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To analyze the unpredictability of Boolean chaos, the model for chaotic circuit system based on autonomous Boolean network is established. In addition, the equations of the Boolean network with propagation time jitter are deduced. By considering the jitter of propagation time because of phase noise, the time for the growth of entropy for an ensemble of trajectories is analyzed. It is demonstrated that Boolean chaos will be unpredictable after tens of nanoseconds, and less average time for the growth of entropy is required as the jitter strength increased. It is shown that Boolean chaos has physical randomness because of phase noise and it also lays the theoretical foundation for the entropy source of true random number generator using chaotic Boolean network.

In this paper, a deep learning (DL)-based predictive analysis is proposed to analyze the security of a non-deterministic random number generator (NRNG) using white chaos. In particular, the temporal pattern attention (TPA)-based DL model is employed to learn and analyze the data from both stages of the NRNG: the output data of a chaotic external-cavity semiconductor laser (ECL) and the final output data of the NRNG. For the ECL stage, the results show that the model successfully detects inherent correlations caused by the time-delay signature. After optical heterodyning of two chaotic ECLs and minimal post-processing are introduced, the model detects no patterns among corresponding data. It demonstrates that the NRNG has the strong resistance against the predictive model. Prior to these works, the powerful predictive capability of the model is investigated and demonstrated by applying it to a random number generator (RNG) using linear congruential algorithm. Our research shows that the DL-based predictive model is expected to provide an efficient supplement for evaluating the security and quality of RNGs.

Boolean chaos is widely used in physical systems for its digital-like behavior and complex dynamics. However, electronic logic devices limit the bandwidth of Boolean chaos and its development. Based on an autonomous optical Boolean network, a method of generating optical Boolean chaos with 14 GHz bandwidth is proposed, exploring the physical mechanism of the chaos generated by the system and analyzing the influences of external parameters on the dynamic characteristics of the system. The output status is mainly affected by the detection optical power, carrier recovery time of the semiconductor optical amplifier, and difference between the two self-feedback time delays. (C) 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

We propose a scheme for an all-optical comparator which embeds a nonlinear fiber ring resonator in a Mach–Zehnder configuration. Such a resonator accumulates the circulating power of the light traversing the ring, so that the effective nonlinear phase shift in fiber can be significantly enhanced. Numerical results demonstrate that with appropriate choice of the parameters of the Mach–Zehnder configuration and the power of the probe light, the all-optical comparator can exhibit an excellent step-like transfer function. Simultaneously, the configuration reduces the switching threshold by 3 or more orders of magnitude to the level of milliwatt when conventional highly nonlinear fibers are adopted. In addition, our simulations show that this all-optical threshold comparator also has a multiperiodic transfer characteristic and thus may be used to construct multibit analog-to-digital convertors.

We present a real-time scheme for ultrafast random number (RN) extraction from a broadband photonic entropy source. Ultralow jitter mode-locked pulses are used to sample the stochastic intensity fluctuations of the entropy source in the optical domain. A discrete self-delay comparison technology is exploited to quantize the sampled pulses into continuous RN streams directly. This scheme is bias free, eliminates the electronic jitter bottleneck confronted by currently available physical RN generators, and has no need for threshold tuning and post-processing. To demonstrate its feasibility, we perform a proof-of-principle experiment using an optically injected chaotic laser diode. RN streams at up to 7 Gb/s with verified randomness were thereby successfully extracted in real time. With the provision of a photonic entropy source with sufficient bandwidth, the present approach is expected to provide RN generation rates of several tens of gigabits per second.