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We develop a method for generating pseudorandom binary sequences using theBernoulli map on cubic algebraic integers. The distinguishing characteristic ofour generator is that it generates chaotic true orbits of the Bernoulli map byexact computation. In particular, we clarify a way to properly prepare a set ofinitial points (i.e., seeds), which is needed when generating multiplepseudorandom sequences. With this seed selection method, we can distribute theinitial points almost uniformly in the unit interval and can also guaranteethat the orbits starting from them do not merge. We also report results of alarge variety of tests indicating that the generated pseudorandom sequenceshave good statistical properties as well as an advantage over what is probablythe most popular generator, the Mersenne Twister MT19937.

Pseudorandom number generator based on the Bernoulli map on cubic algebraic integers