High-speed Random Number Generator Research Articles

High-efficiency implementation of Toeplitz Strong Extractor for PRNG and QRNG output on CPU/GPU hardware systems

Random Number Generators (RNGs) are devices whose utility spans from cryptography to gambling. Depending on the source of the random seed, RNGs are classified as Pseudo-Random Number Generators (PRNGs), which are based on mathematical algorithms, True Random Number Generators (TRNGs) sourced through seemingly random physical processes, and finally, Quantum Random Number Generators (QRNGs) which harness the intrinsic randomness of measured outcomes of quantum states. To ensure that the output of a QRNG is private and nearly uniform, the raw data undergoes a strong extraction process such as Toeplitz or Trevisan Hashing. The extraction process needs to be extremely efficient to achieve high-speed random number generation. The present work demonstrates state-of-the-art methods for performing information-theoretically provable randomness extraction using variations of the Toeplitz Hashing algorithm. These algorithms are implemented on various hardware for comprehensive analysis. Subsequently, these methods are applied to two raw data sets from a PRNG source and a quantum source. A new benchmark of 19.5 Gbps for Randomness Extraction using the Fast Fourier Transform-based Toeplitz Strong Extractor is demonstrated in this work. The implementation of the algorithm on a GPU-based system demonstrates notably enhanced speed, marking a significant leap beyond the existing state-of-the-art implementations.

Nonlinear dynamics in a circular-sided square microcavity laser

Self-chaotic dual-mode and tri-mode microcavity lasers have been recently proposed and demonstrated for high-speed random number generation. Here, we report the characteristics of irregular pulse packages and self-chaos operation for a dual-mode circular-sided square microcavity laser. In addition to the mode interaction between the fundamental and first-order transverse modes, we observed irregular pulse packages due to the mode beating of near-degenerate modes for the first time to our best knowledge. Moreover, a successive route from periodic-one and periodic-three states to chaos is first experimentally illustrated by increasing injection current. The chaotic state is observed over a current range of 10 mA, and the maximum chaos effective bandwidth of 22.4 GHz is realized with a flatness of ±4 dB. Chaotic characteristics are also investigated for different longitudinal modes, which indicates that the self-chaotic microlaser can provide robust parallel chaotic outputs for practical application.

Self-chaotic microlasers for random bit generation

Semiconductor lasers with optical feedback can produce plentiful non-linear dynamics, including periodic and chaotic oscillations, which are usually applied to microwave signals and physical random number generation, respectively. Chaotic semiconductor lasers are especially successful in generating random numbers compared with pseudorandom numbers generated by a computing process. We report a self-chaotic microlaser based on the internal mode interaction of nearly degenerate modes. A special resonator is designed and demonstrated with the two modes’ frequency intervals on the order of GHz. These modes with strong mode beating result in chaos, and physical random bits are obtained from the laser output power at 10 Gb/s. Our proposals provide a novel scheme to generate laser chaos for high-speed random number generation.

Chaotic microlasers caused by internal mode interaction for random number generation

Chaotic semiconductor lasers have been widely investigated for generating unpredictable random numbers, especially for lasers with external optical feedback. Nevertheless, chaotic lasers under external feedback are hindered by external feedback loop time, which causes correlation peaks for chaotic output. Here, we demonstrate the first self-chaotic microlaser based on internal mode interaction for a dual-mode microcavity laser, and realize random number generation using the self-chaotic laser output. By adjusting mode frequency interval close to the intrinsic relaxation oscillation frequency, nonlinear dynamics including self-chaos and period-oscillations are predicted and realized numerically and experimentally due to internal mode interaction. The internal mode interaction and corresponding carrier spatial oscillations pave the way of mode engineering for nonlinear dynamics in a solitary laser. Our findings provide a novel and easy method to create controllable and robust optical chaos for high-speed random number generation.

A simple high-speed random number generator with minimal post-processing using a random Raman fiber laser

A simple novel method for random number generation is presented, based on a random Raman fiber laser. This laser is built in a half-open cavity scheme, closed on one side by a narrow-linewidth 100 mm fiber Bragg grating. The interaction between the randomly excited lasing modes of this laser, in addition to nonlinear effects such as modulation instability, allow the generation of random bits at rates of up to 540 Gbps with minimal post processing. Evaluation of the resulting bit streams’ randomness by the NIST statistical test suite highlights the importance of evaluating the physical entropy content, as bit sequences generated by this random laser pass all the statistical tests with a significance level of 0.01, despite being generated at more than twice the theoretical entropy generation speed.

Simultaneous Chaos Time-Delay Signature Cancellation and Bandwidth Enhancement in Cascade-Coupled Semiconductor Ring Lasers

Optics chaos has been widely studied and its various applications have also been demonstrated in recent years. To improve the performance of chaos-based applications, several properties of the chaotic signals should be evaluated and enhanced accordingly. In this paper, we consider a chaotic system consisting of three cascade-coupled semiconductor ring lasers (SRLs), where the master SRL is subjected to conventional (parallel) optical feedback, while its output is injected to the intermediate SRL and further to the slave SRL. We focus on the time-delay signature (TDS) and bandwidth of the generated chaos and demonstrate the possibility of the simultaneous realization of TDS elimination and bandwidth enhancement in the parameter space of the injection strength against the frequency detuning. In addition, a proof-of-concept test of randomness is carried out, and it demonstrates that the chaotic properties could be greatly enhanced by the proposed cascade-coupling scheme compared with a single SRL with feedback and thus is suitable for use in high-speed random number generation.

Experimental demonstration of 12.5 GHz wideband chaos in symmetric dual-port EDFRL.

We study the dynamics of chaos in a dual-port erbium-doped fiber ring laser (EDFRL). The laser consists of two erbium-doped fibers, intracavity filters at 1549.32nm, isolators, and couplers. At both ports, the laser transitions into the chaotic regime for pump currents greater than 100mA via the period doubling route. We calculate the largest Lyapunov exponent using Rosenstein's algorithm. We obtain positive values for the largest Lyapunov exponent (≈0.2) for embedding dimensions 5, 7, 9, and 11 indicating chaos. We compute the power spectral density of the photocurrents at the output ports of the laser. We observe a bandwidth of 12.5GHz at both ports. This ultra-wideband nature of chaos obtained has potential applications in high-speed random number generation and communication.

Chaotic laser-based ultrafast multi-bit physical random number generation without post-process

Random numbers have great application value in the fields of secure communications, which are commonly used as secret keys to encrypt the information. To guarantee that the information is absolutely secure in the current high-speed communication, the applied random keys should possess a generation speed not less than the encrypted data rate, according to one-time pad theory found by Shannon (Shannon C E 1949 Bell.Syst.Tech.J. 28 656) Pseudo-random numbers generated by algorithm may easily reach a fast speed, but a certain periodicity makes them difficult to meet the aforementioned demand of information security. Utilizing physical stochastic phenomena can provide reliable random numbers, called physical random number generators (RNGs). However, limited by the bandwidth of the conventional physical sources such as electronic noise, frequency jitter of oscillator and quantum randomness, the traditional physical RNG has a generation speed at a level of Mb/s typically. Therefore, real-time and ultrafast physical random number generation is urgently required from the view of absolute security for high-speed communication today. With the advent of wideband photonic entropy sources, in recent years lots of schemes for high-speed random number generation are proposed. Among them, chaotic laser has received great attention due to its ultra-wide bandwidth and large random fluctuation of intensity. The real-time speed of physical RNG based on chaotic laser is now limited under 5 Gb/s, although the reported RNG claims that an ultrafast speed of Tb/s is possible in theory. The main issues that restrict the real-time speed of RNG based on chaotic laser are from two aspects. The first aspect is electrical jitter bottleneck confronted by the electrical analog-to-digital converter (ADC). Specifically, most of the methods of extracting random numbers are first to convert the chaotic laser into an electrical signal by a photo-detector, then use an electrical ADC driven by radio frequency (RF) clock to sample and quantify the chaotic signal in electronic domain. Unfortunately, the response rate of ADC is below Gb/s restricted by the aperture jitter (several picoseconds) of RF clock in the sample and hold circuit. The second aspect comes from the complex post-processes, which are fundamental in current RNG techniques to realize a good randomness. The strict synchronization among post-processing components (e.g., XOR gates, memory buffers, high-order difference) is controlled by an RF clock. Similarly, it is also an insurmountable obstacle to achieve an accurate synchronization due to the electronic jitter of the RF clock. In this paper, we propose a method of ultrafast multi-bit physical RNG based on chaotic laser without any post-process. In this method, a train of optical pulses generated by a GHz mode-locked laser with low temporal jitter at a level of fs is used as an optical sampling clock. The chaotic laser is sampled in the optical domain through a low switching energy and high-linearity terahertz optical asymmetric demultiplexer (TOAD) sampler, which is a fiber loop with an asymmetrical nonlinear semiconductor optical amplifier. Then, the peak amplitude of each sampled chaotic pulse is digitized by a multi-bit comparator (i.e., a multi-bit ADC without sample and hold circuit) and converted into random numbers directly. Specifically, a proof-of-principle experiment is executed to demonstrate the aforementioned proposed method. In this experiment, an optical feedback chaotic laser is used, which has a bandwidth of 6 GHz. Through setting a sampling rate to be 5 GSa/s and selecting 4 LSBs outputs of the 8-bit comparator, 20 Gb/s (=5 GSa/s4 LSBs) physical random number sequences are obtained. Considering the ultrafast response rate of TOAD sampler, the speed of random numbers generated by this method has the potential to reach several hundreds of Gb/s as long as the used chaotic laser has a sufficient bandwidth.

Experimental Evidence of Time-Delay Concealment in a DFB Laser With Dual-Chaotic Optical Injections

The experimental evidence and characterization of time-delay concealment in a semiconductor laser (SL) with dual-chaotic optical injections (DCOIs) are reported. Autocorrelation function and permutation entropy are employed to extract the time-delay signature (TDS). Our experimental results show that both TDSs associated with the dynamics of master lasers or only one of the two TDSs can be concealed in the SL with DCOI, depending on the choices of the injection ratio and frequency detuning of the two injection lights. The experiments are in good agreement with the simulations. Furthermore, the possibility to use the chaotic signal with no obvious TDS generated by the SL with DCOI for high-speed random number generation is experimentally demonstrated.

Two broadband chaotic signals generated simultaneously by semiconductor ring laser with parallel chaotic injection

Recently semiconductor ring laser (SRL) as a novel device has received much attention, for its special cavity allows the output light to propagate in two opposite directions, namely the clockwise mode and counterclockwise mode. SRL does not require gratings or cleaved facets for optical feedback and can be a candidate for small sized photonic integrated circuits which have been developed for secure data transmission, with chaotic carriers and high rate random bit generated. In this paper, we propose a method to obtain two broadband chaotic signals with high unpredictability degree by utilizing injected slave SRL and further explore the physical mechanism and injection conditions. Based on a conventional master-slave configuration, the proposed method obtains two modes of chaotic signals by master SRL with external cross feedback, which are injected in parallel to a slave SRL correspondingly. According to the well-known Lang-Kobayashi rate equations, we establish rate equations and numerically investigate the influences of frequency detuning and injection strength on bandwidth and unpredictability degree. We adapt the given definition of bandwidth and the normalized permutation entropy to respectively evaluate bandwidth and unpredictability degree of chaotic signals. Furthermore, we reveal the underlying physical mechanism of bandwidth enhancement and asymmetric bandwidth-enhancing region by analyzing the radiofrequency and optical spectra of intensity time series. The results show that two chaotic signals have similar routes to enhancing the bandwidth in frequency domain. In the unlocking injection area, two broadband and unpredictability-enhancing chaotic signals generated by slave SRL are simultaneously achieved by choosing appropriate control parameters. Analyses of optical spectra reveal that high-frequency periodic oscillation generated between injection chaotic signals and slave light via beating is the physical mechanism of bandwidth enhncment. The bandwidthenhancing domains of two chaotic signals are asymmetrical due to redshift of master SRL frequency, with external chaotic signals injected. Bandwidth-enhanced chaotic signals are easier to obtain in the domain of negative frequency detuning. The asymmetrical injections contribute to reducing the locking region and extending the bandwidthenhancing region under high injection strength. This conventional master-slave configuration composed of two SRLs can be easily implemented on chip and save other optical devices. The slave SRL subjected to parallel injection signals from master SRL can be used as a wideband unpredictability-enhancing chaotic source, which is extremely useful for the high capacity security-enhancing multiple chaotic communications, as well as for the potential applications of high speed random number generators.

Fast physical and pseudo random number generation based on a nonlinear optoelectronic oscillator

High speed random number generation (RNG) utilizing a nonlinear optoelectronic oscillator (OEO) is explored experimentally. It has been found that by simply adjusting either the injected optical power or the gain of the modulator driver, low complexity dynamics such as square wave, and more complex dynamics including fully developed chaos can be experimentally achieved. More importantly, physical RNG based on high-speed-oscilloscope measurements and pseudo RNG based on post-processing are implemented in this paper. The generated bit sequences pass all the standard statistical random tests, indicating that fast physical and pseudo RNG could be achieved based on the same OEO entropy source. Our results could provide further insight into the implementation of RNG based on chaotic optical systems.

Photonic generation of polarization-resolved wideband chaos with time-delay concealment in three-cascaded vertical-cavity surface-emitting lasers.

Optical chaos generated by chaotic lasers has been widely used in several important applications, such as chaos-based communications and high-speed random-number generators. However, these applications are susceptible to degradation by the presence of time-delay (TD) signature identified from the chaotic output. Here we propose to achieve the concealment of TD signature, along with the enhancement of chaos bandwidth, in three-cascaded vertical-cavity surface-emitting lasers (VCSELs). The cascaded system is composed of an external-cavity master VCSEL, a solitary intermediate VCSEL, and a solitary slave VCSEL. Through mapping the evolutions of TD signature and chaos bandwidth in the parameter space of the injection strength and frequency detuning, photonic generation of polarization-resolved wideband chaos with TD concealment is numerically demonstrated for wide regions of the injection parameters.

Quantum Random Number Generation for 1.25-GHz Quantum Key Distribution Systems

Security proofs of quantum key distribution (QKD) systems usually assume that the users have access to source of perfect randomness. State-of-the-art QKD systems run at frequencies in the gigahertz range, requiring a sustained gigahertz rate of generation and acquisition of quantum random numbers. In this paper, we demonstrate such a high-speed random number generator. The entropy source is based on an amplified spontaneous emission from an erbium-doped fibre, which is directly acquired using a standard small form-factor pluggable module. The module connects to the field programmable gate array (FPGA) of a QKD system. A real-time randomness extractor is implemented in the FPGA, and achieves a sustained rate of 1.25 Gb/s of provably random bits.

基于数字化带宽增强混沌激光信号的高速随机源

基于数字化带宽增强混沌激光信号的高速随机源

Study on real-time optical sampling of chaotic laser for all-optical physical random number generator

Absolutely secure communication should be implemented only through the ‘one-time pad' proposed by Shannon, requires that physical random numbers with rates matched with the associated communication systems be used as secret keys. With the wide application of the WDM technology in optical communication, the single channel rate of the current digital communication system has exceeded 10 Gb/s and developed towards 100 Gb/s. To ensure the absolute security of such a large capacity communication, a large number of real-time, and secure random numbers are needed.#br#Secure random numbers are commonly produced through utilizing physical random phenomena, called physical random number generators. However, conventional physical random number generators are limited by the low bandwidth of the applied entropy sources such as thermal noise, photon-counting and chaotic electrical circuits, and thus have typical low bit rates of the order of Mb/s.#br#In recent years, chaotic lasers attracted wide attention due to their generation of secure, reliable and high-speed random number sequences, and so due to their coherent merits such as high bandwidth, large amplitude fluctuation and ease of integration. There have been lots of schemes based on laser chaos for high-speed random number generation, but most of them execute the random number extractions from the associated laser chaos in the electrical domain and thus their generation rates are faced with the well-known ‘electrical bottleneck'. On the other hand, all-optical random number generation (AO-RNG) methods are all signal processes in the optical domain, so they can efficiently overcome this rate limitation and have a great potential in generating ultrafast random numbers of several dozens or hundreds of Gb/s. However, there is no experimental report on its realization of AO-RNG. One of the obstacles in the way for the AO-RNG achievement is to implement the fast and real-time all-optical sampling of the entropy signals (i.e., laser chaos).#br#In this paper, we present a principal experimental demonstration of the feasibility in the all-optical sampling of the chaotic light signal through constructing a TOAD-based all-optical sampler with a polarization-independent semiconductor optical amplifier (SOA). Specifically, we experimentally generate chaotic laser signals using an optical feedback semiconductor laser and finally complete a 5 GSa/s real-time and high-fidelity all-optical sampling of the chaotic laser with a bandwidth of 6.4 GHz. Further experimental results show that whether the optical sampling period is proportional to the external cavity feedback time or not has a great effect on the weak periodic suppression of the chaotic signal: only when both of them are out of proportion, can the weak periodicity of the original chaotic signal be effectively eliminated; and this is favorable for the generation of high-quality physical random numbers. To the best of our knowledge, it is the first time to realize all-optical sampling of chaotic signal in experiments.

Robust random number generation using steady-state emission of gain-switched laser diodes

We demonstrate robust, high-speed random number generation using interference of the steady-state emission of guaranteed random phases, obtained through gain-switching a semiconductor laser diode. Steady-state emission tolerates large temporal pulse misalignments and therefore significantly improves the interference quality. Using an 8-bit digitizer followed by a finite-impulse-response unbiasing algorithm, we achieve random number generation rates of 8 and 20 Gb/s, for laser repetition rates of 1 and 2.5 GHz, respectively, with a ±20% tolerance in the interferometer differential delay. We also report a generation rate of 80 Gb/s using partially phase-correlated short pulses. In relation to the field of quantum key distribution, our results confirm the gain-switched laser diode as a suitable light source, capable of providing phase-randomized coherent pulses at a clock rate of up to 2.5 GHz.

Efficient Raman generation in a waveguide: A route to ultrafast quantum random number generation

The inherent uncertainty in quantum mechanics offers a source of true randomness which can be used to produce unbreakable cryptographic keys. We discuss the development of a high-speed random number generator based on the quantum phase fluctuations in spontaneously initiated stimulated Raman scattering (SISRS). We utilize the tight confinement and long interaction length available in a Potassium Titanyl Phosphate waveguide to generate highly efficient SISRS using nanojoule pulse energies, reducing the high pump power requirements of the previous approaches. We measure the random phase of the Stokes output using a simple interferometric setup to yield quantum random numbers at 145 Mbps.

Conceal Time Delay Signature of Chaos in Semiconductor Lasers With Dual-Path Injection

The time delay (TD) signatures of chaotic signals in semiconductor lasers (SLs) with dual-path injection (DPI) are investigated numerically and experimentally based on the autocorrelation function and the permutation entropy function, and are compared with those for chaotic signals in SLs with single-path injection (SPI). Both the intensity and phase chaos are considered. The regions of injection strength and frequency detuning contributing to TD concealment are identified. The optimal selection of injection delays for the DPI case is also suggested. It is found that, for both intensity and phase chaos, the TD signature for the DPI case can be better concealed in wider parameter regions than that for the SPI case, which is highly desirable for security-enhanced chaotic communication systems as well as high-speed random number generators based on chaotic SLs.

Route to broadband optical chaos generation and synchronization using dual-path optically injected semiconductor lasers

The generation and synchronization of broadband optical chaos in dual-path optically injected (DPOI) semiconductor lasers (SLs) are numerically demonstrated. The effective bandwidth enhancement is achieved up to about 35.84GHz, under appropriate injection strength and frequency detuning. We systematically study and compare the bandwidth enhancement in single-path optically injected SLs (SPOI-SLs) and DPOI-SLs, and find that better performance can be obtained for the latter over a larger parameter span. Furthermore, two schemes for synchronization of bandwidth-enhanced chaos generated in two similar or identical (twin) DPOI-SLs are proposed, where the twins are driven by a common DPOI signal injected from another chaotic SL. High-quality chaos synchronization, an isochronous type, is observed between the twin DPOI-SLs. Also, the effect of parameter mismatch and frequency detuning is numerically examined. The simple technique of bandwidth enhancement using dual-path injection may pave way for various applications such as high-speed random number generators (RNGs) and chaos-based communications.

Photonic Approach for Generating Randomness-Enhanced Physical Chaos Via Dual-Path Optically Injected VCSELs

The randomness enhancement of physical chaos generated by slave vertical-cavity surface-emitting lasers (S-VCSEL) subject to dual-path polarization-preserved optical injection (DP-PPOI) from single master VCSEL (M-VCSEL) with variable-polarization optical feedback (VPOF) is investigated numerically. The randomness of chaotic signals is evaluated quantitatively by an information-theory-based quantifier, the permutation entropy. The randomness properties for S-VCSEL with DP-PPOI and S-VCSEL with single-path PPOI are compared, as well as the effects of injection strength, frequency detuning, and VPOF are considered. It is shown that, the PE values for S-VCSELs with two different injection schemes are both much higher than those for M-VCSEL, and increase initially and then decrease until they saturate at a constant level. The region of injection parameter space contributing to randomness-enhanced chaos in S-VCSEL can be greatly broadened by adopting DP-PPOI. The generation of randomness-enhanced chaos via photonic approach is highly desirable for high-speed random number generators based on chaotic VCSELs.