I have a compression issue much closer to my heart that is not being properly addresses: AES-256 encrypted plaintext files. Seriously! If you just figure out th

I have a compression issue much closer to my heart that is not being properly addresses: AES-256 encrypted plaintext files. Seriously! If you just figure out the 256-bit key, it would compress well with any compressor - there's a huge class of files which would only need 256 additional bits! Why isn't there any advance on this front? /s Entropy is not a broken measurement - in fact, it's the perfect measurement (proof: Shannon's source coding theorem and its converse), its only downside is that it is only defined with respect to a model. If you measure it on the output of one model (permutations) with respect to another model (i.i.d) then, duh, it's wrong. And general permutations are so rare, that they might bug the author but there's no incentive to consider them. Non general permutations - e.g., addition-modulo permutations, often ARE reasonably well compressed by markov/tree/fsmx model algorithms and their delta counterparts. (And they're still too rare to consider on their own). Kolmogorov complexity is interesting, but it is too vast and complicated to consider as a whole (proof: equivalence of computing Chaitin's omega to the halting problem), other than as a very useful reasoning device. Therefore, like with the halting problem, we focus on specific subsets that seem interesting. Frankly, this rant reads like "But I don't understand why they don't yet have a car that runs on water". Compression is math, and it's a part of math we understand quite well. BWT, for example, is an amazing algorithm - but if you take a step back, it's just an efficient implementation of a compression scheme that was known before. (IIRC, the last gap in understanding the equivalence was closed by Effros et al in 2002)