The Canetti-Krawczyk (CK) model is a formalism for the analysis of keyexchange protocols, which can guarantee many security properties for the protocols proved secure by this model. But we find this model lacks the ability to guarantee key generation center (KGC) forward secrecy, which is an important security property for key-agreement protocols based on Identity. The essential reason leading to this weakness is that it does not fully consider the attackers capabilities. In this paper, the CK model is accordingly extended with a new additional attackers capability of the KGC corruption in Identity-based systems, which enables it to support KGC forward secrecy.