High-quality Pseudorandom Number Generators Research Articles

Critical exponents testing of a random number generator with the Wolff cluster algorithm

Finite-size scaling (FSS) of critical exponents including γ, β and α of 2D Ising models of sizes up to 327682 are studied using the Wolff clustering algorithm and are used to assess the quality of pseudorandom number generators (PRNGs). Critical exponents of PRNGs with quality issues are found to diverge from their theoretical values at large lattice sizes, similar to previous reports that used the Metropolis algorithm to simulate the Ising lattice. Four high-quality PRNGs, including Mersenne Twister, an additive lagged Fibonacci generator, Xorshift and Xorwow are tested and assessed with their FSS behaviors. Dynamic exponent z is also used to assess the quality of the four tested PRNGs and corroborating results are obtained.

Fast, high-quality pseudo random number generators for heterogeneous computing

Random number generation is key to many applications in a wide variety of disciplines. Depending on the application, the quality of the random numbers from a particular generator can directly impact both computational performance and critically the outcome of the calculation. High-energy physics applications use Monte Carlo simulations and machine learning widely, which both require high-quality random numbers. In recent years, to meet increasing performance requirements, many high-energy physics workloads leverage GPU acceleration. While on a CPU, there exist a wide variety of generators with different performance and quality characteristics, the same cannot be stated for GPU and FPGA accelerators. On GPUs, the most common implementation is provided by cuRAND - an NVIDIA library that is not open source or peer reviewed by the scientific community. The highest-quality generator implemented in cuRAND is a version of the Mersenne Twister. Given the availability of better and faster random number generators, high-energy physics moved away from Mersenne Twister several years ago and nowadays MIXMAX is the standard generator in Geant4 via CLHEP. The MIXMAX original design supports parallel streams with a seeding algorithm that makes it especially suited for GPU and FPGA where extreme parallelism is a key factor. In this study we implement the MIXMAX generator on both architectures and analyze its suitability and applicability for accelerator implementations. We evaluated the results against “Mersenne Twister for a Graphic Processor” (MTGP32) on GPUs which resulted in 5, 13 and 14 times higher throughput when a 240, 17 and 8 sized vector space was used respectively. The MIXMAX generator coded in VHDL and implemented on Xilinx Ultrascale+ FPGAs, requires 50% fewer total Look Up Tables (LUTs) compared to a 32-bit Mersenne Twister (MT-19337), or 75% fewer LUTs per output bit. In summary, the state-of-the art MIXMAX pseudo random number generator has been implemented on GPU and FPGA platforms and the performance benchmarked.

Enhancing Metaheuristic Optimization: A Novel Nature-Inspired Hybrid Approach Incorporating Selected Pseudorandom Number Generators

In this paper, a hybrid nature-inspired metaheuristic algorithm based on the Genetic Algorithm and the African Buffalo Optimization is proposed. The hybrid approach adaptively switches between the Genetic Algorithm and the African Buffalo Optimization during the optimization process, leveraging their respective strengths to improve performance. To improve randomness, the hybrid approach uses two high-quality pseudorandom number generators—the 64-bit and 32-bit versions of the SIMD-Oriented Fast Mersenne Twister. The effectiveness of the hybrid algorithm is evaluated on the NP-hard Container Relocation Problem, focusing on a test set of restricted Container Relocation Problems with higher complexity. The results show that the hybrid algorithm outperforms the individual Genetic Algorithm and the African Buffalo Optimization, which use standard pseudorandom number generators. The adaptive switch method allows the algorithm to adapt to different optimization problems and mitigate problems such as premature convergence and local optima. Moreover, the importance of pseudorandom number generator selection in metaheuristic algorithms is highlighted, as it directly affects the optimization results. The use of powerful pseudorandom number generators reduces the probability of premature convergence and local optima, leading to better optimization results. Overall, the research demonstrates the potential of hybrid metaheuristic approaches for solving complex optimization problems, which makes them relevant for scientific research and practical applications.

Critical Ising system testing of high-quality random number generators

Specialized hardware implemented on field programmable gate array (FPGA) is used to simulate critical 2D Ising lattices up to 40962. Four mainstream, high-quality pseudorandom number generators (PRNGs) including Xorshift, Mersenne Twister, Xorwow, and ALFG are tested on this system, and three of them are found to misbehave with different degree of confidence levels. It is observed that PRNGs with quality issues tend to misbehave in critical Ising systems and the ones with bigger issues start to misbehave in smaller critical Ising systems and vice versa. The size at which a PRNG misbehaves is proposed as a measure of a PRNG’s quality.

Triple-Coupling Cellular Automata and Their Application to Image Encryption

Cellular automaton (CA) as a discrete and deterministic dynamic system has been widely used in cryptography. In this paper, a novel triple-coupling CA model is proposed. We first apply the triple-coupling model to 1D CA to design a high-quality pseudo-random number generator (PRNG). Numerical simulation and analyses show that triple-coupling CA exhibits more complex evolutionary behavior than uncoupling CA. The pseudo-random sequence generated by triple-coupling 1D CA can pass all NIST SP800-22 tests. Subsequently, the triple-coupling model is also applied to 2D CA, and a novel image encryption scheme based on this model is proposed. Thanks to the triple-coupling model, the diffusion operation can be completed between different color channels of the color image. Experimental simulations and extensive cryptanalysis show that the image encryption algorithm using the triple-coupling model has superior security and high efficiency.

Chi-square of Pseudorandom Number Generator of Normal Distribution in C++17

High quality pseudorandom number generators were needed in many software solutions throughout the history of programming. Nowadays, these generators play an even more significant role in software development. Generally, these generators bring a certain level of coincidence in some algorithms which need it. This work focuses on the statistical evaluation of one of the representatives of the generators using Pearson's Chi-square goodness of fit test. The generator of pseudorandom numbers under test is the specific implementation in the modern standard of the programming language of C++ (the standard of C++17). Results presented in this paper inform whether the numbers generated by the selected generator follow the desired probability distribution (normal).

A Study of Chaotic Maps Producing Symmetric Distributions in the Fish School Search Optimization Algorithm with Exponential Step Decay

Inspired by the collective behavior of fish schools, the fish school search (FSS) algorithm is a technique for finding globally optimal solutions. The algorithm is characterized by its simplicity and high performance; FSS is computationally inexpensive, compared to other evolution-inspired algorithms. However, the premature convergence problem is inherent to FSS, especially in the optimization of functions that are in very-high-dimensional spaces and have plenty of local minima or maxima. The accuracy of the obtained solution highly depends on the initial distribution of agents in the search space and on the predefined initial individual and collective-volitive movement step sizes. In this paper, we provide a study of different chaotic maps with symmetric distributions, used as pseudorandom number generators (PRNGs) in FSS. In addition, we incorporate exponential step decay in order to improve the accuracy of the solutions produced by the algorithm. The obtained results of the conducted numerical experiments show that the use of chaotic maps instead of other commonly used high-quality PRNGs can speed up the algorithm, and the incorporated exponential step decay can improve the accuracy of the obtained solution. Different pseudorandom number distributions produced by the considered chaotic maps can positively affect the accuracy of the algorithm in different optimization problems. Overall, the use of the uniform pseudorandom number distribution generated by the tent map produced the most accurate results. Moreover, the tent-map-based PRNG achieved the best performance when compared to other chaotic maps and nonchaotic PRNGs. To demonstrate the effectiveness of the proposed optimization technique, we provide a comparison of the tent-map-based FSS algorithm with exponential step decay (ETFSS) with particle swarm optimization (PSO) and with the genetic algorithm with tournament selection (GA) on test functions for optimization.

Efficient deterministic and non-deterministic pseudorandom number generation

A high performance and high quality pseudorandom number generator is presented in this paper. It takes less than one clock cycle to generate a pseudorandom byte on an Intel core i3 processor and passes all the 6 TestU01 batteries of tests. The generator can work in either deterministic mode or non-deterministic mode. When working in deterministic mode, it can be used for high speed data encryption and in other applications that require deterministic and reproducible pseudorandom sequences. When working in non-deterministic mode, the generator behaves much like a true random number generator, but with the advantages of low cost, high performance, and general availability. It is good for many applications that currently rely on true random number generators

Pseudorandom recursions II

We present our earlier results (not included in Hars and Petruska due to space and time limitations), as well as some updated versions of those, and a few more recent pseudorandom number generator designs. These tell a systems designer which computer word lengths are suitable for certain high-quality pseudorandom number generators, and which constructions of a large family of designs provide long cycles, the most important property of such generators. The employed mathematical tools could help assessing the bit-mixing and mapping properties of a large class of iterated functions, performing only non-multiplicative computer operations: SHIFT, ROTATE, ADD, and XOR.

Periodic orbits of the ensemble of Sinai-Arnold cat maps and pseudorandom number generation

We propose methods for constructing high-quality pseudorandom number generators (RNGs) based on an ensemble of hyperbolic automorphisms of the unit two-dimensional torus (Sinai-Arnold map or cat map) while keeping a part of the information hidden. The single cat map provides the random properties expected from a good RNG and is hence an appropriate building block for an RNG, although unnecessary correlations are always present in practice. We show that introducing hidden variables and introducing rotation in the RNG output, accompanied with the proper initialization, dramatically suppress these correlations. We analyze the mechanisms of the single-cat-map correlations analytically and show how to diminish them. We generalize the Percival-Vivaldi theory in the case of the ensemble of maps, find the period of the proposed RNG analytically, and also analyze its properties. We present efficient practical realizations for the RNGs and check our predictions numerically. We also test our RNGs using the known stringent batteries of statistical tests and find that the statistical properties of our best generators are not worse than those of other best modern generators.

Direct numerical observation of anomalous diffusion in random media

We present computer simulations of anomalous diffusion, , in two dimensions. The Monte Carlo calculations are in excellent agreement with previous renormalization group calculations. Interestingly, use of a high-quality pseudorandom number generator is necessary to observe the anomalous diffusion. A linear-feedback, shift-register method leads to incorrect, superdiffusive motion of the random walkers.