  We consider random Cayley digraphs of order $n$ with uniformly distributed
generating set of size $k$. Specifically, we are interested in the asymptotics
of the probability such a Cayley digraph has diameter two as $n\to\infty$ and
$k=f(n)$. We find a sharp phase transition from 0 to 1 at around $k = \sqrt{n
\log n}$. In particular, if $f(n)$ is asymptotically linear in $n$, the
probability converges exponentially fast to 1.
