Several Generalizations of Shamir's Secret Sharing Scheme

A secret sharing scheme is a system designed to share a piece of information or the secret among a group of people such that only authorized people can reconstruct the secret from their shares. Since Blakley and Shamir proposed threshold secret sharing schemes in 1979 independently, many secret sharing schemes have been constructed. In this paper, we present several threshold schemes that are generalizations of Shamir's secret sharing scheme.