Recovering decimation-based cryptographic sequences by means of linear CAs

TL;DR

This paper presents a method to analyze and recover sequences generated by the shrinking generator, modeling them as outputs of linear cellular automata, revealing their underlying linear structure for cryptanalysis.

Contribution

It introduces an algorithm leveraging the linearity of cellular automata and interleaved m-sequences to recover cryptographic sequences, simplifying analysis of seemingly non-linear generators.

Findings

Sequences can be modeled as linear cellular automata outputs.

The proposed algorithm effectively recovers sequences from the shrinking generator.

Irregular decimated generators are more analyzable than previously thought.

Abstract

The sequences produced by the cryptographic sequence generator known as the shrinking generator can be modelled as the output sequences of linear elementary cellular automata. These sequences are composed of interleaved m-sequences produced by linear structures based on feedback shifts. This profitable characteristic can be used in the cryptanalysis of this generator. In this work we propose an algorithm that takes advantage of the inherent linearity of these cellular automata and the interleaved m-sequences. Although irregularly decimated generators have been conceived and designed as non-linear sequence generators, in practice they can be easily analysed in terms of simple linear structures.