Does anyone know of a Linux backup utility that uses GPG to encypt individual files?

I've recovered files from CRDOMs with bad bits recently, and didn't know it until I tried using them. Storing each file with a checksum would be the answer to that. Also, I'd like to be give backups to almost anyone willing to store them. Encrypting the backups would be the answer to that: "Please keep this somewhere cool and dry" is far less of an imposition than "Hide this forever. It has all my personal email on it".

I think GPG encrypting individual files would provide both encryption and checksum. Is there anything wrong with that idea? And has anyone seen a tool to do this? (I could write a script to do it if had to, but I'm reinventing other wheels.)