  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.
