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.     

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.     

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.     

Cryptanalyzing an improved security modulated chaotic encryption scheme using ciphertext absolute value

This paper describes the security weakness of a recently proposed improved chaotic encryption method based on the modulation of a signal generated by a chaotic system with an appropriately chosen scalar signal. The aim of the improvement is to avoid the breaking of chaotic encryption schemes by means of the return map attack introduced by Pérez and Cerdeira. A method of attack based on taking the absolute value of the ciphertext is presented, that allows for the cancellation of the modulation scalar signal and the determination of some system parameters that play the role of system key. The proposed improved method is shown to be compromised without any knowledge of the chaotic system parameter values and even without knowing the transmitter structure.     

Chaotic synchronization with filter based on wavelet transformation

A kind of chaotic synchronization method is presented in the paper. In the transmitter, part signals are transformed by wavelet and the detail information is removed. In the receiver, the component with low frequency is reconstructed and discrete feedback is used, we show that synchronization of two identical structure chaotic systems is attained. The effect of feedback on chaotic synchronization is discussed. Using the synchronous method, the transmitting signal is transported in compressible way, system resource is saved, the component with high frequency is filtered and the effect of disturbance on synchronization is reduced. The synchronization method is illustrated by numerical simulation experiment.     

On the fractional-order extended Kalman filter and its application to chaotic cryptography in noisy environment

In this paper via a novel method of discretized continuous-time Kalman filter, the problem of synchronization and cryptography in fractional-order systems has been investigated in presence of noisy environment for process and output signals. The fractional-order Kalman filter equation, applicable for linear systems, and its extension called the extended Kalman filter, which can be used for nonlinear systems, are derived. The result is utilized for chaos synchronization with the aim of cryptography while the transmitter system is fractional-order, and both the transmitter and transmission channel are noisy. The fractional-order stochastic chaotic Chen system is then presented to apply the proposed method for chaotic signal cryptography. The results show the effectiveness of the proposed method.     

Secure communication by chaotic synchronization: Robustness under noisy conditions

In this work we present a thorough investigation of the effect of noise (internal or external) on the synchronization of a drive-response configuration system (unidirectional coupling between two identical systems). Moreover, since in every practical implementation of a communication system, the transmitter and receiver circuits (although identical) operate under slightly different conditions it is essential to consider the case of the mismatch between the parameters of the transmitter and the receiver. In our work we consider the non-autonomous second order non-linear oscillator system presented by G. Mycolaitis et al. in Proceedings of Seventh International Workshop on Nonlinear Dynamics of Electronic Systems [Globally synchronizable non-autonomous chaotic oscillator, Denmark, July 1999, pp. 277–280], which is particularly suitable for digital communications. Binary information is encoded by combining square pulses of two different frequencies selected so that the system is always in the chaotic regime independent of the encoded message.     

Nonlinear electronic circuit, Part II: synchronization in a chaotic MODEM scheme

In this work we present a thorough investigation of the effect of noise (internal or external) on the synchronization of a drive-response configuration system (unidirectional coupling between two identical systems). Moreover, since in every practical implementation of a communication system, the transmitter and receiver circuits (although identical) operate under slightly different conditions it is essential to consider the case of the mismatch between the parameters of the transmitter and the receiver. In our work we consider the non-autonomous 2nd order nonlinear oscillator system presented in [G. Mycolaitis, A. Tamasevicious, A. Cenys, A. Namajunas, K. Navionis, A. N. Anagnostopoulos, Globally synchronizable non-autonomous chaotic oscillator, in: Proc. of 7th International Workshop on Nonlinear Dynamics of Electronic Systems, Denmark, July 1999, pp. 277-280] which is particularly suitable for digital communications.Furthermore, we modified the previous chaotic communication system in order to exhibit enhanced security features. The enhancement in the security of the system is achieved by introducing a set of parameters used in the encoding and decoding of the message signal. We also introduce a time delay parameter in the dynamical system which on the one hand improves the chaotic behavior of the system and on the other hand, adds further security in the encoding-decoding scheme.     

Singular observer approach for chaotic synchronization and private communication

Based on the singular system observer, this paper proposes an effective approach for chaotic synchronization and private communication. When the useful information is modulated in a chaotic system and its dynamic equation is not available, we can consider the transmitted signal as an external system state. Then we can design a singular observer which has higher dimension. The advantage of such a design is that we can avoid using the derivation information of the transmitted signal. By adopting the singular system observer approach, the transmitted signal can be recovered successfully by the observer. Numerical simulations show the effectiveness of the proposed method.     

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.     

Nonlinear electronic circuit,Part II: synchronization in a chaotic MODEM scheme

In this work we present a thorough investigation of the effect of noise (internal or external) on the synchronization of a drive–response configuration system (unidirectional coupling between two identical systems). Moreover, since in every practical implementation of a communication system, the transmitter and receiver circuits (although identical) operate under slightly different conditions it is essential to consider the case of the mismatch between the parameters of the transmitter and the receiver. In our work we consider the non-autonomous 2nd order nonlinear oscillator system presented in [G. Mycolaitis, A. Tamasevicious, A. Cenys, A. Namajunas, K. Navionis, A. N. Anagnostopoulos, Globally synchronizable non-autonomous chaotic oscillator, in: Proc. of 7th International Workshop on Nonlinear Dynamics of Electronic Systems, Denmark, July 1999, pp. 277–280] which is particularly suitable for digital communications.Furthermore, we modified the previous chaotic communication system in order to exhibit enhanced security features. The enhancement in the security of the system is achieved by introducing a set of parameters used in the encoding and decoding of the message signal. We also introduce a time delay parameter in the dynamical system which on the one hand improves the chaotic behavior of the system and on the other hand, adds further security in the encoding–decoding scheme.     

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.     

Secure communication via multiple parameter modulation in a delayed chaotic system

The problem of secure communication via parameter modulation in a chaotic system is considered. Information signals are used to modulate various parameters of a chaotic system. The resulting chaotic signal is later demodulated and the information signals are recovered using an adaptive demodulator. The convergence of the demodulator is established and simulation results validate the theoretical predictions.     

Secure communication via parameter modulation in a class of chaotic systems

The problem of secure communication via parameter modulation in a class of chaotic systems is studied. Information signal is used to modulate one parameter of a chaotic system. The resulting chaotic signal is later demodulated and the information signal is recovered using an adaptive demodulator. The convergence of the demodulator is established. We show that the proposed scheme is robust with respect to noise and parameter mismatch. Computer simulation on the Chua circuit is given to validate the theoretical prediction.     

A new secured transmission scheme based on chaotic synchronization via smooth adaptive unknown-input observers

We present a new scheme for the secured transmission of information based on master–slave synchronization of chaotic systems, using unknown-input observers. Our approach improves upon state-of-the-art schemes by being compatible with information of relatively large amplitude while improving security against intruders through an intricate encryption system. In addition, our approach is robust to channel noise. The main idea is to separate the encryption and synchronization operations by using two cascaded chaotic systems in the transmitter. Technically, the scheme is based on smooth adaptive unknown-input observers; these have the advantage to estimate the (master) states and to reconstruct the unknown inputs simultaneously. The performance of the communication system is illustrated in numerical simulation.     

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.     

A chaotic system in synchronization and secure communications

In this paper we deal with the synchronization and parameter estimations of an uncertain Rikitake system and its application in secure communications employing chaotic parameter modulation. The strategy consists of proposing a receiver system which tends to follow asymptotically the unknown Rikitake system, refereed as transmitter system. The gains of the receiver system are adjusted continually according to a convenient high order sliding-mode adaptative controller (HOSMAC), until the measurable output errors converge to zero. By using HOSMAC, synchronization between transmitter and receiver is achieved and message signals are recovered. The convergence analysis is carried out by using Barbalat’s Lemma.     

Secure digital communication using controlled projective synchronisation of chaos

A new approach to chaos communication is proposed to encrypt digital information using controlled projective synchronisation. The scheme encrypts a binary sequence by manipulating the scaling feature of synchronisation from the coupled system. The transmitted signal therefore embeds only a single set of statistical properties. This prevents cryptanalysts from breaking the chaotic encryption scheme by using characteristic cryptanalysis that aims to detect switching of statistical properties in the intercepted information carrier signal. Pseudo-random switching key is incorporated into the scheme to masked out the deterministic nature of the underlying coupled system.     

Hyperchaotic secure communication via generalized function projective synchronization

This paper presents two different hyperchaotic secure communication schemes by using generalized function projective synchronization (GFPS), where the drive and response systems could be synchronized up to a desired scaling function matrix. The unpredictability of the scaling functions can additionally enhance the security of communication. First, a hyperchaotic secure communication scheme applying GFPS of the uncertain Chen hyperchaotic system is proposed. The transmitted information signal is modulated into the parameter of the Chen hyperchaotic system in the transmitter and it is assumed that the parameter of the receiver system is unknown. Based on the Lyapunov stability theory and the adaptive control technique, the controllers are designed to make two identical Chen hyperchaotic systems with unknown parameter asymptotically synchronized; thus, the uncertain parameter of the receiver system is identified. The information signal can be recovered accurately by the estimated parameter. Secondly, another secure communication scheme by the coupled GFPS of the Chen hyperchaotic system is introduced. The information signal transmitted can be extracted exactly through simple operation in the receiver. The corresponding theoretical proofs and numerical simulations demonstrate the validity and feasibility of the proposed hyperchaotic secure communication schemes.     

Synchronization of chaotic solid-state Nd:YAG lasers: Application to secure communication

In this paper, the synchronization problem of coupled chaotic lasers in master–slave configuration is numerically studied. The approach used allows to give a simple design procedure for the slave laser. In particular, we consider a complex system composed by two chaotic Nd:YAG lasers coupled through the first state variable of the master laser. Synchronization of chaotic Nd:YAG lasers is achieved by injecting the chaotic signal from the master Nd:YAG laser into the slave Nd:YAG laser. The robustness of synchronization is discussed when a mismatch of parameters occurs, and the effects of the channel noise on recovered information are showed. A potential application of chaotic synchronization of Nd:YAG lasers to transmit encrypted digital information is also given.