/usr/lib/x86_64-linux-gnu/libnettle.so is in nettle-dev 3.2-1ubuntu0.16.04.1.
This file is owned by root:root, with mode 0o777.
It is a symlink to /usr/lib/x86_64-linux-gnu/libnettle.so.6.2
/usr/lib/x86_64-linux-gnu/libnettle.so.6.2