I'd say that science and cryptanalysis both share the ideal of (or can be viewed as) trying to approximate Bayesian updating on a Solomonoff prior. In cryptanalysis, you have the disadvantage that your opponent is intelligent and malicious (from your perspective), but you have the advantage that the encryption process doesn't have much computing power (since ciphers have to be fast to minimize computing costs). In science, nature is not malicious, but it's not limited in computing power either. Yes, they are basically similar, but each is specialized to its domain of inquiry, so I doubt science can learn much from cryptanalysis.
I just remembered EY's post that alien message, and I don't think I'm making too dissimilar an argument: In EY's story, the aliens aren't as smart as humans, so we can infer the patterns in their messages, predict new ones, and inject new code.
As aliens were to those humans, so is nature to us.
Short version: Why can't cryptanalysis methods be carried over to science, which looks like a trivial problem by comparison, since nature doesn't intelligently remove patterns from our observations? Or are these methods already carried over?
Long version: Okay, I was going to spell this all out with a lot of text, but it started ballooning, so I'm just going to put it in chart form.
Here is what I see as the mapping from cryptography to science (or epistemology in general). I want to know what goes in the "???" spot, and why it hasn't been used for any natural phenomenon less complex than the most complex broken cipher. (Sorry, couldn't figure out how to center it.)
EDIT: Removed "(cipher known)" requirement on 2nd- and 3rd-to-last rows because the scientific analog can be searching for either natural laws or constants.