1. I don't understand the example given on page 350. I understand the general idea, but I don't understand how knowing two points on the curve can give you a third. Also, we get the intersection point Q. Why not make that our third point instead of it's reflection across the x axis, P_3?
2. I am intrigued by this. I really can't see, just from reading this section, how elliptic curves will be useful in cryptography. Hopefully I'm not supposed to be able know this at this point. The Addition Law given on page 352 makes things nice. Even though I don't understand why it's true yet, I like it.
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