BeDCV: Blockchain-Enabled Decentralized Consistency Verification for Cross-Chain Calculation

With the increase of data stored on the blockchain, the efficiency of storage and calculation of blockchain has gradually become a bottleneck restricting the development of blockchain. By storing data on multiple chains, blockchains can request data from other chains for calculation and the storage pressure can be alleviated. But the transfer of a large amount of data between chains suffers from low transfer efficiency and poor security. A reasonable design is to perform the calculation on the data storage chain and only transfer the results across chains. However, since the calculation process is invisible, blockchains cannot judge the consistency of calculation results from other chains. In this article, we provide a blockchain-enabled decentralized consistency verification scheme for cross-chain calculation (BeDCV). Considering the decentralized characteristic of blockchain, we adopt the blockchain called supervision chain for decentralized auditing. We modify paillier homomorphic encryption to encrypt data involved in the calculation for correctness verification. Then, we aggregate the ciphertexts of data to generate the audit proof for integrity verification. Besides, we verify whether the data involved in the calculation are real-time by leveraging a counting bloom filter. The supervision chain can check the correctness, integrity, and real-time performance of cross-chain data calculation without revealing any original information about the data. The theoretical and experimental analysis demonstrates that BeDCV can verify the consistency of cross-chain data calculation result effectively, realizing secure and reliable expansion of blockchain.