A New Test for Hamming-Weight Dependencies

TL;DR

This paper introduces a novel statistical test capable of detecting biases caused by Hamming-weight dependencies in pseudorandom number generators, even those passing existing tests, especially for $ extbf{F}_2$-linear based generators.

Contribution

The paper presents a new test that uncovers biases in PRNGs related to Hamming-weight dependencies, surpassing the detection capabilities of current methods.

Findings

Detects biases in $ extbf{F}_2$-linear PRNGs like dSFMT, xoroshiro1024+, and WELL512.

Identifies dependencies undetected by existing state-of-the-art tests.

Effective in revealing subtle biases affecting pseudorandomness.

Abstract

We describe a new statistical test for pseudorandom number generators (PRNGs). Our test can find bias induced by dependencies among the Hamming weights of the outputs of a PRNG, even for PRNGs that pass state-of-the-art tests of the same kind from the literature, and in particular for generators based on $\mathbf F_2$-linear transformations such as the dSFMT, xoroshiro1024+, and WELL512.