Does Fanuc CRX 10 or CRX 25 support secure FTP protocol (SFTP or FTPS) ?

AFAIK, only plain (non-secure) FTP is supported on Fanuc controllers.

Can you also secure this, so that not everyone can access these files?

If you have passwords enabled on the controller, you'll have to log in using a username and password over FTP as well. I think at least setup level access, but I'm not sure. Anonymous login won't work.

Quote from TitusLepic

If you have passwords enabled on the controller, you'll have to log in using a username and password over FTP as well. I think at least setup level access, but I'm not sure. Anonymous login won't work.

Okay, but if someone push a USB stick in, could someone else always copy the AOA?

All file operations can be blocked with the password protection option.

The new R-50iA controllers support SFTP (and HTTPS, etc.).