I've read that encryption produces random data and compression works by removing patterns in data and as a consequence, encrypted data has high entropy. I'm a bit confused, though.
The reason I'm confused is that I thought that all encryption was supposed to do is make it as difficult as brute forcing the key to go from the cipher text to the plain text. It seems to me like there could be an AES key that would produce an all 0 ciphertext given a certain plaintext.
So, long as you couldn't use the all 0 ciphertext to figure out the plain text without brute forcing the key, it wouldn't break any of the goals of encryption.
Is it really that encryption is supposed to produce uncorrelated data to the plaintext, as though every bit was random, and this just happens on large plaintexts, for the most part, to produce high entropy ciphertexts?