A joint encryption and error correction scheme based on chaos and LDPC

Although some cryptosystems based on error correction code have been presented, the security and efficiency must be overcome before it can be realized. In this paper, a novel method of combined encryption and error correction based on hyperchaotic system and lower-density parity check (LDPC) code is proposed to provide both of the security and efficiency. The proposed system adopts a pseudorandom sequence generator based on hyperchaotic system for scrambling the plaintext and constructing the dynamic permutation box. The message is encoded by the LDPC encoder after it was scrambled and then encrypted by the permutation box. Different permutation patterns generated for different message blocks help to provide high security, while the encoder helps to provide capacity of error correction. MATLAB simulations reveal that the proposed scheme is more secure and effective than the existing joint encryption and error correction coding scheme. Moreover, the full error correction ability of LDPC is kept without confliction. So, the proposed scheme is suitable for secure communication system.     

A novel secure image transmission scheme based on synchronization of fractional-order discrete-time hyperchaotic systems

In this paper, a secure image transmission scheme based on synchronization of fractional-order discrete-time hyperchaotic systems is proposed. In this scheme, a fractional-order modified-Hénon map is considered as a transmitter, the system parameters and fractional orders are considered as secret keys. As a receiver, a step-by-step delayed observer is used, and based on this one, an exact synchronization is established. To make the transmission scheme secure, an encryption function is used to cipher the original information using a key stream obtained from the chaotic map sequences. Moreover, to further enhance the scheme security, the ciphered information is inserted by inclusion method in the chaotic map dynamics. The first contribution of this paper is to propose new results on the observability and the observability matching condition of nonlinear discrete-time fractional-order systems. To the best of our knowledge, these features have not been addressed in the literature. In the second contribution, the design of delayed discrete observer, based on fractional-order discrete-time hyperchaotic system, is proposed. The feasibility of this realization is demonstrated. Finally, different analysis are introduced to test the proposed scheme security. Simulation results are presented to highlight the performances of our method. These results show that, our scheme can resist different kinds of attacks and it exhibits good performance.     

A single adaptive controller with one variable for synchronizing two identical time delay hyperchaotic Lorenz systems with mismatched parameters

Time delays are ubiquitous in real world and are often sources of complex behaviors of dynamical systems. This paper addresses the problem of parameter identification and synchronization of uncertain hyperchaotic time-delayed systems. Based on the Lyapunov stability theory and the adaptive control theory, a single adaptive controller with one variable for synchronizing two identical time-delay hyperchaotic Lorenz systems with mismatch parameters is proposed. The parameter update laws and sufficient conditions of the scheme are obtained for both linear feedback and adaptive control approaches. Numerical simulations are also given to show the effectiveness of the proposed method.     

Remote sensing image compression and encryption based on block compressive sensing and 2D-LCCCM

Nonlinear Dynamics - This paper proposes a remote sensing image compression and encryption algorithm based on block compressive sensing and multiple S-boxes that utilize a novel hyperchaotic...     

Spatiotemporal combination synchronization of different nonlinear objects

This paper proposes a novel secure communication scheme based on the Karhunen–Loéve decomposition and the synchronization of a master and a slave hyperchaotic Lü systems. First, the Karhunen–Loéve decomposition is used as a data reduction tool to generate data coefficients and eigenfunctions that capture the essence of grayscale and color images in an optimal manner. It is noted that the original images can be reproduced using only the most energetic eigenfunctions; this results in computational savings. The data coefficients are encrypted and transmitted using a master hyperchaotic Lü system. These coefficients are then recovered at the receiver end using a sliding mode controller to synchronize two hyperchaotic Lü systems. Simulation results are presented to illustrate the ability of the proposed control law to synchronize the master and slave hyperchaotic Lü systems. Moreover, the original images are recovered by using the decrypted data coefficients in conjunction with the eigenfunctions of the image. Computer simulation results are provided to show the excellent performance of the proposed scheme.     

Phase and antiphase synchronization of two identical hyperchaotic complex nonlinear systems

A scheme is designed to achieve phase synchronization (PS) and antiphase synchronization (APS) for an n-dimensional hyperchaotic complex nonlinear system. For this scheme, we have used the idea of an active control technique based on Lyapunov stability analysis to determine analytically the complex control functions which are needed to achieve PS and APS. We applied this scheme, as an example, to study PS and APS of hyperchaotic attractors of two identical hyperchaotic complex Lorenz systems. These complex systems appear in many important fields of physics and engineering. Our scheme can also be applied to two different hyperchaotic complex systems, for which PS and APS have not been investigated, as far as we know, in the literature. Numerical results are plotted to show phases and amplitudes of these hyperchaotic attractors, thus demonstrating that PS and APS are achieved. The bifurcation diagrams are computed for a wide range of parameters of the system parameters and are found to be symmetrical about the horizontal axis for APS, while they lack any symmetry for PS.     

A time-varying hyperchaotic system and its realization in circuit

A hyperchaotic system is often used to generate secure keys or carrier wave for secure communication and the realistic hyperchaotic circuit often is made of capacitor, nonlinear resistor unit and induction coil. Parameters are often fixed in these hyperchaotic circuits and the hyperchaotic property of the system can be estimated by using a scheme of synchronization and time series analysis. In this paper, a time-varying hyperchaotic system is proposed by introducing changeable electric power source into the circuit; the changeable electric power source is combined with induction coil or capacitor in series to generate changeable output signals to excite the system. The diagrams of improved circuit are illustrated and critical parameters in experimental circuits are presented; the Lyapunov exponent spectrum vs. external applied electric power source is calculated. It is confirmed that the improved circuit always holds two positive Lyapunov exponents when the external electric power source works, and the chaotic attractors are much too different from the original one; thus, a more changeable hyperchaotic system is constructed in experiment.     

An image encryption scheme based on chaotic tent map

Image encryption has been an attractive research field in recent years. The chaos-based cryptographic algorithms have suggested some new and efficient ways to develop secure image encryption techniques. This paper proposes a novel image encryption scheme, which is based on the chaotic tent map. Image encryption systems based on such map show some better performances. Firstly, the chaotic tent map is modified to generate chaotic key stream that is more suitable for image encryption. Secondly, the chaos-based key stream is generated by a 1-D chaotic tent map, which has a better performance in terms of randomness properties and security level. The performance and security analysis of the proposed image encryption scheme is performed using well-known ways. The results of the fail-safe analysis are inspiring, and it can be concluded that the proposed scheme is efficient and secure.     

Modified function lag projective synchronization of a financial hyperchaotic system

This paper presents a new type synchronization called modified function lag projective synchronization (MFLPS), where the drive and response systems could be synchronized up to a desired scale function matrix with time-delay. With MFLPS it achieves self-synchronization of a financial hyperchaotic system when the parameters are known and unknown, respectively. The corresponding numerical simulations are performed to verify and illustrate the analytical results.     

Robust adaptive full state hybrid synchronization of chaotic complex systems with unknown parameters and external disturbances

This paper studies the robust adaptive full state hybrid projective synchronization (FSHPS) scheme for a class of chaotic complex systems with uncertain parameters and external disturbances. By introducing a compensator and using nonlinear control and adaptive control, the robust adaptive FSHPS scheme is derived, which can eliminate the influence of uncertainties effectively and achieve adaptive FSHPS of the chaotic (hyperchaotic) complex systems asymptotically with a small error bound. The adaptive laws of the unknown parameters are given, and the sufficient conditions of realizing FSHPS are derived as well. Moreover, we also discuss the case that parameters of chaotic complex system are complex. Finally, the complex Chen system and Lü system, and the hyperchaotic complex Lorenz system are taken as two examples and the numerical simulations are provided to verify the effectiveness and robustness of the proposed control scheme.     

Generalized projective synchronization of the fractional-order Chen hyperchaotic system

In this paper, we numerically investigate the hyperchaotic behaviors in the fractional-order Chen hyperchaotic systems. By utilizing the fractional calculus techniques, we find that hyperchaos exists in the fractional-order Chen hyperchaotic system with the order less than 4. We found that the lowest order for hyperchaos to have in this system is 3.72. Our results are validated by the existence of two positive Lyapunov exponents. The generalized projective synchronization method is also presented for synchronizing the fractional-order Chen hyperchaotic systems. The present technique is based on the Laplace transform theory. This simple and theoretically rigorous synchronization approach enables synchronization of fractional-order hyperchaotic systems to be achieved and does not require the computation of the conditional Lyapunov exponents. Numerical simulations are performed to verify the effectiveness of the proposed synchronization scheme.     

Design and application of an S-box using complete Latin square

Since a substitution box (S-box) is the nonlinearity part of a symmetric key encryption scheme, it directly determines the performance and security level of the encryption scheme. Thus, generating S-box with high performance and efficiency is attracting. This paper proposes a novel method to construct S-box using the complete Latin square and chaotic system. First, a complete Latin square is generated using the chaotic sequences produced by a chaotic system. Then an S-box is constructed using the complete Latin square. Performance analyses show that the S-box generated by our proposed method has a high performance and can achieve strong ability to resist many security attacks such as the linear attack, differential attack and so on. To show the efficiency of the constructed S-box, this paper further applies the S-box to image encryption application. Security analyses show that the developed image encryption algorithm is able to encrypt different kinds of images into cipher images with uniformly distributed histograms. Performance evaluations demonstrate that it has a high security level and can outperform several state-of-the-art encryption algorithms.

     

A novel fractional-order hyperchaotic system stabilization via fractional sliding-mode control

In this paper we numerically investigate the fractional-order sliding-mode control for a novel fractional-order hyperchaotic system. Firstly, the dynamic analysis approaches of the hyperchaotic system involving phase portraits, Lyapunov exponents, bifurcation diagram, Lyapunov dimension, and Poincaré maps are investigated. Then the fractional-order generalizations of the chaotic and hyperchaotic systems are studied briefly. The minimum orders we found for chaos and hyperchaos to exist in such systems are 2.89 and 3.66, respectively. Finally, the fractional-order sliding-mode controller is designed to control the fractional-order hyperchaotic system. Numerical experimental examples are shown to verify the theoretical results.     

The alternating between complete synchronization and hybrid synchronization of hyperchaotic Lorenz system with time delay

The various cases of synchronization in two identical hyperchaotic Lorenz systems with time delay are studied. Based on Lyapunov stability theory, the sufficient conditions for achieving synchronization of two identical hyperchaotic Lorenz systems with time delay are derived, and a simple scheme only with a single linear controller is proposed. When the parameters in the response system are known, the alternating between complete synchronization and hybrid synchronization (namely, coexistence of antiphase and complete synchronization) is observed with the control feedback gain varying. Furthermore, when the parameters in the response system are unknown, for the same feedback controller, the complete synchronization and the hybrid synchronization can be obtained, respectively, as the associated parameters updated laws of the unknown parameters are chosen. Numerical simulation results are presented to demonstrate the proposed chaos synchronization scheme.     

Projectively lag synchronization and uncertain parameters identification of a new hyperchaotic system

This paper investigates projectively lag synchronization of a new hyperchaotic system (proposed by Yang et al. in Nonlinear Anal., Real World Appl., 10:1601, 2009), with certain/uncertain parameters. Based on the Lyapunov function constructing method and application of the Babarǎt lemma, projectively lag synchronization is achieved for the new hyperchaotic system by designing nonlinear controllers. Furthermore, a novel method is proposed to identify unknown parameters based on projectively lag synchronization of the new hyperchaotic system. Finally, several numerical simulations are given to verify and test the correctness and effectiveness of the novel methods we proposed.     

Theoretical analysis and circuit implementation of a novel complicated hyperchaotic system

This article presents a new hyperchaotic system of four-dimensional quadratic autonomous ordinary differential equations, which has one equilibrium point and two quadratic nonlinearities. Some basic dynamical properties are further investigated by means of Poincaré mapping, parameter phase portraits, and calculated Lyapunov exponents and power spectra. The existence of the hyperchaotic system is verified not only by theoretical analysis but also by conducting a novel fourth-order electronic circuit experiment. Various attractors of experimental results show that this 4D hyperchaotic system is different from the historically proposed system and has good engineering application prospects.     

Synchronization between integer-order chaotic systems and a class of fractional-order chaotic system based on fuzzy sliding mode control

In this paper, we focus on the synchronization between integer-order chaotic systems and a class of fractional-order chaotic system using the stability theory of fractional-order systems. A new fuzzy sliding mode method is proposed to accomplish this end for different initial conditions and number of dimensions. Furthermore, three examples are presented to illustrate the effectiveness of the proposed scheme, which are the synchronization between a fractional-order Lü chaotic system and an integer-order Liu chaotic system, the synchronization between a fractional-order hyperchaotic system based on Chen??s system and an integer-order hyperchaotic system based upon the Lorenz system, and the synchronization between a fractional-order hyperchaotic system based on Chen??s system, and an integer-order Liu chaotic system. Finally, numerical results are presented and are in agreement with theoretical analysis.     

Finite-time chaos control and synchronization of fractional-order nonautonomous chaotic (hyperchaotic) systems using fractional nonsingular terminal sliding mode technique

In this paper, a novel fractional-order terminal sliding mode control approach is introduced to control/synchronize chaos of fractional-order nonautonomous chaotic/hyperchaotic systems in a given finite time. The effects of model uncertainties and external disturbances are fully taken into account. First, a novel fractional nonsingular terminal sliding surface is proposed and its finite-time convergence to zero is analytically proved. Then an appropriate robust fractional sliding mode control law is proposed to ensure the occurrence of the sliding motion in a given finite time. The fractional version of the Lyapunov stability is used to prove the finite-time existence of the sliding motion. The proposed control scheme is applied to control/synchronize chaos of autonomous/nonautonomous fractional-order chaotic/hyperchaotic systems in the presence of both model uncertainties and external disturbances. Two illustrative examples are presented to show the efficiency and applicability of the proposed finite-time control strategy. It is worth to notice that the proposed fractional nonsingular terminal sliding mode control approach can be applied to control a broad range of nonlinear autonomous/nonautonomous fractional-order dynamical systems in finite time.     

Lag synchronization of hyperchaotic complex nonlinear systems

In this paper, we study the lag synchronization (LS) of n-dimensional hyperchaotic complex nonlinear systems. The idea of the nonlinear control technique based on the complex Lyapunov function with lag in time is used to propose a scheme to investigate LS of hyperchaotic attractors of these systems. Both complex Lyapunov and control functions are introduced. For illustration, the scheme is applied to two hyperchaotic complex Lorenz systems. The real and complex control functions are derived analytically to achieve LS and to show that the complex error dynamical systems are globally stable. Numerical results are calculated to test the validity of the analytical expressions of control functions to achieve LS of two identical hyperchaotic attractors.     

A new 5D hyperchaotic system based on modified generalized Lorenz system

This paper reports a new five-dimensional (5D) hyperchaotic system with three positive Lyapunov exponents, which is generated by adding a linear controller to the second equation of a 4D system that is obtained by coupling of a 1D linear system and a 3D modified generalized Lorenz system. This hyperchaotic system has very simple algebraic structure but can exhibit complex dynamical behaviors. Of particular interest are the observations that the hyperchaotic system has a hyperchaotic attractor with three positive Lyapunov exponents under a unique equilibrium, three or infinite equilibria, and there are three types of coexisting attractors of this new 5D hyperchaotic system. Numerical analysis of phase trajectories, Lyapunov exponents, bifurcation, Poincaré projections and power spectrum verifies the existence of the hyperchaotic and chaotic attractors. Moreover, stability of hyperbolic or non-hyperbolic equilibria and two complete mathematical characterization for 5D Hopf bifurcation are rigorously studied. Finally, some electronic circuits are designed to implement the 5D hyperchaotic system.