The paper considers the consensus problem in a partially synchronous system with Byzantine processes. In this context, the literature distinguishes (1) authenticated Byzantine faults, where messages can be signed by the sending process (with the assumption that the signature cannot be forged by any other process), and (2) Byzantine faults, where there is no mechanism for signatures (but the receiver of a message knows the identity of the sender). The paper proposes an abstraction called weak interactive consistency (WIC) that unifies consensus algorithms with and without signed messages. WIC can be implemented with and without signatures. The power of WIC is illustrated on two seminal Byzantine consensus algorithms: the Castro-Liskov PBFT algorithm (no signatures) and the Martin-Alvisi FaB Paxos algorithms (signatures). WIC allows a very concise expression of these two algorithms. Moreover, using a implementation of WIC without signatures allows us to derive a signature-free variant of FaB Paxos.