16.5, due on December 9

1. I don't remember how to make sure the message is a point on the curve, and this section didn't explain it (that I could understand).

2. It was good to read this after already talking about it in class a couple times. It made sense. :)

16.4, due on December 7

1. I don't really understand what is going on when we add three points only to then add two points to find something that adds to infinity. I'm also having a hard time grasping the concept of working over a finite field GF(2^n).

2. This is random and unimportant, but I liked learning that a singularity is a point "where the partial derivatives with respect to x and y simultaneously vanish." I don't know if I've ever heard of that, but I think it sounds cool and interesting.

16.3, due on December 4

1. I didn't really understand the algorithm for factoring using elliptic curves. You just choose random curves until one of them works for you? How long do you wait before you deem one ineffective?

2. This section kind of felt like a lot of random things about the elliptic curve factoring algorithm without actually doing a good job of explaining how the algorithm itself works. But it could have been there and just went all over my head.

16.2, due on December 2

1. I don't really understand how to map a message to a point and how to get the message back from a point on an elliptic curve.

2. These elliptic curve things are kind of weird.

16.1, due on November 30

1. This is all a little more abstract than I'm able to grasp. Also, why do you take the negative of the y? I'm sure it's just how we choose to define addition, but why?

2. I'm interested to see how this applies to cryptography . . .

18.1-18.2, due on November 24

1. I didn't understand most of the section about error correcting codes, specifically how a code C can detect a certain number of errors.

2. I thought the part about ISBN numbers was really interesting. I had heard about it before, but never really got it. It helped to learn about it in the context of other error correcting codes.

2.12, due on November 23

1. I don't understand the set-up of Enigma, which I think makes it hard for me to understand the method of breaking it, although that seems to be hard to understand regardless.

2. I remember cyclic groups from 371, which I thought was cool. I also enjoyed the movie The Imitation Game, although I know that it is not completely accurate. 

19.1-19.2, due on November 18

1. I don't really understand how quantum bits work at all.

2. This is a cool overlap of math and physics. It's exciting that developments on this are happening right now!

14.1-14.2, due on November 14

1. I didn't understand the part about I and H(I||j) and why it works. I also had difficulty understanding why the Feige-Fiat-Shamir Identification Scheme actually works.

2. This seems really applicable and useful. That's something I like about this class. While it is just a lot of number theory, I like that it has context in the real world.

Exam Review, due on November 13

• Which topics and ideas do you think are the most important out of those we have studied?
• I think the most important topics are the different cryptosystems that we learned about and specific attacks on those systems. Most of the other stuff that we learned seemed to lead up to them.
• What kinds of questions do you expect to see on the exam?
• It's hard for me to know what to expect, because I feel like we used computers an awful lot in this unit. Even the concepts behind them seem to require bigger numbers, which we aren't really able to work with without a strong computer.
• What do you need to work on understanding better before the exam?
• I need to work on understanding Fermat's Little Theorem and Euler's theorem and how to apply them.
• I need to review all the different primality tests as well as attacks on the different cryptosystems.

12.1-12.2, due on November 11

1. I had a hard time following the notation and set-up of the Shamir threshold scheme.

2. This is all so cool to me. It just makes me feel like a spy, which I love. :)

9.1-9.4, due on November 7

1. It was hard for me to understand fully the set up of the RSA and ElGamal signatures and how they work between two people to produce the desired outcome.

2. I finally see how a hash function is useful. I know you said multiple times in class that signatures was one way that they were used, but I had a hard time understanding how until now.

8.4-8.5 and 8.7, due on November 6

1. I still don't really understand hash functions, so all of this was a little bit unclear. But I especially didn't understand that part about multicollisions.

2. I thought the birthday paradox was so cool!! I think it's awesome.

8.1-8.2, due on November 4

1. I didn't understand the Proposition on page 221 or the set-up of hash functions in general.

2. I'm so tired right now, that every time it says hash, I think of delicious chopped up and cooked potatoes. I'm hoping it means more tomorrow in class.

7.3-7.5, due on November 2

1. I didn't understand the part about the machines that do Diffie-Hellman problems/ElGamal decryption.

2. It's nice to see that the things we've learned in the past couple of classes lead up to something.

7.2, due on October 30

1. I don't understand the part in the Pohlig-Hellman Algorithm where you break x into x0 + x1q1 . . . and why it works. I also didn't really understand the Computing Discrete Logs Mod 4.

2. I had the thought as I was reading that cryptography is just a lot of number theory. I also had the thought, "this is much funner than just plain number theory." It's because this points to something and has cool applications. It's not just proofs! :)

6.5-6.7 and 7.1, due on September 28

1. I was somewhat confused by the discrete logarithms section. I don't really understand how they work.

2. I think the thing with decrypting your message with your key and then encrypting it with their key, so that they decrypt with their key and then encrypt with your key to get the message is really clever.

6.4.1-6.4.2, due on October 26

1. I didn't understand the part about putting the prime factor powers in a matrix and finding linear dependencies (I don't fully remember this), and how the numbers that they got were 0 (mod 2).

2. I found the quadratic sieve method of factoring interesting. I'm impressed someone came up with that.

6.4, due on October 23

1. I didn't really understand how The p-1 Factoring Algorithm works or how it gives us a factor of n.

2. This is just a fun fact: I'm giving a presentation on Fermat tomorrow in my History of Math class, and it's just kind of cool to see his influence in so many different places, specifically here in number theory that relates to Cryptography.

6.3, due on October 21

1. I didn't understand the part about how to pick a prime number.

2. Is this used to make sure we pick good p's and q's?