Physical Random Number Generator Research Articles

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.

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

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

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.

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.

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.

Optical Chaos KEY generator for Cryptosystems

Chaotic structures are ideally appropriate for the construction of cryptographic schemes, because random numbers are an inseparable part of every encryption scheme as a safety mechanism. The optical chaotic circuit is an ultra-fast physical Random number generator, which is illustrated using the CW laser that generates optical signal at 193.1 THz and M-Z modulator that works on an interferometric principle. The circuit generates truly high random bit sequences at different higher bit rates of 320Gb/s and 640 Gb/s. These generated random bits have passed the NIST statistical tests and Diehard battery tests, indicating their randomness for different practical applications. Further, the random number generated by optical chaos circuit is used to secure the image data using RC4 ciphering method.

Entropy rate of chaos in an optically injected semiconductor laser for physical random number generation.

We evaluate the (ɛ, τ) entropy of chaotic laser outputs generated by an optically injected semiconductor laser for physical random number generation. The vertical resolution ɛ and sampling time τ are numerically optimized by comparing the (ɛ, τ) entropy with the Kolmogorov-Sinai entropy, which is estimated from the Lyapunov exponents using linearized model equations. We then investigate the dependence of the (ɛ, τ) entropy on the optical injection strength of the laser system. In addition, we evaluate the (ɛ, τ) entropy from the experimentally obtained chaotic temporal waveforms in an optically injected semiconductor laser. Random bits with an entropy close to one bit per sampling point are extracted to satisfy the conditions of physical random number generation. We find that the extraction of the third-most significant bit from eight-bit experimental chaotic data results in an entropy of one bit per sample for certified physical random number generation.

Autonomous Boolean network and physical random number generator based on XOR gate

As a controllable nonlinear system, autonomous Boolean network which is easy to generate chaotic signals has become a hot research topic. We realize an 18-node autonomous Boolean network circuit which can generate high entropy chaos by using the nonlinear characteristics of two-input XOR gate, and establish an improved mathematical model for the circuit by introducing the filter coefficient. Through numerical simulation and circuit comparison experiment, we study the influence of filter coefficient and delay parameters on network dynamic characteristics of this model. The numerical simulation results are basically consistent with those of the experimental phenomena. When the transmission delay between nodes is not equal, the filter coefficient has a modulation effect on the generation of chaos, which well indicates that the introduction of the filter coefficient makes the improved mathematical model more objective to describe the physical phenomena in the circuit. In addition, using bifurcation diagram, Lyapunov exponent and permutation entropy, we further analyze the nonlinear characteristics and randomness of the autonomous Boolean network. The output chaotic sequence of the network has the characteristics of high bandwidth, high entropy and strong robustness, which is used to generate high speed physical random sequences and has passed the NIST SP 800-22 randomness tests of National Institute of Standards and Technology of America.

A large-scale comprehensive evaluation of single-slice ring oscillator and PicoPUF bit cells on 28-nm Xilinx FPGAs

Lightweight implementation of security primitives, e.g., physical unclonable functions (PUFs) and true random number generator, in field programmable gate array (FPGA) is crucial replacement of the conventional decryption key stored in battery-backed random access memory or E-Fuses for the protection of field reconfigurable assets. A slice is the smallest reconfigurable logic block in an Xilinx FPGA. The entropy exploitable from each slice of an FPGA is an important factor for the design of security primitives. Previous research has shown that the locations of slices can impact the quality of delay-based PUF designs implemented on FPGAs. To investigate the effect of the placement of each single-bit PUF cell free from the routing resource constraint between slices, single-bit ring oscillator (RO) and identity-based PUF design (Pi-coPUF) cells that can each be fully fitted into a single slice are evaluated. To accurately evaluate their statistical performance, data from a large number of devices are required. To this end, 217 Xilinx Artix-7 FPGAs has been employed to provide a large-scale comprehensive analysis for the two designs. This is the first time single-slice disorder-based security entities have been investigated and compared on 28-nm Xilinx FPGA. Uniqueness, uniformity, correlation, reliability, bit-aliasing and min-entropy of each type of cell are evaluated for four different types of cell placement. Our experimental results corroborate that the location of both cell types in the FPGA affects their performances. For both cell types, the lower the correlation between devices, the higher the min-entropy and uniqueness. Overall, the min-entropy, correlation and uniqueness of PicoPUF are slightly higher than those of RO. Otherwise, the uniformity, bit-aliasing and reliability of the PicoPUF are slightly lower than those of the RO. Comparing the resource usage and metrics of the PicoPUF, ring oscillator PUF and some existing memory-based PUF implementations, PicoPUF stands out as a lightweight FPGA-based weak PUF design. The raw data for the PicoPUF design are made publicly available to enable the research community to use them for benchmarking and/or validation.