16.3, due December 3

1. I thought I understood elliptic curves until I read this section. I understood the first few paragraphs and that's about it. In the first example, why are we trying to compute 10!P? It's probably a bad sign that I don't even see how this relates to the goal of factoring n. Also, I don't quite understand the significance of smoothness in this factorization method. Singular curves were also confusing.

2. I like the concept of utilizing differences in p and q in order to factor n=pq. Assuming I follow what it is saying, the very last statement in this section was interesting. Does it mean that the p-1 method and trial division are a part of the algorithm? Or that performing the algorithm is equivalent to doing both methods?

16.3, due December 1

1. This section was surprisingly understandable. One thing I'm a little unclear about is the subsection on discrete logarithms on elliptic curves. How exactly is this the same as the discrete logarithm problem? Also, are we going to learn how this problem can be solved using Pohlig-Hellman or Baby Step Giant Step attacks?

2. It was cool to begin to see how this seemingly obscure and unrelated concept may be used to factor large numbers. I still don't know exactly why elliptic curves mod a composite number could help in factoring the large number, but hopefully we will find that out soon. I also liked the method for manipulating a message so that it lies along an elliptic curve. It's nice.

16.1, due on November 29

1. I don't understand the example given on page 350. I understand the general idea, but I don't understand how knowing two points on the curve can give you a third. Also, we get the intersection point Q. Why not make that our third point instead of it's reflection across the x axis, P_3?

2. I am intrigued by this. I really can't see, just from reading this section, how elliptic curves will be useful in cryptography. Hopefully I'm not supposed to be able know this at this point. The Addition Law given on page 352 makes things nice. Even though I don't understand why it's true yet, I like it.

2.12, due on November 23

1. Near the end of the section, when they start talking about permutations and how to find the three letter daily key, I start to get confused. We just started talking about cycles in abstract algebra, and I'm still not quite comfortable with them. Once we know AD, BE and CF, how do we find the key? Also, how does this key necessarily add to the security? It seems to me like it detracts from it. Can't the cryptanalysts simply start frequency analysis on the 7th character?

2. It's really cool to be learning about a system that played such a big role in World War II. I also liked that it was cracked. Go England. This is the first cryptosystem we've talked about which conceptually actually requires a machine, and the fact that it requires a machine makes me wonder if, with such strides in technology the world is making, there are newer variations of enigma which are harder to break.

19.3, due on November 22

1. There are some days when I understand why the general public hates math. Today is one of those days. I did not understand a word of the reading in the book. The explanation given online mostly made since, but as soon as we started talking about Fourier transformations I was lost. Maybe it's the fact that I'm computer retarded and don't even understand how classical computing works. Let alone quantum computing. Sure hope this is one heck of a lecture or I'll be a lost cause on the homework.

2. That clock analogy was really interesting. What a clever way to describe the concept behind such a monstrously ugly mathematical result. However, I'm afraid it didn't really work on me. I still don't know what the heck is going on. I suppose it is cool, however, that there in theory a quantum computer can do things so quickly.

19.1-19.2, due on November 19

1. Maybe I kind of just freaked out as soon as I read the word quantum. One thing I don't understand is how we know that photons will pass through certain polarized films around 1/2 of the time. I know quantum mechanics is heavily based on probability, but I didn't understand the book's explanation of this. I also don't really get the vectors involved.

2. Wow, I never would have related quantum theory to cryptography. It's amazing that the relationship exists, but I don't understand why we would need to use the quantum key distribution over something like the Diffie-Helman key exchange. Doesn't the fact that eavesdropping causes communication errors make this method not incredibly valuable?

14.1-14.2, due on November 17

1. As soon as we started applying hash functions to this seemingly simple and understandable concept, things went downhill. I didn't understand the second half of page 320 on. It seems like this confusing part is somewhat of an extension of the previous concepts of section 14.2. Also, I'm getting all of the sequences of numbers confused. The s's, v's, and j's all get jumbled together.

2. The broad concepts discussed are really interesting. I like the fact that something can be verified with a very high probability without any useful information being released to Victor, and therefore, by Eve. I'm curious to know if the Feige-Fiat-Shamir Identification Scheme is really what is used in ATM and other machines which must verify the identity of a person.