[progval]

> This is not uniformly true for cryptosystems--it is not naively the case that P(Q(X)) is a secure form of encryption, just because P/Q is. A contrived example is when P and Q are inverses

If P and Q are inverses, then Q is not secure, because you could just apply P to its output.

The same holds true for encryption: if you have two independant keys K1 and K2, then if Mallory can crack P(Q(X, K2), K1), then she can crack Q(X, K2) just by picking a K1 at random and computing P(Q(X, K2), K1).