16.5, due on December 9

• In this section, I had a hard time going through the application of ElGamal digital signatures on an elliptic curve. The outline seems very similar to the signature we already learned (outside of elliptic curves), and maybe that's why its tripping me up. It is so similar that I'm having a hard time making the distinctions.
  
• I really loved this section as well. It helps me to apply a new concept to an older one that I already understand. That helps me to understand both subjects better. The only thing I would've liked to have seen more of in this section is examples. I followed the outlines pretty well, except that of the signature. Elliptic curves are still pretty new and are still taking some getting used to. It would have been wonderful for me to see more examples.
  

16.4, due on December 7

• The only thing I found a little bit difficult was the addition of points in a field on an elliptic curve. I followed what was said in the book, but it is still a little bit unclear how to do it.
  
• This section of reading was really neat because it brought back fields and presented a new approach to using them. I didn't understand fields at first, but after receiving some help and explanation I really feel like I've got them. It was nice to be able to take a relatively new concept and apply it to a relatively old one. Putting the two together helped my understanding of fields as well as my understanding of elliptic curves.
  

16.3, due on December 4

• I'm still a little bit unclear as to how elliptic curves work. I follow along in lecture and understand the examples, but I'm still a little cloudy. The fact that elliptic curves can be singular is also a stumbling block for me.
  
• This section of reading referred back to two other methods of factoring n. It referred back to the p-1 method as well as the Quadratic Sieve. I was intrigued at how similar this "elliptic curve" factorization was to the P-1 method.
  

16.2, due on December 2

• The most difficult part of this reading for me was the plaintext section. I couldn't really follow how to encode plaintext and how to get it back. Hopefully this will be cleared up in lecture on Wednesday.
  
• The best part about this reading is that it brought back discrete logs. Not that I love them terribly, but they are doable. It didn't go too far into detail about it, but I can do discrete logs. And, a modified Pohlig-Helman algorithm wouldn't be too hard to work through. I also enjoyed the first part of the reading, where we learned about elliptic curves mod p. I've also got a feeling that we can use this method to help us factor n. Not that I want to, but I think it may lead to that.

16.1, due on November 30

• The hardest thing to understand about this section was the "infinity" concept. I understand where they're saying infinity is on the graph, but I'm having trouble understanding the addition with infinity. Its really close, but not quite. Lecture should help clear this one up. I also wasn't sure what "abelian group" meant. I learned it in 371 last year, but I can't remember what an abelian group is...
  
• This section of reading really reminded me of differential equations. They took implicit derivatives, they found the slope of the tangent line to a curve, and so on. I also really liked that they clarified the origin of an elliptic curve. At first, I thought it had something to do with ellipses, which it does. But it didn't deal directly with ellipses like I originally thought.
  

2.12, due on November 24

• I'm not really into machinery very much. Maybe that's why I am not quite visualizing what's going on with Enigma. Although I'm not really understanding the process yet, I love the concept. I'll definitely need a review of cycles and a run-through of how the whole process works.
  
• Its amazing that Enigma was broken 30 years before anyone knew it was broken! And, how sneaky of those Englishmen to sell broken parts to people who didn't know they were broken... Enigma seems to be a fairly complicated system with rotors and a keyboard and a plugboard. But it is nice to have something physical to look at instead of having "quantum" theories floating around. It's nice to have something to touch and feel and visualize. I also really love that Enigma uses cycles. That was one of my favorite parts of Math 371. It was one of the things I understood the best. :)
  

Online article and 19.3, due on November 23

• Okay, so if I'm understanding this right, Shor's Algorithm is another way to factor a number n, which has two large prime factors, p and q. So, this is basically a quantum way to solve an RSA system? It was great to read the article online, and very nice of Scott Aaronson to explain it in a way that was understandable. Reading through section 19.3, I felt that I already understood what it was saying, because I had had an introduction to it already. Although Aaronson did bring the discussion full-circle, to come back and relate how this "parallel universe" thing works in Shor's Algorithm, he didn't give any examples or anything. I imagine this would be hard to do, but it was a little bit hard for me to understand the full circle without seeing an example.
  
• I completely understood the thumbtack analogy. It was an interesting way to find a period. I had to read that section about 3 times before it started to make any sense. And then I wondered: "If I didn't have school or church or meetings at all, what would be my typical day? How long would my period be?" It got me thinking that my typical would probably be shorter than 24 hours. If I were locked in room without a clock and without a window, it might be different, but when I'm bored I try to sleep. But, that could also have something to do with being pregnant. :)
  

19.1-19.2, due on November 20

• The book was totally right. I understand NOTHING about quantum mechanics. I do understand light and the example they gave was more understandable to me. I understood when they were talking about the lenses and the light going through the lenses. The part where I got lost is where they started talking about WHY the light can go through all three lenses, but not through just two. Not a physics person...
• It was cool to see how they can use this quantum mechanics to generate conversation between two parties. Not that I understand that all the way either, but it was interesting to read about anyway. The new notation was throwing me off a little bit, too.

14.1-14.2, due on November 18

• I read through the material for lecture today, but really didn't understand any of it. Maybe I read through it too fast or maybe its just a little tough to get. But, I'm not really understanding the whole "door" analogy. Peggy wants to fool Victor as to which way she's going to go and wants him to think she knows how to get into the door? Not sure if that's what I was supposed to get out of that scenario. I also didn't really understand the Feige-Fiat-Shamir Identification Scheme. I'm really looking forward to lecture.
• I'm always wondering if anyone has access to my information after I used my check card for a purchase, and type in my PIN. Its a scary thing to think about. You always see those commercials on TV where the person's identity was stolen without them even knowing it. Now their credit score is horrible and their life is ruined. I appreciate there being methods out there to help protect us from this kind of fraud.

12.1,12.2, due on November 16

• I really like the idea of being able to split a secret among a group of people. Its sad to say that, at least in these days, people in general aren't too trustworthy. Its nice to have a method of splitting the key to make people depend on each other. I also really like that we're using matrices again for some of the threshold schemes. I really love matrices!

Test Review, due on November 13

• The topics we've studied that I feel are the most important are the various factorization methods as well as the primality testing methods we learned. Actually, most of the things we went over seems important in different ways. I just feel that we've had the most practice with factorization and primality testing. Another thing that seems important, and that we've done A LOT, is RSA.
• I sort of expect to see a few things on the exam. When I say sort of, I mean I have really no idea. But I think we will have some factorization questions as well as some questions that will ask us to test for primality. I expect to see some Jacobi symbols on the exam as well as RSA. We'll probably also have some theoretical questions on the exam, similar to the theoretical questions that were on the last exam.
• I definitely need to work on understanding hash functions better before next week. I also need to work on a couple of the factorization algorithms. Aside from those, I just need a general review of the material.
• I came into this course kind of blind. I didn't really expect anything as far as topics are concerned. If the question asks if there's something that I would like to continue to study that we've studied already, I really like RSA. I think its because we've had so much practice with it, but I do like it.

8.3,9.5, due on November 11

• Holy cow! There are so many new symbols to know! We've been introduced to one or two of them before, but now there are so many things to remember about hash functions. They're still pretty fuzzy for me anyway. Some good study time should clear it up. And, I'll just have to read and reread my notes from lecture so that I can catch up on all of the symbols and what they mean.
• The Digital Signature Algorithm really does remind me a lot of the ElGamal method. The way the two are laid out in the book makes them out to be extremely similar. Having completed the homework for this week already, and computing some problems with ElGamal, I feel good about algorithms such as these.
  

8.4-8.5,8.7, due on November 6

• The hard part about this reading was still hash functions. I missed the first part of the reading about hash functions, so this is still a little bit cloudy for me. I understand the lectures in class that talk about hashes, but I'm still a little bit behind. So, when the book started discussing hashes as a means of encryption, I read it, but didn't really get it.
• The only part of the reading that I really understood was why the birthday attack works. I understand the logic behind it and I understand that the BSGS method would work better and be more precise. It was fun to read about and see how it works. The last time I heard of the birthday attack (although it was called by some other name) was a couple of years ago and at that time it was presented as only a theory. It was kind of mentioned in casual conversation. Its fun to know exactly why it works.

8.1-8.2, due on November 4

I didn't get a chance to read the material for today. I was in the middle of it, when I threw up. I don't have the flu, but I'm pregnant and trying to wein myself off of anti-nausea pills. Please send me an email if there's any way I can make this up. Thanks.

7.3-7.5, due on November 2

• I'm still pretty rusty on calculating discrete logs, so section 7.3 is a little bumpy for me. I understand it conceptually, but once I better understand how to do the discrete log thing, I'll be more comfortable. The ElGamal Cryptosystem is also a little bit jumbled in my head. It seems so similiar to a lot of things we've done, but just slightly different.
• Once again, it was nice to be at least introduced to the reading before reading it. The Diffie-Hellman exchange made a lot more sense after hearing a brief intro yesterday. The problems with this exchange seem deeply linked to discrete logs, which I'm still struggling with, but again, after practice it will get better.

6.5-6.7 and 7.1, due on October 28

• The backward RSA system is a little confusing for me. I understand the Ek and Dk from studying AES, and I understand that they cancel each other out. I'm not quite clear though, why, if Ek is known, that it will be difficult to find Dk. That's pretty much the only thing getting me still. The rest of it is pretty familiar, having already studied RSA.
• Discrete logs make sense to me. Not perfectly, but I understand most of it. I'm sure when we go over it in lecture I'll understand it better. But for now, I'm understanding how to go through the process and it seems like an easier way to find primitive roots, which is nice and helpful. :)

6.4.1, due on October 26

• Really, the only difficult part of this reading assignment was that I don't really understand why this all works. I understand that it works and I can understand how to get through it all. Its just very hard to see why it works. Not sure if I'll actually ever understand that part, but it is nice that I can understand and follow the procedure from the book.
• The fun part about this reading section was using matrices. I LOVE matrices. And I love anytime we get to use matrices. I understand them so well, probably partly because I had to take linear algebra twice. :) But matrices always make things a little easier for me to carry out.
  

6.4, due on October 23

• I'm a little bit confused still about the The p-1 Factoring Algorithm. I hope it helps to hear about it in class, but for now, I'm a little lost. It always feels this way for me when we begin to read about new material. And, usually, it is pretty well cleared up for me when we go over the material in class.
• I really like the Fermat factorization method. It seems very logical and I understand and follow the method. I know it isn't meant for two primes that aren't close together. If we tried it in that case, it would take us forever! But, for two primes that are close, I like the method a lot. Its very simple.

6.3, due on October 21

• I'm looking forward to going over the Miller-Rabin Primality Test today in class. It is a little bit confusing to me. I understand how it follows from Fermat's Primality Test, but it goes a little farther and beyond what I can understand at this point. It will be nice to have it clarified in lecture.
• I really enjoyed reading about primality testing. We used theorems and principles that we were already familiar with, such as successive squaring and Fermat's Little Theorem. It was nice to take things we're already familiar with and put them together to find another result.

3.10, due on October 19

• The Jacobi Symbol part was a little shaky for me to understand. The whole thing just seems so "do it the way you want to". I understand the process of using the 5 rules of the Jacobi Symbols to reduce and flip the fractions, but the problem for me stems all the way back to the face that (2/n) = +1 is n is congruent to 1 or 7 mod 8 and = -1 if n is congruent to 3 or 5 mod 8. I'm not sure whether I'm supposed to be able to calculate that to see it or if I'm just supposed to take it as fact because its part of a theorem.
• I'm not too sure about the Legendre symbol either. We went over it briefly in class, so I recognized it when I saw it, but I'm stuck on it for the same reason as being stuck on the Jacobi symbol. All of the properties just seems so random that I think I may have a hard time remembering them all.