On the complexity of asynchronous agreement against powerful adversaries

Abstract

We introduce new techniques for proving lower bounds on the running time of randomized algorithms for asynchronous agreement against powerful adversaries. In particular, we define a strongly adaptive adversary that is computationally unbounded and has a limited ability to corrupt a dynamic subset of processors by erasing their memories. We demonstrate that the randomized agreement algorithms designed by Ben-Or and Bracha to tolerate crash or Byzantine failures in the asynchronous setting extend to defeat a strongly adaptive adversary. These algorithms have essentially perfect correctness and termination, but at the expense of exponential running time. In the case of the strongly adaptive adversary, we show that this dismally slow running time is inherent : we prove that any algorithm with essentially perfect correctness and termination against the strongly adaptive adversary must have exponential running time. We additionally interpret this result as yielding an enhanced understanding of the tools needed to simultaneously achieving perfect correctness and termination as well as fast running time for randomized algorithms tolerating crash or Byzantine failures.

On the Round Complexity of Randomized Byzantine Agreement

“…Connection to the full-information model. The public-randomness model can be viewed as a restricted form of the full-information model [17,8,32,5,9,35,38,44,41,45]. In the latter model, the adversary is computationally unbounded and has complete access to all the information in the system, i.e., it can listen to all transmitted messages and view the internal states of honest parties (such an adversary is also called intrusive [17]).…”

On the Round Complexity of Randomized Byzantine Agreement

“…Connection to the full-information model. The public-randomness model can be viewed as a restricted form of the full-information model [17,7,32,5,9,33,37,43,40,44]. In the latter model, the adversary is computationally unbounded and has complete access to all the information in the system, i.e., it can listen to all transmitted messages and view the internal states of honest parties (such an adversary is also called intrusive [17]).…”