Recent technological advances have given rise to the popularity and success of cloud storage. However, the prospect of outsourcing an increasing amount of data to a third party and the abstract nature of the cloud foster the proliferation of security and privacy challenges, namely, the remote data possession checking. This paper addresses this critical security concern, when storing sensitive data in a cloud storage service, and the need for users to trust commercial cloud providers. It proposes a deterministic Proof of Data Possession (PDP) scheme based on Interactive Proof System(IPS) and an original usage of the GPS scheme. Our approach has several advantages. First, it supports public verifiability which releases data owners from the burden of a periodical verification. Second, it provides constant communication complexity, where the exchanged messages between the storage server and the client are composed of constant number of group elements. Third, our solution is efficient and provably secure, as it is resistant to the fraudulence of the prover and the leakage of verified data