Gaussian Filtering for Noisy Hyperchaotic System: Synchronization and Secure Communication

Abstract

To achieve secure communication, transmitted data is often subjected to unpredictable transformations that obscure its original structure. One effective method involves mapping the original information onto a chaotic system, thereby complicating unauthorized decryption when sent through public channels. Synchronization between the sender and receiver enables the reconstruction of the original signal using appropriate estimation techniques. This study presents an advanced Gaussian filtering strategy designed to achieve both hyperchaotic synchronization and secure communication under conditions of parameter uncertainty and channel disturbances. At the receiver end, a Gaussian-based estimator is deployed to retrieve the original signal. The proposed framework leverages a hyperchaotic system as the transmitter, embedding the message signal within it. The resulting composite chaotic signal is then transmitted through a public medium to the receiver. Simulation experiments employ a fourdimensional Lorentz-Stenflo system as the transmitting chaotic generator. A detailed dynamical analysis, including bifurcation diagrams, confirms the system's chaotic nature. The results validate the efficacy of the proposed method, demonstrating enhanced estimation accuracy and successful recovery of the embedded signal at the receiver. © 2025 IEEE.