Given the Keccak-f permutation I am interested in the following property: What bits in the output are influenced by what bits of the input? That is, if I change for example say the second bit of the input, what bits of the output are influenced by this?
Put another way: Assume I have the first 256 bits of the output of the Keccak function. Then, because Keccak-f is bijective, there are only 1600-256 preimages that can still map to an output with the "right" first 256 bits. Is there a way to estimate how many bits are the same across all 1600-256 remaining values?