The attribute-based encryption algorithm is widely used in cloud computing to make encrypted data outsourced by data providers to be shared or accessed only by users possessing specific credentials (or attributes). However, the standard ABE system could not ensure secure de-duplication, which leads to less storage space and network bandwidth due to duplicate copies of identical data. An attribute-based storage system is introduced which helps to overcome de-duplication in hybrid cloud storage, where a private cloud is responsible for duplicate detection and a public cloud handles the storage. The core advantages of this system are, primarily it can be used to confidentially share data with users by scrutinizing their specific credentials rather than sharing decryption keys. Also, the system attains the standard notion of semantic security for data privacy while existing systems can only achieve this through weaker security notion. Also, the equality checking algorithm will help in detecting de-duplication and confiscate the duplicate copy in private cloud storage.