16.2, Due on December 1

The first portion of the section where the authors describe how we are going to use elliptical curves to factor large numbers was very interesting. "The situation where gcd(b,n)=1 fails... form the key to using elliptical curves for factorization" (pg. 353). I like that little teaser and it's making me moderately excited to read section 16.3.
I also found the first portion to be a review of what we went over on class on Monday. It's nice to approach the reading having already seen an example in class.
The hardest section for me was the last one about representing plaintext. This confuses me. I thought we were using the elliptical curves to factor n, not to encrypt anything. I also had a question about the example on page 353. Where did the equations for what x3 and y3 are congruent to come from? I see where the values came from but not the equations.

16.1, Due on November 29

I kept waiting for the cyrptography application in this section but it never came. Hopefully in the later sections I will see how it relates. I enjoyed reading the historical point on page 349, and it cleared up some confusion about the naming of elliptical curves for me. I also found the very last sentence of the section to be interesting, that infinity is the identity element of the abelian group. I will be very interested in hearing your explanation of that. It reminds me of complex analysis.
The hardest part for me to understand was the addition of elements in the group. I didn't quite follow the group what see what the point was. I struggled with this section a little bit just because I didn't see the motivation for the math. It seemed like the authors were just babbling on and I wasn't sure why. Are all the points on an 'elliptical' curve an abelian group with infinity as the identity?

2.12, Due on November 23

I always enjoy reading about the history and application of the different cryptosystems we have learn about. I liked reading about how the British sold Enigma machines to other countries without telling them it had been cracked. I also liked reading about the different aspects of the machine that made the different combinations plentiful. It's interesting to learn about early, physical cryptography machines, especially in light of the Quantum Computing we read about earlier.
One question I have is that it seems this is just a substitution cipher? I thought that at first, then it sounded like there was more going on, but then on the last page I read about Rejewski and his colleagues creating a code book for the different combinations, and therefore "the effect of the plugboard was then merely a substitution cipher"(pg. 55). What is going on here that makes this different from a substitution cipher?

Shor Reading and 19.3, Due on November 22

I enjoyed the reading on the web about Shor's Algorithm. It was written in a very lighthearted manner tailored to the layman. His analogies were very good and he brought up some great points. It's interesting to me to think about modulo exponentiation and factoring large values of n.
The part about the reading that confused me was the the clock example. I understood the 'experiment' but I didn't understand what we can deduce from the results.
The book reading was not very easy to follow. If I were to ask one question about it I would ask where the Fourier Transform came from? It seems pretty crucial to the Shor Algorithm but I found its explanation to be less than satisfactory. I am also confused about how the graph relates to the algorithm.

19.1 and 19.2, Due on November 19

One big question I have is regarding the strange physics notation. I have never seen vectors represented that way and I'm a little confused as to what they mean. Another question I have is: What does this have to do with cryptography? I was so confused by the reading that I didn't even see it's application to cryptography.
The thing I'm most looking forward to in this unit is the actual experiments in class. I get that we are representing light as a vector but I think it will make more sense in class when we actually do the experiment. I also like the idea of using light as a medium for sending hidden messages, even if I don't understand why or how.

14.1 and 14.2, Due on November 17

The first sections was the most easily understood by me. I enjoyed reading about the Zero-Knowledge Protocol and the Tunnel diagram was very helpful. It's interesting to me how useful different mathematical ideas are in real contexts. The notion of finding square roots as a tool to secure information is really cool to me.
The second section was less easy for me to follow. I didn't catch all the steps, such as what Peggy and Victor need to check. I am wondering if this Feige-Fiat-Shamir identification scheme is meant to be a cryptosystem. I think it is not. I am also curious to know where else I might see Zero-Knowledge Techniques in place. It seems like an interesting idea and a quick Wikipedia search taught me a little more about it. I found it not so ironic that the example on Wikipedia used Victor and Peggy as well. Those must be real mathematical terms.

12.1 and 12.2, Due on November 15

One confusing part for me was in the example at the bottom of page 299-300. By using the Lagrange interpolating polynomial they came up with some numbers but I don't understand where the numbers came from. I'm not sure why they divided some of the large integers by 5 either. I understood most of the example except for that part. I also didn't understand the Vandermonde Matrix. That probably led to me being confused about the Lagranfe interpolating polynomial.
The interesting part of these sections for me was the different approaches to solving the same problem. As a mathematics education major we are always taught to represent things in multiple ways. The book did a nice job of explaining how to break this secret in three different ways. I also liked the first section because it was explained well and not too difficult.