Abstract: This paper presents a big data dynamic storage integrity verification scheme. This scheme, based on lattice problem--a difficult problem even for the quantum computers, has high security, supports dynamic changes of big data, and is also very efficient. In order to support the dynamic characteristics of big data, this scheme adopts the Merkle hash tree technique. This paper has demonstrated the correctness and security of this scheme which shows that it could be widely applied to verify the dynamic storage integrity.of big data.