Tightly-Secure Authenticated Key Exchange

We construct the first Authenticated Key Exchange (AKE) protocol whose security does not degrade with an increasing number of users or sessions. We describe a three-message protocol and prove security in an enhanced version of the classical Bellare-Rogaway security model. Our construction is modular, and can be instantiated efficiently from standard assumptions (such as the SXDH or DLIN assumptions in pairing-friendly groups). For instance, we provide an SXDH-based protocol whose communication complexity is only 14 group elements and 4 exponents (plus some bookkeeping information). Along the way we develop new, stronger security definitions for digital signatures and key encapsulation mechanisms. For instance, we introduce a security model for digital signatures that provides existential unforgeability under chosen-message attacks in a multi-user setting with adaptive corruptions of secret keys. We show how to construct efficient schemes that satisfy the new definitions with tight security proofs under standard assumptions.