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arXiv · 2006.16686

Revisiting Asynchronous Fault Tolerant Computation with Optimal Resilience

Ittai Abraham·Danny Dolev·Gilad Stern
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Abstract

The celebrated result of Fischer, Lynch and Paterson is the fundamental lower bound for asynchronous fault tolerant computation: any 1-crash resilient asynchronous agreement protocol must have some (possibly measure zero) probability of not terminating. In 1994, Ben-Or, Kelmer and Rabin published a proof-sketch of a lesser known lower bound for asynchronous fault tolerant computation with optimal resilience against a Byzantine adversary: if $n\le 4t$ then any t-resilient asynchronous verifiable secret sharing protocol must have some non-zero probability of not terminating. Our main contribution is to revisit this lower bound and provide a rigorous and more general proof. Our second contribution is to show how to avoid this lower bound. We provide a protocol with optimal resilience that is almost surely terminating for a strong common coin functionality. Using this new primitive we provide an almost surely terminating protocol with optimal resilience for asynchronous Byzantine agreement that has a new fair validity property. To the best of our knowledge this is the first asynchronous Byzantine agreement with fair validity in the information theoretic setting.

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Ittai Abraham, Danny Dolev, Gilad Stern. 2020-06-30. Revisiting Asynchronous Fault Tolerant Computation with Optimal Resilience. https://arxiv.org/abs/2006.16686

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