Implementation of chaotic secure communication systems based on OPA circuits

In this paper, we proposed a novel three-order autonomous circuit to construct a chaotic circuit with double scroll characteristic. The design idea is to use RLC elements and a nonlinear resistor. The one of salient features of the chaotic circuit is that the circuit with two flexible breakpoints of nonlinear element, and the advantage of the flexible breakpoint is that it increased complexity of the dynamical performance. Here, if we take a large and suitable breakpoint value, then the chaotic state can masking a large input signal in the circuit. Furthermore, we proposed a secure communication hyperchaotic system based on the proposed chaotic circuits, where the chaotic communication system is constituted by a chaotic transmitter and a chaotic receiver. To achieve the synchronization between the transmitter and the receiver, we are using a suitable Lyapunov function and Lyapunov theorem to design the feedback control gain. Thus, the transmitting message masked by chaotic state in the transmitter can be guaranteed to perfectly recover in the receiver. To achieve the systems performance, some basic components containing OPA, resistor and capacitor elements are used to implement the proposed communication scheme. From the viewpoints of circuit implementation, this proposed chaotic circuit is superior to the Chua chaotic circuits. Finally, the test results containing simulation and the circuit measurement are shown to demonstrate that the proposed method is correct and feasible.     

Adaptive synchronization of chaotic systems and its application to secure communications

This paper addresses the adaptive synchronization problem of the drive–driven type chaotic systems via a scalar transmitted signal. Given certain structural conditions of chaotic systems, an adaptive observer-based driven system is constructed to synchronize the drive system whose dynamics are subjected to the system’s disturbances and/or some unknown parameters. By appropriately selecting the observer gains, the synchronization and stability of the overall systems can be guaranteed by the Lyapunov approach. Two well-known chaotic systems: Rössler-like and Chua’s circuit are considered as illustrative examples to demonstrate the effectiveness of the proposed scheme. Moreover, as an application, the proposed scheme is then applied to a secure communication system whose process consists of two phases: the adaptation phase in which the chaotic transmitter’s disturbances are estimated; and the communication phase in which the information signal is transmitted and then recovered on the basis of the estimated parameters. Simulation results verify the proposed scheme’s success in the communication application.     

An improved chaos-based secure communication technique using a novel encryption function with an embedded cipher key

In this paper, a secure communication technique, using a chaotic system with a single adjustable parameter and a single observable time series, is proposed. The chosen chaotic system, which is a variant of the famous Rikitake model, has a special structure for which the adjustable parameter appears in the dynamic equation of the observable time series. This particular structure is used to build a synchronization-based state observer that is decoupled from the adaptive parameter identifier. A local Lyapunov function is used to design the parameter identifier, with an adjustable convergence rate that guarantees the stability of the overall system. A two-channel transmission method is used to exemplify the suggested technique where the secret message is encoded using a nonlinear function of both the chaotic states and the adjustable parameter of the chaotic system that acts as a secret key. Simulations show that, at the receiver, the signal can be efficiently retrieved only if the secret key is known, even when both the receiver and the transmitter are in perfect synchronization. The proposed technique is demonstrated to have improved security and privacy against intruders, when compared to other techniques reported in the literature, while being simple to implement using both analog and digital hardware. In addition, the chosen chaotic system is shown to be flexible in accommodating the transmission of signals with variable bandwidths, which promotes the superiority and versatility of the suggested secure communication technique.     

Global chaos synchronization of new chaotic systems via nonlinear control

Nonlinear control is an effective method for making two identical chaotic systems or two different chaotic systems be synchronized. However, this method assumes that the Lyapunov function of error dynamic (e) of synchronization is always formed as V (e) = 1/2e^Te. In this paper, modification based on Lyapunov stability theory to design a controller is proposed in order to overcome this limitation. The method has been applied successfully to make two identical new systems and two different chaotic systems (new system and Lorenz system) globally asymptotically synchronized. Since the Lyapunov exponents are not required for the calculation, this method is effective and convenient to synchronize two identical systems and two different chaotic systems. Numerical simulations are also given to validate the proposed synchronization approach.     

An adaptive feedback control for chaos synchronization of nonlinear systems with different order

This paper deals with the chaotic synchronization of fourth-order system and second driven oscillators. Such a problem is related to the synchronization of strictly different chaotic systems. We show that the dynamical evolution of second-order driven oscillators can be synchronized with the projection on canonical planes of a fourth-order chaotic system. In this sense, it is said that the synchronization is achieved in reduced-order. Based on the Lyapunov approach, the adaptation law is determined to tune the controller gain vector in order to track a predetermined linearizing feedback control. An application to secure chaotic communication is also discussed. Numerical simulations are presented to demonstrate the efficiency of the proposed synchronization and secure communication schemes.     

一个新混沌系统及错位投影同步通讯方案

提出了一个新的混沌系统,该系统含有五个参数,每个状态方程均含有非线性乘积项.通过理论推导,数值仿真,Lyapunov指数、Lyapunov维数、分岔图研究其基本的动力学特性,并分析了改变参数时系统的动力学行为的变化.本文研究了该系统的错位投影同步,设计了非线性控制器,实现了两个初值不同的新系统的错位投影同步.另外,将该系统及错位投影同步方法应用到保密通信中,基于改进的混沌掩盖通讯原理,在发送端使用新系统信号对信息信号进行加密及传送,最后在同步后的接收端不失真地恢复出有用信号.数值仿真表明所设计的新的混沌系统具有复杂的动力学特性,适用于保密通讯.     

Adaptive fuzzy observer based synchronization design and secure communications of chaotic systems

This paper proposes a synchronization design scheme based on an alternative indirect adaptive fuzzy observer and its application to secure communication of chaotic systems. It is assumed that their states are unmeasurable and their parameters are unknown. Chaotic systems and the structure of the fuzzy observer are represented by the Takagi–Sugeno fuzzy model. Using Lyapunov stability theory, an adaptive law is derived to estimate the unknown parameters and the stability of the proposed system is guaranteed. Through this process, the asymptotic synchronization of chaotic systems is achieved. The proposed observer is applied to secure communications of chaotic systems and some numerical simulation results show the validity of theoretical derivations and the performance of the proposed observer.     

Counteracting the dynamical degradation of digital chaos via hybrid control

Chaotic systems would degrade owing to finite computing precisions, and such degradation often seriously affects the performance of digital chaos-based applications. In this paper, a chaotification method is proposed to solve the dynamical degradation of digital chaotic systems based on a hybrid structure, where a continuous chaotic system is applied to control the digital chaotic system, and a unidirectional coupling controller that combines a linear external state control with a modular function is designed. Moreover, we proof rigorously that a class of digital chaotic systems can be driven to be chaotic in the sense that the system is sensitive to initial conditions. Different from the existing remedies, this method can recover the dynamical properties of system, and even make some properties better than those of the original chaotic system. Thus, this new approach can be applied to the fields of chaotic cryptography and secure communication.     

Observer-based synchronization of uncertain chaotic system and its application to secure communications

Within the drive-response configuration, this paper considers the synchronization of uncertain chaotic systems based on observers and chaos-based secure communication. Even if there are unknown disturbances and parameters in the drive system, a robust adaptive observer can be used as response system to realize chaotic synchronization. The proposed method is then applied to secure communication. The transmitter is constructed by injecting the information into the drive system with proper manner and one of the transmitting signal is the sum of one of the output and the information signal. The Lur’e chaotic system is considered as an illustrative example to demonstrate the effectiveness of the proposed approaches.     

A fast and efficient chaos-based keyed hash function

This paper proposes a new chaotic keyed hash function based on a single 4-dimensional chaotic cat map whose irregular outputs are used to compute a hash value. The suggested scheme is fast, efficient and flexible. It takes an input message of arbitrary length and returns a hash value of a fixed length n, where n is a multiple of 32 (by convention, n is usually one of the numbers 128, 160, 256, 512, and 1024). Simulation results are presented to demonstrate the suggested hashing scheme’s high sensitivity to the original message and the secret key, as well as its strong capability for confusion and diffusion, and very strong collision resistance. In comparison with existing work, especially those based on chaotic maps, the proposed scheme exhibits superior performance.     

Fast synchronization of non-identical chaotic modulation-based secure systems using a modified sliding mode controller

In this paper, a secure communication scheme based on chaotic modulation is proposed using a reversible process and a robust controller with efficient cost and complexity to synchronize two different chaotic systems. In the controller design, a sliding mode control with an adaptive rule is used for non-linear inputs. The adaptive rule is applied to ensure the synchronization when uncertainties, non-modeled dynamics or external distortions are at work. The message signal is recovered at the receiver using a recursive process at the end. The effectiveness of the proposed algorithm is confirmed via the simulation results for the synchronization of the transmitted signal modulated by Chen chaotic system at the transmitter and Genesio chaotic system at the receiver, and those for the information recovery process.     

Exponential synchronization of discontinuous chaotic systems via delayed impulsive control and its application to secure communication

This paper investigates drive-response synchronization of chaotic systems with discontinuous right-hand side. Firstly, a general model is proposed to describe most of known discontinuous chaotic system with or without time-varying delay. An uniform impulsive controller with multiple unknown time-varying delays is designed such that the response system can be globally exponentially synchronized with the drive system. By utilizing a new lemma on impulsive differential inequality and the Lyapunov functional method, several synchronization criteria are obtained through rigorous mathematical proofs. Results of this paper are universal and can be applied to continuous chaotic systems. Moreover, numerical examples including discontinuous chaotic Chen system, memristor-based Chua’s circuit, and neural networks with discontinuous activations are given to verify the effectiveness of the theoretical results. Application of the obtained results to secure communication is also demonstrated in this paper.     

Synchronization and secure communication of chaotic systems via robust adaptive high-gain fuzzy observer

This paper proposes an alternative robust adaptive high-gain fuzzy observer design scheme and its application to synchronization and secure communication of chaotic systems. It is assumed that their states are immeasurable and their parameters are unknown. The structure of the proposed observer is represented by Takagi–Sugeno fuzzy model and has the integrator of the estimation error. It improves the performance of high-gain observer and makes the proposed observer robust against noisy measurements, uncertainties and parameter perturbations as well. Using Lyapunov stability theory, an adaptive law is derived to estimate the unknown parameters and the stability of the proposed observer is analyzed. Some simulation result of synchronization and secure communication of chaotic systems is given to present the validity of theoretical derivations and the performance of the proposed observer as an application.     

An application of Chen system for secure chaotic communication based on extended Kalman filter and multi-shift cipher algorithm

In recent years chaotic secure communication and chaos synchronization have received ever increasing attention. In this paper a chaotic communication method using extended Kalman filter is presented. The chaotic synchronization is implemented by EKF design in the presence of channel additive noise and processing noise. Encoding chaotic communication is used to achieve a satisfactory, typical secure communication scheme. In the proposed system, a multi-shift cipher algorithm is also used to enhance the security and the key cipher is chosen as one of the chaos states. The key estimate is employed to recover the primary data. To illustrate the effectiveness of the proposed scheme, a numerical example based on Chen dynamical system is presented and the results are compared to two other chaotic systems.     

A chaotic secure communication scheme using fractional chaotic systems based on an extended fractional Kalman filter

In recent years chaotic secure communication and chaos synchronization have received ever increasing attention. In this paper, for the first time, a fractional chaotic communication method using an extended fractional Kalman filter is presented. The chaotic synchronization is implemented by the EFKF design in the presence of channel additive noise and processing noise. Encoding chaotic communication achieves a satisfactory, typical secure communication scheme. In the proposed system, security is enhanced based on spreading the signal in frequency and encrypting it in time domain. In this paper, the main advantages of using fractional order systems, increasing nonlinearity and spreading the power spectrum are highlighted. To illustrate the effectiveness of the proposed scheme, a numerical example based on the fractional Lorenz dynamical system is presented and the results are compared to the integer Lorenz system.     

Chaotic secure communication based on particle filtering

Applying the particle filtering technique, this paper considers the problem of chaotic secure communication. Even if there exist system noise and measurement noise in chaotic maps, the modulated messages can be estimated by a modified particle filter algorithm, i.e. a particle filter with message estimation. Furthermore, the driving signal can be arbitrarily nonlinear, which improves the security level for communication. Simulation results of Holmes map verify our main result.     

Chaotic secure communication based on particle filtering

Applying the particle filtering technique, this paper considers the problem of chaotic secure communication. Even if there exist system noise and measurement noise in chaotic maps, the modulated messages can be estimated by a modified particle filter algorithm, i.e. a particle filter with message estimation. Furthermore, the driving signal can be arbitrarily nonlinear, which improves the security level for communication. Simulation results of Holmes map verify our main result.     

Effect of bounded noise on the chaotic motion of a Duffing Van der pol oscillator in a ϕ6 potential

This paper investigates the chaotic behavior of an extended Duffing Van der pol oscillator in a ϕ⁶ potential under additive harmonic and bounded noise excitations for a specific parameter choice. From Melnikov theorem, we obtain the conditions for the existence of homoclinic or heteroclinic bifurcation in the case of the ϕ⁶ potential is bounded, which are complemented by the numerical simulations from which we illustrate the bifurcation surfaces and the fractality of the basins of attraction. The results show that the threshold amplitude of bounded noise for onset of chaos will move upwards as the noise intensity increases, which is further validated by the top Lyapunov exponents of the original system. Thus the larger the noise intensity results in the less possible chaotic domain in parameter space. The effect of bounded noise on Poincare maps is also investigated.     

Modified generalized projective synchronization of a new fractional-order hyperchaotic system and its application to secure communication

This paper presents a new fractional-order hyperchaotic system. The chaotic behaviors of this system in phase portraits are analyzed by the fractional calculus theory and computer simulations. Numerical results have revealed that hyperchaos does exist in the new fractional-order four-dimensional system with order less than 4 and the lowest order to have hyperchaos in this system is 3.664. The existence of two positive Lyapunov exponents further verifies our results. Furthermore, a novel modified generalized projective synchronization (MGPS) for the fractional-order chaotic systems is proposed based on the stability theory of the fractional-order system, where the states of the drive and response systems are asymptotically synchronized up to a desired scaling matrix. The unpredictability of the scaling factors in projective synchronization can additionally enhance the security of communication. Thus MGPS of the new fractional-order hyperchaotic system is applied to secure communication. Computer simulations are done to verify the proposed methods and the numerical results show that the obtained theoretic results are feasible and efficient.     

A chaos secure communication scheme based on multiplication modulation

A secure spread spectrum communication scheme using multiplication modulation is proposed. The proposed system multiplies the message by chaotic signal. The scheme does not need to know the initial condition of the chaotic signals and the receiver is based on an extended Kalman filter (EKF). This signal encryption scheme lends itself to cheap implementation and can therefore be used effectively for ensuring security and privacy in commercial consumer electronics products. To illustrate the effectiveness of the proposed scheme, a numerical example based on Genesio-Tesi system and also Chen dynamical system is presented and the results are compared.