Probabilistic Analysis of AIS.31 Statistical Tests for TRNGs and Their Applications to Security Evaluations

Abstract

SP 800-90B of NIST(USA) and AIS.31 of BSI(Germany) are representative statistical tests for TRNGs. In this paper, we concentrate on AIS.31 which is under the ongoing international standardization process. We examine the probabilistic meaning of each statistic of the test in AIS.31 and investigate its probability distribution. By changing significance level and the length of sample bits, we obtain formalized accept region of the test. Furthermore we propose the accept regions for some iterative tests, that are not mentioned in AIS.31, and provide some simulations.

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