Pseudorandom number generation using chaotic true orbits of the Bernoulli map

We devise a pseudorandom number generator that exactly computes chaotic true orbits of the Bernoulli map on quadratic algebraic integers. Moreover, we describe a way to select the initial points (seeds) for generating multiple pseudorandom binary sequences. This selection method distributes the initial points almost uniformly (equidistantly) in the unit interval, and latter parts of the generated sequences are guaranteed not to coincide. We also demonstrate through statistical testing that the generated sequences possess good randomness properties.