An Efficient Multi-secret Sharing Scheme with the Quasi-threshold Multipartite Access Structure

In real world, there are many important applications for the secret sharing with the quasi-threshold multipartite access structure. But there was still not a very efficient scheme proposed in the past. In this paper, we combine the multi-secret sharing and the quasi-threshold multipartite access structure, and present an efficient multi-secret sharing scheme with the quasi-threshold multipartite access structure based on Shamir's secret sharing scheme. In this scheme, the participants of any authorized subset can reconstruct multiple secrets by repeatedly using the Lagrange interpolation formula during a sharing process, but any non-authorized subset cannot recover any secret. In addition, the share is the same size of the single shared secret. Thus, it is an efficient and ideal multi-secret sharing scheme with the quasi-threshold multipartite access structure.