Can't update/upgrade du to "Could not execute 'apt-key' to verify signature"

Changing the permission of /tmp back to their defaults worked for me:

sudo chmod 1777 /tmp

I had the same problem on my Ubuntu droplet at Digital Ocean (after a distro upgrade).

Just upgrade your kernel in the digital ocean administration site (yes, it's weird). There is a "kernel" option in the menu on the left side where you can select a new kernel image.

In my case the upgrade was from 3.x to 4.x series