On asymptotically optimal tests for random number generators
This work addresses the need for rigorous statistical tests in cryptographic systems, though it appears incremental as it builds on existing asymptotic theory for RNG testing.
The paper tackles the problem of constructing effective statistical tests for random number generators by deriving an asymptotic estimate for the p-value of an optimal test under a known stationary ergodic alternative hypothesis and describing a family of tests with this property for any unknown stationary ergodic source.
The problem of constructing effective statistical tests for random number generators (RNG) is considered. Currently, statistical tests for RNGs are a mandatory part of cryptographic information protection systems, but their effectiveness is mainly estimated based on experiments with various RNGs. We find an asymptotic estimate for the p-value of an optimal test in the case where the alternative hypothesis is a known stationary ergodic source, and then describe a family of tests each of which has the same asymptotic estimate of the p-value for any (unknown) stationary ergodic source.