  Privacy-preserving federated learning allows multiple users to jointly train
a model with coordination of a central server. The server only learns the final
aggregation result, thus the users' (private) training data is not leaked from
the individual model updates. However, keeping the individual updates private
allows malicious users to perform Byzantine attacks and degrade the accuracy
without being detected. Best existing defenses against Byzantine workers rely
on robust rank-based statistics, e.g., median, to find malicious updates.
However, implementing privacy-preserving rank-based statistics is nontrivial
and not scalable in the secure domain, as it requires sorting all individual
updates. We establish the first private robustness check that uses high break
point rank-based statistics on aggregated model updates. By exploiting
randomized clustering, we significantly improve the scalability of our defense
without compromising privacy. We leverage our statistical bounds in
zero-knowledge proofs to detect and remove malicious updates without revealing
the private user updates. Our novel framework, zPROBE, enables Byzantine
resilient and secure federated learning. Empirical evaluations demonstrate that
zPROBE provides a low overhead solution to defend against state-of-the-art
Byzantine attacks while preserving privacy.
