Privacy-preserving efficient M+1st-price sealed bid auction in cross-chain communication

Cross-chain communication is a cryptographic technology that allows communication between different blockchains. Cross-chain communication is a technology that is gaining attention to expand the potential of blockchains, but it is difficult to construct securely and efficiently. The construction of the M+1st-price sealed bid auction in cross-chain communication is also one of the difficult schemes to realize. The existing M+1st-price sealed bid auction scheme uses a commitment scheme that needs to open the winner’s bid amount after the auction is finished, which does not protect privacy. Furthermore, it is inefficient to construct it using the existing commitment scheme since there are multiple blockchain participants as bidders in cross-chain communication. In this paper, we propose a privacy-preserving and efficient M+1st-price sealed bid auction in cross-chain communication. To achieve privacy-preserving, we propose a scheme that can determine the maximum bid amount without disclosing the largest bidder using a vector commitment scheme. Furthermore, the vector commitment scheme allows the verifier to aggregate multiple bid values into one commitment. Thus, efficiency can be achieved by aggregating the multiplier commitment value by using a vector commitment scheme. Also, by combining the vector commitment scheme and encryption scheme, only the verifier can compare the bid value. Finally, we compare our scheme and other existing schemes to emphasize the contribution of our scheme.