Section 8.1-2

It was interesting to read about how a hash function can be strongly collision free. It seems that in most cryptosystems it is highly unlikely that two ciphertexts will match when the messages do not. For hash functions it is hard to ensure this.

It is difficult to understand how discrete logs apply to hash functions and how the proposition described in 8.1 works.

Section 7.3-7.5

It is interesting that a way has been devised to commit to the information that is transferred as in the dilemma with football games, so that neither party can change the message. It seems that cryptographers have thought of everything.

It was very confusing to read through the explanation of El Gamal. It seems very similar to RSA, but using discrete logs.

Section 7.2

I am thoroughly confused by procedure illustrated for pohlig-Hellman algorithm.

The part about the index calculus was very interesting. It is interesting that series of relations allows us to solve for the discrete log.

Sections 6.5-7 and 7.1

It was really interesting to read about trapdoors and their usefulness and pitfalls.

I was intrigued by discrete logs but i didn't really understand the discussion of one-way functions and why they are only "probably" one way?

Section 6.4.1 and 6.4.2

The quadratic Seive is a very interesting method. It is interesting that the setup works for any modulus. However, it seems difficult to find the squares.

The universal exponent factorization method is very complicated. I didn't understand where the value of u came from.

Section 6.4

I was thoroughly confused by the p-1 factoring algorithm. What is B! And how does it affect the factors of n?

It is interesting to see the connection between a difference of squares and factoring numbers.

Section 6.3

I think it is interesting that the Fermat primality test tells when a number is composite and when its not true tells that a number is probably prime. This seems like a very vague condition for mathematics.

I didn't understand the Miller-Rabin Primality test. I don't understand why the process associated with it. 

Section 3.10

It is very interesting how the properties of the Jacobi symbols allows us to solve a large value problem in only a few steps. The definition is barely used.

I didn't understand the final explication about how jacobi and legendre symbols applies to RSA. What is quadratic residuosity?

Section 3.9

It was hard to understand the proof for square roots mod n. I don't follow the logic.

It is interesting that finding the square roots of a number that is relatively prime to n is as easy as factoring n.

Mathematics of Voting procedures

Dr. Jenkins,
I wrote this last week, but i just realized it didn't post. Sorry.

Dr. Saari, explained a way that each of three "candidates" can win based on the type of voting method, plurality, pairwise, or a runoff election. The question is what does that do to democracy? These types of phenomena is surprisingly likely. Plurality method is one point for first place and zero for all others. Another method is to weight each place with a certain number of points. One conclusion is that anything is possible no matter the voting method. Dr. Saari could fix any election using mathematics.
One way to measure good voting procedures is to see if actual ties are made to be ties using the voting procedures. In the end, it is clear that voting is arbitrary and very vulnerable and that Voting is everywhere.

Section 6.2

The discussion of timing attacks was very interesting. Who knew that that kind of thing was possible.

It was hard to follow the short plaintext attack. I didn't understand about OAEP.

Section 3.12

The theorem in this section is very interesting. It is a very interesting way to express an irrational number.

However, I'm still wondering how we are going to use repeated fractions in cryptography.

Section 6.1

It was super interesting to read about RSA and its capability to be decrypted by the receiver, but not cracked if intercepted by the enemy.

I understood how the algorithm worked, but i just couldn't understand why it works.

Sections 3.5-3.6

I was very interested to learn about primitive roots. It is very cool that numbers can work that way. Is it just a coincidence? How does that work?

I didn't understand the proof of Euler's function.