Upgrading Frequency Test for Overlapping Vectors and Fill Tree Tests
Abstract
Randomness testing is one of the essential and easiest tools for evaluating cryptographic primitives. The faster we can test with more refined tests, the greater volume of data that can be reliably tested.
This paper we analyze three tests. Starting with a range of observations made for a well-known frequency test for overlapping vectors in binary sequence testing, for which we have obtained precise chi-square statistic computed in $O \left(dt 2^{dt} \right)$ instead of $O\left( 2^{2dt}\right)$ time, without precomputed tables.
Next we focused on two tests from Dieharder: the DAB Fill Tree Test and the DAB Fill Tree 2 Test — for which the probability functions originally were determined empirically. We also draw attention to the errors found in their implementations and the insufficient exploration of the tested sequence in the second test. Even though these tests have been in the package for over 10 years, their significant shortcomings have not been noticed until now.
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