Multi-stage multi-secret sharing scheme for hierarchical access structure

Hierarchical threshold secret sharing (HTSS) schemes can be thought as a generalization of classical threshold secret sharing schemes, and they have been extensively in the literature. In an HTSS, participants are classified into different security levels, and the threshold value of a higher level is smaller than that of a lower level. Participants in each level can recover the secrets, if the number of shares is equal to or more than the corresponding threshold value. Share of a higher level participant can be used to reconstruct the secret at lower level. In this paper, we proposed first hierarchical threshold multi-secret sharing scheme based on polynomial interpolation. Proposed scheme is a variation to HTSS schemes based on the CRT suggested by Singh et al. and Harn et al. Novelty of the proposed scheme is that each participant requires to keep only one secret share and multiple secrets can be shared separately without refreshing the secret share. Also, secrets are recovered in stage by stage. Our scheme which is unconditionally secure, is based on Lagrange interpolation polynomial and one-way function.

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