Byzantine fault-tolerant distributed set intersection with redundancy
CoRR(2024)
摘要
In this report, we study the problem of Byzantine fault-tolerant distributed
set intersection and the importance of redundancy in solving this problem.
Specifically, consider a distributed system with n agents, each of which has
a local set. There are up to f agents that are Byzantine faulty. The goal is
to find the intersection of the sets of the non-faulty agents.
We derive the Byzantine set intersection problem from the Byzantine
optimization problem. We present the definition of 2f-redundancy, and
identify the necessary and sufficient condition if the Byzantine set
intersection problem can be solved if a certain redundancy property is
satisfied, and then present an equivalent condition. We further extend our
results to arbitrary communication graphs in a decentralized setting. Finally,
we present solvability results for the Byzantine optimization problem, inspired
by our findings on Byzantine set intersection. The results we provide are for
synchronous and asynchronous systems both.
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