Yeah, but this is not what most people think of when they think secure, is it? That is, this proves that people have to actually break an algorithm to know what it is protecting. This does nothing to show that an algorithm is unbreakable.

(As an example of my understanding, rot13 does nothing to randomize distribution of characters, so it "leaks" information about what it has modified. This sort of leakage can be proven as absent from your algorithm. Anything else is a bit tougher.)