Security arguments for the UM key agreement protocol in the NIST SP 800-56A standard

Abstract

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. Copyright 2008 ACM.