Chaos Synchronization using Nonlinear Observers with applications to Cryptography

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.