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

03/23/2019

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by   Pawel Lorek, et al.

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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 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.