Title: BPFL: Towards Efficient Byzantine-Robust and Provably Privacy-Preserving Federated Learning. Abstract: Federated learning (FL) is an emerging distributed learning paradigm without sharing participating clients' private data. However, existing works show that FL is vulnerable to both Byzantine (security) attacks and data reconstruction (privacy) attacks. Existing FL defenses only address one of the two attacks, and also face the efficiency issue. We propose BPFL, an efficient Byzantine-robust and provably privacy-preserving FL method that addresses all the issues. Specifically, we draw on the state-of-the-art Byzantine-robust FL method and use similarity metrics to measure the robustness of each participating client  in FL. The validity of clients are formulated as circuit constraints on similarity metrics  and verified via a zero-knowledge proof. Moreover, the client models are masked by a shared random vector, which is generated based on homomorphic encryption. In doing so, the server receives the masked client models rather than the true ones, which are proven to be private. BPFL is also efficient due to the usage of non-interactive zero-knowledge proof. Experimental results on various datasets show that our BPFL is efficient, Byzantine-robust, and privacy-preserving.