Protocol Overview. The basic protocol operates in two phases, after which a possible decision is taken. Each pro- cess maintains an estimate. In the first phase, each process broadcasts its estimate using a reliable broadcast service, bv-broadcast (discussed below), as introduced previously [1]. The protocol uses a rotating coordinator; whoever is the as- signed coordinator for a round broadcasts its estimate with a special designation. All processes then wait until they receive at least one mes- sage, and until a timer expires. (The timeout is increased with each iteration, so that eventually once the network stabilizes it is long enough.) If a process receives a message from the coordinator, then it chooses the coordinator’s value to “echo”, i.e., to rebroadcast to everyone in the second phase. Other- wise, it simply echoes all the messages received in the first phase. − − At this point, each process pi waits until it receives enough compatible ECHO messages. Specifically, it waits to receive at least (n t0) messages sent by distinct processes where every value in those messages was also received by pi in the first phase. In this case, it adopts the collection of values in those (n t0) messages as its candidate set. In fact, if a − process pi receives a set of (n t0) messages that all contain exactly the coordinator’s value, then it chooses only that value as the candidate value. Finally, the processes try to come to a decision. If process pi has only one candidate value v, then pi adopts that value v as its estimate. In that case, it can decide v if it matches the parity of the round, i.e., if v = ri mod 2. Otherwise, if pi has more than one candidate value, then it adopts as its estimate ri mod 2, the parity of the round. − − To see that this ensures agreement (when t < n/3), consider a round in which some process pi decides value v = ri mod 2. Since pi receives (n t0) echo messages containing only the value v, we know that every honest process must have value v in every possible set of (n t0) echo messages, and hence every honest process included v in its candidate set. Every honest process that only had v as a candidate also decided
Protocol Overview b 3 l n 3 m + 1 runs as follows4: The rst run of the reduced protocol proceeds in The e cient protocol consists of executing the reduced protocol in sequence for the same way as the basic protocol (with the di erence that it only proceeds for b communication rounds). In every subsequent run (say the m-th run) of the reduced protocol the rst communication round of the protocol is omitted. Instead of receiving a value from the dealer, every player p assigns the resolved root value computed at the end of the previous run to the root node of his reduced IG-tree: tree(m)(d) := resolve(m 1)(d) :
Protocol Overview. The e cient protocol consists of executing the reduced protocol in sequence for n 3
Protocol Overview b 3 ln 3 m + 1 runs as follows4: The rst run of the reduced protocol proceeds in The e cient protocol consists of executing the reduced protocol in sequence for
