Multi-secret sharing scheme for level-ordered access structures

Abstract

The secret sharing scheme by Dileep et al. [19] uses Level ordered access structure which is missing in the existing access structures. In their scheme, sequential reconstruction of the secret is achieved by adding a virtual player at all the levels except at the first level. In this paper, we propose a variation of sequential secret sharing scheme for level ordered access structure (LOAS) [19], where multisecrets are distributed to multilevels each corresponding to a level by using the concepts of quadratic residues and discrete logarithm problem. The method consists of sharing of m secrets in m levels, each corresponding to a level. The distribution of secrets is based on quadratic residues concept and that of the discrete logarithm problem. The reconstruction of secrets is such that players of different levels find their respective level secrets individually only after they get their immediate higher level permission. Verification phase is also added at all the levels which guarantees the correctness of the shares in the presence of any cheater. The comparison of the proposed secret sharing scheme with existing secret sharing schemes, time complexity of the scheme and security analysis of the scheme for passive adversary model are discussed.