Second-level NIST randomness tests for improving test reliability

Testing Random Number Generators (RNGs) is as important as designing them. Here we consider the NIST test suite SF 800-22 and we show that, as suggested by NIST itself, to reveal non-perfect generators a more in-depth analysis should be performed using the outcomes of the suite over many generated sequences. Testing these second-level statistics is not trivial and, relying on a proper model that takes into account the errors due to the approximations in the first level tests, we propose a tuning of the parameters in the simplest cases. The validity of our consideration is widely supported by experimental results on several RNG currently employed by major IT players, as well as a chaos-based RNG designed by authors.