Linear solutions for cryptographic nonlinear sequence generators

TL;DR

This paper demonstrates that linear cellular automata can generate solutions to linear difference equations, revealing that certain cryptographic generators like shrinking generators are insecure due to their linear nature.

Contribution

It introduces a simple algorithm to linearize shrinking generators, showing their inadequacy for cryptographic security.

Findings

Linear cellular automata generate solutions to linear difference equations.

Shrinking generators can be linearized, compromising their cryptographic security.

The paper provides a full description of the linearization algorithm.

Abstract

This letter shows that linear Cellular Automata based on rules 90/150 generate all the solutions of linear difference equations with binary constant coefficients. Some of these solutions are pseudo-random noise sequences with application in cryptography: the sequences generated by the class of shrinking generators. Consequently, this contribution show that shrinking generators do not provide enough guarantees to be used for encryption purposes. Furthermore, the linearization is achieved through a simple algorithm about which a full description is provided.