Mutually trusted authority-free secret sharing schemes (Q1382145)

The traditional approach to secret sharing assumes existence of a trusted authority responsible for initial phase, i.e. generation and distribution of shares to authorized sets of participants. In the paper the problem of establishing secret schemes for a given access structure that do not require such mutually trusted authority (MTA) is studied. Previously, design of MTA-free schemes was restricted to complete access structures only, moreover the basic protocol used there seems not to be able to offer a way to construct MTA-free scheme for a predetermined access structure. In the paper the problem is studied in a more general setting, namely to establish an MTA-free secret sharing scheme for a given access structure which is not necessarily complete. The construction protocol for MTA-free schemes for any access structure is given and its components are then analyzed with respect to three efficiency measures proposed. It is shown that the basic protocol can be improved with respect to each of these measures and for threshold schemes optimal constructions are given. However, improvement with respect to more than one measure is still an open problem, as pointed out in the final section of the paper.