Key Replicating Attack on an Identity-Based Three-Party Authenticated Key Agreement Protocol

In 2009, Mengbo Hou and Qiuliang Xu found the key replicating attack in the BR93 security model on a Certificateless two-party authenticated key agreement protocol proposed by Y.J Shi and J.H Li. In 2010, Marko Hölbl, Tatjana Welzer and Boštjan Brumen proposed a one-round identity-based three-party authenticated key agreement protocol using pairings called IDAK3-P1 and declared that the protocol had the attributes of known-key security, forward secrecy, key-compromise impersonation resilience, unknown key-share resilience and key control. In this paper, we make a systematic analysis on IDAK3-P1 and find it has similar structure as the Y.J Shi and J.H Li's protocol. We introduce Mengbo Hou and Qiuliang Xu's attack method in identifying the vulnerability of IDAK3-P1. Our analysis shows that the IDAK3-P1 is vulnerable to the key replicating attack in the BR model. Therefore, it doesn't possess the security attributes of implicit key authentication and key control as declared.