Related papers: Non-Archimedean Ergodic Theory and Pseudorandom Ge…
We develop a Perron-Frobenius type theory for products of random quantum channels acting on finite-dimensional matrix algebras sampled from a stationary and ergodic stochastic process, which, in keeping with the literature, we call ergodic…
In this paper we study a class of dynamical systems generated by iterations of multivariate permutation polynomial systems which lead to polynomial growth of the degrees of these iterations. Using these estimates and the same techniques…
Quality randomness is fundamental to cryptographic operations but on embedded systems good sources are (seemingly) hard to find. Rather than use expensive custom hardware, our ERHARD-RNG Pseudo-Random Number Generator (PRNG) utilizes…
Pseudorandom number generators are required for many computational tasks, such as stochastic modelling and simulation. This paper investigates the serial CPU and parallel GPU implementation of a Linear Congruential Generator based on the…
An equidistribution is a theoretical quality criteria that measures the uniformity of a linear pseudo-random number generator (PRNG). In this work, we first show that all existing linear cellular automaton (CA) based pseudo-random number…
We propose a simple algorithm for generating normally distributed pseudo random numbers. The algorithm simulates N molecules that exchange energy among themselves following a simple stochastic rule. We prove that the system is ergodic, and…
A novel Mathematical Random Number Generator (MRNG) is presented here. In this case, "mathematical" refers to the fact that to construct that generator it is not necessary to resort to a physical phenomenon, such as the thermal noise of an…
We present results of an extensive test program of a group of pseudorandom number generators which are commonly used in the applications of physics, in particular in Monte Carlo simulations. The generators include public domain programs,…
We develop a method for generating pseudorandom binary sequences using the Bernoulli map on cubic algebraic integers. The distinguishing characteristic of our generator is that it generates chaotic true orbits of the Bernoulli map by exact…
In this work, Pseudo-Random Bit Generation (PRBG) based on 2D chaotic mappings of logistic type is considered. The sequences generated with two Pseudorandom Bit Generators (PRBGs) of this type are statistically tested and the computational…
An operating system kernel uses cryptographically secure pseudorandom number generator for creating address space localization randomization offsets to protect memory addresses to processes from exploration, storing users' password securely…
In this paper we present a new pseudorandom number generator (PRNG) on graphics processing units (GPU). This PRNG is based on the so-called chaotic iterations. It is firstly proven to be chaotic according to the Devaney's formulation. We…
Pseudo-random number generators are widely used in many branches of science, mainly in applications related to Monte Carlo methods, although they are deterministic in design and, therefore, unsuitable for tackling fundamental problems in…
In this survey we summarize properties of pseudorandomness and non-randomness of some number-theoretic sequences and present results on their behaviour under the following measures of pseudorandomness: balance, linear complexity,…
We study the ability of Transformer models to learn sequences generated by Permuted Congruential Generators (PCGs), a widely used family of pseudo-random number generators (PRNGs). PCGs introduce substantial additional difficulty over…
Pseudo-random number generators (PRNGs) play an important role to ensure the security and confidentiality of image cryptographic algorithms. Their primary function is to generate a sequence of numbers that possesses unpredictability and…
Generating random and pseudorandom numbers with a deterministic system is a long-standing challenge in theoretical research and engineering applications. Several pseudorandom number generators based on the inversive congruential method have…
Pseudo-random number generators (PRNGs) are widely used in modern computing and are expected to exhibit excellent statistical performance and repeatability. This study evaluates and compares modern PRNGs used in high performance computing…
A central question in derandomization is whether randomized logspace (RL) equals deterministic logspace (L). To show that RL=L, it suffices to construct explicit pseudorandom generators (PRGs) that fool polynomial-size read-once (oblivious)…
Currently, statistical tests for random number generators (RNGs) are widely used in practice, and some of them are even included in information security standards. But despite the popularity of RNGs, consistent tests are known only for…