Federated learning is a machine learning method that supports training models on decentralized devices or servers, where each holds its local data, removing the need for data exchange. This approach is especially useful in healthcare, as it enables training on sensitive data without needing to share them. The nature of federated learning necessitates robust security precautions due to data leakage concerns during communication. To address this issue, we propose a new approach that employs selective encryption, homomorphic encryption, differential privacy, and bit-wise scrambling to minimize data leakage while achieving good execution performance. Our technique FAS (fast and secure federated learning) is used to train deep learning models on medical imaging data. We implemented our technique using the Flower framework and compared with a state-of-the-art federated learning approach that also uses selective homomorphic encryption. Our experiments were run in a cluster of eleven physical machines to create a real-world federated learning scenario on different datasets. We observed that our approach is up to 90% faster than applying fully homomorphic encryption on the model weights. In addition, we can avoid the pretraining step that is required by our competitor and can save up to 46% in terms of total execution time. While our approach was faster, it obtained similar security results as the competitor.