Evolving Secret Sharing with Essential Participants

Abstract

Komargodski et al. introduced Evolving Secret Sharing which allows an impartial participant, called dealer, to share a secret among unbounded number of participants over any given access structure. In their construction for evolving secret sharing over general access structure, the size of share of the ith participant happens to be exponential \((\mathscr {O}(2^{i-1}))\). They also provided constructions for \((k,\infty )\) threshold secret sharing. We consider the problem of evolving secret sharing with t essential participants, namely, over t-\((k,\infty )\) access structure, a generalization of \((k,\infty )\) secret sharing \((t=0)\). We further generalize this access structure to a possible case of unbounded number of essential participants and provide a construction for secret sharing on it. Both the constructions are information theoretically secure and reduce the share size of the construction due to Komargodski et al. over general access structure, exponentially. Moreover, the essential participants receive ideal (and hence, optimal) shares in the first construction.