Testing a cellular automata construction method to obtain 9-variable cryptographic Boolean functions

TL;DR

This paper introduces a method to construct 9-variable cryptographic Boolean functions using 5-variable cellular automata and analyzes how cryptographic properties are preserved during this extension.

Contribution

It presents a novel construction method for 9-variable Boolean functions from cellular automata and evaluates property preservation across equivalence classes.

Findings

Certain cellular automata rules preserve cryptographic properties after extension

Proportion of rules preserving properties varies across equivalence classes

Method provides a systematic way to generate cryptographically strong Boolean functions

Abstract

We propose a method for constructing 9-variable cryptographic Boolean functions from the iterates of 5-variable cellular automata rules. We then analyze, for important cryptographic properties of 5-variable cellular automata rules, how they are preserved after extension to 9-variable Boolean functions. For each cryptographic property, we analyze the proportion of 5-variable cellular automata rules that preserve it for each of the 48 affine equivalence classes.