Polynomial Time Byzantine Agreement with Optimal Resilience


Seth Pettie October 22, 2022.


“One thing that distinguishes (theoretical) computer science from other scientific disciplines is its full-throated support of a fundamentally adversarial view of the universe. Malicious adversaries, with unbounded computational advantages, attempt to foil our algorithms at every turn and destroy their quantitative guarantees. However, there is one strange exception to this world view and it is this: the algorithm must accept its input as sacrosanct, and may never simply reject its input as illegitimate. But what if some inputs really are illegitimate? Is building a ““fraud detector”” for algorithms a good idea?

In this talk I will present a protocol for asynchronous Byzantine Agreement against the ““strongest”” adversary, which is omniscient, computationally unbounded, and can adaptively corrupt players as the protocol progresses. The protocol reduces Byzantine Agreement to a coin-flipping game in which the nominal goal is to collectively flip a fair coin, in the presence of malicious parties that attempt to fix its outcome. However, in the short term the malicious parties have an insurmountable advantage. The true goal of the game is to build a sound ““fraud detector”” that identifies which parties are not playing according to protocol, and ““blacklist”” them. The final result is a polynomial time Byzantine Agreement protocol against an adaptive, all-knowing adversary that can corrupt up to f<n/3 players. The previous-best protocol against f<n/3 corruptions took exponential time. Moreover, the problem cannot be solved with f >= n/3 corruptions.

Joint work with Leqi Zhu and Shang-En Huang. https://arxiv.org/abs/2206.15335.”

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