Chaos Synchronization with Dynamic Filters: Two Way is Better Than One Way

TL;DR

This paper explores how two-way interaction with dynamic private filters enhances chaos synchronization and security, showing that mutual exchange outperforms one-way drive in complex systems and secure communications.

Contribution

It demonstrates that dynamic private filters prevent synchronization in one-way systems, highlighting the superiority of two-way interaction for secure chaos-based communication.

Findings

Two-way interaction enables synchronization with public parameters.

Private filters prevent synchronization, enhancing security.

Dynamic filters make the chaotic trajectory unrecoverable.

Abstract

Two chaotic systems which interact by mutually exchanging a signal built from their delayed internal variables, can synchronize. A third unit may be able to record and to manipulate the exchanged signal. Can the third unit synchronize to the common chaotic trajectory, as well? If all parameters of the system are public, a proof is given that the recording system can synchronize as well. However, if the two interacting systems use private commutative filters to generate the exchanged signal, a driven system cannot synchronize. It is shown that with dynamic private filters the chaotic trajectory even cannot be calculated. Hence two way (interaction) is more than one way (drive). The implication of this general result to secret communication with chaos synchronization is discussed.