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

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