sections 6.1 and 6.2, due December 2

I think that both of these sections were entirely over my head. The picture in the first example (above where the section actually started) made sense and I thought I understood what an elliptical curve meant, but the next picture seemed to have nothing in common with the first. It also seemed like they were using some words with a definition different than the one I am used to or maybe I just don't know how to apply those definitions to this case. (order, characteristic) The cool thing was that it said this is used in cryptosystems and that is the same thing that impossible book problem referenced so I'm interested about how/if this applies to cryptography (or I will be once I understand it).