An Efficient Verifiable Threshold Multi-Secret Sharing Scheme With Different Stages

Secret sharing is one of the most important cryptographic primitives used for data outsourcing. The threshold-based secret sharing scheme is one of the well-known secret sharing schemes in cryptography. A single secret sharing scheme has low efficiency and multiple secret sharing schemes can greatly improve the efficiency of secret sharing. We present an efficient verifiable threshold multi-secret sharing scheme with different stages in which multiple secrets are shared among participants during one sharing process. In such a way, some qualified subsets of participants can collectively recover these secrets. The verifiable nature means that the participant can verify his/her own share. Our proposed scheme can share multiple secrets and each secret has its own threshold access structure. Moreover, each participant only keeps one share, and however they can reconstruct all secrets in recovery stages. This scheme is a multi-stage-use secret sharing scheme, in which the size of the participant’s share is the same as that of each secret and the amount of information disclosed reaches the optimal lower bound. Compared with the previous verifiable$(t,n)$-threshold multi-secret sharing scheme, this scheme is of stronger computational security and practicability.