Cloud storage is now an important development trend in information technology. However, information security has become an important problem to impede it for commercial application, such as data con-fidentiality, integrity, and availability. In this paper, we revisit the two private PDP schemes. We show that the property of correctness cannot be achieved when active adversaries are involved in these auditing systems. More specifically, an active adversary can arbitrarily tamper the cloud data and produce a valid auditing. Moreover, the malicious CSS can put the auditing right to entrust to anyone and control the delegation key and lead to the failure of the subsequent validation work. Finally, we propose a solution using key agreement to resolve the weakness. Our scheme is high efficiency due to removing expensive bilinear computing. Moreover, the verifier is stateless and independent from cloud storage server, which is an important secure property in PDP schemes.