A distributed secret sharing system is considered that consists of a dealer, @math storage nodes, and @math users. Each user is given access to a certain subset of storage nodes where it can download the data. The dealer wants to securely convey a specific secret s j to user @math via storage nodes, for @math = 1, 2,…, m, in such a way that no user gets any information about other users' secrets in an information-theoretic sense. To this end, we propose to study protocols where the dealer encodes secrets into several secret shares and loads them into the storage nodes. Given a certain number of storage nodes we find the maximum number of users that can be served in such protocols and construct schemes that achieve this. We further define two major properties for such distributed secret sharing systems; communication complexity is defined as the total amount of data that needs to be downloaded by users in order to reconstruct their secrets; and storage overhead is defined as the total amount of data loaded by the dealer into the storage nodes normalized by the total size of secrets. Lower bounds on minimum communication complexity and storage overhead are characterized given any @math and @math . Furthermore, we construct distributed secret sharing protocols, under certain conditions on the system parameters, that attain these lower bounds thereby providing schemes that are optimal in terms of both the communication complexity and storage overhead.
In this paper we show how to divide data D into n pieces in such a way that D is easily reconstructable from any k pieces, but even complete knowledge of k - 1 pieces reveals absolutely no information about D . This technique enables the construction of robust key management schemes for cryptographic systems that can function securely and reliably even when misfortunes destroy half the pieces and security breaches expose all but one of the remaining pieces.