Chaos-based Communication Scheme Research Articles

A novel four-wing chaotic system with multiple equilibriums: Dynamical analysis, multistability, circuit simulation and pseudo random number generator (PRNG) based on the voice encryption

Recently, there has been tremendous interest worldwide in the possibility of using chaos in communication systems. Many different chaos-based secure communication schemes have been proposed up until now. However, systems with strong chaoticity are more suitable for chaos-based secure communication. From the viewpoint of Lyapunov exponents, a chaotic system with a larger positive Lyapunov exponent is said to be more complex. This paper constructing a multistable chaotic system that can produce coexisting attractors is an attractive field of research due to its theoretical and practical usefulness. An innovative 3D dynamical system is presented in this research. It can display various coexisting attractors for the same values of parameters. The new system is more suitable for chaos-based applications than recently reported systems since it exhibits strong multistable chaotic behavior, as proved by its large positive Lyapunov exponent. Furthermore, the accuracy of the numerical calculation and the system's physical implementations are confirmed by analog circuit simulation. Finally, implementing the proposed voice encryption is done using a four-wing chaotic system based on the PRNG.

N-Dimensional Polynomial Chaotic System With Applications

Designing high-dimensional chaotic maps with expected dynamic properties is an attractive but challenging task. The dynamic properties of a chaotic system can be reflected by the Lyapunov exponents (LEs). Using the inherent relationship between the parameters of a chaotic map and its LEs, this paper proposes an <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula>-dimensional polynomial chaotic system (<inline-formula> <tex-math notation="LaTeX">$n\text{D}$ </tex-math></inline-formula>-PCS) that can generate <inline-formula> <tex-math notation="LaTeX">$n\text{D}$ </tex-math></inline-formula> chaotic maps with any desired LEs. The <inline-formula> <tex-math notation="LaTeX">$n\text{D}$ </tex-math></inline-formula>-PCS is constructed from <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> parametric polynomials with arbitrary orders, and its parameter matrix is configured using the preliminaries in linear algebra. Theoretical analysis proves that the <inline-formula> <tex-math notation="LaTeX">$n\text{D}$ </tex-math></inline-formula>-PCS can produce high-dimensional chaotic maps with any desired LEs. To show the effects of the <inline-formula> <tex-math notation="LaTeX">$n\text{D}$ </tex-math></inline-formula>-PCS, two high-dimensional chaotic maps with hyperchaotic behaviors were generated. A microcontroller-based hardware platform was developed to implement the two chaotic maps, and the test results demonstrated the randomness properties of their chaotic signals. Performance evaluations indicate that the high-dimensional chaotic maps generated from <inline-formula> <tex-math notation="LaTeX">$n\text{D}$ </tex-math></inline-formula>-PCS have the desired LEs and more complicated dynamic behaviors compared with other high-dimensional chaotic maps. In addition, to demonstrate the applications of <inline-formula> <tex-math notation="LaTeX">$n\text{D}$ </tex-math></inline-formula>-PCS, we developed a chaos-based secure communication scheme. Simulation results show that <inline-formula> <tex-math notation="LaTeX">$n\text{D}$ </tex-math></inline-formula>-PCS has a stronger ability to resist channel noise than other high-dimensional chaotic maps.

Performance of Improved-DCSK system over land mobile satellite channel under effect of time-reversed chaotic sequences

Among non-coherent chaos-based communication schemes, improved-differential chaos-shift keying (I-DCSK) with the use of time-reversed chaotic sequences shows good achievement in bit-error-rate (BER) performance and spectral efficiency. To date, BER performance of the I-DCSK system has been investigated over various transmission channels in the presence of Gaussian noise and Rayleigh fading. In this paper, we studied for the first time the performance of the I-DCSK system over a land mobile satellite channel. Discrete-time models of the transmitter and receiver over a two-state Lutz channel typically describing satellite environments are studied. We point out that there are differences in cross-correlation characteristics between the time-reversed and conventional chaotic sequences. From this aspect, BER performance of the studied system is analyzed in scenario of taking into account the cross-correlation effect of time-reversed chaotic sequences. BER expressions are verified by Monte Carlo simulations. Performance comparison between I-DCSK and DCSK-based schemes over the studied channel is carried out. Obtained results prove that the I-DCSK system is able to be used as a physical-layer modulation method using chaos for land mobile satellite applications.

Complex-enhanced chaotic signals with time-delay signature suppression based on vertical-cavity surface-emitting lasers subject to chaotic optical injection

A chaotic system is constructed on the basis of vertical-cavity surface-emitting lasers (VCSELs), where a slave VCSEL subject to chaotic optical injection (COI) from a master VCSEL with the external feedback. The complex degree (CD) and time-delay signature (TDS) of chaotic signals generated by this chaotic system are investigated numerically via permutation entropy (PE) and self-correlation function (SF) methods, respectively. The results show that, compared with master VCSEL subject to optical feedback, complex-enhanced chaotic signals with TDS suppression can be achieved for S-VCSEL subject to COI. Meanwhile, the influences of several controllable parameters on the evolution maps of CD of chaotic signals are carefully considered. It is shown that the CD of chaotic signals for S-VCSEL is always higher than that for M-VCSEL due to the CIO effect. The TDS of chaotic signals can be significantly suppressed by choosing the reasonable parameters in this system. Furthermore, TDS suppression and high CD chaos can be obtained simultaneously in the specific parameter ranges. The results confirm that this chaotic system may effectively improve the security of a chaos-based communication scheme.

Design and Analysis of an OFDM-based Differential Chaos Shift Keying Communication System

In this paper, a new non-coherent chaos-based communication scheme, named orthogonal frequency division multiplexing based different chaos shift keying (OFDM-DCSK), is presented inspired by multi-carrier direct sequence code- division multiple access (MC-DS-CDMA) system, multi-carrier DCSK (MC-DCSK) system, and channel estimation of OFDM system. In this scheme, all of the occupied subcarriers are grouped into several groups. In each group, one chaotic reference is transmitted over the central subcarrier, while multiple modulated data streams are transmitted over the remaining subcarriers. Therefore, this transmitter structure increases the spectral efficiency, compared with the conventional DCSK system. At the receiver side, no radio frequency delay circuits are needed to demodulate the received data, which makes the system easy to implement in practice. The bit error rate (BER) performance of the OFDM-DCSK system is derived based on Gaussian approximation under additive white Gaussian noise (AWGN) channel. Simulation results are given under AWGN and two-path Rayleigh flat fading channel, which confirm the effectiveness of this new design.

Hybrid chaos-based communication system consisting of three chaotic semiconductor ring lasers

We report on the realization of a hybrid chaos-based communication scheme using three chaotic semiconductor ring lasers (SRLs). In this scheme, two slave SRLs (S-SRLs) are identically driven by a master SRL (M-SRL) subject to delayed optical feedback. Under proper conditions, the S-SRLs are completely synchronized with each other due to the symmetric operation, and they are also synchronized with the M-SRL through the injection-locking effect. The results also show that a message encrypted through chaos shift keying at the M-SRL end can be successfully decrypted by the two S-SRLs, while the two uncoupled S-SRLs allow for dual-channel chaos communication when both counterpropagating modes of one S-SRL are encoded with a message.

Simultaneous unidirectional and bidirectional chaos-based optical communication using hybrid coupling semiconductor lasers

A simultaneous unidirectional and bidirectional chaos-based optical communication scheme based on a hybrid coupling semiconductor laser system that consists of one center semiconductor laser (CSL) and multiple side semiconductor lasers (SSLs) is proposed numerically. In this scheme, the SSLs oriented in a linear chain mutually couple with the adjacent SSLs and they are subjected to identical unidirectional injections from the CSL which is a chaotic external cavity semiconductor laser. We theoretically analyze the conditions for different types of chaos synchronization based on the symmetry operation mechanism and injection-locking mechanism, and numerically investigate the influences of operation parameters, parameter mismatch robustness, chaos pass filtering effects and communication performance of the hybrid coupling semiconductor laser system. The simulation results demonstrate that with proper selection of the unidirectional and mutual coupling conditions, the SSLs can synchronize with each other isochronally and simultaneously synchronize to the CSL completely or laggardly, which enables the proposed system to achieve a unidirectional broadcasting communication from the CSL to the SSLs and a bidirectional communication among the SSLs simultaneously. The proposed scheme is beneficial to the implementation of optical chaos communication networks.

High-Efficiency Differential-Chaos-Shift-Keying Scheme for Chaos-Based Noncoherent Communication

In this brief, a new noncoherent chaos-based communication scheme, named high-efficiency differential chaos shift keying (DCSK) (HE-DCSK), is proposed. By recycling each reference sample in DCSK, 2 bits of data can be carried in one data-modulated sample sequence, which offers our scheme double bandwidth efficiency and nonrepeated transmitted signal less prone to interception in comparison to DCSK. The bit-error performance of the proposed scheme is studied analytically based on Gaussian approximation for discrete-time implementations. Simulations in additive-white-Gaussian-noise channel are performed and compared with DCSK and correlation delay shift keying (CDSK) schemes. Results show that the bit-error rate performance of HE-DCSK can always outperform CDSK and be even better than DCSK with typical spreading factors and at reasonable E <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sub> /N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</sub> levels.

Chaotic optical cryptographic communication using a three-semiconductor-laser scheme

In this paper, a secure optical chaos-based communication scheme is proposed. A semiconductor laser (SL) subjected to polarization-rotated optical feedback serves as the drive laser (DL), and two identical or near-identical SLs act as the transmitter laser (TL) and receiver laser (RL). The TL and the RL receive identical polarization-rotated optical injection from the DL. Two channels are used, and the TM mode of the DL, after being rotated by 90°, serves as the perturbation quantity. The communication performance is numerically studied. More importantly, the high fidelity and high degree of privacy of the proposed scheme are verified in detail, and the failure of two potential attacker scenarios is demonstrated, even if the attacker can get access to both channels simultaneously.

Security of chaos-based secure communications in a large community

In this paper, we present an attack on a cryptosystem designed by using a spatiotemporal chaotic system. We show that the decryption system proposed in (Phys. Rev. E 66, 065202 (2002)) degenerates to the one-dimensional map under the constant input, and it is insensitive to the slight perturbations to input in specially selected intervals. Consequently, the attacker can use a very simple optimization algorithm to obtain the proper input value within only hundreds of iterations. Furthermore, we prove that there exits a linear dependency between the secret key and the obtained input value, so that the attacker can break this spatiotemporal chaos-based secure communication scheme easily. Both theoretical and experimental results show that the lack of security discourages the use of these cryptosystems for practical application.

Multiaccess Optical Chaos Communication Using Mutually Coupled Semiconductor Lasers Subjected to Identical External Injections

A chaos-based communication scheme allowing for multiaccess message transmission is proposed. In this scheme, two mutually coupled semiconductor lasers (MCSLs) are identically driven by an external cavity semiconductor laser (ECSL). The MCSLs isochronally synchronize with each other through symmetric operation, and they laggardly synchronize to the ECSL through injection-locking. When external modulation is adopted, strong chaos pass filtering effects that are not restricted by the relaxation oscillation frequencies of the MCSLs are observed, which enables us to achieve high bit-rate multiaccess chaos communication. Moreover, the security can be improved by making use of the multiaccess ability. This scheme can be used as a rudiment of chaos communication networks.

Chaotic communication on a satellite formation flying—The synchronization issue in a scenario with transmission delays

Chaos-based communication schemes have drawn increasing attention in the last years. The intrinsic complexity embedded on the chaotic dynamics with its hallmark property of sensitive dependence on initial conditions provides a masterful framework that can be exploited to develop remarkably fast, efficient and robust communication systems at low cost. As so, they can be used to support intensive communication among process distributed over a network, which is the scenario that may exist when the concept of satellite formation flying is used. In this configuration, the set of satellites operates as a “massive virtual” satellite with a very large capability that would require a huge, complex and expensive monolithic satellite. In this work, we analyze a key issue to accomplish a chaotic based communication system—the synchronization among the communication agents. To allow communication, all of the agents must have their chaotic dynamics synchronized with each other. However, in a scenario involving a satellite formation flying, it is necessary to deal with substantial signal delays on the communication among the satellites. These delays impose severe restrictions or even do not allow the accomplishment of the synchronization process if common strategies are used. Here, we propose an approach that allows to properly obtain synchronization among the communication agents on the satellites of the formation, despite the communication delays. It is based on the optimal linear feedback control theory and takes in consideration the “mean field” of the population of chaotic oscillators.

Information Encoding and Decoding Using Unidirectionally Coupled Chaotic Semiconductor Lasers Subject to Filtered Optical Feedback

We present a detailed numerical study of the dynamics of two unidirectionally coupled semiconductor lasers subject to filtered optical feedback. We show that this chaos-based communication scheme allows for an improvement in the decoding of encrypted messages in comparison with the conventional feedback scheme. We found that the performance of the system is optimal when the closed-loop configuration and similar filters are used in the emitter and receiver systems.

CRYPTANALYSIS OF CHAOTIC COMMUNICATION SCHEMES BY DYNAMICAL MINIMIZATION ALGORITHM

This paper addresses the cryptanalysis of three chaos-based secure communication schemes recently proposed by Yu et al. [2007]. Attacks with adaptive observers designed by the dynamical minimization algorithm are assumed. Considering Kerckhoff's principle, i.e. assuming that the basic structure of a cryptosystem is known but some user-specified parameters remain in secret, it is demonstrated that the covered messages in all these schemes can be estimated and hence their securities are challenged.

Simultaneous bidirectional message transmission in a chaos-based communication scheme

We introduce a chaos-based communication scheme allowing for bidirectional exchange of information. Coupling [corrected] two semiconductor lasers through a partially transparent optical mirror, placed in the pathway connecting the lasers [corrected] delay dynamics is induced in both lasers. We numerically demonstrate that this dynamics can be identically synchronized, and moreover, information introduced on both ends of the link can be simultaneously transmitted. This scheme allows one to negotiate a key through a public channel.

A modified chaos-based communication scheme using Hamiltonian forms and observer

In this work, a modified chaos-based communication scheme is presented. In particular, we use the modified scheme proposed by López-Mancilla and Cruz-Hernández (2005), that improves the basic scheme for chaotic masking using a single transmission channel proposed by Cuomo and coworkers (1993). It is extended for a special class of Generalized Hamiltonian systems. Substantial differences that signi.cantly affect the reception quality of the sent message, with or without considering noise effect in the transmission channel are given. We use two Hamiltonian Lorenz systems unidirectionally coupled, the first like a master/transmitter system and the other like a slave/receiver system in order to illustrate with numerical simulations the effectiveness of the modified scheme, using chaos synchronization with Hamiltonian forms and observer.

Breaking a chaos-based secure communication scheme designed by an improved modulation method

Recently Bu and Wang [Chaos, Solitons & Fractals 19 (2004) 919] proposed a simple modulation method aiming to improve the security of chaos-based secure communications against return-map-based attacks. Soon this modulation method was independently cryptanalyzed by Chee et al. [Chaos, Solitons & Fractals 21 (2004) 1129], Wu et al. [Chaos, Solitons & Fractals 22 (2004) 367], and \'{A}lvarez et al. [Chaos, Solitons & Fractals, accepted (2004), arXiv:nlin.CD/0406065] via different attacks. As an enhancement to the Bu-Wang method, an improving scheme was suggested by Wu et al. by removing the relationship between the modulating function and the zero-points. The present paper points out that the improved scheme proposed by Wu et al. is still insecure against a new attack. Compared with the existing attacks, the proposed attack is more powerful and can also break the original Bu-Wang scheme. Furthermore, it is pointed out that the security of the modulation-based schemes is not so satisfactory from a pure cryptographical point of view. The synchronization performance of this class of modulation-based schemes is also discussed.

COMMUNICATION BETWEEN SYNCHRONIZED RANDOM NUMBER GENERATORS

In most published chaos-based communication schemes, the system's parameters used as a key could be intelligently estimated by a cracker based on the fact that information about the key is contained in the chaotic carrier. In this paper, we will show that the least significant digits (LSDs) of a signal from a chaotic system can be so highly random that the system can be used as a random number generator. Secure communication could be built between the synchronized generators nonetheless. The Lorenz system is used as an illustration.

Controlling fast chaos in delay dynamical systems.

We introduce a novel approach for controlling fast chaos in time-delay dynamical systems and use it to control a chaotic photonic device with a characteristic time scale of approximately 12 ns. Our approach is a prescription for how to implement existing chaos-control algorithms in a way that exploits the system's inherent time delay and allows control even in the presence of substantial control-loop latency (the finite time it takes signals to propagate through the components in the controller). This research paves the way for applications exploiting fast control of chaos, such as chaos-based communication schemes and stabilizing the behavior of ultrafast lasers.

Ergodic chaos-based communication schemes.

Recent studies have shown the applicability of synchronized chaotic systems to the area of communications in different ways. At the same time synchronization based signal recovery and estimation of parameters severely suffer due to the presence of channel noise. By exploiting the ergodic properties of chaotic signals effectively, a simple technique called the mean-value method is introduced. This method is shown to be capable of estimating chaos system parameters from the transmitted chaotic signal efficiently for a low signal-to-noise ratio. A suitable demodulator has been designed for ergodic chaotic parameter modulation scheme for digital signal communication. Further, the mean-value technique incorporates a noncoherent receiver to recover analog information signal from the chaos masked signal efficiently. It is found that the proposed chaotic masking scheme is robust even in the presence of strong noise. In addition, this scheme has the potential advantage of a very simple hardware realization, which promises enhanced signal recovery performances.