Evolutionary generation and degeneration of randomness to assess the indepedence of the Ent test battery

Randomness tests are a key tool to assess the quality of pseudo-random and true random (physical) number generators. They exploit some properties of random numbers to quantify to what extent the observed behavior of the tested sequence approximates the expected one. Given the many sides of randomness, there is not an unique test providing the whole picture, instead a suite of tests assessing different aspects randomness. A robust test suite must include independent tests, otherwise tests would assess the same property, providing redundant information. This paper addresses the independence assessment of a popular test suite named Ent. To this end we generate a large number of pseudo-random numbers with different degrees of randomness by evolving them with a Genetic Algorithm. The numbers are generated to maximize their diversity attending different criteria based on Ent output, used as fitness. We encourage diversity by maximizing and minimizing randomness measures. Once a diverse set of pseudo-random numbers is generated, the Ent test suite is run on them, and their statistics studied by means of a classical correlation analysis. The results show high correlation among some statistics used in the literature, which could be overestimating the quality of their randomness source.