Class Progress Questions, due on September 30

1. I have usually spent about three to four hours on the homework, although I'm not understanding everything. The lecture and the reading help with the homework, but not to the point that I know what I'm doing the first or second times I look at it. I have to really dive into it to attempt it.

2. I think when I'm doing the homework correctly and thoroughly, that contributes to my overall learning in the class. I have also learned a lot by working with other people on the homework. When I try to keep up with the lectures, that also helps me to learn.

3. I think I would learn more effectively if I had taken a math class more recently, but that's not something that I can fix now. Going forward, I really need to try to keep with the lectures. I often feel like the topics covered in class are covered very quickly. I need to stay up with them, so I can ask questions when the topic arises instead of being clueless later.

Section 3.11, due on September 27

1. The main thing that I didn't quite understand from the reading was all of the conditions for a field. Initially it was the three conditions given on page 95. However, on page 97, there are another three conditions that are said to be used to construct a finite field. What is the difference between those two sets of conditions?

2. I really enjoyed reading about polynomials and fields. I have always been able to understand polynomials better than the modulus function, so hopefully that will help me with this section. I was also intrigued to be introduced to the idea of fields, but they make sense.They potentially seem very powerful.

Sections 4.5-4.8 due on September 25

1. I'm not sure I really understand salt. I understand its aim, but I don't understand the process or computation behind salt.

2. I liked learning about the computations behind a meet-in-the-middle attack because I had learned about them in a few of my classes, but I didn't know exactly what was going on. It's interesting that even though you can double and triple encrypt the plaintext, the level of security still isn't that high and definitely not high enough that you would trust your message to be completely secure.

Sections 4.1, 4.2, 4.4 due on September 23

1. How is/was DES secure when you use the same Initial Permutation and Expansion Permutation tables every time? I realize that computing capabilities were limited in 1974, but as they increased, I feel like the tables should have changed, especially since DES is not a group.

2. One thing I found interesting was the lack of trust people had of the NSA. It seems like that's a recurring theme. I also was intrigued by expander functions. I had never seen those before, but they are definitely effective. As I read about both DES and the simplified DES-type algorithm, I realized how deep into computers both security and hacking has gotten. We are learning about how to encrypt a set of bits of information, which seems so tiny, when in reality, it could be hacked.

Sections 2.9-2.11, due September 20

1. For the LFSR, and for other cryptosystems we've learned about, it seems like there's a certain amount of educated guessing. For the LFSR, it's guessing the length of the recurrence. Is there a systematic way to guessing what the length of the recurrence is, or should I just start from 1 and work my way up?

2. My first thought was "Blum-Blum-Shub? Who names anything, let alone a pseudo-random bit generator, something like "Blum-Blum-Shub?" Anyway, I had never heard of a linear feedback shift register, so I found it really interesting. The use of binary is easier and harder to understand in some ways than using letters. For example, I'm glad to be working with mod 2 now instead of mod 26, but these ciphers are more difficult to decrypt because of the limited characters that could be repeating.

Sections 2.5-2.8, 3.8 due September 18

1. The book mentions the concepts of confusion and diffusion and relates them to some of the systems we've learned about. However, the classical cryptosystems were not mentioned. My question is do all block ciphers have the properties of confusion and diffusion? Do the Playfair and ADFGX ciphers have those properties?

2. I am really enjoying how the book logically builds up to more complex cryptosystems. It's very easy to follow. I specifically appreciated the review of inverting a matrix and learning about the Playfair cipher, which I had heard referenced in movies, but I didn't really know what it was. I also enjoyed the Sherlock Holmes reference, which helped me realize how widespread and well-used encryption methods really are.

2.1-2.2, 2.4 due September 13

1. The part of this reading that I had the most trouble understanding was the affine cipher. I understand the encryption method, but the decryption got me confused. I understand congruence, but I didn't understand why we were finding a multiplicative inverse of x (mod 26). Could there be more than one desired inverse?

2. I have always been fascinated with substitution ciphers, so I was happy to read 2.4. I loved the reference to U.S. historical figures, and their uses of substitution ciphers. More specifically, I'm glad that the book went through an example of trying to break a cipher through frequency counts. Although knowing which letter e is replaced with is helpful, it still does not tell us the remainder of the cipher. Unless someone has access to a computer (which almost everyone does these days) or they really want to know the message, the substitution cipher is a decent deterrent to discovering the message.

Guest Lecturer, due on September 13

1. One topic that I didn't really understand was the message that was never delivered related to plural marriages not being stopped outside of the U.S. I can definitely see the negative ramifications if it had been sent, but I think that if that was actually the way it was divinely supposed to be, the message would have gotten through another medium. I suppose I don't really understand any kickback or excitement about that story.

2. I really enjoyed the guest lecturer, in part because I had heard of things like the Deseret alphabet, but I had never known what they were used for. The examples she gave of Parley P. Pratt writing to his wife and John Smith writing to Brigham Young were fascinating uses of the Deseret alphabet to learn about. The use of the mason code and simple substitution ciphers also made me think that there must be other, lesser known uses of codes by members of the Church. I had never heard of the secret names in the Doctrine and Covenants either, so I was excited to learn about that.

3.2-3.3, due on September 9

1. I honestly don't really understand the extended Euclidean algorithm. I can follow what the example is doing, but I'm not sure that I'd be able to replicate it. I specifically got lost after it says "an easy calculation shows" because I don't understand why we plug in x5 and y5 instead of continuing with the sequences. I'm getting lost in the details.

2. I was really interested in 3.3 because congruences have come up a couple of times in my studies - both in programming and in networking. We can figure out how many bits are leftover once a certain storage capacity is filled using the mod function. I was glad to learn more about something I had already learned about.

1.1-1.2 and 3.1, due on September 6

1. (Difficult) The most difficult part of this reading was getting used to reading theorems and proofs again. I haven't taken a real math class in over two years, and so 3.1 was a nice re-introduction. I could understand most of the theorems and proofs, but I had a hard time following the proof of the last corollary of the section. I understand what the corollary is saying, but I am barely understanding the proof.

2. (Reflective) I have learned a little bit about cryptography in an information security class I took as part of my program, so reading this section made me excited to approach cryptography from a mathematical standpoint instead of an information security standpoint. In programming basic business applications, we have tried to include some checks for data integrity and authentication, but being able to incorporate more cryptography will be beneficial.

Introduction, due on September 6

My name is Heather Dunnigan. I'm a graduate information systems student. I'm doing the integrated 5-year program, so I will be graduating this April with a bachelor's degree and a master's degree. Beyond calculus, I   have taken Math 290, Math 341, and Math 313. I am taking this class because I got permission to use this class as the last requirement for my math minor, and I saw a flyer for it four years ago when I was a freshman, and I have wanted to take it ever since. It complements my major nicely, and it sounds fun.

I don't have any experience with a computer algebra system, but I do have experience with programming. I have taken a few classes in Java, and I have gotten a little bit of exposure to other languages. I am completely comfortable using SAGE to complete homework assignments.

I had the same math professor for both 290 and 341, and I thought he was very effective. He allowed time for questions to be answered in class, and he was very easy to approach outside of class. He was willing to explain things over again, even if he had just explained it. I could tell he respected his students, and he truly wanted them to understand.

As for something interesting about me, I am from a suburb of Detroit, MI, and this past summer I interned at Deloitte in San Francisco.