I. Introduction
Cloud service enables the users outsource their data to CS for storage, which can liberate the users from the lumbersome burden of data storage [1]. Meanwhile, the users can access and use their data anytime and anywhere [2]. However, once the users’ data are outsourced to CS, cloud data integrity cannot be ensured because of software/hardware breakdown and internal mistakes in the CS [3], [4], [5], [6]. Thus, remote data integrity auditing techniques are utilized to verify whether the data is intactly stored by the CS. Generally, users prefer to entrust a Third Party Auditor (TPA) with substantial computing resources to execute data integrity auditing task [7], [8], [9], [10]. User pays TPA according to the workload of TPA. Thus, user requires to pay high fee for auditing service if plenty of cloud files are audited.