## 60 Citations

### Xorshift1024*, Xorshift1024+, Xorshift128+ and Xoroshiro128+ Fail Statistical Tests for Linearity

- Computer ScienceJ. Comput. Appl. Math.
- 2019

### Unveiling patterns in xorshift128+ pseudorandom number generators

- Computer Science, MathematicsJournal of Computational and Applied Mathematics
- 2022

### Scrambled Linear Pseudorandom Number Generators

- Computer Science, MathematicsACM Trans. Math. Softw.
- 2021

A new test for Hamming-weight dependencies that is able to discover subtle, previously unknown biases in existing generators (in particular, in linear ones), and a number of scramblers, that is, nonlinear functions applied to the state array that reduce or delete the linear artifacts.

### A random number generator for lightweight authentication protocols: xorshiftR+

- Computer ScienceTurkish J. Electr. Eng. Comput. Sci.
- 2017

Three reduced versions of the xorshift+ generator are built and the best of them demonstrated great suitability for lightweight devices considering its randomness, performance, and resource usage.

### Conversion of Mersenne Twister to double-precision floating-point numbers

- Computer ScienceMath. Comput. Simul.
- 2019

### Predicting the PCG Pseudo-Random Number Generator In Practice

- Computer Science, Mathematics
- 2020

This article presents a practical algorithm that recovers all the hidden parameters and reconstructs the successive internal states of the Permuted Congruential Generators, and enables us to predict the next “random” numbers, and output the seeds of the generator.

### Practical seed-recovery for the PCG Pseudo-Random Number Generator

- Computer Science, MathematicsIACR Trans. Symmetric Cryptol.
- 2020

This article presents a practical algorithm that recovers all the hidden parameters and reconstructs the successive internal states of the Permuted Congruential Generators, and enables us to predict the next “random” numbers, and output the seeds of the generator.

### Again, random numbers fall mainly in the planes: xorshift128+ generators

- Mathematics, Computer ScienceArXiv
- 2019

It is shown that in the 3D plots generated by the pseudo random number generators with eight sets of parameters, points concentrate on planes, ruining the randomness.

### CIPRNG: A VLSI Family of Chaotic Iterations Post-Processings for $\mathbb {F}_{2}$ -Linear Pseudorandom Number Generation Based on Zynq MPSoC

- Computer ScienceIEEE Transactions on Circuits and Systems I: Regular Papers
- 2018

The main contribution of this paper is to propose two post-processing modules in hardware, to improve the randomness of linear PRNGs while succeeding in passing the TestU01 statistical battery of tests.

### It is high time we let go of the Mersenne Twister

- Computer ScienceArXiv
- 2019

This paper surveys the results for the non-specialist, providing new, simple, understandable examples, and it is intended as a guide for the final user, or for language implementors, so that they can take an informed decision about whether to use the Mersenne Twister or not.

## 18 References

### An Experimental Exploration of Marsaglia's xorshift Generators, Scrambled

- MathematicsACM Trans. Math. Softw.
- 2016

The space of possible generators obtained by multiplying the result of a xorshift generator by a suitable constant is explored, finding choices of parameters providing periods of length 21024 − 1 and 24096 − 1.

### On the xorshift random number generators

- MathematicsTOMC
- 2005

It is found that the vast majority of xorshift generators with only threexorshift operations, including those having good equidistribution, fail several simple statistical tests.

### Note on Marsaglia's Xorshift Random Number Generators

- Mathematics
- 2004

Marsaglia (2003) has described a class of Xorshift random number generators (RNGs) with periods 2n - 1 for n = 32, 64, etc. We show that the sequences generated by these RNGs are identical to the…

### Some long-period random number generators using shifts and xors

- Mathematics, Computer ScienceArXiv
- 2010

Marsaglia's xorshift generators are generalised to obtain fast and high quality random number generators with extremely long periods to be implemented in a free software package xorgens.

### Improved long-period generators based on linear recurrences modulo 2

- Computer ScienceTOMS
- 2006

This article proposes new generators of that form with better equidistribution and “bit-mixing” properties for equivalent period length and speed and illustrates how this can reduce the impact of persistent dependencies among successive output values, which can be observed in certain parts of the period of gigantic generators such as the Mersenne twister.

### A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications

- Computer Science, Mathematics
- 2000

Some criteria for characterizing and selecting appropriate generators and some recommended statistical tests are provided, as a first step in determining whether or not a generator is suitable for a particular cryptographic application.

### TestU01: A C library for empirical testing of random number generators

- Computer Science, MathematicsTOMS
- 2007

We introduce TestU01, a software library implemented in the ANSI C language, and offering a collection of utilities for the empirical statistical testing of uniform random number generators (RNGs).…

### Xorshift RNGs

- Mathematics
- 2003

Description of a class of simple, extremely fast random number generators (RNGs) with periods 2 k − 1 for k = 32 , 64 , 96 , 128 , 160 , 192. These RNGs seem to pass tests of randomness very well.

### Uniform random number generators for supercomputers

- Computer Science
- 1992

A class of random number generators which have good statistical properties and can be implemented eciently on vector processors and parallel machines is proposed.

### Random number generation and Quasi-Monte Carlo methods

- Computer Science, MathematicsCBMS-NSF regional conference series in applied mathematics
- 1992

This chapter discusses Monte Carlo methods and Quasi-Monte Carlo methods for optimization, which are used for numerical integration, and their applications in random numbers and pseudorandom numbers.