  Some of the recent blockchain proposals, such as Stellar and Ripple, use
quorum-like structures typical for Byzantine consensus while allowing for open
membership. This is achieved by constructing quorums in a decentralised way:
each participant independently chooses whom to trust, and quorums arise from
these individual decisions. Unfortunately, the theoretical foundations
underlying such blockchains have not been thoroughly investigated. To close
this gap, in this paper we study decentralised quorum construction by means of
federated Byzantine quorum systems, used by Stellar. We rigorously prove the
correctness of basic broadcast abstractions over federated quorum systems and
establish their relationship to the classical Byzantine quorum systems. In
particular, we prove correctness in the realistic setting where Byzantine nodes
may lie about their trust choices. We show that this setting leads to a novel
variant of Byzantine quorum systems where different nodes may have different
understanding of what constitutes a quorum.
