International Association
for Cryptologic Research

The synchrony model allows Byzantine Agreement (BA) protocols to be deterministic, tolerate minority faults, and achieve the asymptotically optimal $O(n)$ rounds, and $O(n^2)$ bits of communication where $n$ is the number of parties. We study the deterministic BA problem in a model in which every communication link is either synchronous or partially synchronous. Our main result for this model is that feasibility implies optimality: For every $\frac{n}{3}\leq f<\frac{n}{2}$, the minimal network conditions required for BA to be solvable against $f$ byzantine faults, are also sufficient for it to be solvable optimally, i.e., with $O(f)$ rounds and $O(f^2)$ communication. In particular, BA against minority byzantine faults can be solved when the synchronous links in the network form a mere path ($f$ synchronous links) as efficiently (up to constant factors) as when all communication links are synchronous ($\Omega(f^2)$ synchronous links).