Physical Random Number Research Articles

Broadband chaotic signal generation with a solitary microcavity laser

We have proposed and experimentally demonstrated a novel chaotic signal generator using a solitary deformed square microcavity laser. The carrier density in the microcavity laser exhibits periodic or chaotic oscillation due to the interaction between the cavity modes, as long as the frequency difference between the modes is comparable to the relaxation oscillation frequency of the laser. The oscillation of carrier density leads to the variation of the Fermi level and, consequently, the applied voltage. The electrical signal can then be extracted directly from the electrode of the microcavity laser without the need for optical-electrical conversion. The obtained chaotic signal has a standard bandwidth of 9.6 GHz, and physical random numbers can be generated from the temporal waveform with simple post-processing methods. The scheme demonstrated here requires simple hardware, making it a promising solution for chaotic signal generators in various applications.

Entropy analysis on chaos excited through destabilization of semiconductor lasers at period-one nonlinear dynamics for physical random number generation.

This study analyzes entropy of broadband chaos excited in a semiconductor laser subject to intensity-modulated optical injection for random number generation with guaranteed unpredictability. It is identified that the flattening of spectral profile around the laser relaxation resonance blurs the periodicity it brings, and thus leads to a high entropy value and a high random number generation rate. The effect of measurement device noise on entropy suggests that both the power of chaos needs to be kept at a level to achieve an adequate signal-to-noise ratio, 24 dB or more, and the entropy contribution of the measurement device noise is excluded in order to assert entropy that can be extracted solely from the intrinsic property of chaos. The effect of data sampling rate on entropy shows that entropy reaches its maximum at the Nyquist rate, which is two times the standard bandwidth of chaos, and the rate of change in entropy is much slower than that in sampling rate as the sampling rate varies, which leads to the dominance of the sampling rate, not entropy, in determining the random number generation rate. It is highly likely that modest oversampling (i.e., a sampling rate modestly higher than the Nyquist rate) gives rise to a higher random number generation rate while entropy slightly decreases.

Multi-channel broadband optical chaos generation assisted by phase modulation and CFBG feedback

In this paper, we propose a novel and simple multi-channel broadband optical chaos generation scheme based on phase modulation and chirped fiber Bragg grating (CFBG). Firstly, phase modulation is introduced to generate more new frequency components to broaden the spectrum of the phase chaos. Meanwhile, the accumulated dispersion from CFBG distorts the intensity chaos, converts phase chaos to intensity chaos, and weakens the laser relaxation oscillation. This process would lead to energy redistribution in the power spectrum, effectively increasing the chaotic bandwidth. Then, the wavelength detuning between CFBG and the semiconductor laser is introduced to enhance the chaotic bandwidth further. The experiment results show that the 10 dB bandwidths of the five channels are up to 31.0 GHz, 34.3 GHz, 36.3 GHz, 40 GHz, and 40 GHz, respectively. Note that the maximum bandwidth of the PD in our experiment is limited to 40 GHz. In addition, the multi-channel chaotic signals obtained from the experiment system are used to generate multi-channel physical random numbers. After the post-processing operations, the total rate of five parallel high-speed physical random number generation channels is 4.64 Tbit/s (160 GSa/s × 5bit × 1 channel + 160 GSa/s × 6bit × 4 channels). As far as we know, this is the highest record of using external cavity feedback semiconductor lasers to generate random numbers, which has great potential to meet the security requirements of next-generation Tbit/s optical communication systems.

Experimental estimation of sample entropy in a semiconductor laser with optical feedback for random number generation

Estimating the entropy rate of physical random number generators with uncertainty is crucial for information security applications. We evaluate the sample entropy of chaotic temporal waveforms generated experimentally by a semiconductor laser with time-delayed optical feedback. We demonstrate random number generation with uncertainty using a quantitative measurement of the entropy rate.

Entropy Computation for Oscillator-based Physical Random Number Generators

In this paper, we provide a complete set of algorithms aimed at the design and security evaluation of oscillator-based True Random Number Generators (TRNG). While depending on some TRNG design assumptions, the proposed algorithms use as inputs the statistical parameters of the underlying random physical process such as the clock jitter originating from the thermal noise and give a lower bound of the entropy rate of the generated bit stream as output. We describe the general structure of a TRNG composed of multiple free-running oscillators and samplers, the outputs of which are post-processed by an entropy conditioner. Depending on the specification of the entropy conditioner, which can usually be any Boolean function, we describe several algorithmic optimizations. We then explain how to compute and efficiently manage the entropy rate at the output of such a post-processing block and at the output of the generator as a whole.

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>

Stability of Characteristics of Physical Random Number Generators

The development of technologies leads to the need of revising the methods used to obtain cryptographic keys. The randomness parameters of sequences generated by physical random sequence generators are affected by the physical parameters of the recording equipment and the environment. The requirements for the randomness of the sequence, when passing the binary test, are obtained. It is shown that as the sequence length increases, the requirements for possible deviations from the equiprobable distribution of 0 and 1 increase. The randomness stability of the sequences generated by the generator based on the study of photons is estimated. The oscillator under study consists of an LED and a compact silicon photomultiplier designed to detect low-power light radiation. Possible physical processes leading to the deterioration of the randomness of sequences are shown. The possibility of using a generator of random numerical sequences based on a small-sized silicon photomultiplier for cryptographic purposes is estimated.

On multiplexing in physical random number generation, and conserved total entropy content

In the current article, we use a random supercontinuum based on a random Raman distributed feedback laser to investigate the generation of random numbers by spectrally demultiplexing the broad supercontinuum spectrum in parallel channels. By tuning the spectral separation between two independent channels, we test the most typically used statistical tests’ abilities to identify the required minimum spectral separation between channels, especially after the use of post-processing steps. Out of all the tests that were investigated, the cross-correlation across channels using the raw data appears to be the most robust. We also demonstrate that the use of post-processing steps, either least significant bits extraction or exclusive-OR operations, hinders the ability of these tests to detect the existing correlations. As such, performing these tests on post-processed data, often reported in literature, is insufficient to properly establish the independence of two parallel channels. We therefore present a methodology, which may be used to confirm the true randomness of parallel random number generation schemes. Finally, we demonstrate that, while tuning a single channel’s bandwidth can modify its potential randomness output, it also affects the number of available channels, such that the total random number generation bitrate is conserved.

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.

Tbps parallel random number generation based on a single quarter-wavelength-shifted DFB laser

We propose and experimentally demonstrate a parallel physical random number generator (Ph-RNG) based on a single quarter-wavelength-shifted distributed feedback laser (QWS-DFB LD). Though simply connecting the two output ports of the QWS-DFB LD to form a cross-coupled perturbation, we simultaneously produce two paths of complex optical chaotic signals with a bandwidth above 10 GHz. Furthermore, a dual-channel Ph-RNG with a bit rate of order terabit per second (Tbps) is implemented by combining a multi-bit extraction method. Final results show that our generated physical random numbers can successfully pass standard benchmark tests for randomness.

400 Gb/s physical random number generation based on deformed square self-chaotic lasers

A circular-sided square microcavity laser etched a central hole has achieved chaos operation with a bandwidth of 20.8 GHz without external optical feedback or injection, in which the intensity probability distribution of a chaotic signal with a two-peak pattern was observed. Based on the self-chaotic microlaser, physical random numbers at 400 Gb/s were generated by extracting the four least significant bits without other complex post-processing methods. The solitary chaos laser and minimal post-processing have predicted a simpler and low-cost on-chip random number generator in the future.

On the Difficulty of Testing for Psychokinesis Using Physical Random Number Generators

On the Difficulty of Testing for Psychokinesis Using Physical Random Number Generators

Hyperchaos, Intermittency, Noise and Disorder in Modified Semiconductor Superlattices.

Weakly coupled semiconductor superlattices under DC voltage bias are nonlinear systems with many degrees of freedom whose nonlinearity is due to sequential tunneling of electrons. They may exhibit spontaneous chaos at room temperature and act as fast physical random number generator devices. Here we present a general sequential transport model with different voltage drops at quantum wells and barriers that includes noise and fluctuations due to the superlattice epitaxial growth. Excitability and oscillations of the current in superlattices with identical periods are due to nucleation and motion of charge dipole waves that form at the emitter contact when the current drops below a critical value. Insertion of wider wells increases superlattice excitability by allowing wave nucleation at the modified wells and more complex dynamics. Then hyperchaos and different types of intermittent chaos are possible on extended DC voltage ranges. Intrinsic shot and thermal noises and external noises produce minor effects on chaotic attractors. However, random disorder due to growth fluctuations may suppress any regular or chaotic current oscillations. Numerical simulations show that more than 70% of samples remain chaotic when the standard deviation of their fluctuations due to epitaxial growth is below 0.024 nm (10% of a single monolayer) whereas for 0.015 nm disorder suppresses chaos.

Weaknesses in ENT Battery Design

Randomness testing is a key tool to analyse the quality of true (physical) random and pseudo-random number generators. There is a wide variety of tests that are designed for this purpose, i.e., to analyse the goodness of the sequences used. These tests are grouped in different sets called suites or batteries. The batteries must be designed in such a way that the tests that form them are independent, that they have a wide coverage, and that they are computationally efficient. One such battery is the well-known ENT battery, which provides four measures and the value of a statistic (corresponding to the chi-square goodness-of-fit test). In this paper, we will show that this battery presents some vulnerabilities and, therefore, must be redefined to solve the detected problems.

Benchmark Performance of Digital QKD Platform Using Quantum Permutation Pad

Quantum permutation pad or QPP is a set of quantum permutation gates. QPP has been demonstrated for quantum secure encryption in both classical and quantum computing systems recently, even at a noisy 5-qubit IBMQ systems. In a classical computing system, QPP encryption is implemented as a permutation gate matrix multiplication with information state vectors. In a quantum computing system, QPP is compiled into a quantum encryption circuit in a native quantum computer and encryption is performed through QPP circuit. Leveraging its quantum mechanical characteristics, we report a digital QKD or D-QKD platform using QPP as a quantum mechanical algorithm implemented in classical systems to distribute quantum entropy, generated from physical quantum random number generators or QRNG, and quantum key over the internet. D-QKD interfaces have been developed to support the photonic QKD standard ETSI-014. This makes any systems with ETSI QKD standards compatible with D-QKD. D-QKD offers point-to-point quantum entropy and quantum key distributions as well as point-to-multi-points quantum key synchronizations with speeds 1000x faster than photonic QKD. This paper reports benchmark performance tests and randomness quality tests for pure quantum entropy generated by a QRNG and expanded entropy using the QPP protocol. The work has been funded by the PlanQK <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> project and deployed within the OpenQKD <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> testbed Berlin, operated by Deutsche Telekom.

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

&lt;sec&gt;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.&lt;/sec&gt;&lt;sec&gt;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).&lt;/sec&gt;

(Invited) Single-Electron Manipulation in an Attofarad-Capacitor DRAM

Miniaturization of Si field-effect transistors (FETs) has continuously increased the performance of data processing circuits and expanded semiconductor markets. This trend is expected to accelerate with the advent of the internet-of-things (IoT) society supported by new technologies such as the 5th-generation mobile network and artificial-intelligence systems. In the meantime, since the number of electronic devices will increase with the development of the IoT society, their total energy consumption will increase, which will give rise to serious issues in the near future.Here, aiming for sustainable development of the IoT society, we introduce a single-electron device based on a dynamic random access memory (DRAM) in which a single electron is used as one bit of information. In the DRAM, the motion of a single electron is controlled and then the electron is stored in an attofarad capacitor using a FET in which leakage current is suppressed to the theoretical limit. The charge signal of the electron is amplified by another FET integrated in the DRAM. Miniaturization of the DRAM enables such operation based on single electrons to be performed at room temperature.Such single-electron manipulation in the DRAM makes it function as a multilevel memory. Since the DRAM can manipulate the number of electrons in the capacitor, it can store data information according it. This feature provides the DRAM with a multilevel-memory function, in which each memorized state is represented by one electron. In addition, extremely long retention time is also possible because charge leakage from the capacitor can be suppressed to the theoretical lower limit. These functions are not available in conventional DRAMs.Another application based on the nature of an electron is also demonstrated. Since the motion of a single electron is essentially random, this randomness is used as physical random numbers for data processing based on the spin-glass model. This model promises efficient data processing for image restoration and optimization problems. Using random motion of individual electrons and its average controllability using the FETs, random flipping of spins is emulated by electron motion and the interaction between spins are represented by the average motion of electrons. As a result, we have succeeded in demonstrating data restoration.In these applications, one electron is used as one bit of information. However, the power consumption in electronic devices does not simply decrease if the number of electrons representing one bit is reduced. Thermodynamically, the lower limit of energy consumption is given by kTln2 (k is the Boltzmann constant; T is absolute temperature), which is known as Landauer’s limit. Landauer’s limit provides the fundamental relationship between "Information" and "Energy" and has a strong implication of "Energy" for dealing with "Information". On the other hand, a more substantive idea linking "Information" and "Energy" is Maxwell's demon, which is a thought experiment proposed by James C. Maxwell. Therefore, we believe that in order to achieve the ultimate reduction of power consumption in electronic devices, it is very important to understand Landauer’s limit and Maxwell’s demon and to expand their concepts to devices. For this purpose, we demonstrated power generation in an analogy to Maxwell’s demon. Using the DRAM for single-electron manipulation, random motions of electrons are monitored, and the electrons are guided in a certain direction in which the potential energy is high. Since this demonstration is achieved by using FETs, we can expect not only other demonstrations of proposals for lowering the power consumption of data processing but also applications inspired from such demonstrations in the future.Since the use of nanometer-scale FETs guarantees high stability and controllability, the device can be used as an optimum platform for carrying out demonstrations of some theoretical proposals. Since a small structure is essential for realizing this device and others like it, FETs fabricated with future advanced fabrication technology as well as other small materials such as graphene, carbon nanotubes, and molecules are promising for further progress in this field.

Consideration for Affects of an XOR in a Random Number Generator Using Ring Oscillators.

A cloud service to offer entropy has been paid much attention to. As one of the entropy sources, a physical random number generator is used as a true random number generator, relying on its irreproducibility. This paper focuses on a physical random number generator using a field-programmable gate array as an entropy source by employing ring oscillator circuits as a representative true random number generator. This paper investigates the effects of an XOR gate in the oscillation circuit by observing the output signal period. It aims to reveal the relationship between inputs and the output through the XOR gate in the target generator. The authors conduct two experiments to consider the relevance. It is confirmed that combining two ring oscillators with an XOR gate increases the complexity of the output cycle. In addition, verification using state transitions showed that the probability of the state transitions was evenly distributed by increasing the number of ring oscillator circuits.

Designing Hyperchaos and Intermittency in Semiconductor Superlattices.

Weakly coupled semiconductor superlattices under dc voltage bias are excitable systems with many degrees of freedom that may exhibit spontaneous chaos at room temperature and act as fast physical random number generator devices. Superlattices with identical periods exhibit current self-oscillations dueto the dynamics of charge dipole waves but chaotic oscillations exist on narrow voltage intervals. They disappear easily due to variation in structural growth parameters. Based on numerical simulations, we predict that inserting two identical sufficiently separated wider wells increases superlattice excitability by allowing wave nucleation at the modified wells and more complex dynamics. This system exhibits hyperchaos and varieties of intermittent chaos in extended dc voltage ranges. Unlike in ideal superlattices, our chaotic attractors are robust and resilient against noises and against controlled random disorder due to growth fluctuations.

High-entropy chaos generation using semiconductor lasers subject to intensity-modulated optical injection for certified physical random number generation.

This study investigates high-entropy chaos generation using a semiconductor laser subject to intensity-modulated optical injection for certified physical random number generation. Chaos with a continuous spectral profile that is not only widely distributed but also broadly flattened over a bandwidth of 33 GHz is generated. The former suggests that the chaos can be sampled at a high rate while keeping sufficient un-correlation between data samples, and the latter indicates that the chaos possesses high entropy, both of which enhance the generation rate of physical random numbers with guaranteed unpredictability. A minimum entropy value of 2.19 bits/sample is obtained without any post-processing and by excluding the contribution from measurement noise, suggesting that, to the least extent, the chaotic source can be used as a 2-bit physical random number generator at a rate of 160 Gbits/s.