From O ( n 2 ) to O ( n ) : An Efficient Deterministic Algorithm for Byzantine Agreement

In this paper, we introduce an efficient deterministic agreement algorithm that solves the multi-valued Byzantine agreement problem deterministically for networks of arbitrary size n ≥ 4 and up to t < n/3 failures. This paper considers the “broadcast” version of the agreement problem, wherein the goal is for the nodes in the network to agree on the values that a certain source node wants to broadcast to them. The per-bit communication complexity of an agreement algorithm is defined as the worst case communication complexity for achieving agreement for l bits divided by the message length l. Our algorithm achieves per-bit complexity arbitrarily close to n(n−1)/(n−t) for large value of l. For large l, by using a multi-valued approach, it not only breaks the quadratic lower bound Ω(n) for perbit complexity from the prior work, it is also the most efficient among the known Byzantine agreement algorithms, including the ones that achieve agreement just probabilistically. Moreover, we believe that, besides being order-optimal, the proposed algorithm is in fact also optimal in the sense of minimizing the per-bit cost.