Partition-Resilience. Algorand agreement proposed by Xxxx et al. [5] is a synchronous protocol. In their work, they propose a new property, called partition-resilience: a Byzantine agreement protocol is partition-resilient (PR) if the agreement always holds even if the network is asynchronous, and the termination holds if the network becomes synchronous and all the delayed messages delivered. Notice that “a syn- chronous BA with PR” is different from “an asynchronous BA.” For the former, the protocol is still parameterized by a 2In fact, even the weakly fair validity cannot be achieved. We will elucidate it in Section III. time-bound λ and some properties3 other than the agreement may still rely on λ. On the other hand, an asynchronous BA performs qualitatively the same no matter the condition of the network. The network nowadays in highly reliable, so a synchronous BA with PR enjoys all the desired properties depending on λ most of the time, while the agreement still holds even if the occasional failure happens. When applying to blockchains, the agreement guarantees that the chain will not fork. Thus, PR is a reasonable requirement of a BA protocol for building a blockchain.
Partition-Resilience. We design two mechanisms to achieve this. First, at any time, at most one value can be locked by a supermajority of nodes. Once the supermajority of node locks on a value, all honest nodes in the supermajority will only vote on the value for the first phase in the following iterations. Then, it is impossible that a new value will be locked. Hence, the honest nodes never decide on different values even if the partition exists. Second, to ensure node can process in the same iteration even network partition sometimes happened, nodes will jump to the newest iteration if it receives a majority of votes in the first phase of that iteration. That is, each node will update the locking value not only by the timing bound from the synchronous network but also the condition of valid votes is received asynchronously to against network partition.
Partition-Resilience. In the second experiment, the network operates in two modes: the normal mode and the partition mode. In the normal mode, all the nodes are con- nected with the delay sampled from (250ms, 50ms). In the partition mode, the network is divided into three distinct sets of size | n ∫ or | n ∫ + 1. Within the set, the delay is sampled Fig. 2: The histogram of latency of HBA. from (250ms, 50ms). For the messages between two sets, G the delays are sampled from (4000ms, 1000ms). All the protocols are executed with λ = 1000ms. Thus, when the network is in the partition mode, the delay between different sets exceeds λ. The protocols are executed in the partition mode for 60 seconds. Then, the network becomes the normal mode. The result is shown in Figure 4. G Notice that the partition is “benign” in this model. Except that the delays are sampled from (4000ms, 1000ms), there is no adversary that re-schedules or delay the messages to break the protocols maliciously. The benign partition captures the case that the Internet cables breaks so that the alternative route is saturated. rarely happens in practice if the network is not manipulated maliciously. As for PBFT, the timeout scales up when the view change confirm time (second) 0 # nodes → 16 32 64 16 32 64 16 32 64 16 32 64 HBA PBFT ADD+19 Algorand 15 happens, so once the timeout exceeds the delay, the protocol terminates. For ADD+19, the protocol is design for the syn- chronous network, and the partition-resilience is not claimed 10 in their paper, but the protocol terminates after the partition is resolved 6. As Xxxxxxxx claimed, the protocol terminates immediately after the network is recovered.
