Well Hashing is pretty straight forward. I have personally implemented SHA-1 so I am pretty aware of how everything works. The their is a proof in the section, that while not hard, would be the hardest to follow.
The most interesting thing is how it mentions that the sometimes hash functions are allowed to have viable birthday attacks and still be considered feasible. It makes sense, especially when you realize that even with SHA-1 a birthday attack take 2^80 iterations to find, and what you find isn't even viable as a different message.
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