Signed Diffie-Hellman Key Exchange with Tight Security.

We propose the first tight security proof for the ordinary two-message signed Diffie-Hellman key exchange protocol in the random oracle model. Our proof is based on the strong computational Diffie-Hellman assumption and the multi-user security of a digital signature scheme. With our security proof, the signed DH protocol can be deployed with optimal parameters, independent of the number of users or sessions, without the need to compensate any security loss. We abstract our approach with a new notion called verifiable key exchange.