On the use of dynamical systems in cryptography

TL;DR

This paper reviews the use of chaotic dynamical systems in cryptography, introduces an attack algorithm for chaos-based stream ciphers, and advocates for integrating complexity theory to improve security standards.

Contribution

It provides a new attack algorithm for chaos-based stream ciphers and promotes applying modern cryptographic complexity concepts to chaos cryptography.

Findings

New algorithm effectively tests chaos-based stream cipher security

Highlights weaknesses in existing chaos cryptography systems

Encourages formal complexity-theoretic approaches in chaos cryptography

Abstract

Ever since the link between nonlinear science and cryptography became apparent, the problem of applying chaotic dynamics to the construction of cryptographic systems has gained a broad audience and has been the subject of thousands of papers. Yet, the field has not found its place in mainstream cryptography, largely due to persistent weaknesses in the presented systems. The goal of this paper is to help remedy this problem in two ways. The first is by providing a new algorithm that can be used to attack -- and hence test the security of -- stream ciphers based on the iteration of a chaotic map of the interval. The second is to cast discrete dynamical systems problems in a modern cryptographic and complexity theoretic language, so that researchers working in chaos-based cryptography can begin designing cryptographic protocols that have a better chance of meeting the extreme standards of modern cryptography.