Protocol Optimal-ABA Sample Clauses

Protocol Optimal-ABA. Our protocol Optimal-ABA uses the so-called player-elimination framework, along with several novel ideas. So far player-elimination [16] has been used only in the context of synchronous and asynchronous MPC [16, 2, 24]. Ours is the first non- MPC application of player-elimination. We would refer it by party-elimination, rather than player-elimination in our context (as we use the term party in place of player). In the party-elimination framework, the computation of Optimal-ABA t is divided into t segments, where in each segment the parties agree on an A bit, t considering A bits of their original input as the input message of the segment. In particular, the parties divide their original message into t blocks, each of size t t A bits and in αth segment Sα, the parties reach agreement on an A bit message, considering only the αth block as the input message. Each segment terminates t eventually with the parties having common output of A bits; moreover if the t honest parties start a segment with the same block of A bits, then they agree on that common input. t P P P The computation of a segment is carried out in a non-robust fashion, in the sense that if all the parties including the corrupted parties behave according to the protocol then the segment successfully achieves its task; otherwise the segment may fail in which case it outputs a triplet of parties among which at least one is corrupted. In the former case, the next segment will be taken up for computation for reaching agreement with next block of A bits as input. In the latter case, the same segment will be repeated among the set of parties after excluding the parties in the triplet and this continues until the segment becomes successful. It is to be noted that though the computations in a segment may be done among a subset of parties from (as parties in triplet might be eliminated from ), the agreement in the segment is finally attained over all honest parties in . It is now easy to see that the t segments may fail at most t times in total as t is the upper bound on the number of corrupted parties. After t failures, all the corrupted parties will be removed and therefore there will be no more failure. S S ∈ { }

Protocol Optimal-ABA. Our protocol Optimal-ABA uses the so-called player-elimination framework, along with several novel ideas. So far player-elimination [16] has been used only in the context of synchronous and asynchronous MPC [16, 2, 24]. Ours is the first non- MPC application of player-elimination. We would refer it by party-elimination, rather than player-elimination in our context (as we use the term party in place of player). In the party-elimination framework, the computation of Optimal-ABA t is divided into t segments, where in each segment the parties agree on an A bit, t considering A bits of their original input as the input message of the segment. In particular, the parties divide their original message into t blocks, each of size t

Protocol Optimal-ABA