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

## TL;DR

This paper introduces a novel pseudorandom binary sequence generator based on the Bernoulli map on cubic algebraic integers, ensuring chaotic orbits through exact computation and demonstrating superior statistical properties over traditional generators.

## Contribution

It presents a new method for generating pseudorandom sequences using the Bernoulli map on cubic algebraic integers with a seed selection technique for uniform distribution and non-merging orbits.

## Key findings

- Sequences exhibit good statistical properties
- Generator outperforms Mersenne Twister MT19937
- Method guarantees non-merging chaotic orbits

## Abstract

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