Non-interactive zero-knowledge and applications two round authenticated key agreement

In this paper we propose a two-round authenticated key agreement protocol using non-interactive zero-knowledge (NIZK) proofs. Essentially, a NIZK proof allows a prover to convince a verifier about the correctness of a statement without interaction. An obvious application of this is in a two-round key agreement protocol where each participant proves non-interactively the knowledge of the private key and a shared secret. Our key agreement protocol is based on this idea and is secure assuming the hardness of the Diffie-Hellman problem (DHP) and another related problem in bilinear maps.