Efficient multistage secret sharing scheme using bilinear map

In a multistage secret sharing (MSSS) scheme, the authorised subsets of participants could recover a number of secrets in different stages. A one-stage multisecret sharing (OSMSS) scheme is a special case of MSSS schemes in which all the 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 the MSSS and OSMSS schemes provide computational security. In this study, the authors show that in the OSMSS schemes any unauthorised coalition of the participants can reduce the uncertainty of the secrets. In addition, in MSSS schemes recovering a secret causes reducing uncertainty of the unrecovered secrets. Furthermore, by introducing a new multi-use MSSS scheme based on weil pairing, they reduce the number of public values comparing with the previous schemes.