Prior efforts in enhancing federated learning (FL) security fall into two categories. At one end of the spectrum, some work uses secure aggregation techniques to hide the individual client's updates and only reveal the aggregated global update to a malicious server that strives to infer the clients' privacy from their updates. At the other end of the spectrum, some work uses Byzantine-robust FL protocols to suppress the influence of malicious clients' updates. We present a federated learning protocol F2ED-LEARNING, which, for the first time, offers bidirectional defense to simultaneously combat against the malicious centralized server and Byzantine malicious clients. To defend against Byzantine malicious clients, F2ED-LEARNING provides dimension-free estimation error by employing and calibrating a well-studied robust mean estimator FilterL2. F2ED-LEARNING also leverages secure aggregation to protect clients from a malicious server. One key challenge of F2ED-LEARNING is to address the incompatibility between FilterL2 and secure aggregation schemes. Concretely, FilterL2 has to check the individual updates from clients whereas secure aggregation hides those updates from the malicious server. To this end, we propose a practical and highly effective solution to split the clients into shards, where F2ED-LEARNING securely aggregates each shard's update and launches FilterL2 on updates from different shards. The evaluation shows that F2ED-LEARNING consistently achieves optimal or close-to-optimal performance and outperforms five secure FL protocols under five popular attacks.