Open AccessA New Multi-stage Secret Sharing Scheme for Hierarchical Access Structure with Existential Quantifier
Author(s) -
Guizhi Xu,
Jiangtao Yuan,
Xingxing Jia
Publication year - 2021
Publication title -
informacinės technologijos ir valdymas
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.286
H-Index - 19
eISSN - 2335-884X
pISSN - 1392-124X
DOI - 10.5755/j01.itc.50.2.27789
Subject(s) - secret sharing , access structure , computer science , scheme (mathematics) , theoretical computer science , disjoint sets , verifiable secret sharing , cover (algebra) , homogeneous , mathematics , cryptography , algorithm , discrete mathematics , programming language , mechanical engineering , mathematical analysis , set (abstract data type) , combinatorics , engineering
Multi-stage secret sharing scheme is practical in the case that there is a security system with m ordered checkpoints.It is natural to divide the m checkpoints into m different levels. There are m different secrets, and eachof them with a different importance corresponds to a checkpoint/level. The participants are also divided intom disjoint levels as they do in the hierarchical threshold access structure. Hierarchical threshold access structurewith the existential quantifier ( HTAS∃ ) does not cover the common practice that at least a few numbersof high-ranking participants are required to be involved in any recovery of the secret. The popular schemeswith hierarchical access structure were needed to check many matrices for non-singularity. We propose amulti-stage secret sharing scheme for HTAS∃ , and the tools are based on the linear homogeneous recurrencerelations (LHRRs) and one-way functions. We give the HTAS∃ a modification, so that this hierarchical accessstructure can satisfy the common practice. In our scheme, if the participants are divided into m levels, thereusually has m secrets. But before the (j − 1)-th secret is recovered, the j-th secret cannot be recovered. Ourscheme is a computational secure. The proposed scheme requires a share for each participant and the shareis as long as each secret. Our scheme has high efficiency by comparing with the state-of-the-art hierarchicalsecret sharing schemes.