The Linux version of checksum lacks many (most) of the Windows' version's coolest features. It has everything I needed, which is how checksum on Windows started, until I started thinking about it more, asking questions and answering your questions about it. More recently, people have started asking me about the Linux side of checksum, as the popularity of NAS boxes increases, I guess. So I've done more work on this since.
For now, you can grab a copy of the latest checksum for Linux zip, as well as check out the script itself (Note: I've added a .sh extension to these web files so the server knows what to do with them).
checksum recognizes the name of the symlink it was called from and switches to that mode, you see.
There are a couple of demo shortcuts and symlinks in there, too, for reference and inspiration. For more information, open the checksum script itself (/usr/local/bin/checksum) in a decent text editor, or click checksum.sh, above.
There is still a lot to be done. The verify output is poor in the console (it was designed to be run from my KDE desktop), in that it doesn't give a clear indication of failures at the end of the potentially long list of results, forcing the user to scroll, the scripter to parse.
;o)