Provable Data Possession (PDP) schemes enable users to efficiently check the integrity of their data in the cloud. Support for massive and dynamic sets of data and adaptability to third-party auditing are two key factors that affect the practicality of existing PDP schemes. We propose a secure and efficient PDP system called IDPA-MF-PDP, by exploiting the characteristics of real-world cloud storage environments. The cost of auditing massive and dynamic sets of data is dramatically reduced by utilizing a multiple-file PDP scheme (MF-PDP), based on the data update patterns of cloud storage. Deployment and operational costs of third-party auditing and information leakage risks are reduced by an auditing framework based on integrated data possession auditors (DPAs), instantiated by trusted hardware and tamper-evident audit logs. The interaction protocols between the user, the cloud server, and the DPA integrate MF-PDP with the auditing framework. Analytical and experimental results demonstrate that IDPA-MF-PDP provides the same level of security as the original PDP scheme while reducing computation and communication overhead on the DPA, from linear the size of data to near constant. The performance of the system is bounded by disk I/O capacity.