Rational Secret Sharing Scheme Based on Probability Encryption without Trusted Center

Abstract

Considering the case of players’ deceptions, traditional secret sharing scheme can not resolve the security issues. To address these security issues, the paper proposes a rational secret sharing scheme against cheating based on game theory. Under the conditions of the rational, applying the idea of threshold, the scheme is composed of key generation, share encryption, verification and secret reconstruction. In the process, the scheme firstly utilizes secure multiparty computation function instead of trusted center for key generation and share validation; secondly uses probability encryption which can effectively solve the problem of players keeping silent in the final iteration; thirdly without revealing the secret, employs the commitment to detect the cheat in the scheme; finally, the scheme can reconstruct the secret in the meaningful encryption. In conclusion, the scheme is safe and effective.