It's often possible to distinguish random data from encrypted data using something like a chi square test. However, if you just encrypted random bytes, then it would look just as encrypted as your real data (because it is). Alternatively, you could just encrypt spam emails (it'd be cute if a system like this encrypted and sent every spam email that you received).
...system like this encrypted and sent every spam email that you received
I wanted to like this proposal, but then I realized these encrypted spams have to be sent somewhere. Any ethical target would be too easy for "the bad guys" to filter. Oh well.
