A Penny For Your Thoughts: Compatability of Open Source and my (future) Startup

I love the idea of Open Source, and I (think I would) love to release my startup's code as Open Source, both for moral/worldview reasons and because I believe doing so would (indirectly) make the company more profitable.

But I can't seem to get rid of one last concern: user security.

[Note: I won't go into too much detail about what my future startup will be because a) at this point I'm honestly just not comfortable doing so, and b) leaving such variables undefined means others with similar concerns but different startups can gain more from this discussion.]

Among other things, my startup will involve such "features" as user login (id/password), user-to-user communication (not just text but files, etc. as well), and user storage (again, files etc.). In essence, given the nature of my startup, user security will be a big issue for buyers, as well it should be.

So, the ultimate question becomes: Is it possible to release all code as open source without risking security issues? Or should I just release all code unrelated to security as open source? If the latter, how can I be certain which code could risk security if released open source and which code would not?

Thanks in advance for all comments.