Study on the Pass Rate of NIST SP800-22 Statistical Test Suite

NIST SP800-22 is a statistical test suite for determining whether given sequences are random or not for each statistical test. The statistical test suite has been used widely. However, it was not mentioned in the statistical test suite how many the ratio of passing all the 15 kinds of tests should be for the target generator to be regarded as the ideally true random number generator. In this paper, the ratio of passing all the 15 kinds of tests for the ideally true random number sequences is derived by the theoretical analysis. To verify the theoretical deduction, the statistical tests have been performed on several well known random number generators, such as AES, 3DES, SHA1, stream ciphers wined in eStream project, and some perfect pseudo-random number generator recommended by NIST. The result of the numerical simulations is accord with the theoretical analysis.