Automation of Statistical Tests on Randomness to Obtain Clearer Conclusion

Statistical testing of pseudorandom number generators (PRNGs) is indispensable for their evaluation. A common difficulty among statistical tests is how we consider the resulting probability values (p-values). When we observe a small p-value such as 10−3, it is unclear whether it is due to a defect of the PRNG, or merely by chance. At the evaluation stage, we apply some hundred of different statistical tests to a PRNG. Even a good PRNG may produce some suspicious p-values in the results of a battery of tests. This may make the conclusions of the test battery unclear. This paper proposes an adaptive modification of statistical tests: once a suspicious p-value is observed, the adaptive statistical test procedure automatically increases the sample size, and tests the PRNG again. If the p-value is still suspicious, the procedure again increases the size, and re-tests. The procedure stops when the p-value falls either in an acceptable range, or in a clearly rejectable range. We implement such adaptive modifications of some statistical tests, in particular some of those in the Crush battery of TestU01. Experiments show that the evaluation of PRNGs becomes clearer and easier, and the sensitivity of the test is increased, at the cost of additional computation time.