In AES-128, 10 rounds are used with subkeys generated from the 128-bit key. In DES, 48-bit subkeys are generated from a 56-bit key. This seems to be common in symmetric encryption.
I ask this because of my understanding of entropy and randomness. If you were to take a random integer and put it through some function to expand it (the terminology used in the AES standard), aren't you making it more predictable/less random?
If I were to take a random integer and use it as the seed to a PRNG, I'm not getting anything unpredictable from the seed as I retrieve values from it. Surely the stream has the same randomness as the seed alone. I would have thought that it follows that multiple rounds result in encryption with multiple low quality subkeys with significantly less randomness than the original key, assuming the original key was random, or at least we don't know what it is.
(This PRNG and randomness analogy may be misinformed; I'm simply trying to say that you can't make an unpredictable value bigger and be as unpredictable as it was before, which is my understanding.)
Please could someone clarify why using multiple rounds of a lower quality subkey is more desirable than, say, one round with the whole key (in the case where key length is the block length)?