16.5, due on December 11

1. Difficult: I don't understand how (k^-1)kA=(t+tn) and then nA=infinity. Just to much assuming for me to follow.

2. Reflective: It is nice to see how this can be related and slightly modified to fit stuff we previously learned.

16.4, due on December 9

1. Difficult: I had difficulty following the addition in the finite field worked on elliptical curves.

2. Reflective: It's interesting to see how everything even elliptical curves lead to using mod 2 because that is what works on computers the best.

16.3, due on December 6

1. Difficult: I was confused on how the factorial with the P actually worked. I didn't know why the factorial came into place.

2. Reflective: I really like how its comparing what we are learning to do now to what we learned so far this semester when it comes to factoring.

16.2, due on December 4

1. Difficult: I was confused on how discrete logs relate to elliptic curves. I couldn't quite make the connection there.

2. Reflective: I did like that it talked about the same attacks we used on normal discrete logs on elliptic curves and how it just is slightly modified. It makes it nice that we don't have to learn a bunch of new tests.

16.1, due on December 2

1. Difficult: I found almost all of this section difficult. I don't know if I have ever actually studied elliptic curves and if I have I don't remember. It really lost me when it started talking about the points on a line and how to find equations and I just couldn't follow the math in the book.

2. Reflective: Like I said above I have never really done anything with elliptic curves so I don't know how to relate this to anything. But it is confusing to follow so it sounds like something good to use in cryptography.

2.12, due on November 25

1. Difficult: I found it difficult how to follow how they exactly got the products of the cycles from just three simple words.

2. Reflective: I remember working with permutations and finding products of cycles in Abstract Algebra but I don't remember how we did it.

19.1-19.2, due on November 20

1. Difficult: I didn't really get the quantum mechanics. I understood it though the light example but did not understand once arrows and things started to be drawn and used as a key.

2. Reflective: Who would think to use quantum mechanics with cryptography? All I've ever heard is how hard quantum mechanics is but I guess that's what makes it effective in cryptography.

14.1-14.2, due on November 18

1. Difficult. I don't really get how the zero-knowledge is working. I understand that its checking multiple data that is hard to come up with if you don't have it but don't really get how it works.

2. Reflective: I'm glad something is working to keep my bank account info safe and from having my card information and pin from being stolen form me.

Exam 2 Questions, due on November 15

1. Which topics and ideas do you think are the most important out of those we have studied? 

• I think the most important topics we studied are the different types of cryptosystems gone over and all the different ways you can attack them. That is the reason we have gone over everything else.

2. What kinds of questions do you expect to see on the exam? 

• I expect to see different calculations that we can actually do by hand such as the topics with modular arithmetic, Jacobi symbols, and Shamir threshold scheme problems.

3. What do you need to work on understanding better before the exam?

• I need to understand all of the factoring methods better and how exactly to do those by hand without sage. I also need to go over discrete logs and the review says simple discrete logs but how simple. Can you just brute force them?

12.1-12.2, due on November 13

1. Difficult: I didn't really follow how you write the polynomial for threshold schemes and then why putting it back together the way the book describes works.

2. Reflective: I could see why these methods would be useful. It's important to have ways to share important information if there needs to be so many people involved in the process.

9.1-9.4, due on November 11

1. Difficult: I found following the steps for the RSA and ElGamal Signature Schemes hard. There are just so many steps that you have to keep straight.

2. Reflective: It makes sense that we went over the birthday attack before this section. It shows why that attack is important to understand when digitally signing documents.

8.4-8.5 and 8.7, due on November 8

1. Difficult: I found it difficult to follow how the birthday attack and the hash function related and why they were useful together.

2. Reflective: I remember talking about the birthday paradox in my stats class. We had about 23 people in it and we went around the room and we found a birthday match. I didn't really understand why the probability is the way it is until reading this section on birthday attacks.

8.1-8.2, due on November 6

1. Difficult: I don't really understand what a hash function is. I get that it's another way to encrypt messages but how it does that was confusing to me.

2. Reflect: I feel like every new way of coding that comes up I'm lost in the reading but eventually I figure it out/understand it. Hopefully after class this topic will be the same.

7.3-7.5, due on November 4

1. Difficult: The hardest part for me was following the computational and Decision Diffie-Hellman Problems and how those benefit you when it come to breaking ElGamal.

2. Reflective: It's interesting that cryptosystems can be built off of things like factoring and discrete logs just because they are so hard to do.

7.2, due on November 1

1. Difficult: I found following all the steps to computing discrete logs to be confusing. It was hard to follow where numbers where coming from and why it worked the way that it did.

2. Reflective: I don't think I've ever seen anything like this. It seems interesting but don't really know what to do with it.

6.5-6.7 and 7.1, due on October 30

1. Difficult: I found reading about the discrete logarithm to be hard. It just seems like a random concept.

2. Reflective: I just thought it was interesting to look at the treaty verification section. Its cool to see real world applications.

6.4.1-6.4.2, due on October 28

1. Difficult: The most difficult part of this reading was understanding how you found the numbers to use for the quadratic sieve.

2. Reflective: It is just really interesting to see all the ways that have been used to try to factor large numbers. Just because we have been doing it for so long it seems like it should be something easy but it's not.

6.4, due on October 25

1. Difficult: I'm confused on how the p-1 Factoring Algorithm actually works. It is weird to me that you can just pick a bound B and it will work.

2. Reflect: I think its really interesting that there hasn't been an easy way to factor found. We learn about factoring from a young age but getting into this I realize it isn't as easy as we have been lead to believe our whole life.

6.3, due on October 23

1. Difficult: I just had difficulty following all of the different primality test. How they work and why. There is just a lot to comprehend.

2. Reflection: We've been building up to this. It seems nice to have tests that will help us tell if a number is composite or probably prime.

3.10, due on October 21

1. Difficult: I don't really understand why all of this stuff works. It was hard to follow all the properties and why certain things worked.

2. Reflection: I don't think I've ever really seen anything like this. It is always nice to have properties that you can use though.

3.9, due October 18

1. Difficult: I don't really understand how this works to find the square root in mod n. I probably just need to hear somebody talk through it.

2. Reflective: I have no idea how this relates to anything I've done. I've never needed to find the square root of a number mod n.

6.2, due October 16

1. Difficult: I found most of this reading difficult. I felt as though it was a bunch of theorems and equations just thrown at me that I don't quite get what to do with them.

2. Reflective: I do see why we just did continued fractions. That will help us factor n.

3.12, due October 14

1. Difficult: I don't really get how or why the faster method for finding partial quotients works.

2. Reflection: I definitely remember doing partial quotients in probably abstract algebra. I remember finding partial quotients but I don't remember what we did with them except for just find them.

6.1, due October 11

1. Difficult: So I think I understand most of this material but the one thing that kinda confuses me is Bob makes n public and since n is a product of two primes wouldn't that be relatively easy for people to figure out what p and q are. Then anybody can find the decryption exponent d..

2. Reflection: Well after reading this section I realize why we covered the number theory we just did. It allows us to do this.

3.6-3.7, due October 9

1. Difficult: The thing that I found most difficult in this reading assignment was the Euler's function and Euler's Theorem. I just couldn't really follow the explanation of it.

2. Reflection: Before we did this it was important to cover the Chinese Remainder Theorem because it looks as though that plays a significant role with this stuff.

3.4-3.5, due October 7

1. Difficult: What I found difficult to follow was how modular exponentiation worked. I was having difficulty following why certain exponents were chosen and others weren't.

2. Reflection: I remember doing the Chinese Remainder Theorem in Abstract Algebra. It was only covered one day and we had maybe one homework problem on it. Therefore I don't really remember how to do it but I do know I have used it before.

Exam 1 questions, due October 4

1. Which topics and ideas do you think are the most important out of those we have studied? I think the most important ideas are understanding the different types of systems and what their weaknesses are.

2. What kinds of questions do you expect to see on the exam? I expect to see questions like our homework but that are easier to do since we have to do them by hand. They shouldn't be to hard if we know what we are doing.

3. What do you need to work on understanding better before the exam? I need to better understand all the differences between the different systems and how each of them works.

5.1-5.4, due October 2

1. Difficult: The most difficult part for me was following Rijndael in the first place and then trying to understand the decryption method. It's kinda hard to follow decryption when you don't really get the encryption part.

2. Reflection: This is nothing that I have seen before except for the basics we did in class on Monday. It makes sense that the more things you do to plaintext the harder it is for somebody to break.

Questions, due September 30

1. How long have you spent on the homework assignments? Did lecture and the reading prepare you for them? I spend about an hour on each homework assignment, sometimes longer depending on the assignment. For the most part I feel as though lecture and reading prepares me for the homework. There have been a few questions that I had no idea what I was doing though.

2. What has contributed most to your learning in this class thus far? I really like that we have to do the reading before class. That way I know if I don't understand the reading I really need to pay attention in class so that I can understand it.

3. What do you think would help you learn more effectively or make the class better for you? (This can be feedback for me, or goals for yourself.) I need to try better to completely finish homework before class so that I can better pay attention in class.

3.11-3.11.2, due September 27

1. Difficult: The most difficult part for me is wrapping my head around what a field actually is. The rest of the math seemed pretty straight forward though.

2. Reflective: This reminded me of abstract algebra and using modular arithmetic with polynomials. It is something I am fairly good at and understand.

4.5-4.8, due September 25

1. Difficult: I had difficulty following all the modes of operation and how they all work. They all just seem so similar it is hard to keep them separated in my mind.

2. Reflective: It was interesting to read about the breaking of DES. The advances of technology make a difference in our lives. Sometimes it makes our lives easier but those that do cryptography it is harder to create a good system that is resistant to attacks with advancing technology.

4.1-4.2 and 4.4, due September 23

1. Difficult: I had difficulty just following the DES encryption in general. I don't understand where the L and R's are coming from and don't understand all the permutation charts.

2. Reflection: I don't think I've seen anything like this before. So it was interesting to read something new. I did however recognize the group theory at the end from abstract algebra.

2.9-2.11, due September 20

1. Difficult: The most difficult thing for me in the reading was understanding the linear feedback shift register. There were just so many congruences and I didn't know where different things were coming from.

2. Reflection: The section on pseudo-random bit generation had me thinking about how many times I used the function rand() in my computer science class. I didn't realize that it was really that predictable. The text said that it was and I was like wait a minute I thought it was actually a random number.

2.5-2.8 and 3.8, due September 18

1. Difficult: I had difficulty following how the ADFGX cipher works. I understood the original matrix but I got lost when the matrix starts getting arranged.

2. Reflective: I like how in this reading I am starting to see how Linear Algebra is actually important. I went through that class wondering when I would ever use the majority of the topics covered and now I am starting to see the important of inverses of matrices and determinants.

2.3, due on September 16

1. Difficult: I found it difficult to follow the decoding process once it started taking dot products. I then didn't follow very well what the dot product represented how it then becomes useful.

2. Reflective: It seems that pretty clear that frequency of letters are pretty important when it comes to decoding messages. We kinda used them when we decoded the message in class and on homeworks and now it is being used to crack the Vigenere Cipher.

2.1-2.2 and 2.4, due on September 13

1. Difficult: I didn't really understand how the counting diagram worked and how with the frequencies we can just guess the correct letters. It wasn't very clear how we got the table of numbers.

2. Reflective: Like the book figured out frequencies of numbers and used them to their advantage to crack the code I have done the same thing with the couple of codes that I have had to break in this class. I look and see what letters are repeated a lot and guess what the letters correspond to from there.

Guest Lecturer, due on September 11

1. Difficult: Nothing about the lecture was truly difficult. A question I had though was did it not bother people that codes were being sent back and forth and they couldn't read them? I feel as though somebody that didn't like the church would have tried to intercept them and gotten upset because they couldn't read the code.

2. Reflective: This lecture was really interesting just because I had no idea how much codes were actually used in the church. I learned something new about the Doctrine and Covenants that I didn't previously know about unusual names. It was overall a really interesting lecture.

3.2-3.3, due on September 9

1. Difficult: The most difficult part for me to understand was division in modular arithmetic. I've gotten really good at addition, subtraction, and multiplication but I have never really used division. There is just a lot more that goes into division than addition, subtraction, and multiplication.

2. Reflective: I have used a lot of modular arithmetic when I took computer science winter semester. We used it mainly when we had different choices and needed one at random. We would produce a random number and then mod it depending on how many choices there where. Modular arithmetic can make center things so much easier.

1.1-1.2 and 3.1, due on September 6

1. Difficult: The most difficult part of the text was when it started talking about the size of numbers and how log base 10 of n is important and that relates to k^2 somehow. I am having trouble understanding how all these things relate to each other in 1.1.3 on page 8.
2. Reflective: I enjoyed reading about the basic number theory. I feel like I have used all of what was read in multiple classes and have a good handle on that information. It made me excited that there is actually something that I know going into this class when I didn't think I knew anything pertaining to cryptography.

Introduction, due on September 6

• What is your year in school and major? I am a Junior double majoring with Math and Math Ed.
• Which post-calculus math courses have you taken? I have taken Math 341: Theory of Analysis 1, Math 371: Abstract Algebra 1, MathEd 362: Survey of Geometry
• Why are you taking this class? I am taking this class because it fulfills one of the multiple upper level classes needed to be taken for my math major.
• Do you have experience with Maple, Mathematica, Sage, or another computer algebra system? Programming experience? How comfortable are you with using one of these programs to complete homework assignments? I do not have any experience with Maple, Mathematica, Sage or any other computer algebra system. I have programming experience from taking CS 142 this past winter semester. I feel like I will become comfortable with one of those programs as soon as I sit down and start playing around with it and getting use to it.
• Tell me about the math professor or teacher you have had who was the most and/or least effective. What did s/he do that worked well/poorly. One of my favorite math professions gives us a list of objectives from each section that we study. They tend to be long lists but I know what he wants us to get out of each section. He then pulled test questions from the objectives since that was what he wanted to know. But because I had the objectives from the start I could follow and make sure I learned and understood each objective before it was a couple days before the test.
• Write something interesting about yourself. Something interesting about myself is how deeply invested into sports that I am. I love football and basketball. I am at every home game unless work prevents my going. 
• If you are unable to come to my scheduled office hours, what times would work for you? I tend to have work a lot of the times during your office hours but I would be able to almost always come Tuesday and Thursday 3-4 pm or Friday 10-12.