The Internet of Things (IoT) is also known as the Internet of everything. As an important part of the new generation of intelligent information technology, the IoT has attracted the attention both of researchers and engineers all over the world. Considering the limited capacity of smart products, the IoT mainly uses cloud computing to expand computing and storage resources. The massive data collected by the sensor are stored in the cloud storage server, also the cloud vulnerability will directly threaten the security and reliability of the IoT. In order to ensure data integrity and availability in the cloud and IoT storage system, users need to verify the integrity of remote data. However, the existing remote data integrity verification schemes are mostly based on the RSA and BLS signature mechanisms. The RSA-based scheme has too much computational overhead. The BLS signature-based scheme needs to adopt a specific hash function, and the batch signature efficiency in the big data environment is low. Therefore, for the computational overhead and signature efficiency issues of these two signature mechanisms, we propose a scheme of data integrity verification based on a short signature algorithm (ZSS signature), which supports privacy protection and public auditing by introducing a trusted third party (TPA). The computational overhead is effectively reduced by reducing hash function overhead in the signature process. Under the assumption of CDH difficult problem, it can resist adaptive chosen-message attacks. The analysis shows that the scheme has a higher efficiency and safety.INDEX TERMS Internet of Things, cloud computing, provable data integrity, privacy preserving, public auditability, short signature, ZSS signature.