/usr/lib/x86_64-linux-gnu/libnettle.so is in nettle-dev 2.7.1-5+deb8u2.
This file is owned by root:root, with mode 0o777.
It is a symlink to /usr/lib/x86_64-linux-gnu/libnettle.so.4.7
/usr/lib/x86_64-linux-gnu/libnettle.so.4.7