App Store Link Works via FTP (Wikipedia). First short reviews are good. http://www.digidna.net/products/fileapp
Works by FTP? Ouch. This isn't the 1990s, you can't just blindly pick whatever network protocols you find easiest to implement and throw them together. The problem here is that FTP offers only basic authentication with no encryption (read: no protection at all), whereas most public wifi access points work with the assumption that all encryption is performed by the transfer protocol (which is not unreasonable, since this is the case with all modern protocols). The result? This app doesn't just share your files with your computer like it claims to, it broadcasts them to absolutely everyone on the network, giving them the ability to read, copy, modify or delete any file they want. Ouch indeed. It's currently free so I can't fault it too much, but this seems like a major oversight on the part of the devs. I'd suggest you add an option of either using USB or a networking protocol with adequate security measures built-in.
I am not such a FTP expert (I only know that it's a robust type of connection with a long tradition), but they write at their features page: and there are several options in the "FileApp Pro Preferences" like "Sharing Password ON/OFF" (default OFF) with User Name and Password as well as an option "Security Passcode Protection ON/OFF" (default OFF; four digits input). You'll need the free app "Cyberduck" on your Mac and can configure security settings there. And I hope that Apple's Security Department has tested those things. BTW I am not the developer and I am not affiliated with the software manufacturerjust passing the info.
The problem isn't that it doesn't offer authentication, it's that the authentication it does offer has the level of security of a wet paper bag. You'd actually be better off emailing the files to yourself.