Common use of (t) Clause in Contracts

(t). In particular, if the network is asynchronous and there are up to ta corruptions, weak validity is achieved: any party that does not output has received at least n ts values with grade 2, and n ts ta > ta of those values correspond to the inputs of honest parties. Moreover, when the network is synchronous and up to ts parties are corrupted, there cannot be honest parties Pi and Pj that output different bits v and 1 − v, respectively. This is because 1) if Pi receives (1 − v, ·) up to ta times, then Pj cannot receive (1 − v, 2) more than ta times, and 2) if Pi receives (v, 2) at least n − ts times, then Pj receives (v, ·) at least n − ts > ta times. GBC We formally describe the protocol below. Let Πt be a gradecast protocol running in s GBC rounds. The n executions of Πt are to be run in parallel to preserve round-efficiency. Security is proven in Section C. WC GBC Protocol Πta,ts Πmax{ta,ts} We describe the protocol from the point of view of party Pj holding input vj. We denote by Πmax{ta,ts}(j) an execution of protocol Πmax{ta,ts} in which party Pj acts as the sender. GBC GBC