Abstract
In the specific value computation scenario of blockchain cross-chain data exchange, participants can organize raw data in the form of data pairs, making the computed specific values become key information for cross-chain collaboration. The main challenges faced in this scenario include: the lack of appropriate privacy protection mechanisms leading to easy leakage of sensitive data; the vulnerability of unencrypted or unvalidated data to tampering or malicious attacks; a crisis of trust among users. To address the above problems, this paper introduces secure multi-party computation (MPC) into the cross-chain data exchange process to ensure the fairness of the computation process and protect data privacy. To address the problem of computing the maximum and minimum values of the sums of keyword-corresponding values in cross-chain interactions, it is transformed into the secure computation scheme of computing the maximum and minimum values of the sums of corresponding elements in the intersection of sets (MMSI). A secure computation scheme for maximum and minimum values based on the fully homomorphic NTRU (FH-NTRU) encryption algorithm is proposed. First, a secure computation protocol for MMSI without a universal set under the semi-honest model is proposed. Then, to address potential malicious behaviors in the protocol, a secure computation protocol for MMSI under the malicious model is proposed, using the cut-and-choose method. The protocol under the malicious model is analyzed for correctness and the security of the protocol is proved using the real/ideal model paradigm. Finally, the efficiency analysis and experimental simulations show that the protocol is efficient and reliable, it can resist malicious adversary attacks and ensure the correctness of the computation results while effectively improving the security during cross-chain interactions.