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Suppose a message $m$ is divided into blocks of length $160$ bits: $m > = M_1 || M_2 || ... || M_l$ And define $h(m) = M_1 \oplus M_2 \oplus ... \oplus M_l$

Which of the three desirable properties of a good cryptographic hash function does h satisfy? Show that it does not satisfy the other two.

Three desirable properties of a cryptographic hash function

I feel like if there is only one, like the question states, it has to be the first one, preimage resistance. However, given a hash $h = 000....0$ I can find a bunch of $m$'s that could give that particular hash. Maybe since there are lots of solutions you can't pin point the specific $m$ that gave that value?

What do you think?

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up vote 6 down vote accepted

I believe that this is a poorly written question: such an $h$ obviously doesn't have either preimage resistance, second preimage resistance or collision resistance.

The inability to rederive the specific value of $m$ based on its hash is not an interesting property; it's pretty much true of any function which generates an output shorter than its input.

I don't know where you're getting these questions from; based on this question, I'd suggest you look elsewhere.

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Old Exams, thanks for the confirmation of my worst fears! – Bobby S Dec 16 '11 at 17:43

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