Encrypted data deduplication is an efficient way to solve the waste of resources caused by duplicated data in cloud storage services without the loss of security. In this chapter, we proposed three data deduplication schemes on encrypted big data with flexible data access control, data deletion, and data update. We integrate data deduplication with secure data access control by applying ownership challenge, proxy re-encryption and attribute-based encryption in deduplication. The proposed three schemes cannot only guarantee the data security and privacy but also be applicable to different cloud data deduplication scenarios. We evaluate their performances through comprehensive analysis on security, computation complexity, and operation time, along with some computer simulations. In addition, we summarize the usage scenarios and limitations of our schemes when being deployed in practice for the purpose of proposing some future research directions.