Note on Marsaglia’s Xorshift Random Number Generators

Some long-period random number generators using shifts and xors

Marsaglia recently introduced a class of “xorshift” random number generators (RNGs) with periods 2n − 1 for n = 32, 64, etc. Here Marsaglia’s xorshift generators are generalised to obtain fast and highquality RNGs with extremely long periods. Whereas RNGs based on primitive trinomials may be unsatisfactory, because a trinomial has very small weight, these new generators can be chosen so that th...

Further scramblings of Marsaglia's xorshift generators

xorshift* generators are a variant of Marsaglia’s xorshift generators that eliminate linear artifacts typical of generators based on Z/2Z-linear operations using multiplication by a suitable constant. Shortly after high-dimensional xorshift* generators were introduced, Saito and Matsumoto suggested a different way to eliminate linear artifacts based on addition in Z/232Z, leading to the XSadd g...

Xorshift random number generators from primitive polynomials

A class of xorshift random number generators (RNGs) are introduced by Marsaglia. We have proposed an algorithm which constructs a full period xorshift RNG from a given primitive polynomial. It is shown there is a weakness present in those RNGs and is suggested its improvement. A separate algorithm is also proposed which returns a full period xorshift generator with desired number of xorshift op...

Using Magma to find good xorshift random number generators

A Pseudo Random Numbers Generator Based on Chaotic Iterations: Application to Watermarking

In this paper, a new chaotic pseudo-random number generator (PRNG) is proposed. It combines the well-known ISAAC and XORshift generators with chaotic iterations. This PRNG possesses important properties of topological chaos and can successfully pass NIST and TestU01 batteries of tests. This makes our generator suitable for information security applications like cryptography. As an illustrative ...