Measuring Random Tests by Conditional Entropy and Optimal Execution Order

Abstract

The demands on the random sequences used in trusted computing environment are stricter than other applications. In practice, we usually produce these sequences using pseudorandom number generators, whose deterministic may cause certain security flaws. So there are various statistical tests to examine the quality of random sequences. NIST proposed a test suite containing 15 tests, which is widely used now. It is meaningful to give an overall comparison among these tests. There are two open problems mentioned by NIST for the requirements of a statistical test suite [13]: how to determine the independence and the coverage of a test suite. These two concepts are abstract and hard to measure. In this paper, we use the conditional entropy to construct a quantitative value for comparing the tests, partly solving these two problems. The result also shows the reasonableness of this approach. Also, we propose a basic method on how to determine the tests’ optimal execution order. With this order we can eliminate the non-random sequences after running the least number of tests in the average case. We show such an order under specific parameters. An interesting finding is that these two different approaches have a high similarity in the ranking of these tests.

This work is supported by the National Nature Science Foundation of China (Grant No. 60573032, 60773092, 61073149), the ministry of educationś doctor foundation (20090073110027) and the 13th PRP of Shanghai Jiao Tong University.