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One of the most challenges in distributed consensus mechanisms is both time complexity and message complexity.

For example, PBFT message complexity is O(n^2) that means that it is only scalable to tens of nodes. Thus, classical BFT (Byzantine Fault Tolerant) consensus mechanisms are not scalable to the large networks.

Nevertheless, I am looking for the most scalable BFT consensus  among all. 

In other words, is there a distributed BFT consensus with less than O(n^2) message complexity?

P.S. I brought up this question before in scicomp.stackexchange.com, but they suggested me to bring up it here. (https://scicomp.stackexchange.com/q/36087/37225)

Questioner
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1 Answers1

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You can turn a lot of consensus algorithms that utilize a "leader" into one that takes only O(n) message complexity in the optimistic case, by sending every message in that iteration to the leader, who then broadcasts your message to everyone. (PBFT should fall into this category, except for the view change). Assuming threshold signatures, we can further get O(n) bit complexity. (See Hotstuff, Jolteon, Tendermint).

IIRC in the pessimistic case, Hotstuff still needs a quadratic pacemaker, so the message complexity is still O(n^2), but one could argue (as they do) that they achieve a O(n) ``view change''.

I would also look at the Algorand style of protocol, which achieves $O(n\lambda)$ communication, where $\lambda$ is a choice of security parameter. (It will end up being about $2500$ servers each doing a multicast every round, with current concrete notions of security).

Vervious
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