Advancing Privacy and Accuracy with Federated Learning and Homomorphic Encryption

This paper presents a novel theoretical framework integrating federated learning (FL) with homomorphic encryption (HE) through the Cheon-Kim-Kim-Song (CKKS) algorithm to address fundamental privacy-accuracy trade-offs in distributed machine learning. Our primary contribution is a Taylor-based diagonal Hessian approximation method that enables efficient gradient computation under encryption constraints while maintaining provable convergence guarantees. The framework incorporates Byzantine-resilient client selection mechanisms and establishes formal security bounds against adversarial attacks. Experimental validation across Fashion-MNIST, medical X-ray, and Non-IID CIFAR-10 datasets demonstrates competitive accuracies (92.5-97.3% ) with superior attack resilience, limiting accuracy degradation to 2-5% under intensive poisoning scenarios compared to 15-25% in conventional approaches. The theoretical foundations and empirical results establish the practical viability of privacy-preserving FL for real-world deployment in sensitive domains.