An efficient multi-stage secret sharing using bilinear map
Mitra Fatemi, Reza Ghasemi, Taraneh Eghlidos, Mohammad Reza Aref · Infoscience (Ecole Polytechnique Fédérale de Lausanne) · 2013
In a Multi-Stage Secret Sharing (MSSS) scheme, the authorized subsets of participants can recover a number of secrets in different stages. A One-Stage Multi-Secret Sharing (OSMSS) scheme is a special case of MSSS schemes in which all secrets are recovered simultaneously. In these schemes, in addition to the individual shares, the dealer should provide the participants with a number of public values associated with the secrets. The less the number of public values, the more efficient is the scheme. It is desired that MSSS and OSMSS schemes provide computational security. In this paper we prove that in OSMSS schemes any unauthorized coalition of the participants can reduce uncertainty about the secrets using their shares. In addition, in MSSS schemes recovering a secret causes reducing the uncertainty about the unrecovered secrets. Furthermore, by introducing a new multi-use MSSS scheme based on bilinear maps, we reduce the number of public values comparing with the previous schemes.