Load Balanced Scalable Byzantine Agreement through Quorum Building, with Full Information

Abstract

Abstract. 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 bad processor may send an unlimited number of messages. The only constraint on the adversary is that it must choose its corrupt processors at the start, without knowledge of the processors' private random bits. A good quorum is a set of O(log n) processors, which contains a majority of good processors. In this paper, we give a synchronous algorithm which uses polylogarithmic time andÕ( √ n) bits of communication per processor to bring all processors to agreement on a collection of n good quorums, solving Byzantine agreement as well. The collection is balanced in that no processor is in more than O(log n) quorums. This yields the first solution to Byzantine agreement which is both scalable and load-balanced in the full information model. The technique which involves going from situation where slightly more than 1/2 fraction of processors are good and and agree on a short string with a constant fraction of random bits to a situation where all good processors agree on n good quorums can be done in a fully asynchronous model as well, providing an approach for extending the Byzantine agreement result to this model. As an additional result, we present a fully asynchronous algorithm that can go from a situation where slightly more than 1/2 fraction of processors are good and and agree on a short string with a constant fraction of random bits, to a situation where all good processors agree on n good quorums, and can do this in a load balanced way. This provides an approach for extending the Byzantine agreement result above to the asynchronous model, with an additional log n factor in the number of bits communicated.

Recent Results in Scalable Multi-Party Computation

“…A quorum is a polylogarithmic set of parties, where the number of corrupted parties in each quorum is guaranteed not to exceed a certain fraction. King et al [KLST11] show how to use BA to efficiently create a collection of quorums.…”

“…The protocol is unconditionally-secure against a Byzantine adversary corrupting less than (1/3 − )n of the parties, for some positive constant . The protocol creates a set of quorums using the quorum building algorithm of [KLST11]. For each gate in the circuit, a quorum is used to compute the output of the gate using the MPC of [BGW88] among parties of the quorum.…”

“…As an intermediate result in a Byzantine agreement paper, King et al [KLST11] give a protocol that can be used to bring all parties to agreement on a collection of n quorums. This protocol is based on the almost-everywhere Byzantine agreement 9 of King et al…”

“…In general, one can use any BA algorithm to build a set of quorums as described in [KLST11]. Theorem 5 gives a quorum building protocol using the BA algorithm of Braud-Santoni et al…”

Scalable byzantine computation

“…A single short string with some random bits is sufficient for other interesting purposes, such as providing global coins for Rabin's BA algorithm (as used in [46]), agreeing upon a collection of many small representative sets (quorums) [43], and, in general, choosing from a distribution where a large fraction of choices are good.…”