Physical Random Bit Research Articles

Real-Time Massive Parallel Generation of Physical Random Bits Using Weak-Resonant-Cavity Fabry-Perot Laser Diodes

We experimentally demonstrate a scheme for generating massively parallel and real-time physical random bits (PRBs) by using weak-resonant-cavity Fabry-Perot laser diodes (WRC-FPLDs) with optical feedback. By using external optical feedback to modify the nonlinear dynamic behavior of the longitudinal modes in WRC-FPLDs, the chaotic behavior of each channel can be induced under suitable feedback strength. By filtering these longitudinal modes, a real-time PRBs at 10 Gbits/s can be generated by using field programmable gate array (FPGA) board for the real-time post-processing of a single-channel chaotic signal. Considering the presence of up to 70 longitudinal modes within a broad spectral range exceeding 40 nm, each of these modes can be used to extract chaotic time sequences for random number generation. Therefore, our PRB generation scheme has the potential to achieve a data throughput of over 700 Gbits/s.

Scalable parallel ultrafast optical random bit generation based on a single chaotic microcomb

Random bit generators are critical for information security, cryptography, stochastic modeling, and simulations. Speed and scalability are key challenges faced by current physical random bit generation. Herein, we propose a massively parallel scheme for ultrafast random bit generation towards rates of order 100 terabit per second based on a single micro-ring resonator. A modulation-instability-driven chaotic comb in a micro-ring resonator enables the simultaneous generation of hundreds of independent and unbiased random bit streams. A proof-of-concept experiment demonstrates that using our method, random bit streams beyond 2 terabit per second can be successfully generated with only 7 comb lines. This bit rate can be easily enhanced by further increasing the number of comb lines used. Our approach provides a chip-scale solution to random bit generation for secure communication and high-performance computation, and offers superhigh speed and large scalability.

A Tbit/s parallel real-time physical random number scheme based on chaos optical frequency comb of Si<sub>3</sub>N<sub>4</sub> micro-ring

<sec>Physical random numbers (PRNs) own various advantageous characteristics, including unpredictability, non-repeatability, higher security and reliability. Meanwhile, laser chaos has attracted great attention in the field of PRN. In terms of single channel PRN, laser chaos schemes can achieve a much higher bit-rate than traditional quantum PRN schemes. So far, various laser chaos PRN schemes have been discussed in order to enhance the performance of single channel laser chaos PRN. However, considering the limited bandwidth of laser chaos, especially the bandwidth of digital electronic circuit, the development potential of single channel PRN should be limited and may fall into the trap of high performance and expensive cost. Recently, the applications of multi-channel parallel PRN schemes have been developed. These parallel types may balance the high performance of PRN in a low cost. Recent progress indicates that chaotic micro-comb may have good potential. The micro-comb exhibits highly nonlinear and complex dynamic characteristics, and each comb tooth may show chaotic oscillation. The wavelength division multiplexing technology enables large-scale optical parallel output, providing the possiblity for large-scale parallel PRN generation. However, most of these PRN schemes are offline rather than true online and real-time random numbers. Thus, the development of real, online real-time parallel PRN solutions has great interest and research value in related fields.</sec><sec>Herein we experimentally demonstrat an ultra-high-speed parallel real-time physical random number generator, which is achieved though the combination of chaotic micro-comb of chip-scale Si<sub>3</sub>N<sub>4</sub> ultra-high Q micro-resonator and a high-speed field programmable gate array (FPGA). The results show that the Si<sub>3</sub>N<sub>4</sub> ultra-high Q micro-resonator generates a micro-comb with hundreds of channels, each channel can route into an optically chaotic state, and become an excellent physical entropy source. Using FPGA onboard multi-bit analog-to-digital converter, the filtered optical chaos signal from the micro-comb is discretely sampled and quantized, and resulting in an 8-bit binary bitstream. Taking real-time self-delayed exclusive or (XOR) processing of bitstream and preserving 4 least significant bits, the qualified physical random bitstream with real-time 5 Gbits/s rate is realized experimentally. Considering that there are 294 chaotic comb teeths, our approach anticipates a throughput of 1.74 Tbits/s of real-time physical random bits. Our results could offer a new integrated and ultra-high-speed option for real-time physical random number sources.</sec>

Massive and parallel 10 Tbit/s physical random bit generation with chaotic microcomb

Ultrafast physical random bit (PRB) generators and integrated schemes have proven to be valuable in a broad range of scientific and technological applications. In this study, we experimentally demonstrated a PRB scheme with a chaotic microcomb using a chip-scale integrated resonator. A microcomb contained hundreds of chaotic channels, and each comb tooth functioned as an entropy source for the PRB. First, a 12 Gbits/s PRB signal was obtained for each tooth channel with proper post-processing and passed the NIST Special Publication 800-22 statistical tests. The chaotic microcomb covered a wavelength range from 1430 to 1675 nm with a free spectral range (FSR) of 100 GHz. Consequently, the combined random bit sequence could achieve an ultra-high rate of about 4 Tbits/s (12 Gbits/s × 294 = 3.528 Tbits/s), with 294 teeth in the experimental microcomb. Additionally, denser microcombs were experimentally realized using an integrated resonator with 33.6 GHz FSR. A total of 805 chaotic comb teeth were observed and covered the wavelength range from 1430 to 1670 nm. In each tooth channel, 12 Gbits/s random sequences was generated, which passed the NIST test. Consequently, the total rate of the PRB was approximately 10 Tbits/s (12 Gbits/s × 805 = 9.66 Tbits/s). These results could offer potential chip solutions of Pbits/s PRB with the features of low cost and a high degree of parallelism.Graphical

Modeless Raman fiber laser

The discrete multi-longitudinal mode structure and temporal periodic fluctuation are the intrinsic features of conventional lasers. However, longitudinal mode spacing limits the maximum resolution in high-resolution laser sensing systems. In addition, temporal periodic fluctuation reduces the security of secure communication and deteriorates the randomness in fast physical random bit generation. Therefore, it still remains an open challenge to realize a laser source without discrete longitudinal mode and temporal periodic fluctuation. Here, a modeless Raman fiber laser (RFL) with high efficiency was demonstrated. The output cavity mirror adopts a fiber Bragg grating with ultralow reflectance of −27dB. Due to the modulation instability, the discrete multi-longitudinal modes in the RFL gradually broaden with the increase of intracavity Stokes wave power and eventually fully overlap. At high power levels, the RFL no longer has discrete longitudinal modes like a conventional laser but generates a quasi-continuous spectrum. Benefiting from the modeless nature, the RFL can achieve extremely low relative intensity noise, favorable temporal stability, and rather low coherence. Modeless RFLs are expected to be ushered as ideal light sources into secure communication, optical sensing, and optical imaging.

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.

Fast True Random Bit Generation With an SOA-Based Random Fiber Laser

Physical random bits are generated at rates up to 40 Gbps using an 8-bits digital oscilloscope acquiring the optical intensity at the output of an SOA-based random fiber laser. The simple and minimal off-line post-processing (the selection of 4 LBS) can be easily implemented in real time. The true random bits sequences passed all NIST tests.

Fast physical random bit generation based on a chaotic optical injection system with multi-path optical feedback.

Based on the chaotic signal provided by a simple chaotic system, a random bit sequence with a rate of 640 Gb/s is generated through adopting the circulating exclusive-or (CXOR) post-processing method. Such a simple chaotic system is built via a slave semiconductor laser subject to optical injection of a chaotic signal originated from a master semiconductor laser under multi-path optical feedback. First, through inspecting the dependences of the time-delay-signature (TDS) and bandwidth of the chaotic signal on some key operation parameters, optimized parameters are determined for generating a high-quality chaotic signal with a large bandwidth and low TDS. Second, the high-quality chaotic signal is converted to an 8-bit digital signal by sampling with a digital oscilloscope at 80 GSa/s. Next, through adopting the CXOR post-processing method, a bit sequence with a rate of 640 Gb/s is obtained. Finally, the randomness is estimated by the National Institute of Standard Technology (NIST) Special Publication 800-22 statistical tests, and the results demonstrate that the obtained random bit sequence can pass all the NIST tests.

Ultrafast and real-time physical random bit extraction with all-optical quantization

Optical chaos generated by perturbing semiconductor lasers has been viewed, over recent decades, as an excellent entropy source for fast physical random bit generation (RBG) owing to its high bandwidth and large random fluctuations. However, most optical-chaos-based random bit generators perform their quantization process in the electrical domain using electrical analog-to-digital converters, so their real-time rates in a single channel are severely limited at the level of Gb/s due to the electronic bottleneck. Here, we propose and experimentally demonstrate an all-optical method for RBG where chaotic pulses are quantized into a physical random bit stream in the all-optical domain by means of a length of highly nonlinear fiber. In our proof-of-concept experiment, a 10-Gb/s random bit stream is successfully generated on-line using our method. Note that the single-channel real-time rate is limited only by the chaos bandwidth. Considering that the Kerr nonlinearity of silica fiber with an ultrafast response of few femtoseconds is exploited for composing the key part of quantizing laser chaos, this scheme thus may operate potentially at much higher real-time rates than 100 Gb/s provided that a chaotic entropy source of sufficient bandwidth is available.

Fast physical random bit generation using a millimeter-wave white noise source.

A broadband millimeter-wave (MMW) white noise signal generated by optical heterodyning of two Fabry-Perot laser diodes (FP-LDs) subject to optical feedback is demonstrated and employed for fast physical random bit generation with a simple least significant bits (LSBs) retaining method. Firstly, under suitable feedback conditions, two external-cavity feedback FP-LDs can be easily driven into chaotic states. In this process, the optical spectra of multi-longitudinal modes are significantly broadened. Then, two spectral broadening multi-longitudinal chaotic signals are mixed and converted into an MMW white noise signal through the heterodyne beating technique combined with a fast photodetector. With such an approach, a high dimensional broadband chaos with perfect characteristics of MMW white noise (3-dB bandwidth beyond 50 GHz without any time-delay signature) is experimentally achieved. Finally, taking the generated MMW white noise as the entropy source, 640 Gb/s physical random bit generation is realized by directly selecting 4-LSBs at 160 GS/s sampling rate after an 8-bit analog-digital-convertor.

Fast physical random bit generation of wideband flat chaos signal based on filter feedback

<sec>Chaotic lasers feature wide spectrum and noise-like features, and extensively used in various fields, such as secure communications and random bit generation (RBG). Since the physical RBG using optical chaos was demonstrated first by Uchida et al., the optical chaos has been widely investigated in terms of chaos bandwidth and flatness, which determines the rate and randomness of RBG. Owing to the natural stability of semiconductor lasers, external perturbation is required to generate chaotic signals, such as optical injection, current modulation, and optical feedback. Among them, a semiconductor laser with optical feedback has attracted wide attention because of its simple structure and rich dynamic behaviors. Nonetheless, this configuration suffers the influence of the relaxation oscillation, which results in a limited bandwidth (a few GHz) and an uneven power spectrum. To obtain broad-spectrum chaotic signals, considerable efforts have been made in recent years. However, these solutions are associated with complex structures that require delicate manipulation because multiple parameters should be matched, so the cost of some of these schemes in terms of the system complexity can potentially outweigh the benefits.</sec><sec>In this work, we incorporate an optical filter and an amplifier into the feedback loop of a conventional optical feedback system to generate broadband chaotic signals. The effects of the filter detuning frequency and feedback power on the bandwidth and flatness of the chaotic output are investigated experimentally. The experimental results demonstrate that by appropriately adjusting the feedback power and detuning frequency, both the low-frequency components and the high-frequency components of the chaotic output power spectrum can be increased, and the maximum chaotic bandwidth can reach 24.4 GHz with a flatness of 5.7 dB. This phenomenon is attributed to the physical process of beating between the filtered mode and the internal modes of the laser. Furthermore, the optimized chaotic output is processed by retaining the 4 least significant bits and implementing the delayed exclusive-OR (XOR) operation. Our scheme is capable of generating physical random number of the bit rate of 320 Gbit/s, and successfully passes the standard randomness test, i.e. the NIST test (NIST SP 800-22).</sec>

Ultra-high speed random bit generation based on Rayleigh feedback assisted ytterbium-doped random fiber laser

In this paper, we propose an ultra-high speed random bit generator without the time-delay signature based on an ytterbium-doped random fiber laser (YRFL) with Rayleigh scattering feedback. The spectrum of the YRFL has a relatively broad bandwidth (0.35 nm) and the lasing temporal intensity shows random fluctuations without cavity induced time-delay signatures (TDS), which are essential for ultra-high speed random bit generation The chaotic signal and its time-delayed signal sampling at 40 Giga samples per second (GS/s) are converted to digital 8-bit signals. By selecting 5 least significant bits from each 8-bit digital signal and using bitwise exclusive-OR operation, we experimentally achieve 200 Gbps physical random bit generation based on ytterbium-doped random fiber laser with the verified randomness. The combination of broadband emission and free of TDS makes random fiber lasers new promising sources for high performance random bit generation in a simple and compact configuration, which has a great potential in cryptography and secure communication applications.

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.

Experimental investigation of the time-delay signature of chaotic output and dual-channel physical random bit generation in 1550 nm mutually coupled VCSELs with common FBG filtered feedback.

Here we propose and experimentally demonstrate mutually coupled 1550 nm vertical-cavity surface-emitting lasers (VCSELs), subject to common fiber Bragg grating (FBG) feedback (FMC-VCSELs), to conceal the time-delay signature (TDS) of chaotic outputs. The autocorrelation function and delayed mutual information are used to quantitatively identify the TDS of chaotic output. For comparison, the evolution of the TDS of chaotic output in mutually coupled VCSELs (MC-VCSELs) is also presented. The effects of injection power, frequency detuning between two VCSELs, and frequency detuning between FBG and VCSELs on the TDS concealment are experimentally measured. Experimental results show that FMC-VCSELs have a better TDS suppression performance than MC-VCSELs for varying injection power. In addition, for the FMC-VCSELs system, the TDS can be suppressed to below 0.1 when the VCSELs x-polarization component is located at the edge of the main FBG lobe. Furthermore, dual-channel physical random numbers with verified randomness at a rate of 800 Gbps (2×5LSBs×80GHz) are achieved by utilizing the chaotic outputs with a low TDS from two VCSELs in the FMC-VCSELs system.

Embedding information in physically generated random bit sequences while maintaining certified randomness

Ultrafast physical random bit generation at hundreds of Gb/s rates, with verified randomness, is a crucial ingredient in secure communication and has recently emerged using optics-based physical systems. Here we examine the inverse problem and measure the ratio of information bits that can be systematically embedded in a random bit sequence without degrading its certified randomness. These ratios exceed 0.01 in experimentally obtained long random bit sequences. Based on these findings we propose a high-capacity private-key cryptosystem with a finite key length, where the existence as well as the content of the communication is concealed in the random sequence. Our results call for a rethinking of the current quantitative definition of practical classical randomness as well as the measure of randomness generated by quantum methods, which have to include bounds using the proposed inverse information embedding method.

2.24-Tb/s Physical Random Bit Generation With Minimal Post-Processing Based on Chaotic Semiconductor Lasers Network

Multi-channel physical random bit generator (RBG) based on a chaotic semiconductor lasers (SLs) network is proposed and experimentally demonstrated. In experiments, a small ring network consisting of three SLs mutually coupled with heterogeneous delays is constructed to obtain chaotic temporal waveforms. The results show that the time-delay signature of chaotic intensities in all the three SLs can be well concealed over wide range of parameters. Through linear combination of the three chaotic outputs, seven channels of chaotic entropy sources can be obtained. Furthermore, by introducing a minimal post-processing technique and directly extracting four least significant bits at 80-GS/s sampling rate, seven channel random bit sequences with verified randomness can be simultaneously achieved, and the total bit rate is 2.24 Tb/s. The proposed RBGs enabling such high generation rate have potential applications in the one-time pad encryption for the high-speed optical communication networks.

Fast Physical Random Bit Generation Based on a Broadband Chaotic Entropy Source Originated From a Filtered Feedback WRC-FPLD

Taking the broadband chaotic output from a weak-resonant-cavity Fabry–Perot laser diode (WRC-FPLD) under filtered feedback as a chaotic entropy source, we propose and experimentally demonstrate a scheme for generating fast physical random bits (PRBs) at a rate up to 240 Gbits/s. First, we investigate the dependence of the dynamical properties of the filtered feedback WRC-FPLD on the system parameters, and determine the optimized parameter region for generating wavelength-tunable and broadband chaotic signals. Second, a broadband chaotic signal with a bandwidth beyond 20 GHz output from the WRC-FPLD is sampled and transferred to a digital bit sequence by an 8-bit analog-to-digital converter at a rate of 40 GS/s. Finally, by utilizing multi-bit post-processing method, PRBs is generated at a rate up to 240 Gbits/s, which can pass all the 15 NIST statistics tests and meet the strict criteria of the statistical bias and the serial correlation coefficient.

Time-delay signature concealment and physical random bits generation in mutually coupled semiconductor lasers with FBG filtered injection

We propose and demonstrate experimentally the generation of chaos with suppressed time-delay signature (TDS) and physical random bits in two mutually coupled semiconductor lasers (MCSL) by introducing an auxiliary fiber Bragg grating (FBG) filtered injection path. The measurements show that, even by simply adding a single FBG path, the TDS of chaotic signals generated by both lasers in our proposed scheme can be better concealed compared to the conventional MCSL system. Moreover, better TDS concealment can be achieved in the laser with smaller wavelength. Additionally, two random bit streams extracted from the two chaotic lasers in the proposed scheme are achieved with minimal post-processing. The total generation rate reaches 640-Gbps.

Flat chaos generated by optical feedback multi-mode laser with filter

<sec> Optical chaos has a wide range of applications in communications, such as secure communication, high-resolution lidar ranging, optical time domain reflectometer, and high-rate physical random bit generator.</sec><sec> In recent years, external-cavity feedback semiconductor lasers (ECLs) are the most common chaotic laser generation systems due to their characteristics of wide bandwidth, large amplitude, and simple structure, and the dynamic characteristics of chaotic signals have attracted much attention. However, limited by the relaxation oscillation of the laser, the energy of the chaotic signal directly generated by ECL is mainly concentrated at high relaxation oscillation frequency. Thus, the low-frequency component encounters the problem of energy loss.</sec><sec> In practical applications, the signal detection/acquisition device usually responds to a 3-dB low-pass filtering characteristic. Therefore, the available effective bandwidth of the chaotic signal should actually be 3-dB bandwidth. The lack of low-frequency components will limit the energy utilization rate of chaotic signals and restrict the relevant performances of chaotic applications (such as reliability and transmission of chaotic secure communication, randomness and generation rate of physical random bits, measurement accuracy and range of lidar ranging or optical time-domain reflectometer).</sec><sec> In the paper, we propose a broadband chaos generation scheme with simple structure and losing no low-frequency components. Specifically, we experimentally analyze the radio frequency (RF) spectra of the single-mode and the multi-mode output from an optical feedback Fabry-Perot (FP) semiconductor laser after and before filtering. The experimental results show that comparing with the multi-mode chaotic signal, the low-frequency energy of the single-mode chaotic spectrum is enhanced by 25 dB, and the 3-dB bandwidth of the single-mode chaotic signal can reach 6 GHz. Further theoretical analysis demonstrates that the enhancement of low-frequency component in the single-mode chaotic signal is caused by the mode-competing in multi-mode laser. It is concluded that this method can well solve the problem of low-frequency energy loss in conventional optical feedback chaotic systems, and is beneficial to improving the energy utilization rate of chaotic signals, which is of great significance for improving the performance of chaotic secure communication, random bit generation, lidar ranging, optical time domain reflectometer, and other relevant applications. </sec>

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 40GS/s with 8-bit resolution and use self-delay bitwise exclusive-or operation as a post-processing method. The randomness of the resulting 320Gbps 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.