Elementary Cellular Automata as Non-Cryptographic Hash Functions

TL;DR

This paper explores elementary cellular automata as non-cryptographic hash functions, identifying specific rules with desirable properties like error minimization, efficient hashing, and applications in image processing.

Contribution

It introduces a novel approach using elementary cellular automata rules as hash functions, with a detailed analysis of their properties and potential applications.

Findings

Identified 10 cellular automata rules with error minimization and maximization properties.

Developed a Java implementation capable of hashing 2-byte RGB bitmaps.

Demonstrated applications in edge detection and efficient hashing algorithms.

Abstract

A subset of 10 of the 256 elementary cellular automata (ECA) are implemented as a hash function using an error minimization lossy compression algorithm operating on wrapped 4x4 neighborhood cells. All 256 rules are processed and 10 rules in two subsets of 8 are found to have properties that include both error minimization and maximization, unique solutions, a lossy inverse, efficient retroactive hashing, and an application to edge detection. The algorithm parallels the nested powers-of-two structure of the Fast Fourier Transform and Fast Walsh-Hadamard Transform, is implemented in Java, and is built to hash any 2 byte RGB code bitmap.