Information on calculator Random Number Generators from PPC Journal articles

[Paul Dale]

There are a number of programs available for testing randomness. Knuth is a decent start but there has been a lot more work done over the intervening years.

NIST describes their current process in SP 800-90B draft 2. They also have a Python script that does the analysis. The description is a draft and the examples contain errors but most of the algorithms are properly described, I believe the Python script has correct implementations although there is one case where two sided normal distribution critical values are used and they probably should be single sided. These tests make a reasonable effort, do not require a huge amount of data and attempt to provide an estimate of the entropy present in the samples. However, it isn't difficult to trick them into passing.

The ent program is another testing utility that is very fast and doesn't require a lot of data. In my experience it overestimates the entropy present and shouldn't be given too much weight. A failure here is a definite indication of non-randomness.

The dieharder suite is the defacto standard for testing randomness. It requires a substantial amount of data and can be very slow. It provides a decent battery of tests. Due to the number of tests and the critical values used, some tests usually produce a weak result even for true random numbers.

The current state of the art is the TestU01 suite. It requires a lot of data and is quite discriminating. It usually runs a little faster than the Dieharder suite.

My \( x_{n+1} = frac ( e^{2 x_n + 1} ) \) passes the NIST tests and ent. Dieharder hints at there being a problem with a couple too many weak results and TestU01 fails it outright.


Pauli