Chaos Synchronization using Nonlinear Observers with applications to Cryptography

Abstract: The goal of this survey paper is to provide an introduction to chaos synchronization using nonlinear observers and its applications in cryptography. I start with an overview of cryptography. Then, I recall the basics of chaos theory and how to use chaotic systems for cryptography, with an introduction to the problem of chaos synchronization. Then, I present the theory of non-linear observers, which is used for the synchronization of chaotic systems. I start with an explanation of the observability problem. Then, I introduce some of the classical observers: Kalman filter, Luenberger observer, Extended Kalman filter, Thau's observer, and High gain observer. I finish by introducing the more advanced observers: Adaptive observers, Unknown inputs observers, Sliding mode observers and ANFIS (Adaptive Neuro-Fuzzy Inference Systems) observers.