[unrelated output]
Get:1 http://archive.canonical.com precise Release.gpg [198 B]                 
Hit http://archive.canonical.com precise Release                               
Err http://archive.canonical.com precise Release
[unrelated output]
W: A error occurred during the signature verification. The repository is not updated and the previous index files will be used. 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://us.archive.ubuntu.com precise Release: The following signatures were invalid: BADSIG 40976EAF437D05B5 Ubuntu Archive Automatic Signing Key <ftpmaster@ubuntu.com>
W: Failed to fetch http://archive.canonical.com/ubuntu/dists/precise/Release  

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