1. So, I guess I still have a hard time seeing why we use hash functions since there can be so much collision and whatnot. I guess using the stronger algorithms take out the times where two completely different items can get the same hash, but maybe we could cover in class a bit more on why they are useful? I know that it's a fast way to verify and can be a sort of signature, but how sure can we really be?
2. I do like the birthday problem, just since it would always seem like "No, there's no way it's that likely" when you don't look at it mathematically. It is pretty interesting that it can be used to attack discrete log problems though--that's a pretty good idea!
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