If you have the cyclic group of integers modulo $p$, where $p$ is not a safe prime, as well as a generator $g$ with which for all factors $q$ of $(p-1)$,
$g^{(p-1)/q} \ne 1$,
This answer says that given $g$ and $g^x \bmod p$, we can determine $x \bmod q$ in $O(\sqrt{q})$ time.
What algorithm lets us do that?
