Enhanced secure strategy for electro-optic chaotic systems with delayed dynamics by using fractional Fourier transformation

Ultrafast electro-optic time-frequency fractional Fourier imaging at the single-photon level

The Fractional Fourier Transform (FRT) corresponds to an arbitrary-angle rotation in the phase space, e.g., the time-frequency (TF) space, and generalizes the fundamentally important Fourier Transform. FRT applications range from classical signal processing (e.g., time-correlated noise optimal filtering) to emerging quantum technologies (e.g., super-resolution TF sensing) which rely on or benefit from coherent low-noise TF operations. Here a versatile low-noise single-photon-compatible implementation of the FRT is presented. Optical TF FRT can be synthesized as a series of a spectral disperser, a time-lens, and another spectral disperser. Relying on the state-of-the-art electro-optic modulators (EOM) for the time-lens, our method avoids added noise inherent to the alternatives based on non-linear optical interactions (such as wave-mixing, cross-phase modulation, or parametric processes). Precise control of the EOM-driving radio-frequency signal enables fast all-electronic control of the FRT angle. In the experiment, we demonstrate FRT angles of up to 1.63 rad for pairs of coherent temporally separated 11.5 ps-wide pulses in the near-infrared (800 nm). We observe a good agreement between the simulated and measured output spectra in the bright-light and single-photon-level regimes, and for a range of pulse separations (20 ps to 26.7 ps). Furthermore, a tradeoff is established between the maximal FRT angle and optical bandwidth, with the current setup accommodating up to 248 GHz of bandwidth. With the ongoing progress in EOM on-chip integration, we envisage excellent scalability and vast applications in all-optical TF processing both in the classical and quantum regimes.

Fingerprint construction of optical transmitters based on the characteristic of electro-optic chaos for secure authentication

In this paper, an optical transmitter authentication method using hardware fingerprints based on the characteristic of electro-optic chaos is proposed. By means of phase space reconstruction of chaotic time series generated by an electro-optic feedback loop, the largest Lyapunov exponent spectrum (LLES) is defined and used as the hardware fingerprint for secure authentication. The time division multiplexing (TDM) module and the optical temporal encryption (OTE) module are introduced to combine chaotic signal and the message to ensure the security of the fingerprint. Support vector machine (SVM) models are trained to recognize legal and illegal optical transmitters at the receiver. Simulation results show that LLES of chaos has the fingerprint characteristic and is highly sensitive to the time delay of the electro-optic feedback loop. The trained SVM models can distinguish electro-optic chaos generated by different feedback loops with a time delay difference of only 0.03ns and have a good anti-noise ability. Experimental results show that the recognition accuracy of the authentication module based on LLES can reach 98.20% for both legal and illegal transmitters. Our strategy can improve the defense ability of optical networks against active injection attacks and has high flexibility.

Physical-layer security of optical communication based on chaotic optical encryption without an additional driving signal

We propose and numerically demonstrate a scheme for physical-layer security based on chaotic phase encryption, where the transmitted carrier signal is used as the common injection for chaos synchronization, so there is no need for additional common driving. To ensure privacy, two identical optical scramblers consisting of a semiconductor laser and a dispersion component are used to observe the carrier signal. The results show that the responses of the optical scramblers are highly synchronized but are not synchronized with the injection. By properly setting the phase encryption index, the original message can be well encrypted and decrypted. Moreover, the legal decryption performance is sensitive to the parameter mismatch, since it can degrade the synchronization quality. A slight drop in synchronization induces an evident deterioration in decryption performance. Therefore, without perfectly reconstructing the optical scrambler, the original message cannot be decoded by an eavesdropper.

Electro-optic chaotic system based on time delay feature hiding and key space enhancement based on chaotic post-processing

To improve the output performance of the classical all-optical chaotic system and solve the security problems of its key exposure and small key space, a new chaotic system, to the best of our knowledge, based on logistic map post-processing is proposed. In terms of the general output performance of the system, the spectrum of the proposed system is flatter than the classical system. Through a bifurcation diagram and permutation entropy analysis, it is found that the output of the system is extremely complex. In terms of security, the simulation results show that, with a reasonable selection of system parameters, key hiding can be achieved under a large parameter range. Moreover, through the sensitivity analysis of logistic parameters, it can be seen that the introduction of logistic parameters can improve the key space of the system and further improve the security of the system.

A time-delay signature elimination and broadband electro-optic chaotic system with enhanced nonlinearity by deep learning

In this paper, a novel electro-optic chaotic system with enhanced nonlinearity by deep learning (ENDL) is proposed to achieve time-delay signature (TDS) elimination. A long-short term memory network (LSTM) is trained by a specially designed loss function to enhance the nonlinear effect that can hide the TDS of the system. For the first time, the trained deep learning module is put into a single feedback loop to participate in chaos generation. Simulation results show that the ENDL system can eliminate TDS and increase the bandwidth to more than 31GHz when the feedback intensity is very low (α = 4V). Moreover, the complexity of the chaotic output can be improved with permutation entropy (PE) reaching 0.9941. The synchronization result shows that the ENDL system has high sensitivity to TDS but has low sensitivity to the feedback intensity, thus the system has both high security and high robustness. This system has an uncomplicated synchronization structure and high flexibility, and it opens up a new direction for high-quality chaos generation.

Characterizing the chaotic dynamics of a semiconductor nanolaser subjected to FBG feedback

Nonlinear dynamics of semiconductor nanolasers subjected to distributed feedbacks from fiber Bragg grating (FBG) are investigated through modified rate equations, which include the unique Purcell cavity-enhanced spontaneous emission factor F and spontaneous emission coupling factor β. In the analysis, the effects of F, β, frequency detuning, feedback strength, feedback delay, FBG bandwidth and length on chaotic performance are evaluated. It is observed that the approach of FBG feedback outperforms mirror feedback in terms of concealing time-delay signature and increasing effective bandwidth by choosing intermediate feedback strength and frequency detuning. Additionally, chaotic regions and the corresponding chaotic characteristics are revealed by dynamical mappings of nanolasers subjected to FBG feedback. The results show that decreased F, β and increased FBG bandwidth can extend the parameter range of chaos. However, the variation of feedback delay and FBG length has no obvious effect on TDS suppression and effective bandwidth enhancement. Most importantly, high quality optical chaos with low TDS and high effective bandwidth induced by increased dispersion is obtained within broad parameter regions considered, which is beneficial to achieving chaos-based applications.

Physical secure optical communication based on private chaotic spectral phase encryption/decryption

We propose and demonstrate a novel physical, secure high-speed optical communication scheme based on synchronous chaotic spectral phase encryption (CSPE) and decryption (CSPD). The CSPE is performed by a module composed of two dispersion components and one phase modulator (PM) between them, and the CSPD is carried out by a twin module with reverse dispersions and inverse PM driving signals. The PM driving signals of the CSPE and CSPD modules are privately synchronized chaotic signals that are independently generated by local external-cavity semiconductor lasers subject to common injection. The numerical results indicate that with the CSPE, the original message can be encrypted as a noise-like signal, and the timing clock of the original message is efficiently hidden in the encrypted signal. Based on the private synchronization of the chaotic PM driving signals, only the legal receiver can decrypt the message correctly, while the eavesdropper is not able to intercept a useful message. Moreover, the proposed scheme can also support secure symmetric bidirectional high-speed WDM transmissions. This work shows a prospective way to implement high-speed secure optical communications at the physical layer.

Chaos synchronization and communication in closed-loop semiconductor lasers subject to common chaotic phase-modulated feedback

We propose and demonstrate a closed-loop chaos system composed of external-cavity semiconductor lasers subject to common chaotic phase-modulated optical feedback (CCPMOF). The efficient-bandwidth and time-delay signature (TDS) characteristics of the chaotic carrier, the properties of chaos synchronization, as well as the performance and security of chaos communication are systematically investigated. The numerical results demonstrate that wideband chaotic carrier with effective TDS suppression can be easily obtained, high-quality chaos synchronization with considerable mismatch robustness, frequency detuning tolerance, and phase fluctuation tolerance can be achieved in a wide operation range, and high-speed chaos communication is available. With respect to the conventional closed-loop systems, the bandwidth and complexity of chaotic carrier is greatly enhanced, and the performances of chaos synchronization and communication are obviously improved.

Ultrafast physical random bit generation from a chaotic oscillator with a silicon modulator

We demonstrate physical random bit (PRB) generation from two chaotic optoelectronic oscillators (OEOs) with silicon Mach-Zehnder and microring resonator modulators. The carrier-injection modulation and the beam interference provide the nonlinearity for the OEO. We digitalize the chaotic waveforms from the two OEOs at 40 GS/s with 8-bit resolution and use self-delay bitwise exclusive-or operation as a post-processing method. The randomness of the resulting 320 Gbps PRB sequences is verified by the National Institute of Standards and Technology Special Publication 800-22 statistical tests. With the progress of silicon photonic circuits, there is a potential to fabricate a monolithic chaotic OEO chip for compact PRB generation.

Analysis and characterization of chaos generated by free-running and optically injected VCSELs

We report on the dynamics of free-running and optically injected VCSELs. In particular, the powerful measures including the 0-1 test for chaos and permutation entropy are used for locating the chaotic dynamics in a free-running VCSEL, which illustrates the effects of some key parameters on the chaotic region. In order to enhance chaotic dynamics, the output of the free-running VCSEL (master) is injected to another free-running VCSEL (slave). Our results show that the chaotic dynamics of the slave VCSEL can be greatly enhanced, i.e., both the bandwidth and complexity, while this occurs only outside of the injection locking region where the correlation between the mater and slave lasers is low. To take advantage of these enhanced chaotic dynamics exhibiting extremely high complexity and broadband bandwidth, a three-laser synchronization scheme is proposed and demonstrated. These findings pave the way to the generation of high-quality chaos (no time-delay signature, high bandwidth and complexity) and notably chaos-based applications based on free-running and optically injected VCSELs.

Multi-Gbit/s optical phase chaos communications using a time-delayed optoelectronic oscillator with a three-wave interferometer nonlinearity

We propose a chaos communication scheme based on a chaotic optical phase carrier generated with an optoelectronic oscillator with nonlinear time-delay feedback. The system includes a dedicated non-local nonlinearity, which is a customized three-wave imbalanced interferometer. This particular feature increases the complexity of the chaotic waveform and thus the security of the transmitted information, as these interferometers are characterized by four independent parameters which are part of the secret key for the chaos encryption scheme. We first analyze the route to chaos in the system, and evidence a sequence of period doubling bifurcations from the steady-state to fully developed chaos. Then, in the chaotic regime, we study the synchronization between the emitter and the receiver, and achieve chaotic carrier cancellation with a signal-to-noise ratio up to 20 dB. We finally demonstrate error-free chaos communications at a data rate of 3 Gbit/s.

Generation of flat wideband chaos with suppressed time delay signature by using optical time lens

We propose a flat wideband chaos generation scheme that shows excellent time delay signature suppression effect, by injecting the chaotic output of general external cavity semiconductor laser into an optical time lens module composed of a phase modulator and two dispersive units. The numerical results demonstrate that by properly setting the parameters of the driving signal of phase modulator and the accumulated dispersion of dispersive units, the relaxation oscillation in chaos can be eliminated, wideband chaos generation with an efficient bandwidth up to several tens of GHz can be achieved, and the RF spectrum of generated chaotic signal is nearly as flat as uniform distribution. Moreover, the periodicity of chaos induced by the external cavity modes can be simultaneously destructed by the optical time lens module, based on this the time delay signature can be completely suppressed.

A new switching parameter varying optoelectronic delayed feedback model with computer simulation

In this paper, a new switching parameter varying optoelectronic delayed feedback model is proposed and analyzed by computer simulation. This model is switching between two parameter varying optoelectronic delayed feedback models based on chaotic pseudorandom sequences. Complexity performance results show that this model has a high complexity compared to the original model. Furthermore, this model can conceal the time delay effectively against the auto-correlation function, delayed mutual information and permutation information analysis methods, and can extent the key space, which greatly improve its security.