Federated Learning (FL) is a promising privacy-preserving machine learning paradigm that allows data owners to collaboratively train models while keeping their data localized. Despite its potential, FL faces challenges related to the trustworthiness of both clients and servers, especially in the presence of curious or malicious adversaries. In this paper, we introduce a novel framework named \underline{\textbf{F}}ederated \underline{\textbf{L}}earning with \underline{\textbf{U}}pdate \underline{\textbf{D}}igest (FLUD), which addresses the critical issues of privacy preservation and resistance to Byzantine attacks within distributed learning environments. FLUD utilizes an innovative approach, the $\mathsf{LinfSample}$ method, allowing clients to compute the $l_{\infty}$ norm across sliding windows of updates as an update digest. This digest enables the server to calculate a shared distance matrix, significantly reducing the overhead associated with Secure Multi-Party Computation (SMPC) by three orders of magnitude while effectively distinguishing between benign and malicious updates. Additionally, FLUD integrates a privacy-preserving, voting-based defense mechanism that employs optimized SMPC protocols to minimize communication rounds. Our comprehensive experiments demonstrate FLUD's effectiveness in countering Byzantine adversaries while incurring low communication and runtime overhead. FLUD offers a scalable framework for secure and reliable FL in distributed environments, facilitating its application in scenarios requiring robust data management and security.