Asynchronous Veri able Secret Sharing Sample Clauses

Asynchronous Veri able Secret Sharing. A secret sharing protocol (either synchronous or asynchronous) consists of two protocols: a sharing protocol, in which a dealer \shares" a secret among the players, and a reconstruction protocol, in which the players \reconstruct" the secret from its shares. An uncorrupted dealer should be able to share a secret while making sure that the reconstructed value will be the correct secret. Further- more, if the dealer is uncorrupted then the shared secret should remain unknown to the adversary, as long as no uncorrupted player has started the reconstruction protocol. We say that a secret sharing protocol is veri able if the following requirements hold: as soon as one uncorrupted player 2An alternative convention may be to invoke the corresponding sub-protocol immediately upon the receipt of the message. We prefer the convention that sub-protocols must be explicitly invoked by other sub-protocols. 3Here and in the sequel the probabilities are taken over the random inputs of the players. successfully completes the sharing protocol, a value r is xed; furthermore, all the uncorrupted players will eventually successfully complete the sharing protocol. The value reconstructed by the players in the reconstruction protocol will be r, even if the dealer is corrupted. In De nition 2 we formalize the requirements from a veri able secret sharing protocol for our asynchronous setting. More precisely, let a Share-Reconstruct (SR) protocol be a protocol that consists of two sub- protocols, denoted Sh and Rec. It will be convenient to regard these sub-protocols as independent sub-protocols. Also, there is a distinguished player called the dealer and denoted D. An execution of an SR protocol proceeds as follows:
Sample 1
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