Maybe a good analogy is if you take a "giant" rainbow table, you can usually compress the unencrypted side of the table to something quite a bit smaller than you'd think.

Maybe another way to phrase it is something like encrypting plain text english is now mathematically proven to be not as secure as encrypting a zip (or other format) compressed version of the same english text. (edited to add that its early in the morning and the specific example of a zip file is a great known plaintext attack 0x04034b50 and all that, but "compressing in general" is a good idea. The mistake I made was like calling all photocopiers, "Xerox machines", or all nose tissues "Kleenex").

Crypto is very well taught for algorithms, classes of algos, history, couple other things, but the classes of apps of crypto technology is (intentionally?) very poorly documented and taught. Something that screws up screws up digital sigs probably has little to do with the issues in encryption or authentication or whatever. Its an area ripe for someone to write a book, or a startup to do "something" probably something educational.

no, it means knowing the algorithm allows you to infer more information from the encrypted data, because the "real" entropy (as opposed to the apparently now defunct Shannon entropy) will be much smaller than you expect (you have to try less brute force guesses.)