Shared secret reconstruction
Traditional approaches to the secret sharing problem are focused to the problem of how to divide a secret into shares distributed among a set of users in such a way that only a qualified subset of users can reconstruct the secret while any unqualified group of users have no information about the secret. However, known secret sharing schemes do not prevent cheating in the reconstruction phase -- e.g. it may happen that cheating member of a qualified group of users can recover the secret while the rest of the group cannot. In the paper the problem of how to prevent cheating in the reconstruction phase of a secret sharing scheme is studied. Emphasis is given to the fair reconstruction of a shared secret, i.e. after completion of the reconstruction phase all users involved should have an (almost) equal information about the shared secret. To accomplish this, the authors propose to make use of a known verifiable secret sharing (VSS) scheme. While the VSS scheme cannot be used in its original form to solve the problem, a multi-stage use of a VSS scheme suffices. The authors first show how to solve the problem using a VSS as a basic building block when there is at most one cheater in the group. Then it is shown how to use the approach to deal with more cheaters (up to the case when all except one are cheaters). Description of the proposed scheme is given as well as its detailed analysis. Finally, some open questions and topics for future investigations are briefly reviewed.
scientific article; zbMATH DE number 1202994