Real-time online photonic random number generation

Private correlated random bit generation based on synchronized wideband physical entropy sources with hybrid electro-optic nonlinear transformation

We propose and experimentally demonstrate a novel, to the best of our knowledge, private correlated random bit generation (CRBG) scheme based on commonly driven induced synchronization of two wideband physical entropy sources, which employs an open-loop distributed feedback laser followed by a hybrid electro-optic nonlinear transformation hardware module for effective bandwidth expansion and privacy enhancement. A Mach-Zehnder interferometer followed by an electro-optic self-feedback phase modulation loop as well as a dispersion element are constructed as a private hardware module to perform post-processing and nonlinear transformation of the synchronized signal. A record high rate of 5.2-Gb/s CRBG is successfully achieved between two synchronized wideband physical entropy sources with an enhanced entropy source rate and hardware key space. The demonstrated scheme may provide a new way for CRBG in future high speed secure communication systems.

Min-entropy estimation for semiconductor superlattice true random number generators

Semiconductor superlattice true random number generator (SSL-TRNG) has an outstanding practical property on high-throughput and high-security cryptographic applications. Security in random number generators is closely related to the min-entropy of the raw output because feeding cryptographic applications with insufficient entropy leads to poor security and vulnerability to malicious attacks. However, no research has focused on the min-entropy estimation based on the stochastic model for SSL-TRNG, which is a highly recommended method for evaluating the security of a specific TRNG structure. A min-entropy estimation method is proposed in this paper for the SSL-TRNG by extending the Markov stochastic model derived from the memory effects. By calculating the boundary of the transition matrix, the min-entropy result is the average value of each sample (1 bit) is 0.2487. Moreover, the experimental results show that the estimator is accurate enough to adjust compression rate dynamically in post-processing to reach the required security level, estimating entropy on the fly rather than off-line.

Broadband laser chaos generation using a quantum cascade laser with optical feedback

We propose a method to generate broadband laser chaos using a quantum cascade laser (QCL). Through numerical simulation, we give the evidence that the QCL with optical feedback can route to chaos through the quasi-periodic path. Furthermore, we investigate the influence of the feedback intensity and the bias current on the chaos bandwidth. Final results demonstrate that the chaos bandwidth can headily reach 43.1 GHz due to the lack of relaxation oscillation phenomena in QCLs.

Real-time all-optical random numbers based on optical Boolean chaos

In this work, a method of generating all-optical random numbers based on optical Boolean chaotic entropy source is proposed. This all-optical random number generation system consists of a Boolean chaotic entropy source and an optical D flip-flop. The Boolean chaotic entropy source is composed of an optical XOR gate and two self-delayed feedback; meanwhile, the optical D flip-flop is composed of two optical AND gates and one SR latch. The optical Boolean chaotic signal possesses the dynamic characteristics of complexity and binarization, so random numbers would be generated only by extracted from chaotic signals with the optical D flip-flop. This all-optical random number generation system achieves the result of 5 Gb/s random numbers that is testable. The whole process of random number generation could be completed in the optical domain without photoelectric conversion, more importantly, the device could be integrated.

Gbps physical random bit generation based on the mesoscopic chaos of a silicon photonics crystal microcavity

We present an experimental and theoretical physical random bit (PRB) generator using the mesoscopic chaos from a photonic-crystal optomechanical microcavity with a size of ∼10µm and very low operating intracavity energy of ∼60 Femto-Joule that was fabricated with CMOS compatible processes. Moreover, two kinds of PRB generation were proposed with rates over gigabits per second (Gbps). The randomness of the large PRB strings was further verified using the NIST Special Publication 800-22. In addition, the Diehard statistical test was also used to confirm the quality of the obtained PRBs. The results of this study can offer a new generation of dedicated PRB solutions that can be integrated on Si substrates, which can speed up systems and eliminate reliance on external mechanisms for randomness collection.

Generation and synchronization of wideband chaos in semiconductor lasers subject to constant-amplitude self-phase-modulated optical injection

We propose a novel wideband chaos generation scheme by using an external-cavity semiconductor laser (ECSL) subject to optical-electronic hybrid feedback. In this scheme, the output of ECSL is photo-detected and used to modulate the output of a continuous wave laser by an electro-optical phase modulator, the constant-amplitude self-phase-modulated light is then injected back into the ECSL. The experimental results indicate that, compared with the chaos generation with conventional optical feedback (COF), significant bandwidth enhancement is achieved in the proposed scheme. The effective bandwidth of generated chaos is increased from a few GHz to over 20 GHz, and moreover, the spectrum flatness and the complexity of generated chaos are also considerably improved. Furthermore, we propose a wideband chaos synchronization system based on the proposed chaos generation scheme. It is experimentally demonstrated that high-quality synchronization between two wideband chaos signals with an effective bandwidth greater than 20 GHz is achieved. This work simultaneously achieves the generation and the synchronization of wideband chaos, which shows valuable potential in chaos-based secure communication, such as enhancing the transmission capacity and improving the security.

Entropy evaluation of white chaos generated by optical heterodyne for certifying physical random number generators

The entropy of white chaos is evaluated to certify physical random number generators. White chaos is generated from the electric subtraction of two optical heterodyne signals of two chaotic outputs in semiconductor lasers with optical feedback. We use the statistical test suites of NIST Special Publication 800-90B for the evaluation of physical entropy sources of white chaos with an eight-bit resolution. The minimum value of entropy is 2.1 for eight most significant bits data. The entropy of white chaos is enhanced from that of the chaotic output of the semiconductor lasers. We evaluate the effect of detection noise and distinguish between the entropy that originates from the white chaos and the detection noise. It is found that the entropy of five most significant bits originates from white chaos. The minimum value of entropy is 1.1 for five most significant bits data, and it is considered that the entropy can be obtained at at least one bit per sample.

Correlated random bit generation based on common-signal-induced synchronization of wideband complex physical entropy sources

We propose and experimentally demonstrate a novel, to the best of our knowledge, correlated random bit generation (CRBG) scheme in virtue of the synchronization of two physical entropy sources that are composed of a continuous-wave laser, a phase modulator that is driven by the output of a local laser subject to constant-amplitude and random-phase (CARP) injection, as well as a dispersive component. It is experimentally indicated that wideband complex physical entropy sources with an effective bandwidth of 22 GHz can be achieved, and high-quality synchronization with a large cross-correlation coefficient (∼0.95) can be achieved by introducing symmetric CARP injections into the local lasers at Alice and Bob ends. Based on this, two distributed CRBSs with a bit rate over 3 Gb/s and satisfactory consistency are independently generated at Alice and Bob ends; the excellent randomness of CRBSs is verified using a test suite of the National Institute of Standards and Technology.

Observation of flat chaos generation using an optical feedback multi-mode laser with a band-pass filter

We demonstrate experimentally that flat and broadband chaotic signals can be easily generated by combining a multi-mode laser diode subject to optical feedback with a band-pass filter. Measurements are made of the RF spectra of multi-mode and single-mode outputs from an external cavity Fabry-Perot (FP) semiconductor laser before and after the filtering procedure. In this way it is found that in the chaos regime the low-frequency energy of the single-mode output is enhanced by about 25 dB comparing with that of the multi-mode output. Moreover, the associated 3-dB chaos bandwidth can reach around 6 GHz for the single mode case. Numerical demonstrations show mode competition is the physical origin of the low-frequency enhancement in the single-mode chaotic outputs.

Semiconductor-laser-based hybrid chaos source and its application in secure key distribution

An analog-digital hybrid optical chaos source and a corresponding secure key distribution (SKD) scheme are proposed. An analog-digital hybrid electro-optic feedback loop is introduced to enhance the robustness of the chaotic semiconductor lasers. The source, which can adopt robust digital synchronization strategies, could generate a broadband analog optical chaotic signal of high dynamical complexity. Furthermore, the source reduces the requirement on the processing speed of digital components and simplifies the hybrid system structure markedly. For demonstrating, we build a SKD system with the proposed chaos source. Since this SKD scheme is compatible with digital optical networks, the commercially available communication techniques can help to make it insensitive to impairments in fiber optic links. This feature has potential in long-haul SKD.

Wideband complex-enhanced chaos generation using a semiconductor laser subject to delay-interfered self-phase-modulated feedback

A wideband complexity-enhanced chaos generation scheme is proposed by using a semiconductor laser subject to delay-interfered self-phase-modulated optical feedback. The influences of feedback strength, phase modulation index, and interference delay on the effective bandwidth and time-delay-signature (TDS) characteristics of the proposed scheme-generated chaos are extensively investigated both experimentally and numerically. The results demonstrate that with the joint effects of phase modulation-induced spectrum expansion and nonlinear filtering of delayed interference, wideband chaos with flat spectrum and excellent TDS suppression characteristics can be generated over a wide dynamic operation range. In comparisons with the relevant chaos generation schemes under conventional optical feedback, individual self-phase modulated optical feedback, and delay-interfered optical feedback, the proposed scheme cannot only significantly enhance the effective bandwidth of chaos but also considerably enhance the complexity of chaos by suppressing the TDS toward an indistinguishable level close to 0.

Generating randomness: making the most out of disordering a false order into a real one

Randomness is far from a disturbing disorder in nature. Rather, it underlies many processes and functions. Randomness can be used to improve the efficacy of development and of systems under certain conditions. Moreover, valid unpredictable random-number generators are needed for secure communication, rendering predictable pseudorandom strings unsuitable. This paper reviews methods of generating randomness in various fields. The potential use of these methods is also discussed. It is suggested that by disordering a "false order," an effective disorder can be generated to improve the function of systems.

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.

Nonlinear dynamics of solitary and optically injected two-element laser arrays with four different waveguide structures: a numerical study

We study the nonlinear dynamics of solitary and optically injected two-element laser arrays with a range of waveguide structures. The analysis is performed with a detailed direct numerical simulation, where high-resolution dynamic maps are generated to identify regions of dynamic instability in the parameter space of interest. Our combined one- and two-parameter bifurcation analysis uncovers globally diverse dynamical regimes (steady-state, oscillation, and chaos) in the solitary laser arrays, which are greatly influenced by static design waveguiding structures, the amplitude-phase coupling factor of the electric field, i.e. the linewidth-enhancement factor, as well as the control parameter, e.g. the pump rate. When external optical injection is introduced to one element of the arrays, we show that the whole system can be either injection-locked simultaneously or display rich, different dynamics outside the locking region. The effect of optical injection is to significantly modify the nature and the regions of nonlinear dynamics from those found in the solitary case. We also show similarities and differences (asymmetry) between the oscillation amplitude of the two elements of the array in specific well-defined regions, which hold for all the waveguiding structures considered. Our findings pave the way to a better understanding of dynamic instability in large arrays of lasers.

Real-time physical random bit generation at Gbps based on random fiber lasers

We demonstrate for the first time, to the best of our knowledge, a high-speed physical random bit generator at gigabits/second without the time-delay signature based on chaotic power fluctuations of a random fiber laser. The random fiber laser is configured using a ring structure with semiconductor optical amplifiers as the optical gain and a fiber random grating as the random feedback medium. The long-length ring cavity provides a large number of densely spaced cavity modes that co-exist within the gain bandwidth tailored by the optical filter. Unlike fixed cavity modes in conventional fiber ring lasers, these modes are less phase-correlated due to the random distributed feedback from the fiber random grating fabricated by a plane-by-plane inscription technique without phase control, leading to intensified lasing output fluctuations with high-dimensional chaotic dynamic natures without specific cavity features, when the random fiber laser is operated slightly above the lasing threshold. Random bit generation at a bit rate up to ∼1.6  Gbps is achieved with verified randomness through standard tests. Different from the previously reported schemes requiring offline post-processing procedures, this physical random number generator can function in real time, offering high-quality randomness and security assurance for pertinent applications.