal method for designing the discrete chaotic system with any desired number of positive Lyapunov exponents is proposed to meet the needs of hyperchaotic systems in chaotic cryptosystem and chaotic secure communication, and three examples of eight-dimensional discrete system with chaotic attractors, eight-dimensional discrete system with fixed point attractors and eight-dimensional discrete system with periodic attractors are given to illustrate how the proposed methods control the Lyapunov exponents. Compared to the previous methods, the positive Lyapunov exponents are used to reconstruct a hyperchaotic system.

Based on the nonlinear feedback approach for realizing any continuous time scalar(hyper)chaotic signal synchronization control,we have designed an adaptive feedback controller for controlling the scalar output signal of a smooth(hyper)chaotic system to synchronize with any continuous time scalar(hyper)chaotic signal under some assumptions.The result,which is rigorously proved by means of stability theory,not only can adaptively estimate the control parameter,but also has some robustness against parameter variations and external disturbances.An application to the synchronization of two(hyper)chaotic systems is given.

In wireless communications, chaotic communications have been a field of interest due to its low complexity in hardware implementation and low power consumption in chaotic signal generation. Among the modulation schemes using the chaotic signal, Differential Chaos Shift Keying (DCSK) is a robust noncoherent technique. Multiple-input multiple-output (MIMO) system is a technology that uses multiple transmit and/or multiple receive antennas in order to improve the system performance in wireless systems. In our paper, we have proposed a new scheme of MIMO-DCSK which utilizes the benefits of MIMO system into the chaotic communication system by transmitting and receiving DCSK modulated signals through multiple antennas. Our analysis and simulation results show how the chaotic communications in the new MIMO-DCSK benefits over the single input single output (SISO) system and the BER performance of DCSK in additive white Gaussian noise (AWGN) channels using Alamouti space-time code and the maximum likelihood decoding is analyzed.

The adaptive synchronized problem of the four-dimensional (4D) Lu hyperchaotic system performed by Elabbasy et al. (Chaos Solitons Fractals 30:1133–1142, 2006) with uncertain parameters by applying the single control input is addressed in this article. Based on the Lyapunov theorem of stability, the single-input adaptive synchronization controllers associated with the adaptive update laws of system parameters are developed to make the states of two nearly identical 4D Lu hyperchaotic systems asymptotically synchronized. Numerical studies are presented to illustrate the effectiveness of the proposed chaotic synchronization schemes.

Adaptive control and synchronization of a new hyperchaotic system with unknown parameters

This paper presents a method based on the state observer design for constructing a chaotically synchronized systems. Fractional-order direct Lyapunov theorem is used to derive the closed-loop asymptotic stability. The gains of the observer and observer-based controller are obtained in terms of linear matrix inequalities (LMIs) formulation. The proposed approach is then applied to secure communications. The method combines chaotic masking and chaotic modulation, where the information signal is injected into the transmitter and simultaneously transmitted to the receiver. Chaotic synchronization and chaotic communication are achieved simultaneously via a state observer design technique. An numerical fractional-order chaotic Lorenz system is given to demonstrate the applicability of the proposed approach.

In this paper, the control of chaotic externalinjection multiplequantumwell laser synchronization via phasecontrollers is presented and external chaos phase shift keying modulation is proposed for secure communication. Chaotic laser synchronization is numerically achieved under controlling by phasecontrollers. Lasing phase shift is controlled via continuous ON/ON chaos shift keying and chaotic laser signal is transmitted by chaos phase shift keying modulation on end. Chaotic laser demodulation is realized by setting a phase shift of the receiver phasecontrollers. ON/ON chaos phase shift keying communications at bit rates of 01 and 05Gbit/s are numerically simulated. ON/ON chaos phase shift keying communication bit rate，the synchronization characterization and the system parameter mismatch are numerically analyzed, in particular.

In recent years, a large amount of work on chaos-based cryptosystems has been published (Kocarev (2001); Millerioux et al. (2008)). A general methodology for designing chaotic and hyperchaotic cryptosystems has been developed using the control systems theory (Grassi et al. (1999); Liao et al. (1999); Yang et al. (1997a;b)). The chaotic communication system is closely related to the concept of chaos synchronization. An overview of chaotic secure communication systems can be found in (Yang (2004)). He classified the continuous-time chaotic secure communication systems into four generations. In the third generation, the combination of the classical cryptographic technique and chaotic synchronization is used to enhance the degree of security. Specifically, Yang et al. proposed a new chaos-based secure communication scheme in an attempt to thwart the attacks (Yang et al. (1997a;b)). They have combined both conventional cryptographic method and synchronization of chaotic systems. Their cryptographic method consists of an encryption function (the multi-shift cipher), a decryption function (the inverse of the encryption function), a chaotic encrypter that generates the key signal for the encryption function, and a decrypter that estimates the key signal. The approach has a limitation since the cryptosystem design may fail if different chaotic circuits are utilized. So far, this generation has the highest security in all the chaotic communication systems had been proposed and has not yet broken. From the control theoretic perspective, the transmitter and the receiver in the chaotic communication system can be considered as the nonlinear plant and its observer, respectively. Grassi et al. proposed a nonlinear-observer-based decrypter to reconstruct the state of the encrypter (Grassi et al. (1999); Liao et al. (1999)). They extended the Chua’s oscillator to the observer-based decrypter. The cryptosystem does not require initial conditions of the encrypter and the decrypter belonging to the same basin of attraction. If we can design a decrypter without the knowledge of the parameters of the encrypter, the chaos-based secure communication systems are not secure, because the parameters of the encrypter is selected as static secret keys in the cryptosystem. Parameter identification and adaptive synchronization methods may be effective for intruders in building reconstruction mechanisms, even when a synchronizing system is not available. Therefore, it is important for secure issues to investigate whether adaptive identifiers without the system information of encrypter can be constructed or not. We have recently designed an observer-based chaotic communication system combining the cryptosystems proposed by Grassi et al. (Grassi et al. (1999)) and by Liao et al. (Liao et al. (1999)) that allows us to assign the relative degree and the zeros of its encrypter system (Matsuo et al. (2004)). Specifically, we constructed three cryptosystems based on a Chua’s circuit by assigning its relative degree and zeros. The cryptosystem consists of 20