This comes following a discussion with a colleague.
My plaintext file
plainconsists of a about 100,000 lines of "all work and no play...". It's size is: 2.2 MB.
Compressed it is: 5.4kB
I encrypt the original:
openssl aes-128-cbc -in plain -out plain.ENC
plain.ENCis marginally bigger than the original, which I would expect.
I compress the encrypted copy:
gzip plain.ENC. But I observe that the compressed copy is now marginally larger than
Assuming the entropy of the original file is on the order of ~1000-10000 bits, why is the corresponding ciphertext incompressable? My intuitive notion of the entropy of a string is the minimal number of bits required to produce that string. If the string is the 3 MB long cipher text, it was generated with a 1000-bit entropy string encrypted with an AES implementation (probably no more than a few thousand bits), as well as a few-hundred bit key. Intuitively, to me, the entropy of the cipher text should be no more than the sum of the entropies of the strings and procedures that generate it.
So, my question is: Is my intuitive notion completely wrong? If we extended the low-entropy file to be orders of magnitude larger, would we begin to observe compressibility in the ciphertext?