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Replicated services accessed via quorums enable each access tobe perfo rmed at only a subset (quorum) of the servers and achieve consistency across accesses by requiring any two quorums to intersect. Recently, b-masking quorum systems, whose intersections contain at least 2b + 1 servers, have been proposed to construct replicated services tolerant of b-arbitrary (Byzantine) server failures. In this paper we consider a hybrid fault model allowing benign failures in addition to the Byzantine ones. We present four novel constructions for b-masking quorum systems in this model, each of which has optimal load (the probability of access of the busiest server) or optimal availability (probability of some quorum surviving failures). To show optimality we also prove lower bounds on the load and availability of any b-masking quorum system in this model.

The load and availability of Byzantine quorum systems