The most recent updates to Ubuntu suddenly started generating warning messages saying that the patches could not be authenticated.
This is apparently a known bug in package bookkeeping. The procedure for fixing it seemed to be:
1. sudo mv /etc/apt/sources.list /etc/apt/sources.list.backup
2. sudo touch /etc/apt/sources.list
3. Run the package manager and check for updates. You should see none; quit the package manager.
4. sudo rm /etc/apt/sources.list
5. sudo mv /etc/apt/sources.list.backup /etc/apt/sources.list
6. Run the package manager again; this time you should be able to install the updates without warnings.