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Internet of things (IoT) is one of the main application scenarios of 5th generation mobile networks (5G). Along with the rapid development of 5G, IoT terminal devices will create big data. Generally, IoT terminal devices are lightweight user equipments, for example, wearable devices. In order to take use of these lightweight terminal devices, it is a feasible way to outsource these created big data to the public cloud. When these data are out of the client's control, it is of crucial importance to ensure the remote data integrity. To solve the weaknesses of the existing remote data integrity checking schemes, we propose the concept of blockchain-based remote data integrity checking (RDIC) scheme for big data. The new concept makes use of blockchain technique which greatly improves the efficiency and security of RDIC. First, the system model and security definition are given for the proposed RDIC scheme by using blockchain. Then, by using efficient modular arithmetic, RSA digital signature, blockchain, etc , we construct a lightweight blockchain-based RDIC scheme. Finally, we analyze its security and performance. The detailed analysis shows that our scheme is provably secure and lightweight. • The concept of blockchain-based RDIC for IoT in 5G Networks. • The first concrete scheme for the model. • Detailed performance analysis and experimental results. [ABSTRACT FROM AUTHOR]