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. 1. A player rst runs sub-protocol Sh on its given input. (The dealer has input value s 2 S where S is some pre-de ▇▇▇ set. All other players have no input.) At a certain point, protocol Sh may output a special symbol `sharing succeeded'. In the sequel, when we colloquially say that protocol Sh completes, we mean that the player outputs `sharing succeeded'. We stress that sub-protocol Sh remains active even after this symbol has been output.