A completely fair secret sharing scheme without dealer

In secret sharing schemes, there is always a special participant called the dealer who controls the distribution of the secret S. It is so powerful that once the dealer is depraved, the whole system is to be paralyzed. In order to solve this problem, it is necessary to cancel the privilege of the dealer and realize completely fair secret sharing. In this paper, we make use of the excellent additivity property of the polynomial and obtain a completely fair secret sharing scheme without the dealer. In this way, we can securely and fairly share a secret without the threat of oversized power.