  We give efficient randomized and deterministic distributed algorithms for
computing a distance-$2$ vertex coloring of a graph $G$ in the CONGEST model.
In particular, if $\Delta$ is the maximum degree of $G$, we show that there is
a randomized CONGEST model algorithm to compute a distance-$2$ coloring of $G$
with $\Delta^2+1$ colors in $O(\log\Delta\cdot\log n)$ rounds. Further if the
number of colors is slightly increased to $(1+\epsilon)\Delta^2$ for some
$\epsilon>1/{\rm polylog}(n)$, we show that it is even possible to compute a
distance-$2$ coloring deterministically in polylog$(n)$ time in the CONGEST
model. Finally, we give a $O(\Delta^2 + \log^* n)$-round deterministic CONGEST
algorithm to compute distance-$2$ coloring with $\Delta^2+1$ colors.
