Stabilizing Consensus with Many Opinions

We consider the following distributed consensus problem: Each node in a complete communication network of size $n$ initially holds an \emph{opinion}, which is chosen arbitrarily from a finite set $\Sigma$. The system must converge toward a consensus state in which all, or almost all nodes, hold the same opinion. Moreover, this opinion should be \emph{valid}, i.e., it should be one among those initially present in the system. This condition should be met even in the presence of an adaptive, malicious adversary who can modify the opinions of a bounded number of nodes in every round. We consider the \emph{3-majority dynamics}: At every round, every node pulls the opinion from three random neighbors and sets his new opinion to the majority one (ties are broken arbitrarily). Let $k$ be the number of valid opinions. We show that, if $k \leqslant n^{\alpha}$, where $\alpha$ is a suitable positive constant, the 3-majority dynamics converges in time polynomial in $k$ and $\log n$ with high probability even in the presence of an adversary who can affect up to $o(\sqrt{n})$ nodes at each round. Previously, the convergence of the 3-majority protocol was known for $|\Sigma| = 2$ only, with an argument that is robust to adversarial errors. On the other hand, no anonymous, uniform-gossip protocol that is robust to adversarial errors was known for $|\Sigma| > 2$

Communication-Efficient BFT Protocols Using Small Trusted Hardware to Tolerate Minority Corruption

Agreement protocols for partially synchronous or asynchronous networks tolerate fewer than one-third Byzantine faults. If parties are equipped with trusted hardware that prevents equivocation, then fault tolerance can be improved to fewer than one-half Byzantine faults, but typically at the cost of increased communication complexity. In this work, we present results that use small trusted hardware without worsening communication complexity assuming the adversary controls a fraction of the network that is less than one-half. Our results include a version of HotStuff that retains linear communication complexity in each view and a version of the VABA protocol with quadratic communication, both leveraging trusted hardware to tolerate a minority of corruptions. Our results use expander graphs to achieve efficient communication in a manner that may be of independent interest

Distributed agreement with optimal communication complexity

We consider the problem of fault-tolerant agreement in a crash-prone synchronous system. We present a new randomized consensus algorithm that achieves optimal communication efficiency, using only O(n) bits of communication, and terminates in (almost optimal) time O(log n), with high probability. The same protocol, with minor modifications, can also be used in partially synchronous networks, guaranteeing correct behavior even in asynchronous executions, while maintaining efficient performance in synchronous executions. Finally, the same techniques also yield a randomized, faulttolerant gossip protocol that terminates in O(log ∗ n) rounds using O(n) messages (with bit complexity that depends on the data being gossiped).