One connection I can draw from these sections is that the hash functions feel a lot like the AES and DES algorithms. Maybe it's the XORing or the three letter acronyms (MD4,MD5) but something about has functions reminds me of those earlier computer algorithms. However, I think the difference comes in the fact that the has functions are one way. I recall finding inverse operations for the different modes of operation in an earlier homework and I don't believe that is possible with has functions.
While there were many confusing parts for me, the one I am most intrigued and eager to learn more about is the proposition on page 221. I don't see why such a vague supposition can lead to the answer to a discrete logarithm problem which we just learned is very hard to solve. It seems that if we have a function that is not surjective we shouldn't be able to solve a discrete logarithm problem. [I think that's what m not equal to m' but h(m)=h(m') implies, although I'll admit it's written differently than I normally see it and I'm not totally convinced myself that it does imply it's not surjective].
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