16.5 due on December 8

1. I think I understood most things which scares me, because I normally don't. I am still not comfortable with adding points and multiplying points with an integer. The the notation for the key exchange is not sitting well with me. I don't understand what the N_A or N_B means. They didn't really explain that.
2. It blows my mind how similar elliptic curves are to discrete logs. From the reading it sounds like a superior system. We probably aren't going to go over weakness, but there has to be some weaknesses of elliptic curves. I am curious because they seem quite useful in many ways.

16.4 due on December 6

1. It must have been a long weekend because I thought I was understanding elliptic curves, but after reading this section, I no longer feel like that. I think the confusion comes from the equation E: y^2+a_1*x*y+a_3*y=x^3+a_2*x^2+a_4*x+a_6. I understand that taking the derivative of the normal form in mod 2 would cause problems, so there needs to be this other form. I just don't under stand how to solve for the points and such. This carried over to the finite fields.
2. I am curious to see how elliptic curves play into the cryptosystems. I guess that is the next section, so I won't have to wait much longer for my curiosity to be soon satisfied. I am always curious how things come about, the historical background of things.

16.3 due December 3

1. I had some difficulty understanding the whole of section 16.3.1; I just couldn't really figure out what the author trying to convey. I also had some trouble understanding the example in 16.3 where factorials where introduced. I also didn't see how that related to the p-1 method and smooth factors and elliptic curves.
2. I did understand and found it cool the part where the reading noted that using elliptic curves to factor a composite number succeeds much more often than the p-1 method. I also just think is really cool that elliptic curves can be used to factor composite numbers. I wonder if it was a purposeful exploration of elliptic curves, or if one just happened to stumble on the fact that elliptic curves are effective in factoring numbers.

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.