A challenging task in cloud is to reduce the amount of storage space and save bandwidth. That can be highly achieved by adopting one of the important data compression techniques for eliminating duplicate copies of repeating data called data de-duplication and has been widely used in cloud storage to. To protect the confidentiality of sensitive data while supporting de-duplication, the convergent encryption technique has been proposed to encrypt the data before outsourcing. To better protect data security, this paper makes the first attempt to formally address the problem of authorized data de-duplication. Different from traditional de-duplication systems, the differential privileges of users are further considered in duplicate check besides the data itself.