Privacy of the clients' data and security against Byzantine clients are key challenges in Federated Learning (FL). Existing solutions to joint privacy and security incur sacrifices on the privacy guarantee. We introduce LoByITFL, the first communication-efficient information-theoretically private and secure FL scheme that makes no sacrifices on the privacy guarantees while ensuring security against Byzantine adversaries. The key components are a small and representative dataset available to the federator, a careful modification of the FLTrust algorithm, and the one-time use of a trusted third party during an initialization period. We provide theoretical guarantees on the privacy and Byzantine resilience, as well as experimental results showing the convergence of LoByITFL.