apt - How to fix GPG in updater

I have asked this question before, but it was closed as a "duplicate." I can assure you that my scenario is original, as it does not refer to third party PPA's. I am having GPG problems with system updates. It says there is no public key available, and I have also been warned that my update information is outdated. Here's the terminal text:

W: A error occurred during the signature verification.
The repository is not updated and the previous index files will be used. GPG error:http://extras.ubuntu.com quantal Release: 
The following signatures couldn't be verified because the public key is not available: NO_PUBKEY 16126D3A3E5C1192


W: GPG error: http:// archive.canonical.com quantal Release: The following signatures couldn't be verified because the public key is not available: NO_PUBKEY 40976EAF437D05B5 NO_PUBKEY 3B4FE6ACC0B21F32
W: GPG error: http:// us.archive.ubuntu.com quantal Release: The following signatures couldn't be verified because the public key is not available: NO_PUBKEY 40976EAF437D05B5 NO_PUBKEY 3B4FE6ACC0B21F32
W: GPG error: http:// us.archive.ubuntu.com quantal-updates Release: The following signatures couldn't be verified because the public key is not available: NO_PUBKEY 40976EAF437D05B5 NO_PUBKEY 3B4FE6ACC0B21F32
W: GPG error: http:// us.archive.ubuntu.com quantal-backports Release: The following signatures couldn't be verified because the public key is not available: NO_PUBKEY 40976EAF437D05B5 NO_PUBKEY 3B4FE6ACC0B21F32
W: GPG error: http:// us.archive.ubuntu.com quantal-security Release: The following signatures couldn't be verified because the public key is not available: NO_PUBKEY 40976EAF437D05B5 NO_PUBKEY 3B4FE6ACC0B21F32
W: Failed to fetch http:// extras.ubuntu.com/ubuntu/dists/quantal/Release

W: Some index files failed to download. They have been ignored, or old ones used instead.

I have put spaces in the urls because new users are not allowed more than two hyperlinks per question.

Please don't just close this as a duplicate. It does not refer to third party PPA's, it refers to the standard update packages issued by Canonical.

Run these commands in the terminal:

sudo apt-key adv --recv-keys --keyserver keyserver.ubuntu.com 40976EAF437D05B5
sudo apt-key adv --recv-keys --keyserver keyserver.ubuntu.com 3B4FE6ACC0B21F32

This downloads the missing GPG keys (as mentioned in the original error message) from the Ubuntu GPG keyserver.