1. Difficult - These sections does make a lot of sense. For 8.4 and 8.5, (on birthday attacks), there are many more opportunities for matches (proportional to n^2, where we have n people), instead of trying to find a particular value (which is just proportional to n). The book gave an approximate formula for a match as (1-exp(-r^2/2N)) where r is the number of people and N is the number of of birthdays, and cited an exercise for proof.
Working through the exercise, we approximate ln(1-x) using the taylor polynomial to 1 or 2 degrees. This gives bounds on a sum of ln(1- k/N), so when we exponentiate it, it gives bounds on the desired product [of (1-k/N)]. This is approximated above and below by c_1 exp(-lambda) and c_2 exp(-lambda), where lambda = r^2 / 2N. As N grows, c_1 and c_2 tend toward 1. Hence, the product is approximately exp(-lambda), giving the formula mentioned above.
2. Insteresting - I liked how the analog of OFB came back in 8.7, this time using hash functions. This connects well back to the modes of operation earlier in the semester. The book was mentioning how this was a stream cipher. That's all I have to say about that though.
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