Byzantine Fault Tolerance on General Hybrid Adversary Structures

Adversary structures are a generalization of the classical "at most t-out-of-n" threshold failure model which is used in many published Byzantinetolerant protocols. An adversary structure basically lists all coalitions of parties whose corruption the protocol should tolerate. Using adversary structures it is possible to encode dependent failure models, such as "either all Linux machines fail or all Windows machines but not both at the same time". We describe a general technique that allows to transform an algorithm designed for the threshold model into an algorithm that works for general adversary structures. Our technique is based on several (partly informal) rules which describe how the algorithm and its proof must be augmented so that general adversary structures can be tolerated. We demonstrate the applicability of our approach by transforming an asynchronous Byzantine-tolerant reliable broadcast protocol into one that tolerates Byzantine adversary structures. We also consider similar transformations for hybrid failures (combinations of different fault models) and discuss ways to map adversary structures to the real world and manage them efficiently