This paper presents cutting-edge advancements in exponential synchronization and encryption techniques, focusing on Quaternion-Valued Artificial Neural Networks (QVANNs) that incorporate two-sided coefficients. The study introduces a novel approach that harnesses the Cayley-Dickson representation method to simplify the complex equations inherent in QVANNs, thereby enhancing computational efficiency by exploiting complex number properties. The study employs the Lyapunov theorem to craft a resilient control system, showcasing its exponential synchronization by skillfully regulating the Lyapunov function and its derivatives. This management ensures the stability and synchronization of the network, which is crucial for reliable performance in various applications. Extensive numerical simulations are conducted to substantiate the theoretical framework, providing empirical evidence supporting the presented design and proofs. Furthermore, the paper explores the practical application of QVANNs in the encryption and decryption of color images, showcasing the network's capability to handle complex data processing tasks efficiently. The findings of this research not only contribute significantly to the development of complex artificial neural networks but pave the way for further exploration into systems with diverse delay types.