Generalized Secret Sharing Scheme Based on MDS Codes

Abstract

Secret sharing scheme(SSS) is a well known method with applications in threshold cryptography, e-voting, e-bidding, sensor networks, cloud computing etc. A secret is shared among a set of shareholders or participants by a trusted dealer. Any authorized subset of participants can determine the secret. The set of all such subsets of participants is known as \textit{Access Structure}. In a generalized access structure, any subset of participants can be an authorized subset. A novel ideal SSS based on MDS codes which realizes a strict generalized access structure is proposed. The proposed scheme has an advantage that the participants can choose their own shares and the trusted dealer can verify whether the shares are valid or not. A set of one-way functions are needed in this scheme. The one-way functions are based on hardness assumption of DLP which is an intractable problem. The proposed scheme is computationally perfect scheme.