Solve the error occurred during the signature verification in ubuntu

Solve the error occurred during the signature verification in ubuntu to install a software (I am using the 163 source), but I was told file size mismatch. therefore, the package list: sudo apt-get update... is updated ...... w: A error occurred during the signature verification. the repository is not updated and the previous index files will be used. GPG error: http://security.ubuntu.com lucid-security Release: The following signatures were invalid: BADSIG 40976EAF 437D05B5 Ubuntu Archive Automatic Signing Key <ftpmaster@ubuntu.com> W: A error occurred during the signature verification. the repository is not updated and the previous index files will be used. GPG error: http://us.archive.ubuntu.com lucid Release: The following signatures were invalid: BADSIG 40976EAF437D05B5 Ubuntu Archive Automatic Signing Key <ftpmaster@ubuntu.com> W: A error occurred The signature verification. the repository is not updated and the previous index files will be used. GPG error: http://us.archive.ubuntu.com lucid-updates Release: The following signatures were invalid: BADSIG 40976EAF437D05B5 Ubuntu Archive Automatic Signing Key <ftpmaster@ubuntu.com> even if you execute: sudo apt-get clean sudo apt-get update still has the same error. Solution: sudo apt-get clean cd/var/lib/apt sudo mv lists. old sudo mkdir-p lists/partial sudo apt-get clean sudo apt-get update