If you start to sleep really bad from the simple attacks I can demonstrate and therefore never come close to designing a cryptosystem I've succeeded in my mission, I have just purchased a bunch of sleeping and anti-anxiety pill futures ;-)  On the one hand, yes, the problem here is authentication, but I want to be very careful not to word it so that it reads like "if only they slapped a MAC on this! It'd be fne!" because the resulting cryptosystem is still sixteen different kinds of broken...