7.3-7.5 due November 1

1. I had difficulty understanding how Bob finds the value of b by looking at x mod 4. I followed the example except for that one part. I also didn't understand the Computational Diffie-Hellman Problem and the Decision Diffie-Hellman Problem. What I didn't understand was the significance or how they fit into the rest of it.
2. I was pretty interested in the name of ElGamal. All the algorithms we have covered were named after people. This looked like a code name in Spanish or something. A quick google search revealed this algorithm wasn't any different; it was developed by Dr. Taher ElGamal of Ciaro Egypt, a computer scientist.

7.2 due on October 29

1. What was difficult to understand ... It started at "7.2 Computing Discrete Logs". I felt like I kind of knew what was going in the introductory text, but when I got the the Pohlig-Hellman algorithm, I just got lost. I think the other stuff would follow.
2. Though I didn't understand 7.2.4 the author said that "there is a philosophical reason that we should not expect such an algorithm." It makes wish I understand even more.

6.5-6.7, 7.1 due on October 27

1. I had some difficulty understanding how the treaty verification worked. It raises the question to me is RSA still secure if you compute d and let (n,d) be public but keep e private? It seems me that country B can just gather their own x data and then use it to find d. After that country B can do what they want.
There was also some difficulty understanding the method of authentication and non-repudiation. I didn't follow their explanation.

2. The RSA challenge if funny. I think it would take me a little more than $100 to put in a serious effort to try to decrypt the message. The people that worked on it must have been looking for a challenge. Trapdoors are interesting. They seem like a very easy security breach on a cryptosystem if word ever got, but after reading and thinking about it that is pretty much the case with any cryptosystem.

Talk on Math Minimal Surfaces October 21

1. The lecture seemed quite understanding and fun. My only difficulty is that what do you what do with minimal surfaces and how did they study of minimal surfaces start? I guess the end of the lecture hit home. I am pretty close to be graduating with a math degree, and I have not a clue what to afterward. That is probably the most difficult thing for me chew on.

2. Soap films seem like a lot of fun, but not quite as fun as running through encryption levels of AES. The idea of research sounds fun. I enjoy listening to new things discovered. I am signed up for newsletter that latest breakthroughs in the computing world. I don't know if I could handle doing research especially in mathematics. It seems like there would be a lot of drudgery. I have a hard time getting through homework assignments. Research is probably different from homework though.

6.4 due on October 22

1. I didn't follow the p-1 Factor Algorithm. I keep getting lost with all the subscripts and superscripts. The explanation following didn't make much sense as well; though for some reason the explanation for choosing B did make sense. Maybe because it was left up to the situation.
2.I have heard of elliptic curves used in cryptography, but I don't know much about them. I have also heard a bit about quantum computing as well. I am interested in both of those topics. Hopefully we will cover them ...

6.3 due October 20

1. I did pretty well following the Miller-Rabin Primality Test. I had difficulty following and understanding the material after the pseudo-primes to the Solovay-Strassen Primality Test, the explanation to why the Miller-Rabin test works.
2. It think the important thing to take from the reading is that these are "composite testing" methods. The methods don't really prove something is prime but is a composite. It is interesting how the problem lies in factoring numbers, and it seems like there is a lot of room for finding better algorithms.

3.10 due on October 18

1. I don't quite follow this section. I read over it and got to the end, and I was lost and tried reading it again. The Legendre symbol sort of made sense but then it seemed like the Jacobi symbol was the same symbol but meant something different. I don't kind of lost in those definitions and examples.
2. During the math lecture on primes the Legendre was mentioned. I thought I would gain a bit more understanding, but didn't. I am amazed how people figure this stuff out. Gauss is mentioned in both physics and math; Euler, Fermat. Brains.

Focus On Math - "A Brief History of Primes" by John Friedlander

1. Dr. Friedlander mentioned in  his presentation that checking if a number is prime is fast. I must have dozed off or missed something because it seems like to me that one would have to check a number with all previous primes  and compare the gcd. That doesn't seem very quick.
2. I wish Dr. Friedlander would have gotten into more of what he does. Much of the material covered has been covered in previous classes. Maybe have a brief portion on the future of primes. I have heard of the Riemann Conjecture for some time, but what it was about. It is interesting that the conjectures he presented haven't been proved. They seem so simple, but those are usually the hardest problems.

3.9 due on October 15

1. I didn't follow the follow the portion where the modulus was a composite. I understood how the square roots were solved for the individuals mods, but then the combined part to get the four solutions lost me. The concept or the process of finding the square roots mod n is giving my brains some fits.
2. I thought it was interesting that given n=pq where p,q are primes, when a person finds the solutions to the squares, he/she finds the factors of n. Seeing how we are working with the RSA, this might be another way to attack the algorithm.

6.1 due on October 13

1. I had difficulty understanding the theorems in 6.2.0. I am not sure how they work out. I am sure we'll go over them in class. I was also really confused by the "more sophisticated method of preprocessing the plaintext". It seemed like they jumped from a plaintext attack to this method, and I didn't see quite the need for the method.

2. I seems like RSA is not so secure afterwards though I am sure it is still quite secure. I am in a stats class right now so the last method was intrigueing. It was using some sample variables, means, and deviations to calculate the processing times of the computer. It's genius. Is it an effective attack? I didn't quite figure out how they actually timed the computer, but the concept is cool.

6.1 due on October

1. I don't understand where the polynomial X^2-(n-phi(n)+1)X+n came from. It seems like a real useful polynomial for RSA.  The rest of the section was straight forward after the previous class lectures.
2. The RSA is neat in how simple the concepts are quite simple when compared to DES and AES. It seems like it would be easy to break all you have to do is factor a number, but it isn't the case. It is cool they use just a couple of math theorems for the method.

3.6-3.7 due on October 5

1. I think Fermat's Little Theorem and Euler's Theorem are pretty cool. The really simplify congruences. It is amazing to see that discovered quite a while ago, these theorems play in important role in modern day cryptography.

2. I followed the three-pass protocol the nonmathematical way but the mathematical way was a little more hard to follow. Then primitive roots sections was murky. I understood the example and understand what a primitive root is ... sort of, but the propositions were not so clear.