Enhanced image encryption algorithm based on chaotic hyperbolic PDE systems synchronization

This paper proposes a secure image encryption process using chaotic hyperbolic Partial Differential Equations (PDE) systems synchronization. Chaotic infinite-dimensional systems offer a promising alternative for secure communication since they allow for a larger key space, efficient computation, and more complex dynamics than finite-dimensional ones. Inspired by the backstepping methodology, 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 and therefore synchronization of the transmitter and receiver chaotic PDE systems. Unlike classical approaches, the observer system on the receiver side must be the less robust: the more sensitive it is to a slight change in the encryption key, the more secure the cryptosystem will be. Using the observation data and the encrypted data sent by the transmitter, the receiver can synchronize his own chaotic hyperbolic PDE system and reconstruct the original image. Two modulation-demodulation strategies based on the synchronized chaotic states are proposed. The corresponding cryptosystems are assessed using classical indicators and key sensitivity analysis.