The histogram test for randomness assessment

The number of application areas of random number sequences is constantly increasing, but the desired quality of randomness may and do differ from one application domain to another. This is the reason why there is no single perfect random number generator for every application. Hence the selection of a generator has to rely on a thorough analysis of the entropy source and the randomness properties of the outcome sequences. In computing the degree of suitability of a generator for a certain purpose statistical testing plays an essential role, but the problem is that no finite set of statistical tests can be considered complete and consequently cannot ensure perfect randomness. However, analyzing the sequence from as many different statistical perspectives as one can afford - with costs in processing time and storage capacity - is essential in order to increase the confidence in the tested generator or reject it altogether. The present paper introduces a new perspective in statistical randomness testing in the form of a statistical test based on the concept of histogram, and describes several implementation methods together with benchmark results.