SPDZ-Based Optimistic Fair Multi-Party Computation Detection

The fairness of multi-party computation has been investigated for long time. Classic results demonstrate that fair exchange can be achieved by utilizing cryptographic tools, as most of them are based on garbled circuits. For the secret-sharing schemes, such as SPDZ, it may incur significant overhead to simply apply a fair escrow scheme, since it encrypts all the shares of delivered results. To address this issue, we design a twolevel secret-sharing mechanism. The escrow encryption is only for the first level of sharing and performed in preprocessing. The second level of sharing is used for computation and always handled by plaintexts, such that the online phase is still efficient. Our work also employs a semi-trusted third party (TTP) which provide optimistic escrow for output delivery. The verification and delivery procedures prevent the malicious parties from corrupting the outcome or aborting, when there is at least one honest party. Furthermore, the TTP has no knowledge of output, so even if he is malicious and colluding, we only lose fairness. The escrow decryption is needed only when misconduct is detected for opening the first-level shares.