Second-level NIST Randomness Tests for Improving Test Reliability

Testing random number generators (RNGs) is as important as designing them. The paper considers the NIST test suite SP 800-22 and shows 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, a tuning of the parameters in the simplest cases was propose. The validity of this 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.