Modelling Nonlinear Sequence Generators in terms of Linear Cellular Automata

TL;DR

This paper demonstrates that a broad class of nonlinear sequence generators, specifically CCSGs, can be modeled using linear cellular automata, enabling new analysis and cryptanalysis techniques.

Contribution

It introduces a simple algorithm to convert CCSGs into linear CA models, facilitating their analysis and cryptanalysis.

Findings

CCSGs can be represented by linear CA models

The linear models assist in cryptanalysis of CCSGs

The conversion algorithm is simple and practical

Abstract

In this work, a wide family of LFSR-based sequence generators, the so-called Clock-Controlled Shrinking Generators (CCSGs), has been analyzed and identified with a subset of linear Cellular Automata (CA). In fact, a pair of linear models describing the behavior of the CCSGs can be derived. The algorithm that converts a given CCSG into a CA-based linear model is very simple and can be applied to CCSGs in a range of practical interest. The linearity of these cellular models can be advantageously used in two different ways: (a) for the analysis and/or cryptanalysis of the CCSGs and (b) for the reconstruction of the output sequence obtained from this kind of generators.