Chaos synchronization using non-linear observers with applications to cryptography

Abstract

The subject of this thesis is the synchronization of chaotic systems using non-linear bservers, with applications to cryptography. I present in my thesis a general method to improve the performance of some observers with unknown inputs. I also develop a method to improve the frequency characteristics of chaotic systems such as the Rossler system and the Lorenz system. I also build modifications of a twisting observer for systems with time delay. Among these modifications, there is a method that allows us to consider any unknown input of a system in triangular form as being a fictitious state, which allows us to use state observers for the estimation of an unknown input. I construct also the notion of higher-adaptive-order sliding mode observers. I also present a countermeasure using ANFIS observers and an improved Lorenz system facing an acoustic cryptanalysis attack against RSA, then I combine the chaos theory with the lattice theory to generate new problems in post-quantum cryptography