The time-adaptive statistical testing for random number generators

Currently, there are dozens of random number generators (RNGs) and hundreds of statistical tests designed to test the generators. These tests are often combined into so-called batteries, each of which contains from a dozen to more than a hundred tests. When a battery test is used, it is applied to a sequence generated by the RNG, and the calculation time is determined by the length of the sequence and the number of tests. Generally speaking, the longer the sequence, the smaller deviations from randomness can be found by a specific test. So, when a battery is applied, on the one hand, the "better" tests are in the battery, the more chances to reject a "bad" RNG. On the other hand, the larger the battery, the less time can be spent on each test and, therefore, the shorter the test sequence. In turn, this reduces the ability to find small deviations from randomness. To reduce this trade-off, we propose an adaptive way to use batteries (and other sets) of tests that can be used in such a way as to increase the testing power.