Any ideas? What is wrong with this idea? (something must be, or it would've been done by now, I am guessing.) I don't know the math, so I suspect I must've erred gravely somewhere.
You have indeed erred gravely :-) One of the information theoretical concepts we are dealing with here is that of information density. The whole reason compression works is that in most files, the information density is not "perfect"; that is, there is repeated information in the file. This reflects what we see when we compress a file: the more which is repeated, the better compression is. Graphics compress much better than executeables. Well, one of the reasons encryption works is because I can't tell from the encrypted text what kind of patterns exist. Consider a letter-substitution cipher. If I were to apply one to this message, you could probably decrypt it, because much of the structure is still there: common english words, letter frequencies, etc. This makes letter-substitution a pretty poor cipher. What about DES? Well, this is interesting. Without the key, the information density of an encrypted file looks the same as the density of a compressed file, or of noise. This is why you could claim something was just noise, not encrypted data. It's also why a common "good" PRNG is formed by feeding the numbers through some crypto algorithm, because it makes the numbers appear random. It is because encrypted data appears to have a very high information density that it will not compress much, if at all. Compressing encrypted data, from some standpoints, is tatamount to actually decrypting it. Examples: A is a file with 1000 lines of 79 "A"'s followed by a newline. A.Z is the file, compressed. A.x is the file, encrypted (unix crypt, lame, I know) A.x.Z is the encrypted file, compressed wiht the -f option. -rw-rw-r-- 1 marc 80000 May 21 17:26 A -rw-rw-r-- 1 marc 1466 May 21 17:26 A.Z -rw-rw-r-- 1 marc 80000 May 21 17:47 A.x -rw-rw-r-- 1 marc 106577 May 21 17:47 A.x.Z Note that A.x doesn't compress at all. In fact, it grows! Marc