It is often claimed that Conflict-free Replicated Data Types (CRDTs) ensure consistency of replicated data in peer-to-peer systems. However, peer-to-peer systems usually consist of untrusted nodes that may deviate from the specified protocol (i.e. exhibit Byzantine faults), and most existing CRDT algorithms cannot guarantee consistency in the presence of such faults. This paper shows how to adapt existing non-Byzantine CRDT algorithms and make them Byzantine fault-tolerant. The proposed scheme can tolerate any number of Byzantine nodes (making it immune to Sybil attacks), guarantees Strong Eventual Consistency, and requires only modest changes to existing CRDT algorithms.