Statistical Testing of PRNG: Generalized Gambler's Ruin Problem

Pawel Lorek, Marcin Slowik, Filip Zagórski

Abstract: We present a new statistical test (GGRTest) which is based on the generalized gambler’s ruin problem (with arbitrary winning/losing probabilities). The test is able to detect non-uniformity of the outputs generated by the pseudo-random bit generators (PRNGs). We also propose a new method, called BitTracker, of processing bits of a PRNG. In most of the statistical test-suites, bits are read in 31/32-bit groups. For many tests (e.g., OPERM) only a few first bits of the group are taken into account. Instead of “wasting” bits (in some statistical tests), the method takes into account every single bit of the PRNG’s output.