16.2 due on December 1

1. I didn't quite follow how the explanation for an approximate value for number of points mod p. I also didn't understand the discrete logarithms on elliptic curves. I don't see how B=kA for some integer k relates to a discrete logarithm problem.
2. I actually understood the elliptic curve cryptosystem mentioned worked for the most part. It seems kind of like it isn't all that efficient as there is a possibility of performing many operations to find a square root of x^3+bx+c for x=mK+j. I am interested in an example when there is a mod of a composite such as the example in 16.1 and how elliptic curves can lead to factoring the composite.

2.12 due on November 23

1. I had some difficulty understand the attack. The first part was the daily settings and how that was transmitted. It sounded like it was in a book, so why must that be transmitted? Then I didn't understand at all how the permutation cycles were used to show what letters were mapped to other letters.
2. I found it interesting that the British had been breaking the Enigma throughout World War II. I guess really all I have about the Enigma is from U-571. The movie made it seem like it it was much later in the war that the Enigma was broken, but the book said the British new how to two months before Germany invaded Poland. That was the onset of World War II. 

19.3 and Shor's Explanation due on November 22

1. Shor's algorithm still doesn't make sense to me. The blog helped shed a little bit of light on it, especially the analogy with the clocks on the wall. But, I still don't understand how that helps factor a number n. It appears to me to be a probabilistic algorithm where there are still possibilities of not find a factor of n, so what good is it compared to the classical computer.
2. The theoretical capabilities of quantum computer sounds exciting and cool. I can see how it has become and becoming a popular area of research. I have heard some things about quantum computing it the past but have not really understood. As a soon to be clueless to a career path math graduate, it may be a possible area to pursue.

19.1-19.2 due on November 19

1. I don't quite understand how basis of vector spaces work into quantum computing. Hence, the quantum key distribution did not make much sense. Basis of vector spaces wasn't my strong point of linear algebra as well. I also have difficulty understanding how the quantum key distribution is any different from the digital computing of now; it just seem like they were using different symbols for 0 and 1.
2. This whole topic is interesting; the possibilities that are out there if quantum computing does  work out. I found it interesting, from the quantum key distribution that if Eve listens in, it changes the data sent or the state of the photon. This seems that it quantum computing may offer new security as well as the power to destroy security. It would be a whole new ball game.

14.1-14.2 due on November 17

1. I thought I understood Identification scheme until it got to the point of where it asks 'what if Peggy doesn't know a square root of y?' I didn't follow the guessing process. Then in the actual Feige-Fiat-Shamir Identification Scheme, I came to realize that I really didn't understand it at all. I think it is compute y that gets me.
2. The story about the fake atm was pretty clever. I think it was just recently that there were people installing code on atms that would record and send peoples' information to the thieves. The Zero-Knowledge Proofs are pretty interesting; it seems like it is based of probability. Yet, there are some differences I feel. 

12.1 - 12.2 due on November 15

1. I didn't understand the Shamir Threshold Scheme at all. I was hoping the example would help me understand, but it didn't. I got lost with the Lagrange interpolating polynomial. With the linear system approach I didn't understand the construction of the matrix. I followed the Blakely method better, but I didn't follow how the plane equations were constructed as well.
2. The whole idea of Threshold schemes are pretty cool. I never really thought about situations that would need such a system, but now after reading, it applies to a lot of different life situations. They seem like a very nice solutions to the problems. 

8.3, 9.5 due on November 10

1. When the author said in 8.3 that "the reader is warned that discussion that follows is fairly technical", I knew I was in trouble. I understood until that padding portion of the SHA-1. I didn't get much after that. With the DSA, I didn't quite understand the verification process and the explanation why it works.
2. It is interesting that both sections we read, that speed was mentioned. The DSA removes one step of modular exponentiation from the ElGamal scheme so it is faster. How much faster are we talking about: milliseconds, seconds, minutes? I am sure it depends on the size of message, so what is the Big-O of it is probably the better question to ask.

8,4-8.5, 8.7 due on November 5

1. When I finished the reading, my summary thoughts were "I guess I don't understand how hash functions work." In 8.7 it didn't sound like like the hash function was much different that the modes of operation found in chapter 4. I also didn't understand the multi-collisions section.
2. The birthday attack is really interesting. It is cool that it is using a probability concept in cryptography. It sounds like there a 70% chance that there are two people in the class with the same birthday.

8.1-8.2 due on November 3

1. I have some difficulty understanding the difference between strongly collision-free and weakly collision-free. They seem to be saying the same thing, but I know there is a significant difference. I also had some difficulty following the example of the discrete log hash.
2. I have heard of hash functions and of MD5 separately. I knew that MD5 had something to do with data integrity. It is cool to piece it all together and get a better understanding. It is interesting that some of the popular hash functions have turned out to fail the strong collision-free requirement. It obviously must be hard to determine. I noticed the text said the the discrete log hash function is "probably" strong collision-free.