Synchronization of Chaotic Hyperbolic PDE Systems for Image Encryption Using Backstepping Observer Design

This paper proposes a secure image encryption process using chaotic hyperbolic partial differential equations (PDE) systems synchronization. Using an innovative invertible transform, we design a sensitive observer for an original chaotic system with an increased number of encryption keys. It achieves finite-time stabilization of the error system. Therefore, using the observation data sent by the transmitter, the receiver can synchronize the chaotic observer PDE system. From the encrypted data and observer state, we can then reconstruct the original data. An analytical key sensitivity analysis is illustrated in simulations. Unlike classical approaches, the observer system must be the less robust: the more sensitive it is to a variation of the system's parameters, the more secure the cryptosystem will be. Different modulation strategies based on the synchronized chaotic states are proposed. Their robustness to basic crypto-attacks is assessed on a simple test case.