The methods for supporting dynamic data updates and third-party audit are key factors that affect the practicality of existing provable data possession (PDP) schemes. This article proposes a secure and efficient PDP system called IDPA-MF-PDP for realistic cloud storage environments. The cost of auditing multiple files is dramatically reduced by a multiple-file PDP scheme based on the data update pattern of cloud storage. The requirement for users being online is reduced to the maximum extent by the implicit third-party audit framework and tamper-evident audit logs. The tripartite interaction protocol between the user, the cloud server and the implicit auditor combines MF-PDP with the implicit third-party audit framework. Theoretical analysis and experimental results show that IDPA-MF-PDP has equivalent security property with single-file PDP schemes and the audit log provides a trustworthy history record of audit results; IDPA-MF-PDP reduces the computation and communication overhead of data possession auditing from linear in the number of files to near constant.