Tightly‐secure two‐pass authenticated key exchange protocol using twin Diffie–Hellman problem

Tight security is an important requirement of practical cryptographic schemes. Compared with loosely‐secure schemes, tightly‐secure schemes allow shorter security parameters hence are more efficient. In CRYPTO 2018, Gjøsteen and Jager proposed a tightly‐secure authenticated key exchange (AKE) protocol. They used ‘commitment trick’ to construct a tight security reduction for their protocol. However, this technique leads to a three‐pass execution in their protocol, and their protocol cannot achieve key confirmation unless it is modified to have a four‐pass execution. In this study, the authors propose a tightly‐secure two‐pass AKE protocol. They use the twin Diffie–Hellman problem and the ‘re‐patch’ trick of random oracles to construct a tight security reduction for their protocol. This technique allows their protocol to have a two‐pass execution. Their protocol provides several security properties such as key‐compromise‐impersonation security, unknown‐key‐share security, and weak perfect forward secrecy. Moreover, a three‐pass variant of their protocol provides key confirmation.