Secure Communication Using NAC Based Synchronisation Between Nonidentical Chaotic Systems

This paper focuses on the finite-time generalized synchronization problem of non-identical fractional order chaotic (or hyper-chaotic) systems by a designing adaptive sliding mode controller and its application to secure communication. The effects of both disturbances and model uncertainties are taken into account. A novel fractional order integral sliding mode surface is designed and its stability to the origin is proved in a given finite time. By the aid of the fractional Lyapunov stability theory, a robust controller with adaptive update laws is proposed and its finite-time stability for generalized synchronization between two non-identical fractional-order chaotic systems in the presence of model uncertainties and external disturbances is derived. Numerical simulations are provided to demonstrate the effectiveness and robustness of the presented approach. All simulation results obtained are in good agreement with the theoretical analysis. According to the proposed generalized finite-time synchronization criterion, a novel speech cryptosystem is proposed to send or share voice messages privately via secure channel. Security and performance analyses are given to show the practical effect of the proposed theories.

Chaotic neural networks consisting of a great number of chaotic neurons are able to reproduce the rich dynamics observed in biological nervous systems. In recent years, the memristor has attracted much interest in the efficient implementation of artificial synapses and neurons. This work addresses adaptive synchronization of a class of memristor-based neural chaotic systems using a novel adaptive backstepping approach. A systematic design procedure is presented. Simulation results have demonstrated the effectiveness of the proposed adaptive synchronization method and its potential in practical application of memristive chaotic oscillators in secure communication.

This paper mainly proposes a new disturbance observer (DO) for a secure communication system (SCS) of the chaos-based system (CBS). First, the fractional-order (FO) Chen chaotic system is remodeled by a Takagi–Sugeno (T–S) fuzzy system with the aim of softening in calculation. Second, the robust fixed-time was designed to synchronize two nonidentical chaotic systems. Third, a new disturbance observer was proposed to compensate for the disturbance and uncertainty of the secure communication system. Fourth, the proof of the proposed method based on Lyapunov condition together with simulation are given to illustrate the correctness and effectiveness of the proposed theory. The tested disturbance on the public channel was mostly compensated by the appropriately estimated disturbance value. The states of master and slave systems (MSSs) were closed to each other in fixed-time. These factors are used to confirm that the symmetry of two chaotic systems were obtained by the proposed control methods.

To solve the problem of indeterminate synchronization time in different chaotic systems, this paper presents a time-controllable synchronization scheme. A general synchronization controller and parameter update laws are proposed to stabilize the error system, thus the drive and response systems could be synchronized up to a given scaling matrix at a pre-specified exponential convergence rate. The synchronization time formula is strictly deduced, which suggests that the speed of synchronization is determined by several parameters, such as exponential rate, initial system value and other parameters brought in by the controller. By adjusting these parameters, the performance of the synchronization can be effectively improved. In numerical simulation, two nonidentical 3D autonomous chaotic systems are chosen to verify this method. The error system can be rapidly stabilized, and unknown parameters are also identi?ed correctly. Firally, two groups of time-controllable parameters are given to verify the theory, wherein synchronization of both cases can be obtained quickly and each result of the synchronization is consistent with the theoretical calculation. The synchronization scheme is characterized by high safety and efficiency, and has its potential value in secure communication.

Output synchronization of chaotic systems under nonvanishing perturbations

This paper presents a novel wireless control framework for electric drive systems by employing a fuzzy brain emotional learning neural network (FBELNN) controller in conjunction with a Disturbance Observer (DO). The communication scheme uses chaotic system dynamics to ensure data confidentiality and robustness against disturbance in wireless environments. To be applied to embedded microprocessors, the continuous-time chaotic system is discretized using the Grunwald–Letnikov approximation. To avoid the loss of generality of chaotic behavior, Lyapunov exponents are computed to validate the preservation of chaos in the discrete-time domain. The FBELNN controller is then developed to synchronize two non-identical chaotic systems under different initial conditions, enabling secure data encryption and decryption. Additionally, the DOB is introduced to estimate and mitigate the effects of bounded uncertainties and external disturbances, enhancing the system’s resilience to stealthy attacks. The proposed control structure is experimentally implemented on a wireless communication system utilizing ESP32 microcontrollers (Espressif Systems, Shanghai, China) based on the ESP-NOW protocol. Both control and feedback signals of the electric drive system are encrypted using chaotic states, and real-time decryption at the receiver confirms system integrity. Experimental results verify the effectiveness of the proposed method in achieving robust synchronization, accurate signal recovery, and a reliable wireless control system. The combination of FBELNN and DOB demonstrates significant potential for real-time, low-cost, and secure applications in smart electric drive systems and industrial automation.

In this paper, a nonlinear Model Matching control problem is presented based on feedback linearization technique. For the analysis purpose, the output synchronization case is considered. The proposed synchronization methodology utilizes a control law acquired from graph theory and takes care of the model-matching control for multi-agent systems. Especially, set of non-identical chaotic systems are considered as Plant and Model, combination where the relative degree of the systems is less than the order of the system. The asymptotic convergence error dynamics is proved using the Routh-Hurwitz method. The effectiveness of the proposed procedure is verified using MATLAB simulations. For example, the 3D Lorenz chaotic system and 4D Lüchaotic system are considered to achieve synchronization in multi-agent systems configuration.

This paper investigates the hybrid chaos synchronization of identical Liu systems, identical Lu systems, and non-identical Liu and Lu systems by active nonlinear control. Liu system (Liu et al. 2004) and Lu system (Lu and Chen, 2002) are important models of three-dimensional chaotic systems. Hybrid synchronization of the three-dimensional chaotic systems considered in this paper are achieved through the synchronization of the first and last pairs of states and anti-synchronization of the middle pairs of the two systems. Sufficient conditions for hybrid synchronization of identical Liu, identical Lu, and non-identical Liu and Lu systems are derived using active nonlinear control and Lyapunov stability theory. Since the Lyapunov exponents are not needed for these calculations, the active nonlinear control is an effective and convenient method for the hybrid synchronization of the chaotic systems addressed in this paper. Numerical simulations are shown to illustrate the effectiveness of the proposed synchronization schemes.

International audience

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.

In this work, a secure second-order discrete time delta sigma (ΔΣM) modulator is used to securely modulate two physiological signals for e-health applications. The chaotic system used is a new 3D chaotic system that is used to generate random keys for encryption. Quintic nonlinearity is integrated into the existing sprott chaotic system and then studied via nonlinear dynamics tools, which reveal complex dynamics, including the coexistence of three distinct chaotic attractors and the phenomenon of intermittency. A microcontroller implementation of the system is performed to demonstrate its real-life applicability. The bits generated from the chaotic regime of the proposed oscillator are tested successfully via the NIST-800.22 test. The pseudo random bit streams generated from the chaoticity of the oscillator using the system parameters and initial conditions as secret keys are used in a 2-stage confusion process to encrypt two physiological signals. At the receiving end, the physiological signals are successfully recovered, and some standard metrics, such as key space analysis, key sensitivity, and cross-correlation, are applied to verify the strength of the encryption scheme. A comparison with recent and good standing contributions in the literature is also provide at the end of this work, which shows that the proposed scheme is robust against common attacks. The results obtained in this study open the possibility of applying chaos in digital communication systems for the conception of secure e-health services.p. 2Highlights• A new random chaotic system applicable in information protection is conceived and experimented.• Random encryption data are successfully generated from the chaotic system in its confused state and tested statistically. • Patient's ECG signal is securely transferred via a secure and simple communication scheme.

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.

In this article, a nonlinear active control technique is proposed so as to attain the synchronization of two different chaotic systems. Master and slave configuration is incorporated for the analysis. The main objective is to design Reduced Order Synchronization (ROS) scheme, where the order of the master system is greater than that of the slave system. Initially, active control technique based ROS is achieved and after that the results are extended to address reduced order synchronization in the presence of time delays in the systems. Based on Routh-Hurwitz criterion and Lyapunov stability theorem, the convergent behaviour of the error dynamics is proved. The theoretical results are validated by the detailed simulation results for Lorenz-Stenflo and Lü system.

The main contribution of this paper is to propose a nonlinear robust controller to synchronize general chaotic systems, such that the controller does not need the information of the chaotic system’s model. Following this purpose, in this paper, two methods are proposed to synchronize general forms of chaotic systems with application in secure communication. The first method uses radial basis function neural network (RBFNN) as a controller. All the parameters of the RBFNN are derived and optimized via particle swarm optimization (PSO) algorithm and genetic algorithm (GA). In order to increase the robustness of the controller, in the second method, an integral term is added to the RBF neural network gives an integral RBFNN (IRBFNN). The coefficients of the integral term and the parameters of IRBFNN are also derived and optimized via PSO and GA. The proposed methods are applied to the famous Lorenz chaotic system for secure communication. The performance and control effort of the proposed methods are compared with the recently proposed PID controller optimized via GA. Simulation results show the superiority of the proposed methods in comparison to the recent one in improving synchronization while using smaller control effort.

In this study, the modelling and simulation of chaotic Rossler system has been carried out by using an intelligent system based on neuro-fuzzy modelling technique. Furthermore, the MATLAB simulation of chaotic Rossler system has been carried out for comparison with proposed technique. Structure of the Adaptive Neuro-Fuzzy Inference System (ANFIS) is improved and trained in MATLAB toolbox. A hybrid learning algorithm consists of back-propagation and least-squares estimation is used for training the ANFIS network. Numerical simulations are used in this study. We have used four various data sets for testing the simulation speed of ANFIS and MATLAB. Obtained Results show that the proposed modelling technique has much higher speed and accuracy in comparison with MATLAB simulation. The neuro-fuzzy modelling technique can be simply used in software tools for designing and simulation of the chaotic Rossler system and the other chaotic systems.