Outsourcing an increasing amount of data to a third party raises a number of security and privacy challenges. Remote data possession checking is one of them. It addresses the verification that some previously outsourced data blocks across multiple storing nodes are correctly stored, and fully available. We propose a new set homomorphic proof of data possession, called SHoPS, supporting several operations like aggregation of proofs. ShoPS is a deterministic Proof of Data Possession (PDP) scheme, based on an interactive proof protocol. Our approach has several advantages. First, it supports public verifiability where the verification process can be delegated to another entity, thus releasing the data owner from the cumbersome task of periodical verifications. Second, it enables several proofs to be aggregated and a subset of data files’ proofs to be verified, while providing an attractive communication overhead. Third, SHoPS is efficient and provably secure, as it is resistant to the fraudulence of the prover and the leakage of verified data. We describe a theoretical framework for SHoPS and we experimentally validate the feasibility of our proposed scheme.