Growing Random Strings in CA

TL;DR

This paper introduces a cellular automata method that generates long pseudo-random strings from short seeds, utilizing cryptographic principles and validated through multiple statistical approaches.

Contribution

It presents a novel cellular automata-based technique for producing pseudo-random strings, incorporating cryptographic concepts like diffusion and confusion.

Findings

Strings exhibit pseudo-random properties based on Fourier, entropy, and compression analysis.

The method successfully generates long random strings from short seeds.

Python code implementation is provided for cryptographic applications.

Abstract

We discuss a class of cellular automata (CA) able to produce long random strings, starting from short "seed" strings. The approach uses two principles borrowed from cryptography: diffusion and confusion. We show numerically that the strings are pseudo-random using three approaches based on: Fourier transform, entropy estimation, and compression. An application to cryptography is also included with the corresponding Python code.