I just installed Linux Mint 13 KDE two days ago. Updated once, yesterday, installed GNOME via synaptic prior to that and a few programs using the software manager since. Everything was working fine.
Tonight I was notified of available updates. Ran the update manager and got this:

W: GPG error: http://security.ubuntu.com precise-security Release: The following signatures were invalid: BADSIG 40976EAF437D05B5 Ubuntu Archive Automatic Signing Key <ftpmaster@ubuntu.com>
W: GPG error: http://archive.canonical.com precise Release: The following signatures were invalid: BADSIG 40976EAF437D05B5 Ubuntu Archive Automatic Signing Key <ftpmaster@ubuntu.com>
W: GPG error: http://archive.ubuntu.com precise Release: The following signatures were invalid: BADSIG 40976EAF437D05B5 Ubuntu Archive Automatic Signing Key <ftpmaster@ubuntu.com>

I cannot get the updates, nor can I install via the software manager. The Synaptic Package Manager, however, does work.
Could this be a problem with the update/software source server, or is it something I can fix on my end?
Thanks ahead of time for any assistance. I ran Slackware and AntiX Linux for a couple of years, and then had to use Windows for about a year, so though I'm a bit rusty I still know the bash shell is my friend.

Solved the problem. For anyone who might happen into similar, here's what to run:
sudo apt-get clean
cd /var/lib/apt
sudo mv lists lists.old
sudo mkdir -p lists/partial
sudo apt-get clean
sudo apt-get update