Fair and Efficient Robust Secret Sharing Scheme against Rushing Adversaries

Abstract

Robust secret sharing (RSS) is an extension of secret sharing, which can reconstruct a secret correctly even if any $t$ shares are incorrect. The existing scheme would not effectively achieve fairness. Moreover, even for an optimal scheme, RSS still has the problem that one party is verified by multiple parties, leading to expensive communication costs. In this work, we construct a blockchain-aided RSS scheme that can ensure decentralization and fairness. The central building block for our scheme to handle a rushing adversary is a bulletin board we implement on the InterPlanetary File System. Furthermore, we design a monetary penalty mechanism to impose real penalties on corrupt parties. Each participant either uploads his share correctly or loses his deposit. In addition, our scheme eliminates considerable communication between participants. Compared with the previous schemes, our scheme has a lower communication complexity, which is close to $\tilde{O}\left(n\right)$ . We conduct experiments to show the performance of our scheme. To our knowledge, this is the first implementation of a fair RSS scheme. For shares with a length of 128 bits, the time for each participant to execute the verification phase is 470 ms.