Mutual correlation of NIST statistical randomness tests and comparison of their sensitivities on transformed sequences

Abstract

In addition, we define five new methods for transforming a sequence. Our motivation is to detect those tests whose results are invariant under a certain transformation. To observe the correlation, we use two methods. One is the direct correlation between the tests and the other is the correlation between the results of a test on the sequence and its transformed form. In light of the observations, we conclude that some of the tests are correlated with each other.Furthermore, we conclude that in designing a reliable and efficient suite we can avoid overpopulating the list of test functions by employing transformations together with a reasonable number of statistical test functions.

Measuring Independence between Statistical Randomness Tests by Mutual Information

“…There are many works on the evaluation of the correlation between statistical randomness tests; see [ 9 , 10 , 15 , 23 , 24 ]. In this work, the correlation between the statistical randomness tests of the NIST battery will be evaluated, so only some reported results on the correlation between these tests will be described in order to be able to make comparisons with respect to the results obtained.…”

“…In [ 10 ], studies on the correlations between tests were carried out using Pearson’s correlation coefficient, but this time he divided the tests into two groups: the tests that can be applied to short sequences and those that can be applied to long sequences. The experiments generated 200,000 sequences of bits considered short, and 200 sequences of bits considered long, always bearing in mind that the tests that can be applied to short sequences, can also be applied to long sequences, but not the other way around.…”

“…Since its emergence, the NIST battery [ 5 ] has been widely used due to its standard nature, although it has also received some criticism [ 4 , 10 , 15 ]. Table 1 presents the 17 statistical randomness tests included in this battery, because the two versions of the CUSUM test (forward and backward), and the two versions of the serial test (1 and 2), are included.…”

“…The estimation was made for the two possible cases, correlated variables and independent variables. The pairs of random variables were selected from the p -values of the previously studied test [ 10 , 15 ]. The behavior of the estimated MI values was then analyzed, as the number of observations of each random variable increased.…”

“…Then, the one important problem is to efficiently determine this correlation. In [ 9 , 10 ], the study of the correlations between statistical randomness tests was proposed using Pearson’s correlation coefficient (PCC); however, it does not detect nonlinear correlations. For this reason, the fundamental objective of this work is to design a new general method by using mutual information to detect linear and non-linear correlations.…”