1. Two things I don't understand. I don't understand the proposition about finding discrete logs only given two messages whose hash functions are equal. I got bogged down in some of those steps. Especially because it says "Suppose . . . " Whenever it says something like that, I think "I may suppose that, but does that make it true?" Also, the simple has example they give involves XORing columns in a matrix. I don't understand how this is going to make a unique h(m). It seems to me that working with a mod that is so small, there would be many different messages that would map to the same XORed function.
2. Really the only thing I found interesting was that hash functions are used a lot in digital signatures. I would like to know more about how this works or how hash functions fit into that idea.
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