Let me try to answer your question in a different way. There are two things, security and the perception of security. For arguments sake, even if we assume tha

Let me try to answer your question in a different way. There are two things, security and the perception of security. For arguments sake, even if we assume that the method of simply creating UUIDs for file names is secure (which as several people have said is not a valid assumption), I would argue that it does not provide a good enough perception of security. So, if your users are really concerned about security and afraid that others will look at their files, a simple solution as above would just not cut it. You will have to really convince them that your system is really secure. Now, no matter what you use, UUID, MD5, SHA1/2/256 etc. to them it won't make a difference and that may mean that you will lose users. Based on that, my suggestion would be to do what you said above, make them all private and use authenticated access control. This will provide security as well as perception of security and get you more satisfied users.