Entropy of random numbers generated by ergodic transformation

Abstract

An algorithm for a new pseudorandom number generator is studied from the point of ergodic theory. We choose a piecewise linear map T on the unit interval and a hyperbolic toral automorphism A on the 2-dimensional torus. A discretized version of T defined on $Z_n$, $n=2^{32}$ is used. The Markov partition of the torus for the transformation A is used. The entropy is used for the test of randomness. The Shannon-McMillan-Breiman theorem and the Birkhoff ergodic theorem are used to estimate the entropy.