Byzantine Agreement with Optimal Early Stopping, Optimal Resilience and Polynomial Complexity

We provide the first protocol that solves Byzantine agreement with optimal early stopping (\min\{f+2,t+1\} rounds) and optimal resilience (n>3t) using polynomial message size and computation.
All previous approaches obtained sub-optimal results and used resolve rules that looked only at the immediate children in the EIG (Exponential Information Gathering) tree. At the heart of our solution are new resolve rules that look at multiple layers of the EIG tree.
Joint work with Danny Dolev (to appear in STOC 2015).