Compression of a encrypted stream is possible, dispite the entropy (tell you more one day but ways to reararange the cyphertext into a form more yeildable for compression exist as I wrote one many years ago).
That said many forms of encryption used limited sized keys (and methods) and humans can be very predictable. Get 1000 people and ask them to pick an encryption password form say 10 billion possible combinations and you would think the odds of two people picking the same would be low, yet it happens and above the odd's. This ignore that 5% of them would pick "god" or "jesus" as a password if you have no checks and let them.
As for the actualy decryption, you don't even want to know what they have for rainbow tables, seriously scarey, that ignore the kinks and dents they have seeded in various encryption subsystems over the years. Could spend a lifetime talking about what random truely is and then still find that 256bit encryption is flawed many years later so they net effect is only 64bit encryption with the rest workable. Personly I don't like encryptin that uses even numbers, I'd take 255bit over 256bit, call be silly but time will show method in that madness.