Chaotic Transmitter Research Articles

Design the hyperchaotic cryptosystems via the Gerschgorin theorem

In this paper, we propose a new method to design a feedback controller for synchronizing the hyperchaotic circuits. The main idea of the method is to design a controller by applying a suitable Lyapunov function and Gerschgorin theorem. Therefore, the feedback controller can guarantee that the signal by chaotic masking from the transmitter can be recovered at the receiver. A scheme of the hyperchaotic communication systems is proposed, where the transmitter and receiver are constituted of the coupled Chua’s chaotic circuits in this paper. On the other hand, to enhance the degree of security in chaotic communication systems, the techniques of cipher are also considered in this paper. Therefore, the cryptosystems can be obtained by using the encrypter, and decrypter as the chaotic transmitter–receiver pairs. To the purpose of the synchronization, the concepts of identical and generalized synchronizations are used to achieve the aim that the plaintext signals from the encrypter can be retrieved at the decrypter. Finally, the simulation results are given to demonstrate the performance of the proposed cryptosystems.

Bandwidth-enhanced chaos synchronization in strongly injection-locked semiconductor lasers with optical feedback.

Bandwidth-enhanced chaos synchronization in strongly injection-locked semiconductor lasers with optical feedback is numerically studied based on laser rate equations. The bandwidth of the chaotic carrier frequency in a semiconductor laser with optical feedback is expanded roughly three times by strong optical injection compared with the bandwidth when there is no optical injection. Using a bandwidth-enhanced semiconductor laser as a chaotic transmitter and receiver, we synchronized transmitter and the receiver lasers in a complete chaos synchronization scheme.

Ultrawideband direct chaotic data transmission in the microwave range

A method of wireless, high-rate, direct chaotic transmission of digital data is proposed. The method is based on the use of ultrawideband chaotic oscillations generated directly in the microwave range. Experimental results are presented to demonstrate the possibility of data transmission at a rate of up to 200 Mb/s.

Optical communication with synchronized hyperchaos generated electrooptically

We propose a method based on a scalar second-order difference-differential equation to obtain intensity chaos from a laser diode with a nonlinear delayed feedback. The method can be used for encrypting, transmitting, and decrypting a signal in a chaos-based communication system. The core of the chaotic transmitter and receiver is formed by an electrooptic modulator that is used to generate a strong reproducible nonlinearity and chaotic waveforms of extremely high Lyapunov dimensionality. The system opens the way to ultrafast chaotic communications.

CHAOTIC PHASE SHIFT KEYING IN DELAYED CHAOTIC ANTICONTROL SYSTEMS

Based on the delayed feedback chaotic anticontrol systems, a new chaotic phase shift keying (CPSK) scheme is proposed for secure communications in this paper. The chaotic transmitter is a linear system with nonlinear delayed feedback in which a trigonometric function cos(·) is used. Such system can exhibit rich chaotic behavior with the choice of appropriate parameters. For an M-ary communication system where M=2n, each of these M possible symbols (n-bits) is firstly mapped to 2(m-1)π/M (with m=1, 2, …, M) which is used as the phase argument for the cos(·) function in the nonlinear feedback. Two different kinds of signals can be transmitted. In the first one, an appropriate linear combination of state variables is chosen as the transmitting signal based on the observer theory. In another one, a nonlinear component in the transmitter state equation is chosen. In both schemes, only a scalar chaotic signal is transmitted through the channel. Demodulation is based on the synchronization of the transmitter and the receiver, and different decoded phases correspond to different information signals.

OBSERVABILITY BIFURCATION VERSUS OBSERVING BIFURCATIONS

In this paper we highlight the difference between observability bifurcation and observing bifurcation. From this, we deduce that one way to improve transmission by synchronization of chaotic systems may be chaotic transmitter with also observability bifurcation. We end the paper, with an example of chaotic system with also an observability bifurcation. Moreover this example point out some benefits of the step by step sliding mode observer.

A note on chaotic secure communication systems

This paper presents a new way to transmit and retrieve an information-bearing signal via chaotic systems. In contrast to existing schemes with one transmission line, a two-channel transmission method is adopted for the purpose of faster synchronization and higher security. Basically, an output of the chaotic transmitter is sent for synchronization-only, with no connection to the information signal. The other channel transmits a signal generated from a highly nonlinear function of the chaotic states and the information-bearing signal. While the first channel serves the purpose of efficient synchronization, the second channel is used for complicated encryption and, therefore, improved security/privacy. Simulation results validate the new chaos-based secure communication method.

SYNCHRONIZATION THROUGH FILTERING

We study the synchronization problem in discrete-time via an extended Kalman filter (EKF). That is, synchronization is obtained of transmitter and receiver dynamics in case the receiver is given via an EKF that is driven by a noisy drive signal from a noisy transmitter dynamics. The convergence of the filter dynamics towards the transmitter dynamics is rigorously shown using recent results in extended Kalman filtering. Two extensive simulation examples show that the filter is indeed suitable for synchronization of (noisy) chaotic transmitter dynamics. An application to private communication is also given.

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.

Chaotic dynamics in coupled microwave oscillators

Describes an investigation into possible chaotic behavior in a coupled-oscillator system and the possible control of this behavior for communications. The established mathematical models for these oscillator arrays are demonstrated to exhibit chaos when the coupling strength between oscillators is below the range for phase locking. The complexity and predictability of the array dynamics are analyzed by means of standard dynamical measures such as the Lyapunov exponents, the Kolmogorov-Sinai entropy, and the attractor dimension, the authors show that chaos in these oscillator arrays is low dimensional and well characterized; both necessary conditions for control and possible exploitation of chaos. Finally, the method of occasional proportional feedback is used to stabilize the output from the array while the array is still in the chaotic regime. Possible applications of these chaotic transmitters are also discussed.

Signal masking for chaotic optical communication using external-cavity diode lasers

Amplitude modulation is used to encode a message into the output of a chaotic laser-diode optical transmitter, and decoding of the message by use of a synchronized chaotic laser-diode receiver is demonstrated experimentally. The chaotic carrier is shown to effectively mask the transmitted message.

COMPUTATIONAL VERB SYSTEMS: COMPUTING WITH VERBS AND APPLICATIONS

In the previous work, verbs were modeled by using different linear and nonlinear dynamical systems for characterizing each of them with different dynamics in different contexts, In this paper the problem of computing with verbs (verb computation) is studied. The relationship and compulation between verbs are modeled by relations between different dynamics. The classical “equality” is generalized to verb equality, which is synchronization or generalized synchronization between dynamical systems. Different schemes of synchronization between dynamical systems are presented to show how rich the verb equality can be. Verb computation turns out to be another aspect of linguistic computation besides fuzzy logic. In a word, fuzzy logic answers the questions characterized by “what” while verb computation answers the questions characterized by “how”. Verb computation is a model of the natural way used by human beings to cope with the dynamical aspects of complexities of the nature. Whenever ‘wherever’ a system becomes too complex to get an exact model, and only some linguistic statements containing descriptions or implications of dynamical characteristics exist, verb computation becomes a powerful tool for coping with these complexities. Comparing with fuzzy theory, which copes with vagueness in static relations, verb computation copes with vagueness in dynamical processes. Fuzzy theory and verb computation describe two different aspects of the complexities we should cope with for our survival. To illustrate the application of verb computation, the simulation example of “understand music” is presented to show how emotions and intuitions can be transmitted through music by a process of computing with verbs. Then an actual application of verb computation to unmasking a chaotic secure communication scheme—chaotic shift keying is presented. First a reference system is chosen as the“machinself”. Then the reference system “hears” the transmitted signal and “feels” different styles in the transmitted signal when different bits of the message signal are scrambled. Different feelings of the reference system reveal the scrambled message signal even though the structure and the parameters of the chaotic transmitter are unknown.

Breaking chaotic secure communication using a spectrogram

We present the results of breaking a kind of chaotic secure communication system called chaotic switching scheme, also known as chaotic shift keying, in which a binary message signal is scrambled by two chaotic attractors. The spectrogram which can reveal the energy evolving process in the spectral-temporal space is used to distinguish the two different chaotic attractors, which are qualitatively and statistically similar in phase space. Then mathematical morphological filters are used to decode the binary message signal without the knowledge of the binary message signal and the transmitter. The computer experimental results are provided to show how our method works when both the chaotic and hyper-chaotic transmitter are used.

Cryptanalyzing chaotic secure communications using return maps

In chaotic secure communications, message signals are scrambled by chaotic dynamical systems. The interaction between the message signals and the chaotic systems results in changes of different kinds of return maps. In this paper, we use return map based methods to unmask some chaotic secure communication systems; namely, chaotic shift keying (chaotic switching), chaotic parameter modulation and non-autonomous chaotic modulation. These methods are used without knowing the accurate knowledge of chaotic transmitters and without reconstructing the dynamics or identifying the parameters of chaotic transmitters. These methods also provide a criterion of deciding whether a chaotic secure communication scheme is secure or not. The effects of message signals on the changes of different return maps are studied. Fuzzy membership functions are used to characterize different kinds of changes of return maps. Fuzzy logic rules are used to extract message signals from the transmitted signal. The computer experimental results are provided. The results in this paper show that the security of chaotic secure communication not only depends on the complexity of the chaotic system but also depends on the way the message is scrambled. A more complex chaotic system is not necessary to provide a higher degree of security if the transmitted signal has simple and concentrated return maps. We also provide examples to show that a chaotic system with complicated return maps can achieve a higher degree of security to the attacks presented in this paper.

Chaotic transmission strategies employing artificial neural networks

Two novel chaotic coding and decoding methods based on artificial neural networks (ANNs) are reported which employ the unimodal logistic map (LM) as an example. Coding is carried out by either modulating the LM or by generating the chaotic sequence with ANNs. In simulations speech has been coded and the resulting SNR/sub sig/ for the decoded speech has been evaluated. The results demonstrate that the two proposed methods offer a SNR/sub sig/ improvement of 4 and 20 dB over the SNR/sub sig/ obtained by using the LMS for decoding.

Breaking chaotic switching using generalized synchronization: examples

In a chaotic switching scheme, a binary message signal is scrambled by two chaotic attractors. In this paper we present examples to show how generalized chaotic synchronization (GS) can be used to break chaotic switching schemes. Since GS is a very robust phenomenon, we find that an intruder can recover the binary information signal from chaotic switching schemes without knowing both the structure and parameters of the chaotic transmitter. The breaking method presented in this paper is not sensitive to the order of the transmitter, which means that even in a chaotic switching scheme which uses two hyperchaotic systems, the degree of security may still be low. The simulation results for both low order and high order transmitters are presented.

Encoding and decoding messages with chaotic lasers

We investigate the structure of the strange attractor of a chaotic loss-modulated solid-state laser utilizing return maps based on a combination of intensity maxima and interspike intervals, as opposed to those utilizing Poincar{acute e} sections defined by the intensity maxima of the laser ({dot I}=0,{umlt I}{lt}0) alone. We find both experimentally and numerically that a simple, intrinsic relationship exists between an intensity maximum and the pair of preceding and succeeding interspike intervals. In addition, we numerically investigate encoding messages on the output of a chaotic transmitter laser and its subsequent decoding by a similar receiver laser. By exploiting the relationship between the intensity maxima and the interspike intervals, we demonstrate that the method utilized to encode the message is vital to the system{close_quote}s ability to hide the signal from unwanted deciphering. In this work alternative methods are studied in order to encode messages by modulating the magnitude of pumping of the transmitter laser and also by driving its loss modulation with more than one frequency. {copyright} {ital 1997} {ital The American Physical Society}

Obtaining Synchronization for a Class of Chaotic Systems

An iterative algorithm is proposed for constructing synchronizing receivers for a chosen class of chaotic transmitter systems. A complete knowledge of the transmitter system is not required. Identical synchronization is ensured with the transmitted signal in the constructed receivers. Potential applications of the method are discussed for communications.

A Secure Communications System Using Chaotic Switching

Since previous secure communications methods using chaotic systems require very high SNRs, knowledge of the initial conditions, and/or chaotic systems with the self-synchronization property, their application is limited. In this paper, a new secure communications scheme based on chaotic switching is discussed. The proposed scheme makes decisions on the incoming bits by comparing the power level of the dynamical error for each symbol signal after applying a noise reduction method based on the known system dynamics. A multi-user secure communications scheme is also considered where each user's symbol signal is mapped through a unique scramble matrix. We also examine whether these scramble matrices help to combat against smart jamming. The proposed system does not require self-synchronization between the chaotic receiver and transmitter and exhibits reasonable performance at relatively low SNRs.

Chaotic transmission of waves and "cooling" of signals.

Ray dynamics in waveguide media exhibits chaotic motion. For a finite length of propagation, the large distance asymptotics is not uniform and represents a complicated combination of bunches of rays with different intermediate asymptotics. The origin of the phenomena that we call "chaotic transmission," lies in the nonuniformity of the phase space with sticky domains near the boundary of islands. We demonstrate different fractal properties of ray propagation using underwater acoustics as an example. The phenomenon of the kind of Levy flights can occur and it can be used as a mechanism of cooling of signals when the width of spatial spectra dispersion is significantly reduced. (c) 1997 American Institute of Physics.