With the rapid development of cloud storage and cloud computing technology, users tend to store data in the cloud for more convenient services. In order to ensure the integrity of cloud data, scholars have proposed cloud data integrity verification schemes to protect users’ data security. The storage environment of the Internet of Things, in terms of big data and medical big data, demonstrates a stronger demand for data integrity verification schemes, but at the same time, the comprehensive function of data integrity verification schemes is required to be higher. Existing data integrity verification schemes are mostly applied in the cloud storage environment but cannot successfully be applied to the environment of the Internet of Things in the context of big data storage and medical big data storage. To solve this problem when combined with the characteristics and requirements of Internet of Things data storage and medical data storage, we designed an SM2-based offline/online efficient data integrity verification scheme. The resulting scheme uses the SM4 block cryptography algorithm to protect the privacy of the data content and uses a dynamic hash table to realize the dynamic updating of data. Based on the SM2 signature algorithm, the scheme can also realize offline tag generation and batch audits, reducing the computational burden of users. In security proof and efficiency analysis, the scheme has proven to be safe and efficient and can be used in a variety of application scenarios.