International Association
for Cryptologic Research

We present new lower and upper bounds on the number of communication rounds required for asynchronous Crusader Agreement (CA) and Binding Crusader Agreement (BCA), two primitives that are used for solving binary consensus. We show results for the information theoretic and authenticated settings. In doing so, we present a generic model for proving round complexity lower bounds in the asynchronous setting.

In some settings, our attempts to prove lower bounds on round complexity fail. Instead, we show new, tight, rather surprising round complexity upper bounds for Byzantine fault tolerant BCA with and without a PKI setup.