Chaos-based Communication Research Articles

Optimizing Security and Cost Efficiency in N-Level Cascaded Chaotic-Based Secure Communication System

In recent years, chaos-based secure communication systems have garnered significant attention for their unique attributes, including sensitivity to initial conditions and periodic orbit density. However, existing systems face challenges in balancing encryption strength with practical implementation, especially for multiple levels. This paper addresses this gap by introducing a novel N-level cascaded chaotic-based secure communication system for voice encryption, leveraging the four-dimensional unified hyperchaotic system. Performance evaluation is conducted using various security metrics, including Signal-to-Noise Ratio (SNR), Peak Signal-to-Noise Ratio (PSNR), Percent Residual Deviation (PRD), and correlation coefficient, as well as Field-Programmable Gate Array (FPGA) resource metrics. A new Value-Based Performance Metrics (VBPM) framework is also introduced, focusing on both security and efficiency. Simulation results reveal that the system achieves optimal performance at N = 4 levels, demonstrating significant improvements in both security and FPGA resource utilization compared to existing approaches. This research offers a scalable and cost-efficient solution for secure communication systems, with broader implications for real-time encryption in practical applications.

Complex dynamics in nonlinear small time-delayed optoelectronic oscillator and application in fast reservoir computing and pulse generation

We investigated a time-delayed optoelectronic oscillator (OEO) that displays a wide range of complex dynamic behavior under small time delay. The phase-space trajectory distributions in different dynamic regimes were compared which brings a new perspective on the underlying mechanism of the transition process. It was found that bifurcation is always possible no matter how small the time delay is even if the universal adiabatic approximation model is invalid. Hereby we proposed a versatile simple oscillator which has a potential capacity as memory carrier and high-dimensional state spatial mapping ability that brings 1000 times computing-efficiency improvements of reservoir computing over the large time delay one. Furthermore, we demonstrated a new approach for a tunable optoelectronic pulse generator (repetition rate at 0.2 MHz and 0.25 GHz) which depends critically on time-delayed input electrical pulse. The proposed oscillator is also a promising system for the applications of fast chaos-based communication.

Fractal Tent Map with Application to Surrogate Testing

Discrete chaotic maps are a mathematical basis for many useful applications. One of the most common is chaos-based pseudorandom number generators (PRNGs), which should be computationally cheap and controllable and possess necessary statistical properties, such as mixing and diffusion. However, chaotic PRNGs have several known shortcomings, e.g., being prone to chaos degeneration, falling in short periods, and having a relatively narrow parameter range. Therefore, it is reasonable to design novel simple chaotic maps to overcome these drawbacks. In this study, we propose a novel fractal chaotic tent map, which is a generalization of the well-known tent map with a fractal function introduced into the right-hand side. We construct and investigate a PRNG based on the proposed map, showing its high level of randomness by applying the NIST statistical test suite. The application of the proposed PRNG to the task of generating surrogate data and a surrogate testing procedure is shown. The experimental results demonstrate that our approach possesses superior accuracy in surrogate testing across three distinct signal types—linear, chaotic, and biological signals—compared to the MATLAB built-in randn() function and PRNGs based on the logistic map and the conventional tent map. Along with surrogate testing, the proposed fractal tent map can be efficiently used in chaos-based communications and data encryption tasks.

Coherent Chaotic Communication Using Generalized Runge–Kutta Method

Computer simulation of continuous chaotic systems is usually performed using numerical methods. The discretization may introduce new properties into finite-difference models compared to their continuous prototypes and can therefore lead to new types of dynamical behavior exhibited by discrete chaotic systems. It is known that one can control the dynamics of a discrete system using a special class of integration methods. One of the applications of such a phenomenon is chaos-based communication systems, which have recently attracted attention due to their high covertness and broadband transmission capability. Proper modulation of chaotic carrier signals is one of the key problems in chaos-based communication system design. It is challenging to modulate and demodulate a chaotic signal in the same way as a conventional signal due to its noise-like shape and broadband characteristics. Therefore, the development of new modulation–demodulation techniques is of great interest in the field. One possible approach here is to use adaptive numerical integration, which allows control of the properties of the finite-difference chaotic model. In this study, we describe a novel modulation technique for chaos-based communication systems based on generalized explicit second-order Runge–Kutta methods. We use a specially designed test bench to evaluate the efficiency of the proposed modulation method and compare it with state-of-the-art solutions. Experimental results show that the proposed modulation technique outperforms the conventional parametric modulation method in both coverage and noise immunity. The obtained results can be efficiently applied to the design of advanced chaos-based communication systems as well as being used to improve existing architectures.

Synchronization of Analog-Discrete Chaotic Systems for Wireless Sensor Network Design

The current work is focused on studying the performance of the Pecora–Carroll synchronization technique to achieve synchronization between the analog and discrete chaos oscillators. The importance of this study is supported by the growing applications of chaotic systems for improving the security of data transmission in various communication layers, primarily on the physical layer. The hybrid analog-discrete approach of implementing chaos oscillators opens new possible communication schemes for wireless sensor network (WSN) applications. The analog implementation of chaos oscillators can benefit the simpler sensor node (SN) integration, while the discrete implementation can be used on the gateway. However, the core of such chaos-based communications is synchronizing analog and discrete chaos oscillators. This work studies two key parameters of analog-discrete chaotic synchronization: chaotic synchronization noise immunity and synchronization speed. The noise immunity study demonstrates the quality of synchronization at various noise levels, while the synchronization speed demonstrates how quickly the analog-discrete synchronization is achieved, along with how quickly the two systems diverge when synchronization is no longer present. The two studies use both simulation-based and hardware-based approaches. In the simulation case, the analog oscillator’s circuit is modeled in LTspice XVII, while in the hardware case, the circuit is implemented on the PCB. In both simulation and hardware studies, the discrete model of the oscillator is implemented in MATLAB R2023b. The studies are performed for two pairs of different chaos oscillators to widen the proposed approach application potential: the Vilnius and RC chaos oscillators. The oscillators have been selected due to their simplicity and similar dynamic behavior for model-based and electrical circuit implementation. The proposed approach also allows us to compare the synchronization of different oscillators in the analog-discrete implementation.

FPGA realization of an image encryption system using the DCSK-CDMA technique

This paper describes a four-wing chaotic oscillator-based DCSK-CDMA modulation technique for image encryption and decryption. The system consists of a transmission module for the encrypted and modulated color matrices, and a reception module for the decrypted and demodulated original data. Among our main contributions is the integration for the first time in the state of the art of DCSK chaotic modulation techniques with the CDMA communication scheme, as well as the implementation of our DCSK and CDMA algorithms in VHDL language for Xilinx FPGA cards. The DCSK-CDMA technique enables demodulation and decryption without any loss in the original data. Other contributions arising from this investigation are the encryption process implemented using DCSK-CDMA techniques based on a four-wing chaotic oscillator and the realization on the FPGA of a chaos-based communications system for the secure transmission of images of grayscale and RGB formats using DCSK-CDMA techniques. The system architecture in this work was designed using fixed-point binary arithmetic, with the application of the 4th order Runge–Kutta numerical method for the four-wing chaotic oscillator. The analysis of the correlation coefficients between the original and encrypted information indicates the values of 5.367×10−4 and −2.205×10−7 for grayscale and RGB images, respectively, with a full recovery of the original information. The results of simulations in MATLAB/Simulink coincide with the implementation of the complete system in VHDL on the Xilinx Artix-7 AC701 board.

Design of A Chaos-based Digital Radio over Fiber Transmission Link using ASK Modulation for Wireless Communication Systems

Secured broadband radio communications are becoming increasingly pivotal for high-speed connectivity in radio access networks, playing a crucial role in both mobile information systems and wireless IoT connections. This paper introduces a chaos-based two-channel digital radio communication system utilizing fiber optic radio transmission technology. The system comprises two radio channels operating at up to 1 Gbps using amplitude shift keying (ASK) modulation, followed by modulation with a chaotic sequence before conversion to the optical domain using the MZM modulator. To compensate for fiber loss, the system utilizes an Erbium Doped Fiber Amplifier (EDFA) and employs the optical links through standard ITU-G.655 optical fibers. Numerical simulation of the designed system is performed using the commercialized simulation software Optisystem V.15 to assess and characterize transmission performance. The results demonstrate the system’s effective operation on two channels with a fiber transmission distance of up to 110 km, maintaining a bit error ratio of less than 10−9. This feature ensures reliable performance for high-speed radio connections, particularly in applications such as fronthaul networks in cloud radio access and wireless sensor network connections.

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.

Some Properties of a Discrete Lorenz System Obtained by Variable Midpoint Method and Its Application to Chaotic Signal Modulation

Various discretization effects caused by applying numerical integration techniques to continuous chaotic systems are broadly studied in nonlinear science. Along with the negative impact on the precision of the various finite-difference schemes, such effects may have surprisingly fruitful practical applications, e.g. pseudo-random number generation, image encryption with improved diffusion and confusion properties, chaotic path planning, and many others. One such application is chaos-based communication systems which gained attention in recent decades due to their high covertness and broadband transmission capability. A crucial problem in the design of chaotic communication systems is the modulation of carrier signals. Due to the noise-like properties of chaotic signals, they can barely be modulated using the same methods as conventional harmonic signals. Thus, developing new modulation techniques is of great interest in the field of chaotic communications. In this study, we investigate the discrete model of the Lorenz oscillator obtained using controllable midpoint numerical integration and develop a novel modulation technique for chaos-based communication systems. We discover and analyze the multistability phenomenon in the dynamics of the investigated finite-difference Lorenz model through bifurcation, the basin of attraction, and Lyapunov spectrum analysis procedures. Using a specially designed testbench, we explicitly show that the proposed modulation method outperforms commonly used parametric modulation and is nearly equal to the state-of-the-art symmetry-based modulation in terms of covertness and noise resistivity. In addition, the proposed modulation technique is much easier to implement using computer arithmetics, especially in fixed-point hardware. The reported results may be efficiently applied to designing advanced chaos-based communications systems or improving the characteristics of existing communication system architectures.

Estimating Optimal Synchronization Parameters for Coherent Chaotic Communication Systems in Noisy Conditions

It is known, that coherent chaotic communication systems are more vulnerable to noise in the transmission channel than conventional communications. Among the methods of noise impact reduction, such as extended symbol length and various digital filtering algorithms, the optimization of the synchronization coefficient may appear as a very efficient and simple straightforward approach. However, finding the optimal coefficient for the synchronization of two chaotic oscillators is a challenging task due to the high sensitivity of chaos to any disturbances. In this paper, we propose an algorithm for finding the optimal synchronization parameter K_opt for a coherent chaos-based communication system affected by various noises with different signal-to-noise ratios (SNR). It is shown, that under certain conditions, optimal $K$ provides the lowest possible bit error rate (BER) during the transmission. In addition, we show that various metrics applied to the message demodulation task propose different noise immunity to the overall system. For the experimental part of the study, we simulated and physically prototyped two chaotic communication systems based on well-known Rossler and Lorenz chaotic oscillators. The microcontroller-based prototype of a chaotic communication system was developed to investigate the influence of noise in the real transmission channel. The experimental results obtained using the designed hardware testbench are in good correspondence with the theoretical propositions of the study and simulation results. The suggested evaluation metrics and optimization algorithms can be used in the design of advanced chaos-based communication systems with increased performance.

A Chen-Like Model: High Periodicity Leading to Chaotic Dynamics

The Chen circuit system, a three-dimensional autonomous system with intriguing dynamics, has gained considerable attention due to its potential applications in diverse scientific fields. In this article, a Chen-like system is defined and a comprehensive dynamics studied. The system exhibits chaotic dynamics, limit cycles, and bifurcations, making it a captivating subject of study. By employing numerical simulations and analytical techniques, we explore the system’s stability and identify critical parameter values leading to qualitative changes. Notably, we delve into Hopf bifurcations, which give rise to stability changes and the emergence of limit cycles. Furthermore, we analyze the fractal dimension of the system’s attractor, providing insights into its complexity and self-similarity. Through a systematic examination of the Chen-like system, we deepen our understanding of its intricate dynamics and offer valuable insights into the underlying mechanisms. The findings contribute to the field of dynamical systems and hold potential implications in areas such as chaos-based secure communications, signal processing, and nonlinear control. This work serves as a valuable reference for researchers and practitioners interested in the dynamics and bifurcation analysis of nonlinear systems.

The Intricacies of Sprott-B System with Fractional-Order Derivatives: Dynamical Analysis, Synchronization, and Circuit Implementation.

Studying simple chaotic systems with fractional-order derivatives improves modeling accuracy, increases complexity, and enhances control capabilities and robustness against noise. This paper investigates the dynamics of the simple Sprott-B chaotic system using fractional-order derivatives. This study involves a comprehensive dynamical analysis conducted through bifurcation diagrams, revealing the presence of coexisting attractors. Additionally, the synchronization behavior of the system is examined for various derivative orders. Finally, the integer-order and fractional-order electronic circuits are implemented to validate the theoretical findings. This research contributes to a deeper understanding of the Sprott-B system and its fractional-order dynamics, with potential applications in diverse fields such as chaos-based secure communications and nonlinear control systems.

High-speed chaos-based secure optical communications over 130-km multi-core fiber.

Chaotic optical communication is of great significance for secure data transmission. Despite rapid development over the decades, high-speed (>100 Gbps) and long-distance (>100 km) chaotic optical communication in a single fiber is still full of challenges. Here, we propose and experimentally demonstrate high-speed and long-distance chaos-based secure optical communications using mutual injection of semiconductor lasers and space-division multiplexing (SDM) techniques. The encrypted signals are transmitted through all seven core channels of the multi-core fiber (MCF), which effectively expands the aggregate transmission capacity of a single fiber. A pair of source and synchronization devices based on mutual injection of semiconductor lasers are employed to effectively encrypt and decrypt signals. Chaos-based secure optical communications with 70-Gbps on-off keying (OOK) and 140-Gbps quadrature phase-shift keying (QPSK) signals over a 130-km MCF are successfully demonstrated in the experiment with favorable performance. The demonstration may pave the way for future ultrahigh capacity and ultra-long distance chaotic optical communications by fully exploiting multi-dimensional resources of light waves, including the spatial dimension.

High-entropy-rate broadband chaos generation by using short-resonant-cavity DFB semiconductor laser with optical feedback.

Semiconductor lasers with delayed optical feedback are a promising source of optical chaos for practical applications, owing to simple configurations that are easy to integrate and synchronize. However, for traditional semiconductor lasers, the chaos bandwidth is limited by the relaxation frequency to several gigahertz. Here, we propose and experimentally demonstrate that a short-resonant-cavity distributed-feedback (SC-DFB) laser can generate broadband chaos only with simple feedback from an external mirror. The short distributed-feedback resonant cavity not only enhances laser relaxation frequency but also makes the laser mode more susceptible to external feedback. Experiments obtained a laser chaos with 33.6 GHz bandwidth and a spectral flatness of 4.5 dB. The corresponding entropy rate is estimated as more than 33.3 Gbit/s. It is believed that the SC-DFB lasers will promote development of chaos-based secure communication and physical key distribution.

DPI DCSK Modulation with BCJR Decoding

This paper proposes a novel [Formula: see text]-ary differential permutation index (DPI) differential chaos shift keying (DCSK) by using the Bahl–Cocke–Jeline–Raviv (BCJR) decoding (DPI-DCSK-BCJR) for chaos-based communications. By exploiting the characteristics of differential modulation and quasi-orthogonality of chaotic signals, the proposed DPI-DCSK-BCJR can provide two more calculated energies to decide the transmitted bits. Theoretical analysis of bit-error-rate (BER) is carried out over multipath Rayleigh fading channel and then validated via simulations. The proposed scheme is demonstrated to outperform the conventional DPI-DCSK by 2[Formula: see text]dB for different [Formula: see text]. This performance gain is especially increased over high-delay channels. Furthermore, the advantage of the proposed frequency-modulated DPI-DCSK-BCJR is verified over practical ultra-wideband (UWB) wireless channels. In addition, we investigate the proposed DPI-DCSK-BCJR for more generalized multiuser communications. The simulation result shows that DPI-DCSK-BCJR can achieve performance gains up to 5[Formula: see text]dB as compared to the conventional PI-DCSK and DPI-DCSK for both two and three user systems. Consequently, the proposed DPI-DCSK-BCJR can be considered as a low-cost alternative for low-complexity and high-rate chaotic-based wireless communication.

Highly-secured chaos-based communication system using cascaded masking technique and adaptive synchronization

Highly-secured chaos-based communication system using cascaded masking technique and adaptive synchronization

Prototyping the Symmetry-Based Chaotic Communication System Using Microcontroller Unit

Chaos-based communications are a promising application of chaos theory and nonlinear dynamics. Their key features include concealed transmission, high security, and native broadband signals. Many studies have recently been published devoted to this technology. However, the practical implementations of chaos-based communications are rare due to multiple shortcomings: high hardware requirements, complex signal processing algorithms, and a lack of efficient modulation techniques for chaotic signals. In this study, we consider a simple hardware prototype of a coherent chaos-based communication system based on a novel type of modulation: adaptive symmetry of the finite-difference scheme used in a chaos generator. We explicitly demonstrate the possibility of covertly transmitting data using a chaotic transmitter and receiver implemented in a general-purpose microcontroller unit. A comparison between traditional parameter and symmetry modulation is given through a return map analysis and bit error rate estimation. The communication secrecy is analyzed using quantified return map analysis. The obtained results confirm the possibility of creating chaos-based communication systems based on symmetry modulation.

Chaotic-based Orthogonal Frequency Division Multiplexing with Index Modulation

Orthogonal frequency division multiplexing with index modulation (OFDM-IM), stands out among conventional communication technologies, as it uses the indices of the available transmit entities. Thanks to such an approach, it offers a novel method for the transmission of extra data bits. Recent years have seen a great interest in chaos-based communications. The spectrum-spreading signals used in chaotic signal modulation technologies are orthogonal to the existing mixed signals. This paper presents how well a non-coherent differential chaos shift keying communication system performs across an AWGN. Different types of detection methods are simulated, bit error rate and power spectral density are calculated and then compared with standard OFDM with index modulation. The results of simulations concerning the performance of a DCSK system, adding to the security of the proposed solution and offering a comparable bit error rate performance, are presented in the paper as well.

Encryption and Decryption of Audio Signal and Image Secure Communications Using Chaotic System Synchronization Control by TSK Fuzzy Brain Emotional Learning Controllers.

In this article, a new idea of chaos synchronization and chaos-based secure communication is developed. First, the chaotic master system is used as a transmitter in chaos-based secure communication, then a drive signal is constructed, and the information message is encrypted into the drive signal to form a transmitted signal for secure communication. Second, in the receiver, a recurrent Takagi-Sugeno-Kang (TSK) fuzzy brain emotional learning cerebellar model articulation controller (RTFBECAC) is developed to control the slave system to follow the master system in the transmitter. Third, after descripting the chaotic signal, the embedded information message can be recovered. Besides, the stability problem is analyzed in detail based on the stability theory. Finally, two simulation examples, including audio signal and image, are introduced to illustrate the effectiveness and the advantages of the proposed method.

A filtered Hénon map

In this paper, we use Lyapunov exponents to analyze how the dynamical properties of the Hénon map change as a function of the coefficients of a linear filter inserted in its feedback loop. We show that the generated orbits can be chaotic or not, depending on the filter coefficients. The dynamics of the system presents complex behavior, including cascades of bifurcations, coexistence of attractors, crises, and “shrimps”. The obtained results are relevant in the context of bandlimited chaos-based communication systems, that have recently been proposed in the literature.