Difficult: Nothing, it all made sense. The elliptic curve math is simple, and I am already very familiar with DH and ElGamal.

Reflective: I was sad to see no discussion of message encryption with elliptic curves. It is also sad to just see extensions to known methods that have man-in-the-middle attacks.

Exam Prep:
Important: Math in Z_p, Proofs about the infinitude of primes, how to factor primes, multiplicative functions, characters, encryption, and elliptic curve point addition.

Questions: Pretty much what we have seen so far, but with a focus on encryption.

Understand: There is nothing I actually feel that week on. The biggest problems I have had on the tests to date has been a lack of exactitude, which is my fault and not a problem with what I have learned.

Section 6.3

Difficult: I can read the algorithm just fine, but I feel lost when reading the definition for how they got up to the algorithm. I read it twice, and I still just don't seem to fully grasp it. I can't even tell why.

Reflective: I think it is really cool that we can find medium sized factors of numbers. It makes me think more and more that there must be a quick way to find them. Is there any proof of what time complexity class that factoring numbers belongs to?

Chapter 6.1-6.2

Difficult: This is all pretty familiar since I have taken the cryptography class before. I would like it if we could see you run the material in sage, but I don't think we have a project in class, so that probably won't be possible.

Reflective: It is very interesting to consider these curves. I still find it amazing that we are able to use them for cryptography.

Section 5.4.2

Difficult: I have done these encryptions a lot, so nothing was difficult. I work in the security lab, so cryptography is becoming second nature.

Reflective: It is interesting that we don't make use of an NP-Hard problem for encryption. It isn't even NP-Complete, and could possible live in P. It is interesting that we are depending so much on something we think is hard, but not provably so.

Section 5.4-5.4.1

Difficult: Nothing, I have seen this material before in Math 485.

Reflective: I think it is interesting that they say cryptography is broken up between classical encryption and public key encryption, while completely ignoring symmetric key encryption. Unlike their definition of classical encryption, the algorithm itself can be known, and the security, just as in public key cryptography, is in the key.

Section 5.3.2

Difficult: I feel that I understand each individual equation, but I am having a hard time filling out a complete mental picture of the proof. I don't really know where the disconnect is though.

Reflective: I don't really get why we care so much about Mersenne primes. What applications do they have, besides being huge. I wonder because it seems like we spend a lot of time looking for them, but I havn't heard why we need them.

Section 5.3.1

Difficult: I think I understood the material pretty well. The hardest part was during the proof of the correctness of the Solovay-Strassen primality test. It really wasn't that bad, but did have a lot of parts.

Reflective: It is interesting how reliable these probabilistic tests are. It is trivial to test a large number of paces, and come with a very tight bound on the error. It is also interesting that even deterministic algorithms have error, due to problems with hardware, and so at some point might really not be that much more reliable.