Binary value broadcast Clause Samples

Binary value broadcast. The protocol relies in Phase 1 on a reliable broadcast routine bv-broadcast proposed before [1], which is used to ensure validity, i.e., any estimate adopted (and later decided) must have been proposed by some honest process. Moreover, it guarantees that if every honest process begins a round with the same value, then that is the only possible estimate for the remainder of the execution (if 𝑡 < 𝑛/3). Specifically, bv-broadcast guarantees the following critical properties while 𝑡 < 𝑛/3: (i) every message broadcast by 𝑡0 + 1 honest processes is eventually delivered to every honest process (see Lemma B.2); (ii) every message delivered to an honest process was broadcast by at least 𝑡 + 1 processes (see Lemma B.1). These properties are ensured by a simple echo procedure. When a process first tries to bv-broadcast a message, it broad- casts it to everyone. When a process receives ��0 + 1 copies of a message, then it echoes it. When a process receives 𝑛 − 𝑡0 copies of a message, then it delivers it. Notice that if a mes- sage is not bv-broadcast by at least 𝑡0 + 1 processes, then it is never echoed and hence never delivered. And if a message is bv-broadcast by 𝑡0 + 1 (honest) processes is echoed by every honest process and hence delivered to every honest process. This reliable broadcast routine ensures validity, since a Phase 1 message that is echoed in Phase 2 must have been delivered by bv-broadcast, and hence must have been bv-broadcast by at least one honest process.