  Replicated services accessed via {\em quorums} enable each access to be
performed 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 {\em 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.
