W: GPG error: http://us.archive.ubuntu.com precise Release: The following signatures were invalid: BADSIG 40976EAF437D05B5 Ubuntu Archive Automatic Signing Key

# apt-key adv --keyserver keyserver.ubuntu.com --recv-keys 40976EAF437D05B5

# cd /var/lib/apt
# mv lists lists.old
# mkdir -p lists/partial
# apt-get update