Elementary Cellular Automata as Non-Cryptographic Hash Functions

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.