Assignment 42

1. I like how this section has examples for each specific point with discrete logs. I still don't feel confident doing them on my own, but having those examples help a little.

2. I wonder how people figured that we could use elliptic curves along with the idea of discrete logs in the first place. I am always amazed at how bright some people can be--far beyond me.

Assignment 41

1. I guess for me the hardest part is really that I'm behind because I haven't made it to class-food poisoning is not fun. So, I really need to buckle down and make sure I understand elliptic curves in general better. Since I won't make it today either, I need to study hard on this even moreso.

2. I definitely recognize the setup to GF(4) from abstract algebra, and I find it interesting that it has such a direct correlations to what we are doing here now. It makes sense to this it would be more useful than a curve mod 2.

Assignment 40

1. I am so glad that we have already done a lot with factoring. Otherwise, I would be totally lost right now. I'm still trying to figure out the very first example--how it was explained kind of lost me.

2. It's interesting that we begin by finding several curves--that is definitely different from how we did things before! There are a lot of things that we do differently with elliptic curves, even though other things remain the same.

Assignment 39

1. I feel like the points in this section weren't too difficult. What I still struggle with is the idea of elliptic curves themselves. There are just a few points about it--like coming up with the points at times--that still haven't clicked. It seems like once this is solidified in my mind, I'll be okay with everything else.

2. It is interesting how things like the P-H algorithm can be thwarted in the case of elliptic curves. It definitely does make it seem as though elliptic curve cryptography is more secure. I wonder what attacks we might be able to make on elliptic curves that we can't on our other systems though.

Assignment 38

1. Well this was an interesting read. Isn't addition supposed to be easy? I still have a hard time wrapping my head around the whole concept. For example, it really throws me off to see the graph of an elliptic curve where the ordered pairs don't really seem to make any sense on a normal Cartesian coordinate.

2. One thing that stood out to me reading this was at the beginning. It's cool that we are now moving towards methods that will reduce the workload, so that we can send things more easily and efficiently. If we can get things like this working--and later on, find new things that take even less to work--we should be able to do even more with cryptographical systems.