So I was wondering about what will be the dependence of the outputs when I padded one input with two different strings two times for technically generating two different strings, say the input string is
123 and the first time I have padded
123 $$H(12\mathbin\|234)$$ and next time I have padded '24' before '123' $$H(24\mathbin\|234).$$ Can I safely deduce that the outputs are completely independent even if the inputs are somehow related?
Asking this because I don't completely know the internal mechanisms of sha256 and how they are hashing stuff like this. I have good ideas about universal hash functions but kind of ignorant of cryptographic hash functions. So I have something developed using 3 wise independent hash functions but I am trying to shift everything using sha256 and in order to prove a lot of theoretical part concepts, I was looking for answers like this. I was looking for some sort of rigorous math proof/conceptual proof in this regard. Would appreciate any sort of help.