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

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(logn) processors, which contains a majority of good processors. In this paper, we give a synchronous algorithm which uses polylogarithmic time and Õ(vn) 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(logn) 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.

Fast Byzantine Leader Election in Dynamic Networks

We study the fundamental Byzantine leader election problem in dynamic networks where the topology can change from round to round and nodes can also experience heavy {\em churn} (i.e., nodes can join and leave the network continuously over time). We assume the full information model where the Byzantine nodes have complete knowledge about the entire state of the network at every round (including random choices made by all the nodes), have unbounded computational power and can deviate arbitrarily from the protocol. The churn is controlled by an adversary that has complete knowledge and control over which nodes join and leave and at what times and also may rewire the topology in every round and has unlimited computational power, but is oblivious to the random choices made by the algorithm. Our main contribution is an $O(\log^3 n)$ round algorithm that achieves Byzantine leader election under the presence of up to $O({n}^{1/2 - \epsilon})$ Byzantine nodes (for a small constant $\epsilon > 0$) and a churn of up to \\$O(\sqrt{n}/\poly\log(n))$ nodes per round (where $n$ is the stable network size).The algorithm elects a leader with probability at least $1-n^{-\Omega(1)}$ and guarantees that it is an honest node with probability at least $1-n^{-\Omega(1)}$; assuming the algorithm succeeds, the leader's identity will be known to a $1-o(1)$ fraction of the honest nodes. Our algorithm is fully-distributed, lightweight, and is simple to implement. It is also scalable, as it runs in polylogarithmic (in $n$) time and requires nodes to send and receive messages of only polylogarithmic size per round.To the best of our knowledge, our algorithm is the first scalable solution for Byzantine leader election in a dynamic network with a high rate of churn; our protocol can also be used to solve Byzantine agreement in a straightforward way.We also show how to implement an (almost-everywhere) public coin with constant bias in a dynamic network with Byzantine nodes and provide a mechanism for enabling honest nodes to store information reliably in the network, which might be of independent interest.