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.

12.1-12.2, due on November 15

1. I had a hard time following the Vandermonde matrix, and struggled to understand how a subset of the people can find the secret. Also, is there some kind of theorem which says the minimum number of people who need to get together in order to find the secret for each of these methods? If the matrix is not invertible, it won't work right?

2. Although I did understand the theory behind these concepts, I think it's really interesting that they exist. It seems counterintuitive that any subset of t people can find the message. Are there instances where threshold schemes are used other than military and business? I know these two areas practically run the world, but it would be cool to hear about more situations where this is used.

Exam 2, due on November 12

1. I feel like the most important topics we studied are the RSA and ElGamal crypto systems. Both of these fall under the concept of public key systems. If you don't understand the public key concept, there is no way you can understand RSA or ElGamal. Also, the math behind these systems is important: factoring large numbers, discrete logarithms, etc.

2. Since we won't have maple on the test, I am expecting conceptual questions. For example, if a system is set up in such and such way, how can eve break in and find the message. Or, why is it infeasable for eve to be able to find this parameter? I also expect some number theory problems which don't require maple. Like solving a discrete log problem by hand.

3. I need to understand hash functions better. I guess I still just don't understand the point. Signatures will also be good for me to study a lot. Most of all, however, I need to work on my understanding of the theory behind the algorithms and such. I know that they work, but a lot of times I don't know why they work.

4. I would be interested in studying a bit of coding theory, but I'm not sure that fits in the curriculum. Chapter 13, "games" looks like fun. But maybe the title of the chapter is deceiving, and the material not as fun as it sounds.

8.3, 9.5, due on November 10

1. It would be helpful in class for you to go over each step of the SHA-1 Algorithm. I suppose I understand the main idea of the hash function, but how would one be designed? Why is each step in the SHA-1 Algorithm, for example, necessary? My other question is when will the digital signature algorithm be used?

2. Hash functions amaze me. Not that they are particularly intriguing in and of themselves, but HOW on Earth do people sit down and come up with them? Looking over the SHA-1 Algorithm, all I see is a bunch of seemingly random operations which take an input and produce a smaller output. It's really cool to me that there is an method to this madness.

9.1-9.4, due on November 8

1. I was a little bit confused about the ElGamal signature scheme. Also, I'm really wondering how to escape "blind signatures." They seem necessary, and I'm interested in knowing how to safeguard against the dangers involved in them. One other thing I didn't understand was on page 246 when it explains why s/k is the signed message. After the therefore, it says k^(ed)m^(d)/k=m^d (mod n). I don't see how this is justified.

2. I quite enjoyed reading about birthday attacks on signatures. What a clever way to use probability to get Alice to sign a fraudulent document. I was even more excited about Alice's decision to add a comma. Poor Fred thought he had her fooled, but the joke's on him. He should have paid more attention in English class. RSA signatures were also interesting.

8.4-8.5, 8.7, due on November 5

1. What didn't I understand? The question is what did I understand. I guess I'm still just unsure about hash functions. Also, why would we use the Birthday Attack if baby step giant step is "superior," as the book says? When it's talking about multicollisions, how do we know that we can find the two blocks m_0 and m'_0 in 2^(n/2) steps?

2. I think the birthday paradox is fascinating. It really doesn't make sense intuitively, but I liked the way they explained it as not looking for a match with "your" birthday necessarily, but a match between any two students. I kind of understood the birthday attack on discrete logarithms, and I'm excited to learn more about that in class.