This paper shows that deterministic consensus with written messages is possible in presence of link faults and compromised signatures. Relying upon a suitable perception-based hybrid fault model that provides different categories for both node and link faults, we prove that the authenticated Byzantine agreement algorithms OMHA and ZA of (Gong, Lincoln & Rushby, 1995) can be made resilient to \l link faults per node by adding 3\l and 2\l nodes, respectively. Both algorithms can also cope with compromised signatures if the affected nodes are considered as arbitrary faulty. Authenticated algorithms for consensus are therefore reasonably applicable even in wireless systems, where link faults and intrusions are the dominating source of errors. Keywords: Fault-tolerant distributed systems, fault models, link faults, consensus, Byzantine agreement, written messages, authentication.