Synthesis of all Maximum Length Cellular Automata of Cell Size up to 12

TL;DR

This paper presents an algorithm to generate all maximum length cellular automata rule vectors for cell sizes up to 12, with applications in cryptography, coding, and VLSI testing.

Contribution

It introduces a new algorithm for computing all maximum length CA-rule vectors for up to 12 cells and lists rule vectors for primitive polynomials in GF(2^2) to GF(2^{12}).

Findings

Algorithm successfully computes all maximum length CA-rule vectors.

Rule vectors for primitive polynomials in GF(2^2) to GF(2^{12}) are listed.

Programmable maximum length CA can be used in cryptographic design.

Abstract

Maximum length CA has wide range of applications in design of linear block code, cryptographic primitives and VLSI testing particularly in Built-In-Self-Test. In this paper, an algorithm to compute all $n$-cell maximum length CA-rule vectors is proposed. Also rule vectors for each primitive polynomial in GF(2^2) to GF(2^{12} have been computed by simulation and they have been listed.Programmable rule vectors based maximum length CA can be used to design cryptographic primitives.