Using a reservoir computer to learn chaotic attractors, with applications to chaos synchronisation and cryptography

TL;DR

This paper demonstrates that reservoir computing can effectively emulate chaotic attractors, enabling chaos synchronization and breaking chaos-based cryptography, with applications shown on Mackey-Glass and Lorenz systems.

Contribution

It introduces the use of reservoir computers to emulate chaotic systems and demonstrates their application in chaos synchronization and cryptography cracking.

Findings

Reservoir computers can synchronize with chaotic systems.

Trained reservoirs can emulate chaotic attractors accurately.

Reservoirs can break chaos cryptography based on Mackey-Glass.

Abstract

Using the machine learning approach known as reservoir computing, it is possible to train one dynamical system to emulate another. We show that such trained reservoir computers reproduce the properties of the attractor of the chaotic system sufficiently well to exhibit chaos synchronisation. That is, the trained reservoir computer, weakly driven by the chaotic system, will synchronise with the chaotic system. Conversely, the chaotic system, weakly driven by a trained reservoir computer, will synchronise with the reservoir computer. We illustrate this behaviour on the Mackey-Glass and Lorenz systems. We then show that trained reservoir computers can be used to crack chaos based cryptography and illustrate this on a chaos cryptosystem based on the Mackey-Glass system. We conclude by discussing why reservoir computers are so good at emulating chaotic systems.