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As The Cloud Computing Technology Develops During The Last Decade, Outsourcing Data To Cloud Service For Storage Becomes An Attractive Trend, Which Benefits In Sparing Efforts On Heavy Data Maintenance And Management. Nevertheless, Since The Outsourced Cloud Storage Is Not Fully Trustworthy, It Raises Security Concerns On How To Realize Data Deduplication In Cloud While Achieving Integrity Auditing. In This Work, We Study The Problem Of Integrity Auditing And Secure Deduplication On Cloud Data. Specifically, Aiming At Achieving Both Data Integrity And Deduplication In Cloud, We Propose Two Secure Systems, Namely SecCloud And SecCloud $^+$ . SecCloud Introduces An Auditing Entity With A Maintenance Of A MapReduce Cloud, Which Helps Clients Generate Data Tags Before Uploading As Well As Audit The Integrity Of Data Having Been Stored In Cloud. Compared With Previous Work, The Computation By User In SecCloud Is Greatly Reduced During The File Uploading And Auditing Phases. SecCloud $^+$ Is Designed Motivated By The Fact That Customers Always Want To Encrypt Their Data Before Uploading, And Enables Integrity Auditing And Secure Deduplication On Encrypted Data.