  This paper studies the message complexity of authenticated Byzantine
agreement (BA) in synchronous, fully-connected distributed networks under an
honest majority. We focus on the so-called {\em implicit} Byzantine agreement
problem where each node starts with an input value and at the end a non-empty
subset of the honest nodes should agree on a common input value by satisfying
the BA properties (i.e., there can be undecided nodes). We show that a
sublinear (in $n$, number of nodes) message complexity BA protocol under honest
majority is possible in the standard PKI model when the nodes have access to an
unbiased global coin and hash function. In particular, we present a randomized
Byzantine agreement algorithm which, with high probability achieves implicit
agreement, uses $\tilde{O}(\sqrt{n})$ messages, and runs in $\tilde{O}(1)$
rounds while tolerating $(1/2 - \epsilon)n$ Byzantine nodes for any fixed
$\epsilon > 0$, the notation $\Tilde{O}$ hides a $O(\polylog{n})$ factor. The
algorithm requires standard cryptographic setup PKI and hash function with a
static Byzantine adversary. The algorithm works in the CONGEST model and each
node does not need to know the identity of its neighbors, i.e., works in the
$KT_0$ model. The message complexity (and also the time complexity) of our
algorithm is optimal up to a $\polylog n$ factor, as we show a
$\Omega(\sqrt{n})$ lower bound on the message complexity.
