Second-level testing revisited and applications to NIST SP800-22

The use of second-level testing to reduce Type II errors in RNG validation was suggested from the very beginning though rarely employed in real-world cases. Yet, as security requirements become more critical and the availability of even faster RNG more commonplace, second-level testing will be key to distinguishing RNGs based on the quality of very large chunks of their output. This paper addresses some principles governing the proper design of second-level tests (i.e. how to divide available data into chunks and how to compute second-level p-values) as well as its implications on the design of the underlying basic tests.