No abstract

Randomness testing is a key tool to analyse the quality of true (physical) random and pseudo-random number generators. There is a wide variety of tests that are designed for this purpose, i.e., to analyse the goodness of the sequences used. These tests are grouped in different sets called suites or batteries. The batteries must be designed in such a way that the tests that form them are independent, that they have a wide coverage, and that they are computationally efficient. One such battery is the well-known ENT battery, which provides four measures and the value of a statistic (corresponding to the chi-square goodness-of-fit test). In this paper, we will show that this battery presents some vulnerabilities and, therefore, must be redefined to solve the detected problems.

Random numbers play a key role in a wide variety of applications, ranging from mathematical simulation to cryptography. Generating random or pseudo-random numbers is not an easy task, especially when hardware, time and energy constraints are considered. In order to assess whether generators behave in a random fashion, there are several statistical test batteries. ENT is one of the simplest and most popular, at least in part due to its efficacy and speed. Nonetheless, only one of the tests of this suite provides a p value, which is the most useful and standard way to determine whether the randomness hypothesis holds, for a certain significance level. As a consequence of this, rather arbitrary and at times misleading bounds are set in order to decide which intervals are acceptable for its results. This paper introduces an extension of the battery, named StringENT, which, while sticking to the fast speed that makes ENT popular and useful, still succeeds in providing p values with which sound decisions can be made about the randomness of a sequence. It also highlights a flagrant randomness flaw that the classical ENT battery is not capable of detecting but the new StringENT notices, and introduces two additional tests.