Further investigations of random numbers
Random numbers generated by linear recurrence modulo 2 and correlation and distribution functions
CORRELATION FUNCTION↗
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Reassessing the MCNP Random Number Generator
Random number generators are integral components to Monte Carlo codes. They provide the pseudorandom number sequence used to actually sample the distributions of interest. As a result, they are one of the most important components to the software. The current recommended MCNP random number generator is a 63-bit linear congruential generator (LCG). This generator is quite fast, but it has some drawbacks. First, it only has a period of 2 63 . Due to the necessarily non-optimal usage of random numbers to ensure parallel reproducibility, this amount is too few to guarantee random number sequences are not reused in all configurations the code runs under. As simulation size increases, users will need to be aware of the limitations of the generator and tune configuration variables to best suit their simulations, or they will need to assume that reuse is not negatively affecting their answers. Neither of these are optimal. Second, small LCGs are fairly weak in bit generation quality, and this can have an unknown impact on the quality of the simulation. This paper is an investigation into whether or not more modern random number generators can supersede the current ones. The goal is to find a generator that is similar or superior in speed to the LCGs, has a state space large enough to make strong guarantees about random number reuse, and passes all modern random number test suites. If such a generator is found, it would eliminate the need for the user to even be aware of the limitations of the random number generator and would simplify the use of the code. This paper will be broken into several parts. Sec. 2 will discuss the evolution of the random number generator within the MCNP code. Sec. 3 will go over what a Monte Carlo code needs from a generator to be reproducible and portable and how the current generator behaves in that light. Sec. 4 goes through how each generator was tested. Finally, Sec. 5 will discuss improvements that could be made to the code.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Quantum random number generators
Random number generators include a thermal optical source and detector configured to produce random numbers based on quantum-optical intensity fluctuations. An optical flux is detected, and signals proportional to optical intensity and a delayed optical intensity are combined. The combined signals can be electrical signals or optical signals, and the optical source is selected so as to have low coherence over a predetermined range of delay times. Balanced optical detectors can be used to reduce common mode noise, and in some examples, the optical flux is directed to only one of a pair of balanced detectors.
97 MATHEMATICS AND COMPUTING↗
The RANDOM computer program: A linear congruential random number generator
The RANDOM Computer Program is a FORTRAN program for generating random number sequences and testing linear congruential random number generators (LCGs). The linear congruential form of random number generator is discussed, and the selection of parameters of an LCG for a microcomputer described. This document describes the following: (1) The RANDOM Computer Program; (2) RANDOM.MOD, the computer code needed to implement an LCG in a FORTRAN program; and (3) The RANCYCLE and the ARITH Computer Programs that provide computational assistance in the selection of parameters for an LCG. The RANDOM, RANCYCLE, and ARITH Computer Programs are written in Microsoft FORTRAN for the IBM PC microcomputer and its compatibles. With only minor modifications, the RANDOM Computer Program and its LCG can be run on most micromputers or mainframe computers.
Miles, R. F., Jr.↗
A new portable random number generator wrapper library
Random number generator is an important component of many scientific projects. Many projects are written using programming models (like OpenMP and SYCL) to target different architectures. However, some programming models do not provide a random number generator. In this work, we introduce our random number generator wrapper. It is a header-only library that supports three distributions of random numbers: uniform, normal, and poisson. On the GPU backend, it wraps the cuRAND and rocRAND library, and supports various random number engines. It also wraps random123, a counterbased random number generator, on both CPU and GPU. With this library, we can generate random numbers with a few lines of code and target both GPU and multi-thread CPU with the same code. We also investigate the performance and scalability of this wrapper on different architectures with different engines and the number of cores.
97 MATHEMATICS AND COMPUTING↗
An investigation of the uniform random number generator
Most random number generators that are in use today are of the congruential form X(i+1) + AX(i) + C mod M where A, C, and M are nonnegative integers. If C=O, the generator is called the multiplicative type and those for which C/O are called mixed congruential generators. It is easy to see that congruential generators will repeat a sequence of numbers after a maximum of M values have been generated. The number of numbers that a procedure generates before restarting the sequence is called the length or the period of the generator. Generally, it is desirable to make the period as long as possible. A detailed discussion of congruential generators is given. Also, several promising procedures that differ from the multiplicative and mixed procedure are discussed.
Temple, E. C.↗
A Comparison of Three Random Number Generators for Aircraft Dynamic Modeling Applications
Three random number generators, which produce Gaussian white noise sequences, were compared to assess their suitability in aircraft dynamic modeling applications. The first generator considered was the MATLAB (registered) implementation of the Mersenne-Twister algorithm. The second generator was a website called Random.org, which processes atmospheric noise measured using radios to create the random numbers. The third generator was based on synthesis of the Fourier series, where the random number sequences are constructed from prescribed amplitude and phase spectra. A total of 200 sequences, each having 601 random numbers, for each generator were collected and analyzed in terms of the mean, variance, normality, autocorrelation, and power spectral density. These sequences were then applied to two problems in aircraft dynamic modeling, namely estimating stability and control derivatives from simulated onboard sensor data, and simulating flight in atmospheric turbulence. In general, each random number generator had good performance and is well-suited for aircraft dynamic modeling applications. Specific strengths and weaknesses of each generator are discussed. For Monte Carlo simulation, the Fourier synthesis method is recommended because it most accurately and consistently approximated Gaussian white noise and can be implemented with reasonable computational effort.
Grauer, Jared A.↗
TRIM: AI Guided Random Number Generation for Resource-Constrained IoT Systems
Random numbers often serve as the backbone for many security solutions in diverse domains such as cryptography, side channel leakage prevention, and moving target defense. However, generating true random numbers requires a physical source of entropy (e.g. hardware, quantum, environmental phenomenon) making it difficult to realize at a large scale and at a low cost. On the flip side, pseudorandom number generators (easy to implement) following a specific distribution (e.g. Gaussian) can be easily compromised given a sufficient amount of traces. In this work, we have developed a machine learning-guided generative approach that can be used to create portable, resource-efficient, and cost-effective random number generators with high throughput and true randomness characteristics. We implement the proposed approach as a highly parameterized framework and perform extensive evaluation for different settings. The framework was able to learn from true random sources such as irrational numbers and environmental audio noise and imitate those sources towards generating new good quality random numbers on demand. We have generated more than 1 billion bits and observed robust performance in terms of true randomness metrics obtained from NIST SP 800-22 and FIPS 140-1 randomness test suites achieving a throughput of up to 142.85 Mbps. Compared to the state-of-the-art (SOTA) technique, the iso-cost setup of our framework can achieve more than 500 Mbps in a distributed setting. We have evaluated the efficacy of running the true randomness imitation AI models on target edge devices such as Raspberry Pi 4 (Model B), Nvidia Jetson Nano, Nvidia Jetson Orin Nano and Nvidia Jetson Xavier. We have also looked at the security of the TRIM framework itself against different adversarial threat models.
Cybersecurity↗
Proposal for a quantum random number generator using coherent light and a non-classical observable
The prototype quantum random number (random bit) generator (QRNG) consists of one photon at a time falling on a 50:50 beam splitter followed by random detection in one or the other output beams due to the irreducible probabilistic nature of quantum mechanics. Due to the difficulties in producing single photons on demand, in practice, pulses of weak coherent (laser) light are used. In this paper, we take a different approach, one that uses moderate coherent light. It is shown that a QRNG can be implemented by performing photon-number parity measurements. For moderate coherent light, the probabilities of obtaining even or odd parity in photon counts are 0.5 each. Photon counting with single-photon resolution can be performed through use of a cascade of beam splitters and single-photon detectors, as was done recently in a photon-number parity-based interferometry experiment involving coherent light. We highlight the point that unlike most quantum-based random number generators, our proposal does not require the use of classical de-biasing algorithms or post-processing of the generated bit sequence.
Gerry, Christopher C.↗
Quantum Random Number Generator (QRNG)
The Los Alamos Quantum Random Number Generator (QRNG) is a hardware-based, high-performance Random Number Generator capable of generating 200 Mbit/s or more of true random numbers. Like flipping a coin, it is very much random and essential for information security like encrypting data on the internet, checking email, or purchasing something from an online vendor. The device harvests entropy from fluctuations in an optical source that arise from quantum mechanical properties of light. Qrypt, Inc., a company launched in 2017, began making strategic investments and developing partnerships to advance cutting-edge quantum hardware solutions. One of those key investments was licensing QRNG from Los Alamos and subsequently collaborating with advanced quantum materials and technology researcher Dr. Raymond Newell to create high-quality random keys at scale.
97 MATHEMATICS AND COMPUTING↗
Traceable random numbers from a non-local quantum advantage
The unpredictability of random numbers is fundamental to both digital security and applications that fairly distribute resources. However, existing random number generators have limitations—the generation processes cannot be fully traced, audited and certified to be unpredictable. The algorithmic steps used in pseudorandom number generators are auditable, but they cannot guarantee that their outputs were a priori unpredictable given knowledge of the initial seed. Device-independent quantum random number generators can ensure that the source of randomness was unknown beforehand, but the steps used to extract the randomness are vulnerable to tampering. Here we demonstrate a fully traceable random number generation protocol based on device-independent techniques. Our protocol extracts randomness from unpredictable non-local quantum correlations, and uses distributed intertwined hash chains to cryptographically trace and verify the extraction process. This protocol forms the basis for a public traceable and certifiable quantum randomness beacon that we have launched. Over the first 40 days of operation, we completed the protocol 7,434 out of 7,454 attempts—a success rate of 99.7%. Each time the protocol succeeded, the beacon emitted a pulse of 512 bits of traceable randomness. The bits are certified to be uniform with error multiplied by actual success probability bounded by 2−64. Further, the generation of certifiable and traceable randomness represents a public service that operates with an entanglement-derived advantage over comparable classical approaches.
97 MATHEMATICS AND COMPUTING↗
A random number generator for continuous random variables
A FORTRAN 4 routine is given which may be used to generate random observations of a continuous real valued random variable. Normal distribution of F(x), X, E(akimas), and E(linear) is presented in tabular form.
Guerra, V. M.↗
Gas discharge tube true random number generator
A hardware random number generator comprises a gas discharge tube, an average voltage generator, and a comparator. The gas discharge tube includes first, second, and third terminals and may generate a variable voltage on the second terminal when a supply voltage is applied to the first and third terminals. The average voltage generator receives the variable voltage from the gas discharge tube and may generate an average voltage equal to a moving average value of the variable voltage over successive periods of time. The comparator receives the variable voltage and the average voltage and may generate a random stream of data bits, such that a value of each bit varies according to the relative magnitudes of the variable voltage and the average voltage.
42 ENGINEERING↗
Pseudo-random number generator for the Sigma 5 computer
A technique is presented for developing a pseudo-random number generator based on the linear congruential form. The two numbers used for the generator are a prime number and a corresponding primitive root, where the prime is the largest prime number that can be accurately represented on a particular computer. The primitive root is selected by applying Marsaglia's lattice test. The technique presented was applied to write a random number program for the Sigma 5 computer. The new program, named S:RANDOM1, is judged to be superior to the older program named S:RANDOM. For applications requiring several independent random number generators, a table is included showing several acceptable primitive roots. The technique and programs described can be applied to any computer having word length different from that of the Sigma 5.
Carroll, S. N.↗
A Stochastic Quasi-Newton Method in the Absence of Common Random Numbers
We present Q-SASS, a quasi-Newton method for unconstrained stochastic optimization that does not rely on common random numbers. Most existing quasi-Newton approaches leverage common random numbers to construct second-order updates. However, motivated by challenges in variational quantum algorithms—where such coordination is not possible—we consider the setting in which function values and gradients are accessible only through noisy probabilistic zeroth- and first-order oracles, and no common random numbers can be exploited. We derive high-probability tail bounds on the iteration complexity of our algorithm for nonconvex, convex, and strongly convex (more generally, those satisfying the PL condition) objective functions. Finally, we demonstrate the empirical benefits of our quasi-Newton updating scheme on both synthetic and quantum chemistry problems.
Complexity bound↗
High-speed tunable generation of random number distributions using actuated perpendicular magnetic tunnel junctions
Perpendicular magnetic tunnel junctions (pMTJs) actuated by nanosecond pulses are emerging as promising devices for true random number generation (TRNG) due to their intrinsic stochastic behavior and high throughput. In this work, we demonstrate the tunability and quality of random number distributions generated by pMTJs operating at a frequency of 104 MHz. First, changing the pulse amplitude is used to systematically vary the probability bias. The variance of the resulting bitstreams closely matches the expected binomial distribution, demonstrating consistency with an underlying sequence of Bernoulli trials. Second, the quality of uniform distributions of 8-bit random numbers generated with a probability bias of 0.5 is considered. A reduced chi-square analysis of these data shows that only two XOR operations are sufficient to achieve this distribution with p-values greater than 0.05. Finally, we show that there is a correlation between long-term probability bias variations and pMTJ resistance. These findings suggest that variations in the characteristics of the pMTJ underlie the observed variation of probability bias. In conclusion, our results highlight the potential of stochastically actuated pMTJs for high-speed, tunable TRNG applications, showing the importance of the stability of pMTJ device characteristics in achieving reliable, long-term performance.
Magnetic tunnel junctions↗
Quantum Random Number Generator (QRNG)
The Los Alamos QRNG is a hardware-based high-performance Random Number Generator capable of generating 200 Mbit/s or more of true random numbers. The device harvests entropy from fluctuations in an optical source that arise from quantum mechanical properties of light. These quantum effects are irreducibly random; the resulting numbers are unpredictable and beyond the influence of any adversary. Qrypt, Inc., launched in 2017, has amassed multiple quantum entropy sources to create high-quality random keys at scale. The company is engaging with Los Alamos through license and a Cooperative Research and Development Agreement to facilitate the transition of QRNG technology and deploy the technology into the marketplace.
97 MATHEMATICS AND COMPUTING↗
Generation of pseudo-random numbers
Practical methods for generating acceptable random numbers from a variety of probability distributions which are frequently encountered in engineering applications are described. The speed, accuracy, and guarantee of statistical randomness of the various methods are discussed.
Howell, L. W.↗