#### Theory Seminar

# Byzantine Agreement in Polynomial Expected Time

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How can we build a reliable system out of unreliable parts? Byzantine agreement is fundamental to addressing this question. The Byzantine agreement problem is to devise an algorithm so that n agents, each with a private input can agree on a single common output that is equal to some agent's input. In the classic Byzantine agreement problem, communication is via asynchronous message-passing and the adversary is adaptive with full information. In particular, the adversary can adaptively determine which processors to corrupt and what strategy these processors should use as the algorithm proceeds; the scheduling of the delivery of messages is set by the adversary, so that the delays are unpredictable to the algorithm; and the adversary knows the states of all processors at any time, and is assumed to be computationally unbounded. Such an adversary is also known as strong.

We present a polynomial expected time algorithm to solve asynchronous Byzantine Agreement with a strong adversary that controls up to a constant fraction of the processors. This is the first improvement in running time for this problem since Ben-Or's exponential expected time solution in 1983. Our algorithm is designed so that in order to thwart it, corrupted agents must engage in statistically deviant behavior that is detectable by individual agents. This suggests a new paradigm for secure distributed computing: the design of algorithms that force an attacker into behavior that is statistically deviant in a way that is computationally detectable.