# On testing pseudorandom generators via statistical tests based on the arcsine law

## TL;DR

This paper introduces a new statistical test based on the arcsine law for evaluating pseudorandom number generators, including an error analysis using a Berry-Essen type inequality to ensure test reliability.

## Contribution

It proposes a second-level statistical test for pseudorandom generators based on the arcsine law, with a detailed error approximation framework.

## Key findings

- The test effectively detects weaknesses in pseudorandom generators.
- The Berry-Essen inequality provides accurate error bounds for the test.
- The method enhances confidence in the statistical evaluation of randomness.

## Abstract

Testing the quality of pseudorandom number generators is an important issue. Security requirements become more and more demanding, weaknesses in this matter are simply not acceptable. There is a need for an in-depth analysis of statistical tests -- one has to be sure that rejecting/accepting a generator as good is not a result of errors in computations or approximations. In this paper we propose a second level statistical test based on the arcsine law for random walks. We provide a Berry-Essen type inequality for approximating the arcsine distribution, what allows us to perform a detailed error analysis of the proposed test.