This is heading somewhat offtopic (Perl :-), however...
You should read man gpg. STFW for information on file signing and how it all works.
Understand the way everything works and have another stab at this.
You might find it easier to do this on the command line with a couple of dummy files, then once you have it working, figure out how to achieve the same thing with Perl.

Essentially what you're attempting to do is:

gpg --verify sigfile signed-files
[download]

Where the result from gpg --clearsign random_tarfile is the 'sigfile' (random_tarfile.asc), and the random_tarfile (which is the 'signed-file(s)') remains unchanged.