The increasing demand in promoting cloud computing in either business or other areas requires more security of a cloud storage system. Traditional cloud storage systems fail to protect data integrity information (DII), when the interactive messages between the client and the data storage server are sniffed. To protect DII and support public verifiability, we propose a data integrity verification scheme by deploying a designated confirmer signature DCS as a building block. The DCS scheme strikes the balance between public verifiable signatures and zero-knowledge proofs which can address disputes between the cloud storage server and any user, whoever acting as a malicious player during the two-round verification. In addition, our verification scheme remains blockless and stateless, which is important in conducting a secure and efficient cryptosystem. We perform security analysis and performance evaluation on our scheme, and compared with the existing schemes, the results show that our scheme is more secure and efficient.