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.
  

3.9, due on October 16

• It was a little bit tough for me to understand the breaking down of composite roots. That was the hard part about the reading last time we learned about this. I'm not sure if there's only one way to break down a composite root, or if we can choose which factors to break it down into.
• I think I'm getting a hold of the square rooting concept without the composite roots. The formula makes sense to me and I think I understand it and could do it on my own if I needed to.

3.12 and 6.2, due on October 14

• The hardest part of the text for me to understand was the M Wiener Theorem. I'm not quite understanding the reason behind why they chose that "if d <>
• I really enjoyed the continuing fractions that we learned in class and read about. It was fun to see Dr. Jenkins figuring out everything in Maple. I understood the continuing fractions and how/why it works. And, once again, it was nice to read about something we had already learned about. It made the reading process much easier.

6.1, due on October 9

• I really can't say that anything in this section of reading was super difficult. If I had never before seen the RSA algorithm, it may be difficult for me to understand, but I've seen it before. Even the PGP wasn't too hard to understand.
  
• I remember the RSA algorithm! We practiced it way back in 190 with much smaller numbers. But the algorithm was introduced to us. It was fun to read about something that was vaguely familiar. It was fun to tie in the principle of the PGP. Although RSA isn't fast enough to encrypt anything very long, it tightens the security to encrypt the full message with some other method, but then encrypt the key using RSA, since RSA is pretty hard to break.
  

3.6-3.7, due on October 7

• It took some serious consideration to understand how primitive roots are found. At first, it seemed like a lucky guess. Its still a little bit fuzzy, but I think I'm starting to understand it.
• I enjoyed reading about Fermat's Little Theorem. I remember reading about it back in 190 and loved having a review. I don't remember all of the little shortcuts that the theorem provides for modular arithmetic. Those shortcuts will take remembering and some practice, but I think it will drastically decrease the time it takes to calculate really large numbers. It was also nice to have a preview of the reading last class. It helped me to follow along in the reading and understand what was being said and explained.

3.4-3.5, due on October 5

• I learned about the Chinese Remainder Theorem clear back in Math 190, but I don't remember it being as confusing as this. I am having a hard time remembering how the theorem works and what we need to use it for. I understand the thought process, but it will definitely take some practice before I can feel comfortable using it myself.
• I really enjoyed reading about modular exponentiation. It makes a lot of sense to me--it is a method of making some extremely impossible calculations possible. It makes really intense algebra not so intense. Its kind of a short cut to modular calculations.