Break RSA given $N, e$ and lower half of $d$
If $e$ is small, and if you have $n/4$ least significant bits of $d$, then you can factorize $N$. The attack runs in time polynomial in $e, n$. You can have a look at Boneh Durfee Frankel attack Section 3. So, if $e$ is only 65537, then the attack is certainly feasible.