Periodic orbits of the ensemble of cat maps and pseudorandom number generation

We propose a method for constructing high-quality pseudorandom number generators (RNG) based on an ensemble of hyperbolic automorphisms of the unit two-dimensional torus (Sinai-Arnold map, or cat map) while keeping a part of the information hidden. The single cat map provides the random properties expected from a good RNG and is hence an appropriate building block for an RNG, although some unnecessary correlations are always present in practice. We show that hidden variables suppress these correlations dramatically. Simultaneously, introducing hidden variables complicates deciphering. Relevant correlations for a single cat map are found by the one-dimensional directed random walk test. We analyze the nature of these correlations and show how to diminish them asymptotically. We generalize Percival-Vivaldi theory in the case of the ensemble of maps, find the period of the proposed RNG analytically, and also analyze its properties. We check our predictions numerically. We also test our RNG using a number of standard statistical tests and find no correlations