Title: Secure Byzantine-Robust Federated Learning with Dimension-free Error. Abstract: In the present work, we propose a federated learning protocol with bi-directional security guarantees. First, our protocol is Byzantine-robust against malicious clients. Additionally, it is the first federated learning protocol with a per-round mean estimation error that is independent of the update size (e.g., the size of the model being trained). Second, our protocol is secure against a semi-honest server, as it only reveals sums of the updates. The code for evaluation is provided in the supplementary material.