Chaotic Secure Communication System Research Articles

Exploration of Four-Channel Coherent Optical Chaotic Secure Communication with the Rate of 400 Gb/s Using Photonic Reservoir Computing Based on Quantum Dot Spin-VCSELs

In this work, we present a novel four-channel coherent optical chaotic secure communication (COCSC) system, incorporating four simultaneous photonic reservoir computers in tandem with four coherent demodulation units. We employ a quartet of photonic reservoirs that capture the chaotic dynamics of four polarization components (PCs) emitted by a driving QD spin-VCSEL. These reservoirs are realized utilizing four PCs of a corresponding reservoir QD spin-VCSEL. Through these four concurrent photonic reservoir structures, we facilitate high-quality wideband-chaos synchronization across four pairs of PCs. Leveraging wideband chaos synchronization, our COCSC system boasts a substantial 4 × 100 GHz capacity. High-quality synchronization is pivotal for the precise demasking or decoding of four distinct signal types, QPSK, 4QAM, 8QAM and 16QAM, which are concealed within disparate chaotic PCs. After initial demodulation via correlation techniques and subsequent refinement through a variety of digital signal processing methods, we successfully reconstruct four unique baseband signals that conform to the QPSK, 4QAM, 8QAM and 16QAM specifications. Careful examination of the eye diagrams, bit error rates, and temporal trajectories of the coherently demodulated baseband signals indicates that each set of baseband signals is flawlessly retrieved. This is underscored by the pronounced eye openings in the eye diagrams and a negligible bit error rate for each channel of baseband signals. Our results suggest that delay-based optical reservoir computing employing a QD spin-VCSEL is a potent approach for achieving multi-channel coherent optical secure communication with optimal performance and enhanced security.

Simultaneously enhancing capacity and security in free-space optical chaotic communication utilizing orbital angular momentum

Optical chaotic signals emitted from an external-cavity feedback or injected laser diode enable small-signal information concealment in a noise-like carrier for secure optical communications. Due to the chaotic bandwidth limitation resulting from intrinsic relaxation oscillation frequency of lasers, multiplexing of optical chaotic signal, such as wavelength division multiplexing in fiber, is a typical candidate for high-capacity secure applications. However, to our best knowledge, the utilization of the spatial dimension of optical chaos for free-space secure communication has not yet been reported. Here, we experimentally demonstrate a free-space all-optical chaotic communication system that simultaneously enhances transmission capacity and security by orbital angular momentum (OAM) multiplexing. Optical chaotic signals with two different OAM modes totally carrying 20 Gbps on–off keying signals are secretly transmitted over a 2 m free-space link, where the channel crosstalk of OAM modes is less than −20 dB, with the mode spacing no less than 3. The receiver can extract valid information only when capturing approximately 92.5% of the OAM beam and correctly demodulating the corresponding mode. Bit error rate below the 7% hard-decision forward error correction threshold of 3.8×10−3 can be achieved for the intended recipient. Moreover, a simulated weak turbulence is introduced to comprehensively analyze the influence on the system performance, including channel crosstalk, chaotic synchronization, and transmission performance. Our work may inspire structured light application in optical chaos and pave a new way for developing future high-capacity free-space chaotic secure communication systems.

Coupling Projection Synchronization of Three Chaotic Systems and Its Multilevel Secure Communication via DNA CRNs

The complete synchronization of two chaotic systems and its secure communication have been considered based on DNA chemical reaction networks (DNA CRNs). There are concerns about the security of the single-level chaotic secure communication system. Thereby a multi-level secure communication scheme is put forward via DNA CRNs in this work. Firstly, a three-variable chaotic system that consists of catalysis, double, fasciation, and annihilation modules is constructed using DNA CRNs. Secondly, according to the stability principle of nonlinear systems, DNA CRNs are adopted to realize the coupling projection synchronization of three chaotic systems, and the synchronization results are discussed. Finally, sine and cosine signals are designed using DNA CRNs. These signals are added into three systems to realize multi-level encryption and decryption. Furthermore, the interference terms are taken into consideration to test the robustness of the system. The results show that the proposed scheme has high security, and can efficiently encrypt and decrypt biological signals through multi-level transmission in the presence of interference.

Optical cascaded reservoir computing for realization of dual-channel high-speed OTDM chaotic secure communication via four optically pumped VCSEL.

In this work, we propose a chaotic secure communication system with optical time division multiplexing (OTDM), using two cascaded reservoir computing systems based on multi beams of chaotic polarization components emitted by four optically pumped VCSELs. Here, each level of reservoir layer includes four parallel reservoirs, and each parallel reservoir contains two sub-reservoirs. When the reservoirs in the first-level reservoir layer are well trained and the training errors are far less than 0.1, each group of chaotic masking signals can be effectively separated. When the reservoirs in the second reservoir layer are effectively trained and the training errors are far less than 0.1, the output for each reservoir can be well synchronized with the corresponding original delay chaotic carrier-wave. Here, the synchronization quality between them can be characterized by the correlation coefficients of more than 0.97 in different parameter spaces of the system. Under these high-quality synchronization conditions, we further discuss the performances of dual-channel OTDM with a rate of 4×60 Gb/s. By observing the eye diagram, bit error rate and time-waveform of each decoded message in detail, we find that there is a large eye-openings in the eye diagrams, low bit error rate and higher quality time-waveform for each decoded message. Except that the bit error rate of one decoded message is lower than 7 × 10-3 in different parameter spaces, and those of the other decoded messages are close to 0, indicating that high-quality data transmissions are expected to be realized in the system. The research results show that the multi-cascaded reservoir computing systems based on multiple optically pumped VCSELs provide an effective method for the realization of multi-channel OTDM chaotic secure communications with high-speed.

Toward Chaotic Secure Communications: An RIS Enabled M-Ary Differential Chaos Shift Keying System With Block Interleaving

Chaotic secure communication systems using chaotic waveforms as their spreading carriers can hide the transmitted information bits over a wide frequency range of chaotic waveform, which disguises the transmitted information waveform as noise. In this paper, a reconfigurable intelligent surface (RIS) enabled <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> -ary differential chaos shift keying with block interleaving (RIS-MDCSK-BI) system is proposed for chaotic secure communications, where an RIS is deployed at the transmitter to assist communications and a pair of block interleaving patterns are used to interleave <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> -ary information-bearing signals to enhance security performance. Moreover, we propose a chaotic merging sort algorithm to generate different block interleaving patterns, where these interleaving patterns are encrypted by using the non-periodic and noise-like properties of chaotic signals. To estimate information bits at the legitimate receiver, we propose a sequential detection algorithm and a joint detection algorithm. Then, theoretical bit error rate (BER) performances of the proposed RIS-MDCSK-BI system with the legitimate receiver and the eavesdropping receiver are derived. The security performance metrics, including information leakage and secrecy outage probability, are also analyzed. Monte Carlo simulations are performed to verify the superior BER performance and security performance of the proposed RIS-MDCSK-BI system compared to benchmark systems.

New Design of Secure Communication System Based on Dynamic Linear Receiver

In this paper, the design issues of the chaotic secure communication system will be scientifically explored. Based on time-domain analysis, a new secure communication system with dynamic linear receivers will be constructed. This secure communication system can not only make the error signal close to zero, but also can correctly calculate its exponential convergence rate. Finally, several numerical simulation results are proposed to illustrate the practicability and correctness of the main results.

Research on the Performance of Multimode Optical Chaotic Secure Communication System With Multidimensional Keys and a Complex Entropy Source

In this paper, we design an optical chaotic secure communication system with multi-dimensional keys and a complex entropy source, which can allow secure communication working in different modes such as unicast, multicast, and broadcast. In the proposed scheme, amplified spontaneous emission (ASE) noise of the erbium-doped fiber amplifier (EDFA) with sufficient randomness is used as an entropy source to improve the security of the system. And by using the electro-optic delay feedback loops, the key spaces are introduced and the phase distortion is generated, then the data are masked in both phase and intensity fields. As a frequency-dependent group delay (FDGD) module, Gires-Tournois interferometer (G-T I) in the feedback loop can effectively hide the time delay signature (TDS) and achieve additional 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">36</sup> key spaces. The influence of different key mismatches on decryption function is numerically investigated, and the results indicate that the broadband nature of ASE noise makes the TDS a very sensitive encryption key, which increases the difficulty of illegal third parties stealing information. And with the help of the wavelength converter and wavelength division multiplexer, secure communication in various modes is successfully realized, which greatly improves the communication efficiency and is suitable for various security places.

Three-loop electro-optical phase chaotic secure communication system with time-delay signatures concealment and key space enhancement

A novel three loops electro-optical phase (TLEOP) chaotic secure communication system is proposed, which consists of three mutually coupled electro-optical phase chaotic feedback loops. A pseudo-random binary sequence (PRBS) is introduced in the proposed system scheme. The scheme improves the complexity of the chaotic carriers and completely the time-delay signatures (TDSs) of the system with a small feedback gain coefficient that is easy to reach. The PRBS or the original messages and the chaotic carriers are nonlinearly coupled together and participate in the generation of the chaotic carrier which further improves the complexity and the security of the chaotic system. Multiple TDSs effectively enlarge the key space of the system (about 1012). The synchronization performance of the proposed TLEOP system is discussed. The results show that the TDSs are suitable as the secret key of the system because of the high sensitivity of the chaos synchronization to time-delays. Since the mismatch of the feedback gain coefficient caused by environmental changes has little effect on the chaos synchronization, the proposed system has strong robustness. The proposed scheme has great application prospects in chaotic secure communication.

Design of a Single-Channel Chaotic Secure Communication System Implemented by DNA Strand Displacement.

DNA strand displacement (DSD) is regarded as a foundation for the construction of biological computing systems because of the predictability of DNA molecular behaviors. Some complex system dynamics can be approximated by cascading DSD reaction modules with different functions. In this paper, four DSD reaction modules are used to realize chaotic secure communication based on drive-response synchronization of four-dimensional chaotic systems. The system adopts the communication technology of chaos masking and uses a single-channel synchronization scheme to achieve high accuracy. The simulation results demonstrate that encryption and decryption of the signal are achieved by the design. Moreover, the system is robust to noise signals and interference during the DNA reactions. This work provides a method for the application of DNA molecular computation in the communication field.

Chaotic synchronization based on improved global nonlinear integral sliding mode control☆

In order to avoid integral saturation of integral sliding mode surface, a new integral function which can magnify small errors and minify large errors is designed. Meanwhile, an attenuation function which can decay to zero in a finite time is designed to accelerate the convergence speed of global sliding mode surface. Then, an improved global nonlinear integral sliding mode surface (GNISMS) is constructed, and sliding mode control based on the proposed sliding mode surface is designed to accomplish the synchronization control of chaotic systems with external disturbances and internal parameters uncertainties. Simulation results show that the proposed sliding mode control method has good control performance, and it can be effectively applied to the chaotic secure communication system based on chaos synchronization control.

FPGA Realization of Spherical Chaotic System with Application in Image Transmission

This paper considers a three-dimensional nonlinear dynamical system capable of generating spherical attractors. The main activity is the realization of a spherical chaotic attractor on Intel and Xilinx FPGA boards, with a focus on implementation of a secure communication system. The first major contribution is the successful synchronization of two chaotic spherical systems, in VHDL program, in a master-slave topology using Hamiltonian forms. The synchronization errors show that the two spherical chaotic systems synchronize in a very short time after which the error signals become zero. The second major contribution is the FPGA realization of a spherical chaotic attractor-based secure communication system, which involves encrypting both grayscale and RGB images with chaos and diffusion key at the transmitting system, sending the encrypted image via the state variables, and reconstructing the encrypted image at the receiving system. The Intel Stratix III and Xilinx Artix-7 AC701 results are the same as those of MATLAB. The statistical analyses of the encrypted and received images show that the implemented system is very effective, as it reveals high degree of randomness in the encrypted images with the entropy test, and the obtained correlation coefficient, which is zero, removes relativity between the original and encrypted images. Finally, the transmission system fully recovers the original grayscale and RGB images without loss of information.

Bidirectional digital image secure transmission and recognition based on a long-distance chaos synchronization system with machine learning capability

Based on chaos synchronization of two response lasers (RLs) injected by the common chaos signals from a driving laser (DL) with double optical feedback (DOF) and an additional neural network (NN), a bidirectional chaotic secure communication system with machine learning capability is proposed and the long-distance digital image transmission and recognition performances are numerically investigated. The simulated results show that the time delay signature (TDS) of the driving chaotic signals from DL with DOF is greatly weakened under suitable operation conditions. Two RLs can generate chaos signals with low TDS and broad bandwidth, and the high-quality chaos synchronization between two RLs can be achieved while the synchronization quality between DL and any one of RLs is extremely bad, which is helpful to realize the secure communication. Using the synchronized chaos output signals from two RLs as chaos carriers and chaos masking (CM) encoding method, the bidirectional 10 Gb/s secure communication over 140 km fiber channel can be realized and the effects of the fiber parameters on the communication performances are discussed. After adopting an additional NN, a long-distance digital image transmission and recognition based on this proposed secure communication system can be realized and the communication distance can be extended to 220 km.

Wideband complex-enhanced bidirectional phase chaotic secure communication with time-delay signature concealment.

A novel bandwidth-enhanced bidirectional phase chaotic secure communication system with time-delay signature (TDS) concealment is proposed and analyzed by numerical simulation. This bidirectional system based on two mutually coupled electro-optic (MCEO) phase feedback loops is driven by a common all-optical (AO) chaotic source. The AO driving source makes the amplitude and phase terms in the Ikeda-based MCEO equation chaotic. Two mutually coupled optoelectronic delayed feedback loops also greatly increase the complexity of the chaotic carrier. By replacing the semiconductor laser in the existing bidirectional communication scheme with an electro-optic feedback loop, the problems of narrow carrier bandwidth and poor synchronization performance can be compensated. Compared to the single MCEO system, the permutation entropy of the AO-MCEO cascaded system with a bit rate of 10 Gbit/s is improved by 0.13 to 0.98. The TDS of the AO-MCEO system is suppressed 35 times to less than 0.01 to be completely hidden when the EO gain is reduced by half to 2.75. The chaos effective bandwidth is increased by 5 GHz to 32.05 GHz, and the spectrum flatness is reduced by 0.33 dB/Hz to 0.82 dB/Hz. Meanwhile, the security is further enhanced by reducing the cross-correlation coefficient to 0.001 between the AO driving source and the electro-optical chaotic carrier. The results show that the proposed model has potential applications in bandwidth-enhanced bidirectional secure chaotic systems.

Key space enhancement of a chaos secure communication based on VCSELs with a common phase-modulated electro-optic feedback.

In this paper, a novel chaotic secure communication system based on vertical-cavity surface-emitting lasers (VCSEL) with a common phase-modulated electro-optic (CPMEO) feedback is proposed. The security of the CPMEO system is guaranteed by suppressing the time-delay signature (TDS) with a low-gain electro-optic (EO) feedback loop. Furthermore, the key space is enhanced through a unique secondary encryption method. The first-level encrypted keys are the TDS in the EO feedback loop, and the second-level keys are the physical parameters of the VCSEL under variable-polarization optical feedback. Numerical results show that, compared to the dual-optical feedback system, the TDS of the CPMEO system is suppressed 8 times to less than 0.05 such that they can be completely concealed when the EO gain is 3, and the bandwidth is doubled to over 22 GHz. The error-free 10 Gb/s secure optical transmission can be realized when the time-delay mismatch is controlled within 3 ps. It is shown that the proposed scheme can significantly improve the system performance in TDS concealment, as well as bandwidth and key space enhancement, which has great potential applications in secure dual-channel chaos communication.

Time-delay signature concealment in chaotic secure communication system combining optical intensity with phase feedback

In this paper, we present a cascaded system, with optical intensity chaos and electro-optic phase chaos, to allow for bidirectional communication. In this scheme, we utilize the intensity chaotic signal instead of the traditional continuous wave (CW) to inject into the electro-optic oscillator to produce a phase chaotic signal. Under a suitable feedback intensity, we also demonstrate that the configuration can generate the chaos with high complexity and high dimension by using largest Lyapunov exponents (LLEs) and Lempel–Ziv Complexity (LZC). Using the delay time identification techniques, we show that the configuration can successfully conceal all time delay signatures (TDSs), which correspond to the feedback delays of both laser and electro-optic oscillator. By mutually phase modulating between two output signals at both oscillators, delay dynamics is induced in both sides. We numerically demonstrate that this dynamics can be identically synchronized. Based on the synchronization between transmitter and receiver, the messages introduced at two ends of the link can be simultaneously exchanged. We still find that: under a little mismatch of parameter, the system can maintain good quality of transmission. This scheme provides a possible way to achieve chaotic bidirectional confidential communication.

Design of a secure communication system between base transmitter station and mobile equipment based on finite-time chaos synchronisation

This paper proposes a chaotic secure communication system between a base transmitter station and mobile equipment. To make the chaotic keys, the Chua chaotic systems are used in the mobile equipment and base transmitter station. Chaotic oscillators are perturbed by external disturbances and parametric uncertainties. Based on the Lyapunov stability theory and the finite-time synchronisation concept, a robust terminal sliding mode controller is designed. In the first step, we aimed to achieve chaos synchronisation under external disturbances and parametric uncertainties in a finite time. In the second step, to enhance security in the communication system, a combination of the chaotic encryption method as multi-shift cipher encryption and double chaotic masking has been suggested. The simulation outcomes are presented to show the applicability and performance of the proposed method.

A polynomial-fuzzy-model-based synchronization methodology for the multi-scroll Chen chaotic secure communication system

In this paper, a polynomial-fuzzy-model-based design methodology to synchronize multi-scroll Chen chaotic systems is proposed for secure communication. At first, the architecture of secure communication system (SCS) based on the synchronization of multi-scroll Chen chaotic systems is presented. Then, the master and slave multi-scroll Chen chaotic systems are transformed into the equivalent master and slave polynomial fuzzy models respectively. After that, the H∞ polynomial fuzzy control design is proposed for synchronizing the master and slave multi-scroll Chen chaotic systems as well as restraining external disturbances. Moreover, for practical application, a constraint on the control input is also considered. The H∞ polynomial fuzzy control design is represented in terms of sum-of-squares (SOS) conditions which can be efficiently solved by the polynomial optimization Matlab toolbox SOSOPT. Furthermore, simulation results show the effectiveness of the proposed polynomial-fuzzy-model-based control design methodology. After the control design, the polynomial-fuzzy-model-based chaotic synchronization methodology is applied to implement the SCS. Finally, three experiments are given to demonstrate the practicality of the implemented SCS.

Chaotic Secure Communication Based on Single Feedback Phase Modulation and Channel Transmission

In this paper, a chaotic secure communication system based on single feedback phase modulation is designed, in which phase modulation of feedback light is carried out by using random square wave as communication key, and chaotic light with wide spectrum and no delay signature is generated. Message is modulated into chaotic carrier at transmitter end, through chaotic synchronization and comparison, original message is successfully demodulated at receiver end. In addition, two kinds of message encryption methods, chaos modulation and chaos masking, are studied by comparing synchronization and bit error rate under different channel signal-to-noise rate.

Experiment on 10-Gb/s message transmission using an all-optical chaotic secure communication system

We experimentally demonstrate 10-Gb/s message transmission using an all-optical chaotic secure communication system. In this system, a semiconductor laser subject to mirror optical feedback, operating under a high bias current, is employed as the transmitter. Owing to the high bias current, the transmitter’s relaxation oscillation frequency is greatly increased, and consequently, the carrier bandwidth of the transmitted message is also enhanced. By injecting the bandwidth-enhanced signal into an open-loop receiver, we establish a chaos synchronization with a correlation coefficient of 0.94 between the transmitter and the receiver. Based on the high-quality chaos synchronization, a 10 Gb/s message is experimentally encrypted and decrypted with a bit error ratio (BER) below 3.8 ×10−3, i.e., the hard decision forward error correction (HD-FEC) threshold. Bit error analysis indicates that the transceiver, using chaotic decryption, has a BER below the HD-FEC threshold over a wide parameter region. In this parameter region, it is difficult for an eavesdropper using direct decryption to obtain a message with a BER below the HD-FEC threshold.

Optimization and CMOS design of chaotic oscillators robust to PVT variations: INVITED

Edward Lorenz was an early pioneer of the chaos theory. He discovered that small changes in initial conditions produce large changes in long-term outcome, and introduced a chaotic attractor already known as Lorenz chaotic oscillator, which produces a butterfly-like behavior. This and all kinds of continuous-time chaotic oscillators can be simulated with different numerical methods. However, a bad choice of the step size and/or parameters of the mathematical models can produce errors or even mitigate the chaotic behavior. These issues are related to the main property of chaotic oscillators, the high sensitivity to the initial conditions, which is quantified by evaluating the maximum Lyapunov exponent (MLE). The Lorenz and other representative oscillators like Lü, Chua's circuit and Rössler have been implemented using different discrete electronic devices and few ones with integrated circuits (IC) using CMOS technologies. Designing CMOS chaotic oscillators is challenging because a very small variation in their parameters from their mathematical models or in the sizes of the MOS transistors may suppress the chaotic behavior. This article describes how to perform a successful simulation and optimization, and how to synthesize the mathematical models using CMOS technology. The application of metaheuristics to optimize MLE by varying the parameters of the oscillators, and the optimization of the CMOS IC design to guarantee robustness to process, voltage and temperature (PVT) variations, are discussed. Finally, we discuss issues on the application of chaos generators in random number generators, robotics and chaotic secure communication systems.