# Traversing a n-cube without Balanced Hamiltonian Cycle to Generate Pseudorandom Numbers

## TL;DR

This paper introduces a novel pseudorandom number generator based on traversing an n-cube with a removed Balanced Hamiltonian Cycle, demonstrating promising initial statistical results and highlighting open challenges for larger dimensions.

## Contribution

It proposes a new class of pseudorandom number generators using n-cube traversals without Balanced Hamiltonian Cycles, with automatic construction for small sizes.

## Key findings

- Initial statistical tests show promising randomness qualities.
- Construction is automatic for small n, but remains open for large n.
- The approach offers a new perspective on pseudorandom number generation.

## Abstract

This article presents a new class of Pseudorandom Number Generators. The generators are based on traversing a n-cube where a Balanced Hamiltonian Cycle has been removed. The construction of such generators is automatic for small number of bits, but remains an open problem when this number becomes large. A running example is used throughout the paper. Finally, first statistical experiments of these generators are presented, they show how efficient and promising the proposed approach seems.