Perpetual Secret Sharing from Dynamic Data Structures

In this paper we propose a secret sharing scheme where the access structure changes over time following a dynamic data structure. The proposed scheme can accommodate an unbounded number of new parties and when the number of parties become very large, the scheme utilizes the dynamic data structure to search, add and delete parties which makes the scheme practical. Evolving Secret sharing was proposed in the literature to include unbounded number of parties into the scheme. We introduce a related idea called perpetual secret sharing which has the following advantages over the existing evolving schemes:- our construction reduces the memory usage of a dealer to a large extent and our scheme is implementable by constant-depth circuits $(AC^{0})$. Moreover, the construction is flexible and with some modifications, the construction can handle dynamic and evolving versions of several other multipartite access structures such as hierarchical access structures, compartmental access structures etc.