Complexity Reduction in Analyzing Independence between Statistical Randomness Tests Using Mutual Information

Abstract

The advantages of using mutual information to evaluate the correlation between randomness tests have recently been demonstrated. However, it has been pointed out that the high complexity of this method limits its application in batteries with a greater number of tests. The main objective of this work is to reduce the complexity of the method based on mutual information for analyzing the independence between the statistical tests of randomness. The achieved complexity reduction is estimated theoretically and verified experimentally. A variant of the original method is proposed by modifying the step in which the significant values of the mutual information are determined. The correlation between the NIST battery tests was studied, and it was concluded that the modifications to the method do not significantly affect the ability to detect correlations. Due to the efficiency of the newly proposed method, its use is recommended to analyze other batteries of tests.

Keywords

• mutual information
• complexity
• PRNG
• cryptography