Break RSA given $N, e$ and lower half of $d$ I have full bits of public key $(n,e=65537)$ but from the private key, I have the lower half bits of $d$.

Can I restore the whole RSA private key from that data and use it for decryption?
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.