Section 6.1, due December 2

I found it a little confusing why single points were bad in our scenario. It seems fine to add a single point to itself. It may not be a very interesting curve, but I could not see why it would be banned. Also, I did not quite understand what characteristic 2 meant.

However, I did find it interesting that elliptic curves are all abelian groups. We know abelian groups are really just products of additive groups in Zn, so it seems that we could just classify elliptic curves as such. It may just be too hard to map the points on the curve to their corresponding points in the products of Zn. However, if this was done, it would seem to open up all sorts of opportunities.