I kept waiting for the cyrptography application in this section but it never came. Hopefully in the later sections I will see how it relates. I enjoyed reading the historical point on page 349, and it cleared up some confusion about the naming of elliptical curves for me. I also found the very last sentence of the section to be interesting, that infinity is the identity element of the abelian group. I will be very interested in hearing your explanation of that. It reminds me of complex analysis.
The hardest part for me to understand was the addition of elements in the group. I didn't quite follow the group what see what the point was. I struggled with this section a little bit just because I didn't see the motivation for the math. It seemed like the authors were just babbling on and I wasn't sure why. Are all the points on an 'elliptical' curve an abelian group with infinity as the identity?
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