Brief announcement: fast scalable Byzantine agreement in the full information model with a nonadaptive adversary

We address the problem of designing distributed algorithms for large scale networks that are robust to Byzantine faults. We consider a message passing, full information model: the adversary is malicious, controls a constant fraction of processors, and can view all messages in a round before sending out its own messages for that round. Furthermore, each corrupt processor may send an unlimited number of messages. The adversary is constrained to choose its corrupt processors at the start, without knowledge of the processors' private random bits, but is otherwise adaptive. To the authors' best knowledge, there have been no subexponential protocols in the asynchronous version of this model and no protocols that compute Byzantine agreement without all-to-all communication in this model even a model in which private channels or cryptography are assumed, unless corrupt processors' messages are limited. We announce a polylogarithmic time protocol in the asynchronous model which appeared in SODA 08 and was recently improved to a resilience of n/(3 + ε). We also give a polylogarithmic time protocol for Byzantine agreement using only Õ(n^3/2) total bits of pairwise communication which succeeds with high probability. These results rest on our solution to the problem of selecting a small representative sample of processors (universe reduction). This work extends the authors' work on scalable almost everywhere agreement to everywhere agreement and is an unpublished manuscript.