Assignment 12

1. I'd say I average a couple of hours each assignment up to now, although the last ones have been much longer. Lecture and reading do give me a good basic understanding, but sometimes I still feel a little lost on the last couple of assignments.

2. For me, working with the problems has been most beneficial for me so far. I really enjoy having the chance to decrypt things on my own and try to better understand how the different encryptions actually work.

3. If homework assignments continue at this level, I'm going to need to find more time to work on them. I feel like I'd like to say something else here too, but I'm not sure what it may be. I feel like class time is used pretty well after all. I guess if I get too stuck I'll try to make it to office hours more often, though it can be hard with my schedule at times. It has been really helpful when I can make it though, so thanks for that!

Assignment 11

1. Oh fields. We meet again abstract algebra! Taking it over the spring was hard enough, so I'm here thinking that a review of it in class would be most excellent to have. In the end, I feel that a review would really help my full understanding of what we are preparing to cover. I mean, I remember the basics of fields and whatnot, but (especially since I took it in the spring term and thus at an accelerated rate) a lot of it is eluding me as I read through it. So, I'll definitely be reviewing on my own, but any additional help would be more than welcome.

2. One thing that I find interesting through these readings were when we had equations suddenly pop out, seemingly out of nowhere. For example, when we multiply in GF(2^8), we are dealing with X to the exponents of 8, 4, 3, 1, and 0. Before that, though, we were representing all elements as polynomials of degree 7 or less. I don't quite get yet how this works out, even reading through it again and again. I wonder how they got this, and how it helps us out in the end.

Assignment 7

1. The most difficult parts of this reading was probably the section on block ciphers. I found it to be difficult mostly because of all the terms in there. This says to me that I still need to review all of the ciphers that we have covered before, and learn all of the ciphers that we have not yet covered. I feel that a good review of these ciphers, along with a better understanding of how the other ciphers work, will clear up and misunderstandings I have about this section.

2. I really enjoyed reading through the examples of cryptography being used, whether it was fictional (as in Sherlock Holmes' case) or historical (as with the WWII codes). It still amazes me how people could think of such things for codes. I feel like coming up with this on my own would be out of my league. That's probably why it's so much fun to read about it all.

Assignment 6

1. I feel that the most difficult thing for me from the reading was thinking in terms of matrices and vectors and not seeing them the way I want to think about them there in the text. Once I went off to the side in order to see it in the way I imagined it, it became easier for me to visualize what was being described. I would have like more visuals in the actual text, but it did describe it more than enough for me to figure it out in a way that made sense to me.

2. I found the methods for cracking this cipher to be very interesting. How does somebody come up with that? It makes sense to me to compare expected values against the frequency at which a given character generally appears, but I would not have thought to compare dot products in order to do this. It would be really nice to try using this method once or twice in class!

Assignment 5

1. I thought that the hardest part of this reading was the section on affine ciphers. I am at least somewhat familiar with the shift and substitution ciphers, and this type was just that one step further in terms of sophistication--to me at least. Luckily, we had just gone over modular division, so that part didn't really phase me at all. It just gets a lot more difficult when you suddenly have to keep track of more than one characteristic. Really, if it were up to me, I'd only try to crack codes if they were based on one characteristic unless the code was really important. If only those trying to read my codes thought that way too.

2. Reading through this really makes me think about my project, especially when it comes to determining what a letter may represent based on how often it show up. I hadn't really been thinking of this fully when we were brainstorming how to make a good code, and so ours may fall short of the mark we set for it if Alice were to discover the method by which the code is made. After all, even if each character is represented by three new characters, it can still be blocked off in a similar manner. So, overall, this was a good reading at this point in time in order to hit home how a code needs to avoid such an inspection through a stronger set-up.

Assignment 4

1. I didn't know a lot of the history behind what we went over in class. It was all very interesting, and I feel that she did a very good job at relating it to us, but I do always like to have a good understanding of what is being discussed. For me, the more I know about something, the better able I am to relate to it and make it meaningful. So, while it was very interesting, I kept finding myself wondering more about the stories and histories instead of always focusing on the coding methods.

2. The whole presentation was very interesting to me. I really enjoyed it, and I feel like it was definitely well prepared. I had never really even considered the usage of codes in the early church years. Also, if it was used so much then, I imagine it still is now? I laugh a bit too, because I see myself more-so as the first representative who thought that everyone would be a gentleman like he was: they wouldn't dare to read another's mail, because he would never do so himself! But this really is just naive. It's too bad it is that way and we need codes for anything other than just fun.

Assignment 3

1. I haven't really dealt with modular division much in the past. Instead, I would usually just think my way through the problem in order to find a suitable solution. Because of this, I was somewhat unfamiliar with the thinking process the reading took me through. I definitely prefer for things to feel right for me when I do them, so I had to read over this section a few times before I felt comfortable with it. Now that I've done so, I'm okay with it, but it was the most difficult part of the reading for me.

2. I find the prospect of working with powers in modular math to be pretty intriguing. Like division, it is something I haven't dealt with before. This reading didn't delve into it in depth just yet--which is why it was easier for me to deal with--but I wouldn't be surprised if it was more difficult in the end, especially since it's likely we'll be dealing with large numbers. However, I'm really interested to see how this applies to cryptography. While it's true that I don't really know anything about it just yet, I'm can't help but wonder what it'll be like when we get to that point.

Assignment 2

1.   The most difficult part of this reading was trying to make sense of the different methods and terms that were flung out in the reading that I have not understanding of, such as all of the different algorithms mentioned. This section will undoubtedly make a lot more sense to me once I do know those terms, and I'm sure we'll shortly find out more about most of them, but it was difficult for me now because I kept trying to figure out as much as I could about each of these terms.

2. I really liked how the reading went through the differences between symmetric and public keys. I feel that will be a very important distinction, especially because of their different uses and levels of practicality from case to case. I wonder though--how much data is required before a symmetric key is more efficient? From the next section, I really appreciated the distinction that was made between authentication and non-repudiation. In our discussion in class, they had still seemed pretty similar to me, so this additional reading on the matter was very helpful for me to clear up why we still distinguish between the two. Reading through 3.1, it is apparent that we'll need these basic methods of mathematics in order to really delve into cryptography, but I wonder exactly how we will need them in order to do so. The first chapter talked a lot about different algorithms that make use of factorization, so things like divisibility, primes, and the Euclidean algorithm will definitely be useful, but I wonder exactly how we will wind up using them. I guess, at this point, only time will tell.

Assignment 1

1.   What is your year in school and major?

            I am a senior studying Mathematics Education.

2.   Which post-calculus math courses have you taken?  (Use names or BYU course numbers.)

            I have taken Linear Algebra, Multivariable Calculus, Ordinary Differential Equations, Theory of Analysis, and Abstract Algebra.

3.   Why are you taking this class?  (Be specific.)

            Cryptography sounds like a it'll be a really fun subject to study and better understand. I look forward to learning the mathematics behind the algorithms we use to ensure data integrity.

4.   Do you have experience with Maple, Mathematica, SAGE, or another computer algebra system?  

            Sadly, no. 

5.   Programming experience?  How comfortable are you with using one of these programs to complete homework assignments?

            I have some limited experience with Visual Basic from years gone by. I don't know how well I might be able to complete assignments using this, but I do feel fairly competent as an amateur when it comes to the logic behind programming.

6.   Tell me about the math professor or teacher you have had who was the most and/or least effective.  

             One professor I quite enjoyed was Professor Williams from the Mathematics Education department. I felt he was able to teach the material very well and also was very interested in how well we learned it.

7.   What did s/he do that worked so well/poorly?

             I've had a lot of instructors that I really liked, and only a couple that could have helped me more. In each of these cases, though, I feel that the most prevalent reason was that the professor either did or did not show me that they cared about me learning the subject matter. If they would open themselves up to the class and made themselves approachable while requiring that the material was mastered, I did quite well. On the other hand, those who didn't really want to be there passed that sentiment onto me.

8.   Write something interesting or unique about yourself.

            I have a lot of interests. I really enjoy things like reading, cooking (especially the eating afterwards), and pretty much all sports. Hopefully this helps make me a more rounded person.

9.   If you are unable to come to my scheduled office hours, what times would work for you?

            I may not be able to make the given office hours. If this is the case, I could make it during the hour directly afterwards.

Just some stuff for fun to start...

This explains why Eve became the way she did. I guess here enhanced capabilities as a machine really helped her crack the code.