Federated learning (FL) has come forward as a critical approach for privacy-preserving machine learning in healthcare, allowing collaborative model training across decentralized medical datasets without exchanging clients' data. However, current security implementations for these systems face a fundamental trade-off: rigorous cryptographic protections like fully homomorphic encryption (FHE) impose prohibitive computational overhead, while lightweight alternatives risk vulnerable data leakage through model updates. To address this issue, we present FAS (Fast and Secure Federated Learning), a novel approach that strategically combines selective homomorphic encryption, differential privacy, and bitwise scrambling to achieve robust security without compromising practical usability. Our approach eliminates the need for model pretraining phases while dynamically protecting high-risk model parameters through layered encryption and obfuscation. We implemented FAS using the Flower framework and evaluated it on a cluster of eleven physical machines. Our approach was up to 90\% faster than applying FHE on the model weights. In addition, we eliminated the computational overhead that is required by competitors such as FedML-HE and MaskCrypt. Our approach was up to 1.5$\times$ faster than the competitors while achieving comparable security results. Experimental evaluations on medical imaging datasets confirm that FAS maintains similar security results to conventional FHE against gradient inversion attacks while preserving diagnostic model accuracy. These results position FAS as a practical solution for latency-sensitive healthcare applications where both privacy preservation and computational efficiency are requirements.