AN ACCURATE EVALUATION OF MAURER'S UNIVERSAL TEST Jean-S

Maurer's universal test is a very common randomness test, capable of detecting a wide gamut of statistical defects. The algorithm is simple (a few Java code lines), exible (a variety of parameter combinations can be chosen by the tester) and fast. Although the test is based on sound probabilistic grounds, one of its crucial parts uses the heuristic approximation : c(L;K) = 0:7 0:8 L + 1:6 + 12:8 L K 4=L In this work we compute the precise value of c(L;K) and show that the inaccuracy due to the heuristic estimate can make the test 2.67 times more permissive than what is theoretically admitted. Moreover, we establish a new asymptotic relation between the test parameter and the source's entropy.