Chaos Communication Research Articles

Dynamics-inversion-based optical chaos communication systems with simplified structures and enhanced security

Dynamics-inversion-based optical chaos communication systems with simplified structures and enhanced security

Experimental demonstration on the proactive detection of fiber tapping in optical chaos communication.

Optical chaos communication has a physical-layer security advantage but defends passively against a malicious attack. Here, we conduct a proof-of-concept experiment of detecting the attack proactively by observing performance degradation in optical chaos communication tapped with fiber bending. Influences of the curvature radius of the bent fiber on a chaos synchronization coefficient and bit error rate are investigated. Results show that the synchronization coefficient decreases from 0.958 to 0.904 and the bit error rate increases from 1.31 × 10-4 to 1.73 × 10-3 under a curvature radius of 10 mm, revealing the attack. Bending fiber to this extent leads to a power loss of 1.81%, which is difficult to detect by the optical time-domain reflectometer but causes significant interference to chaos communication due to the concurrent change in the light polarization, jointly decreasing the effective optical injection strength for yielding chaos synchronization.

Improving decryption quality of optical chaos communication using neural networks.

Optical chaos communication is a promising secure transmission technique because of the advantages of high speed and compatibility with existing fiber-optic systems. The deterioration of chaotic synchronization quality caused by fiber optic transmission impairments affects the quality of recovery of information, especially high-order modulated signals. Here, we demonstrate that the use of a convolutional neural network (CNN) with a bidirectional long short-term memory (LSTM) layer can reduce the decryption BER in an optical chaos communication system based on common-signal-induced semiconductor laser synchronization. The performance of a neural network is investigated as a function of network parameters and chaos synchronization coefficient. Experimental results show that the BER of 16-ary quadrature-amplitude-modulation (16QAM) signal after 100-km fiber transmission is decreased from 3.05 × 10-2 to below the soft-decision forward-error-correction (SD-FEC) threshold of 2.0 × 10-2.

Secure Communication via Chaotic Synchronization Based on Reservoir Computing.

Information security occupies a very important part of national security. Chaos communication can provide high-level physical layer security, but its harsh claims on the chaotic system parameters of the transmitter and the receiver resulting in reduced synchronization coefficient and more difficult consistent synchronization of point to multipoint networking. In this article, a chaotic synchronization and communication system based on reservoir computing (RC) has been proposed. In this scheme, the trained RC highly synchronized with the emitter acts as the receiver with simplified structure under the premise of ensuring safety. Simultaneously, the cross-prediction algorithm has been proposed to weaken the accumulation effect of prediction synchronization error of RC and facilitate the realization of long-term communication. Furthermore, the tolerance of the system performance to the signal-to-noise ratio with the variations of the mask coefficients has been investigated, and the optimal operation point under the condition of the adjustable number of nodes and leakage rate of RC has been numerically analyzed. The simulation results show that the normalized mean-square error of synchronization of 10⁻⁶ magnitude and the bit error rate of decryption at 10⁻⁸ level can be obtained. Finally, from the operational perspective, a 100-m short-distance experiment confirms that its communication performance is consistent with the simulation results. We strongly believe that the proposed system offers the opportunity of a new research direction in chaotic secure communications.

Time Delay Signature Extraction of Optical-Feedback-Induced Chaos With Reservoir Computing

The time delay signature is a crucial secure key for chaos communication using optical feedback semiconductor lasers. Herein, we propose a single node-based photonic reservoir computing method for extracting the time delay signature of optical-feedback-induced chaos. Through drawing the phase diagram of the chaotic time series and its delayed copies, we transform the time delay signature into the shape feature of the obtained two-dimensional image. After training the optimized photonic reservoir with these two-dimensional images, we numerically demonstrate that our method can achieve an overall extraction accuracy rate of 97.3% for different optical feedback semiconductor lasers. Considering its good performance and simple configuration, we believe that this single node-based photonic reservoir computing offers a hardware-friendly solution for time delay signature extraction.

Multi-Wavelength Broadband Chaos Generation and Synchronization Using Long-Cavity FP Lasers

Simultaneous generation and synchronization of multiple broadband laser chaos with different wavelengths are numerically demonstrated by using long-active-cavity Fabry-Perot (LC-FP) semiconductor lasers based on multi-mode beating effect. Simulation results show that the LC-FP laser under simple optical feedback can produce broadband chaos with a bandwidth up to 37 GHz with an active cavity length of about 1500um. Furthermore, common-signal-induced chaos synchronization is predicted. Driven by a common chaos from the optical-feedback LC-FP laser, two response LC-FP lasers can reach broadband chaos synchronization with a correlation coefficient beyond 0.98. Meanwhile, the drive-response correlation is low at around 0.4. More interestingly, by optical filtering, parallel multiple broadband chaotic signals at different wavelengths are obtained with bandwidths exceeding 25 GHz and cross-correlation values lower than 0.2. The chaos synchronization keeps for the identical wavelengths. This work will pave a way for increasing capacity of chaos communication.

Secure WDM communication based on second order differential feedback electro-optical chaotic mutual injection synchronization

An optical phase chaos and mutual injection chaos synchronization scheme based on second order differential feedback electro-optical loop is proposed for chaotic communication. The filtered chaotic waves for mutual injection synchronization and multi-channel signals are transmitted through wavelength division multiplexing (WDM) to realize large-capacity confidential communication. The results show that the bandwidth of the optical chaos is 41.38 GHz, the normalized permutation entropy is 0.999, and the chaos has the performance of time delay suppressing (TDS). This scheme achieves up to 7-channel 25 GBaud 16QAM with the multi-modulus algorithm (MMA) algorithm at OSNR of 25 dB after 100 km transmission. The bit-rate distance of 280,000 Gb/s km is successfully realized by 500 km transmission of 4-channel 35 GBaud 16QAM signals at 25 dB OSNR. The analysis proves that the performance of the second order digital differential electro-optical phase feedback (2nd order DEOP) chaos is better than that of the 1st order DEOP chaos and 3rd order DEOP chaos. The 2nd order DEOP chaos can be generated at a smaller feedback coefficient, the bandwidth of radio frequency chaos is wider, and the TDS suppression is better. This scheme realizes high-speed and large-capacity secure optical chaos communication, which can be widely used in WDM networks and has practical feasibility and application value.

Ultra-wideband chaotic optical communication based on electro-optic differential feedback loop

A differential feedback electro-optical phase chaotic system is proposed to generate ultra-wideband optical chaos and realize high-speed long-distance chaotic communication. The nonlinear dynamics of this differential feedback loop are studied in detail. The numerical results show, firstly, in terms of chaos complexity, the highest permutation entropy of 0.993 and the largest spectral entropy of 0.945 are achieved. Regarding the key hiding, the time delay signature of phase chaos on both the autocorrelation function and delayed mutual information can be completely suppressed, so security can be guaranteed. Secondly, the maximum bandwidth of the radio spectrum is 46.75 GHz in the range of 50 GHz, and the minimum flatness is 1.62 dB/GHz. Finally, the reception of format-transparent messages can be realized by combining co-drive synchronization and coherent demodulation. The 50 GBaud QPSK signal can transmit 2400 km and the 25 GBaud 16 QAM signal can transmit 1500 km at an OSNR of 25 dB. This system realizes ultra-wideband high-complexity chaos and chaotic communication, which can greatly improve the security, transmission distance, and transmission rate of chaotic optical communication.

Performance Enhancement of Chaotic Error Correction Coding Using Consecutive Sequences

The use of chaotic dynamics for error correction is the subject of extensive research, as the approach allows to avoid the use of redundant data. This work proposes a new technique for non-coherent chaos communications for modifying error-correction depending on chaotic dynamics. In the proposed system, there are two consecutive sequences created from a comparable chaotic map, with the second series being created as the latest value of the initial one. Generation of a sequential chaotic sequence with a comparable chaotic dynamic delivers additional information to the receiver, allowing it to appropriately recover information and, hence, facilitate the receiver’s bit-error performance. For error correction and for detecting the symbol that is transmitted, a suboptimal technique based on the nearest distance between chaotic map trajectories over the n-dimensional sequence received is utilized. Simulation results show that the proposed error correction approach improves Eb/N0 as the dimension of the trajectory map increases, indicating that the method improves overall error correction performance. With the dimension of 4, a gain of 0.8 dB in Eb/N0 is achieved compared with an approach without any error-correcting schemes, at the bit-error probability of 10−3.

Wideband chaos synchronization using discrete-mode semiconductor lasers.

Optical chaos communication encounters difficulty in high-speed transmission due to the challenge of realizing wideband chaos synchronization. Here, we experimentally demonstrate a wideband chaos synchronization using discrete-mode semiconductor lasers (DMLs) in a master-slave open-loop configuration. The DML can generate wideband chaos with a 10-dB bandwidth of 30 GHz under simple external mirror feedback. By injecting the wideband chaos into a slave DML, an injection-locking chaos synchronization with synchronization coefficient of 0.888 is realized. A parameter range with frequency detuning of -18.75 GHz to approximately 1.25 GHz under strong injection is identified for yielding the wideband synchronization. In addition, we find it more susceptible to achieve the wideband synchronization using the slave DML with lower bias current and smaller relaxation oscillation frequency.

Household chaos and mother-adolescent communication.

Household chaos creates unpredictability and stress in families' lives compromising the quality of family interaction and communication. This study examined how mother and adolescent perceptions of daily household chaos relate to adolescent disclosure of information to mothers. We also explored indirect effects through mother and adolescent responsiveness. Participants included 109 mother-adolescent dyads who completed a 7-day diary study (adolescent age 14-18 years, 49% female, 38% White, 25% Asian, 17% Hispanic, 7% Black, 13% multiple/other ethnicities). Multilevel models revealed that on days when adolescents reported more household chaos than usual, they were more likely to disclose information to their mothers. On days when mothers and adolescents perceived more household chaos, they perceived their relationship partner as less responsive, and on days when mothers and adolescents perceived less responsiveness from their relationship partner, they reported less adolescent disclosure. There was a significant indirect effect among mothers' reports at the daily level, such that on days when mothers reported more household chaos than usual, they reported their adolescents as less responsive, and in turn, as disclosing less information to them. Averages across the week showed that mothers who reported higher average levels of household chaos compared to other families reported less adolescent disclosure. Mothers and adolescents who reported more household chaos compared to other families perceived their relationship partner as less responsive, and less adolescent responsiveness predicted less adolescent-reported and mother-reported adolescent disclosure on average compared to other families. Findings are discussed in terms of relational disengagement in chaotic home environments. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

Chaos synchronization of semiconductor lasers over 1040-km fiber relay transmission with hybrid amplification

Optical chaos communication and key distribution have been extensively demonstrated with high-speed advantage but only within the metropolitan-area network range of which the transmission distance is restricted to around 300 km. For secure-transmission requirement of the backbone fiber link, the critical threshold is to realize long-reach chaos synchronization. Here, we propose and demonstrate a scheme of long-reach chaos synchronization using fiber relay transmission with hybrid amplification of an erbium-doped fiber amplifier (EDFA) and a distributed fiber Raman amplifier (DFRA). Experiments and simulations show that the hybrid amplification extends the chaos-fidelity transmission distance thanks to that the low-noise DFRA suppresses the amplified spontaneous emission noise and self-phase modulation. Optimizations of the hybrid-relay conditions are studied, including launching power, gain ratio of DFRA to EDFA, single-span fiber length, and number of fiber span. A 1040-km chaos synchronization with a synchronization coefficient beyond 0.90 is experimentally achieved, which underlies the backbone network-oriented optical chaos communication and key distribution.

Key Space Enhancement of Chaos Communication Using Semiconductor Lasers with Spectrum-Programmable Optoelectronic Feedback

We propose a scheme for key-space-enhanced chaos secure communication using semiconductor lasers with spectrum-programmable optoelectronic feedback. This feedback consists of multiple parallel optoelectronic feedback loops composed of bandpass filters and radio-frequency amplifiers. The centre frequencies of the filters and gain coefficients of the amplifiers increase the key space. We use 12 parallel filtered feedback loops to analyse the effects of parameter mismatch on the synchronization quality. The simulation result indicates that the key space reaches approximately 2100 at a data rate of 10 Gbit/s, and it can be further enhanced by increasing the number of feedback loops. These results suggest an alternative approach for security-enhanced optical chaos communication.

Performance improvement of coherent optical chaos communication using probabilistic shaping.

We numerically investigate the effects of probabilistic shaping on the performance improvement of coherent optical chaos communication. Results show that the decryption bit-error ratio (BER) of the 16-ary quadrature amplitude modulation (QAM) signal decreases upon increasing the probabilistic shaping factor. It is predicted that the BER of 10-GBd 16QAM can be decreased by one order of magnitude. On the other hand, for the forward error correction threshold of the BER, the requirement for synchronization quality is no longer strict for successful decryption. This means that probabilistic shaping improves the system's tolerance to residual synchronization error. Thus, the transmission rate can be increased by approximately 30∼60%. The side effect of probabilistic shaping is that the valid masking coefficient range is narrowed.

Dual-Channel Secure Communication Based on Wideband Optical Chaos in Semiconductor Lasers Subject to Intensity Modulation Optical Injection

Chaotic optical communication was initially proposed to provide advanced physical layer security for optical communication. Here, we propose and numerically demonstrate an optical chaos communication scheme based on semiconductor lasers subject to intensity modulation optical injection for secure transmission of quadrature amplitude modulation (QAM) messages. In this scheme, two chaotic sources were generated with different modulation parameters and acted as chaotic carriers at the transmitter side, which were subsequently used to drive two receivers in two separate channels. Numerical results demonstrate that this scheme allows for broadband chaos generation and high-quality chaos synchronization can be achieved to simultaneously encrypt two messages for secure communication; a 20 GBaud 16-QAM message was recovered correctly with a transmission distance in standard single mode fiber (SMF) over 120-km, while the other 20 GBaud 64-QAM message was limited to a 20-km fiber transmission distance. The system performance was systematically evaluated by analyzing the bit error ratio (BER) of the recovered message versus the masking coefficient and the transmission distance. Furthermore, our simulations justify the robustness against the mismatch of parameters. Therefore, we hope that this scheme can be experimentally implemented for high-speed chaos communication and secure key distribution.

Incomplete synchronization of chaos under frequency-limited coupling: Observations in single-transistor microwave oscillators

The synchronization of chaotic systems has been extensively studied based on diverse coupling schemes and media which allow almost unaltered energy exchange over the entire spectral range of oscillation. Less is known about the dynamics of systems encompassing couplings that restrict interaction to a narrower frequency interval, such as through band-pass filtering. Here, this situation is systematically investigated in the context of a master–slave pair of single-transistor chaotic oscillators operating in the microwave region. Albeit incomplete, phase synchronization remains detectable down to a fractional bandwidth on the order of 5% when the pass band is centered around the predominant spectral peaks, leading to a well-evident directed causal influence alongside intricate spectral effects. Concordant results are obtained between numerical simulations using an LC network and experimental measurements based on an electrically-tunable filter as a coupling medium. The possibility of maintaining selective locking over a channel shared between two oscillator pairs is shown. It is furthermore demonstrated that, in this circuit, frequency-limited coupling entrains one aspect of the chaotic dynamics, namely damped resonance, without significantly impacting the relaxation process that irregularly excites it. These results demonstrate in a realistic setting that chaos synchronization does not unavoidably require broadband couplings, thus enabling future applications of chaos communication using realistic antennas such as in distributed sensing. Some considerations about the construction of a hypothetical cellular network based on the coupling scheme under consideration are given.

Influence of Linewidth Enhancement Factor on the Nonlinear Dynamics and TDS Concealment of Semiconductor Ring Lasers

In this paper, the influences of linewidth enhancement factor on the output characteristics of a semiconductor ring laser (SRL) are numerically investigated. By constructing a master–slave injection model, we discuss the influence of linewidth enhancement factor on the output characteristics of SRL. In addition, the 0–1 chaos test is introduced to study the effects of linewidth enhancement factor, feedback strength, feedback time delay and normalized injection current on the dynamic characteristics of the master laser. Furthermore, a simulation study is carried out on the suppression of time delay characteristics by the linewidth enhancement factor. The results show that selecting a proper linewidth enhancement factor has a significant effect on the chaotic output of SRL, and a larger linewidth enhancement factor is beneficial for the concealment of time delay signature. Such results are beneficial for achieving the security chaos communication and physical random generators.

Chaotic optical communications of 12.5-Gbaud OOK and 10-Gbaud QPSK signals based on mutual injection of semiconductor lasers.

Chaotic optical communications can provide a high level of security in data transmission. High-speed chaotic optical communications have hardly been implemented so far limited by the bandwidth of chaotic signals and the difficulties of wideband chaos synchronization. Here, we experimentally demonstrate all-optical wideband chaos synchronization and communications based on mutual injection of semiconductor lasers. Both 12.5-Gbaud on-off keying (OOK) signals and 10-Gbaud quadrature phase shift keying (QPSK) signals are successfully encrypted and transmitted over a 10-km and 2-km single-mode fiber (SMF), respectively.

Complex Modified Projective Difference Function Synchronization of Coupled Complex Chaotic Systems for Secure Communication in WSNs

Complex-variable chaotic systems (CVCSs) have numerous advantages over real-variable chaotic systems in chaos communication due to their increased unpredictability, confidentiality, and the ease of implementation. Synchronization between the master and slave systems in CVCSs is key to achieving encryption and decryption. However, existing synchronization schemes for CVCSs require the amplitude of the chaotic signal to be much larger than that of the plaintext. Moreover, traditional chaotic masking of complete synchronization (CS) requires uniformity between the transmitter and receiver ends. Therefore, we propose a complex modified projective difference function synchronization (CMPDFS) of CVCSs to address these issues, where the modified projective matrix helps address the issues with the amplitude. The receiver end is reconstructed without uniformity of the transmitter. We design the CMPDFS controller and propose a new secure communication scheme for wireless sensor networks (WSNs). The basic principle is fundamentally different from traditional chaotic masking. Simulation results and security analysis demonstrate that the CMPDFS communication scheme has a large key space, high sensitivity to encryption keys, high security, and an acceptable encryption speed. Hence, the proposed scheme can improve the security of WSNs. Moreover, it also can be applied to similar communication systems.

An Enhanced Electro-Optic Chaos Secure Communication System Immune to Time Delay Signature Extraction

Time delay signature (TDS) is a key issue that affects the security performance of optical chaos communication. Currently, the autocorrelation function (ACF) and delayed mutual information (DMI) are two crucial methods to extract the TDS. Several strategies have been proposed to resist statistical analysis (i.e., ACF and DMI). However, a dynamic inverse modeling method has been proposed to identify TDS by utilizing the strong nonlinear inversion capability of deep learning, which brings about new threat. To resist this analysis, we propose a stratagem that one can increase the nonlinear dimensionality of the chaos system at the transmitter and concurrently reduce the dimensionality of transmitted signals, leading to “deficiency of data dimensionality”. A three-dimensional chaotic system is designed as the transmitter and only one-dimensional signal is transmitted for communication. Furthermore, a hybrid receiver is designed. The nonlinear model of the response system is realized by cooperation of an analog electro-optical link and a neural network in digital domain. The architecture not only destroys the possibility of TDS extraction but also preserves all necessary information required for chaos synchronization with low-complexity implementation.