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Although many methods have been proposed, they still have their limitations. This paper improves some defects of the previous methods and proposes an efficient cloud data integrity verification scheme based on blockchain. In this paper, we proposed a lattice signature algorithm to resist quantum computing and introduced cuckoo filter to simplify the computational overhead of the user verification phase. Finally, the decentralized blockchain network is introduced to replace traditional centralized audit to publicize and authenticate the verification results, which improves the transparency and the security of this scheme. 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