Vulnerability of two multiple-key agreement protocols

In 2008, Lee et al. proposed two multiple-key agreement protocols, first one based on elliptic curve cryptography (ECC) and the other one, based on bilinear pairings. Shortly after publication, Vo et al. showed that the Lee-Wu-Wang’s pairing-based protocol is vulnerable to impersonation attack then for removing the problem, they proposed an improved protocol. In this paper, first We show that the Lee-Wu-Wang’s ECC-based protocol is insecure against forgery attack and also, if long-term private keys of two entities and one key of the session keys are revealed, the other session keys are exposed too. Then, we demonstrate that the Vo-Lee-Yeun-Kim’s protocol is vulnerable to another kind of forgery attacks and a reflection attack.