> a transformation that would only be possible if the bits are independent, but nowhere in his proof does he state that he is making this assumption. Am I misu

> a transformation that would only be possible if the bits are independent, but nowhere in his proof does he state that he is making this assumption. Am I misunderstanding what you and/or the article means by "independent"? The fact that indexes derived from (non-overlapping) parts of a hash function output are uniformly ((preferably crypographically-secure-)psuedo-)random (and thus uncorrelated with each other and with indexes from other hash invocations) is what the phrase "hash function" means ("avalanche effect" if I remember my terminology correctly).