Two-Level Threshold Secret Sharing Scheme and Monotone Functions

Abstract

The threshold secret sharing scheme(SSS) has been studied widely in the last few years. The traditional threshold SSS such as Shamir's can only handle some simple monotone access structures. But there are some cases of monotone access structures are unable to be realized by traditional (one-level) threshold SSS. However those results are under the assumption of applying the traditional threshold SSS or one-level threshold SSS to monotone access structure. In this paper, we apply the two-level threshold SSS to monotone access structure. The main purpose of using two-level threshold secret scheme is trying to divide a secret through two levels. In the rst level, it only concerns on generating the shares based on the number of user groups. In the second level, it subdivides the secret share from the rst level to each user inside the group. We consider the disjoint case where a user can be randomly assigned into a group only. In this paper, we prove that some monotone access structure cannot be realized by two-level threshold SSS.