Section 16.3, due December 4

It seems like finding these points and finding factors would take longer than the book says. I wasn't quite sure when the book said that they looked at 10000!P. Wouldn't that take a long time to do? This seems like one of those things where you just have to try it yourself to see that it works. Did the book choose convenient cases, or is it pretty fast to factor smaller numbers?

I got a little lost when the book started talking about singular curves. I understand that the equation has multiple roots, but should we try to use a singular curve to factor n or should we avoid them?

Section 16.2, due December 2

Is there any graphical interpretation that we can use to think of elliptic curves mod n? When I graphed the points in the example, I didn't seem to get anything.

It seems like it takes some work just changing our message into plaintext. Most other systems that we have looked at don't seem to have that problem. Does that add a lot of time or is it rather inconsequential?