Assignment 34

1. I think going over how we can add these quantum vectors together could be helpful in order to ensure that I am thinking about it correctly. Other than this, I think I understand it pretty well.

2. This was a pretty fun reading, taking me back to my days in Chemical Engineering. My question on it, though, is how did we come up with it exactly? Why do we use it? It makes sense that it can be secure and all, but it feels like it's coming out of left field. :)

Assignment 33

1. Oh boy, 14.2 brings out the big numbers again. I liked the easy conceptual case. Oh well. Since I understand the concept alright I feel it won't be too bad, but a review on Sage might be nice in order to speed things up a bit for me. I feel like I'm not nearly as good at using Sage as others and that slows me down.

2. I really like this section of reading. It's definitely nice to have something like this to protect us, but it's also cool that it's all based on probability instead of strictly rigid proof. Overall, that is something neat about cryptography--it's (so far) mostly based on attackers being incredibly unlikely to crack the code, whereas other forms of math adhere only to proof.

Assignment 32

1. I feel the most important topic that we have studied so far is the RSA algorithm, as that is what is most commonly used today. It is also good to know the conceptual ideas behind why it works so well and how it is a secure system, as knowing these concepts will help us to be better crypto-thinkers.

2. I expect to see a good deal of computational questions along with questions dealing with systems like RSA and ElGamal, along with discrete logarithms potentially. Really, though, there is just so much to choose from!

3. Really, I feel that I just need to have a good review of everything since there is so much to remember. In particular, I think I need to focus on the Chinese Remainder theorem, primality and all theorems having to do with that, and all of the algorithms.

Assignment 31

1. I feel like I have a pretty good handle on all of the math in these sections, along with the idea. I guess I feel that I'll be good to go after doing a couple of examples and once I'm sure I can do it well with all of the ways presented.

2. This section seems pretty cool to me. I like how it takes us back to things like high school algebra too, since other systems we've been dealing with bring in things like discrete logarithms and whatnot. It's fun to be able to go back to the basics and still do cool cryptosystems.

Assignment 30

1. This was a pretty fun reading. Most everything made good sense to me here too, so I guess my question for today would be why use El Gamal when it seems that everything we've studied generally points to RSA being stronger? Is it because of one or two saving graces it has, or are there other reasons? I guess that's what I struggle with on this reading.

2. The idea of digital signatures is fun to read about, as it has become such a key part of society today. The examples--particularly the one in 9.4--were fun to read about too. Are we going to do some signatures in class too? Because I feel that could be a fun project actually--making sure it can't be forged or something.

Assignment 29

1. So, I guess I still have a hard time seeing why we use hash functions since there can be so much collision and whatnot. I guess using the stronger algorithms take out the times where two completely different items can get the same hash, but maybe we could cover in class a bit more on why they are useful? I know that it's a fast way to verify and can be a sort of signature, but how sure can we really be?

2. I do like the birthday problem, just since it would always seem like "No, there's no way it's that likely" when you don't look at it mathematically. It is pretty interesting that it can be used to attack discrete log problems though--that's a pretty good idea!

Assignment 28

1. So, it seems like every example of a hash given was too slow or not collision resistant enough. What's the point of it then? You can't really use it for signatures if it isn't feasible. I know that the book presents a working method in 8.3, but since we don't read 8.3 for today I assume that there is something more valuable to what we read than what I got out of it, and so now I just wonder what that was. It must have gone over my head.

2. So, it was cool to see that if we know some m that isn't equal to m' where h(m)=h(m'), we can find the discrete logarithm. That definitely piqued my interest since we've spent so much time talking about how we assume it is too hard to find it. Too bad that method is too slow to use!

Assignment 27

1. I guess with these sections I don't quite see, mathematically, how it will be just as hard to compute the discrete log as it would be to do the computational Diffie-Hellman problem. I guess I just don't understand it enough just yet to see how the mathematics of these two problems weave together. It is nice to go over the ElGamal system now too since we have been discussing it a lot in class recently. A few examples of this system would be nice to see too.

2. I like the example of the football game. Does this method get used a lot in the real world these days? What other instances might we use for it?