Most cryptographic algorithms provide a means for secret and authentic communication. However, under many circumstances, the ability to repudiate messages or deny a conversation is no less important than secrecy and authenticity. For whistleblowers, informants, political dissidents and journalists --- to name a few --- it is most important to have means for deniable conversation, where electronic communication must mimic face-to-face private meetings. Off-the-Record Messaging, proposed in 2004 by Borisov, Goldberg and Brewer, and its subsequent improvements, simulate private two-party meetings. Despite some attempts, the multi-party scenario remains unresolved.

The Unified Model (UM) key agreement protocol is an efficient Diffie-Hellman scheme that has been included in many cryptographic standards, most recently in the NIST SP 800-56A standard. The UM protocol is believed to possess all important security attributes including key authentication and secrecy, resistance to unknown key-share attacks, forward secrecy, resistance to known-session key attacks, and resistance to leakage of ephemeral private keys, but is known to succumb to key-compromise impersonation attacks. In this paper we present a strengthening of the Canetti-Krawczyk security definition for key agreement that captures resistance to all important attacks that have been identified in the literature with the exception of key-compromise impersonation attacks. We then present a reductionist security proof that the UM protocol satisfies this new definition in the random oracle model under the Gap Diffie-Hellman assumption.