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On Statistical Tests for Randomness Included in the NIST SP800-22 Test Suite and Based on the Binomial Distribution

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3 Author(s)
Pareschi, F. ; ENDIF-Eng. Dept., Univ. of Ferrara, Ferrara, Italy ; Rovatti, R. ; Setti, G.

In this paper we review some statistical tests included in the NIST SP 800-22 suite, which is a collection of tests for the evaluation of both true-random (physical) and pseudorandom (algorithmic) number generators for cryptographic applications. The output of these tests is the so-called p-value which is a random variable whose distribution converges to the uniform distribution in the interval [0,1] when testing an increasing number of samples from an ideal generator. Here, we compute the exact non-asymptotic distribution of p-values produced by few of the tests in the suite, and propose some computation-friendly approximations. This allows us to explain why intensive testing produces false-positives with a probability much higher than the expected one when considering asymptotic distribution instead of the true one. We also propose a new approximation for the Spectral Test reference distribution, which is more coherent with experimental results.

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Information Forensics and Security, IEEE Transactions on  (Volume:7 ,  Issue: 2 )