相关论文: Implementing 64-bit Maximally Equidistributed $\ma…

The 32-bit Mersenne Twister generator MT19937 is a widely used random number generator. To generate numbers with more than 32 bits in bit length, and particularly when converting into 53-bit double-precision floating-point numbers in…

This paper proposes a type of pseudorandom number generator, Mersenne Twister for Graphic Processor (MTGP), for efficient generation on graphic processessing units (GPUs). MTGP supports large state sizes such as 11213 bits, and uses the…

Sequence generators obtained by linear recursions over the two-element field $\mathbb{F}_2$, i.e., $\mathbb{F}_2$-linear generators, are widely used as pseudorandom number generators. For example, the Mersenne Twister MT19937 is one of the…

We combine the design of two \emph{random number generators}, \emph{Mersenne Twister} and \emph{Xorgens}, to obtain a new class of generators with heavy-weight characteristic polynomials (exceeded only by the {\sc well} generators) and high…

Many simulation applications require the generation of long sequences of pseudo-random numbers. Linear recurrences modulo 2 are commonly used as the fundamental building block for constructing pseudo-random number generators with extended…

In this work it is shown how 128 bit SSE2 multimedia extension registers, present in Pentium IV class 32 bit processors, may be used to generate random numbers at several times greater speed then when regular general purpose registers are…

Parallel stochastic simulations tend to exploit more and more computing power and they are now also developed for General Purpose Graphics Process Units (GP-GPUs). Conse-quently, they need reliable random sources to feed their applications.…

The Mersenne-Twister is one of the most popular generators of uniform pseudo-random numbers. It is used in many numerical libraries and software. In this paper, we look at the Komolgorov entropy of the original Mersenne-Twister, as well as…

$\mathbf F_2$-linear pseudorandom number generators are very popular due to their high speed, to the ease with which generators with a sizable state space can be created, and to their provable theoretical properties. However, they suffer…

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…

The problem of constructing pseudorandom generators that fool halfspaces has been studied intensively in recent times. For fooling halfspaces over the hypercube with polynomially small error, the best construction known requires seed-length…

This paper presents a new distributed approach for generating all prime numbers in a given interval of integers. From Eratosthenes, who elaborated the first prime sieve (more than 2000 years ago), to the current generation of parallel…

Parallel supercomputer-based Monte Carlo applications depend on pseudorandom number generators that produce independent pseudorandom streams across many separate processes. We propose a new scalable class of parallel pseudorandom number…

We obtain new explicit pseudorandom generators for several computational models involving groups. Our main results are as follows: 1. We consider read-once group-products over a finite group $G$, i.e., tests of the form $\prod_{i=1}^n…

The paper study counter-dependent pseudorandom generators; the latter are generators such that their state transition function (and output function) is being modified dynamically while working: For such a generator the recurrence sequence…

We present an iterative approach to constructing pseudorandom generators, based on the repeated application of mild pseudorandom restrictions. We use this template to construct pseudorandom generators for combinatorial rectangles and…

Generalised Mersenne Numbers (GMNs) were defined by Solinas in 1999 and feature in the NIST (FIPS 186-2) and SECG standards for use in elliptic curve cryptography. Their form is such that modular reduction is extremely efficient, thus…

In this note, we give a practical solution to the problem of determining the maximal period of matrix generators of pseudo-random numbers which are based on an integer-valued unimodular matrix of size NxN known as MIXMAX and arithmetic…

The authors prove that the probability of choosing a nonlinear filter of m-sequences with optimal properties, that is, maximum period and maximum linear complexity, tends assymptotically to 1 as the linear feedback shift register length…

Marsaglia recently introduced a class of xorshift random number generators (RNGs) with periods 2n-1 for n = 32, 64, etc. Here we give a generalisation of Marsaglia's xorshift generators in order to obtain fast and high-quality RNGs with…