Assignment 12

• How long have you spent on the homework assignments? Did lecture and the reading prepare you for them?

Personally, I tend to spend 1-2 hours on my homework assignments.  Lecture has been my biggest preparation for homework assignments, though in the last couple of assignments, the book has been more of a help.  I was able to look up the things I didn't understand in lecture and apply them in the homework.

• What has contributed most to your learning in this class thus far?

Honestly, I would say the homework has contributed the most to my learning.  I usually understand the lecture, the reading is decently comprehensible, but when I get to apply it in the homework, things make much more sense.

• What do you think would help you learn more effectively or make the class better for you?

The one thing I can think of is more example problems in class.  I know when we work on problems in class, or split into groups like we did for the substitution cipher we did on the first day of class, I understand the material better because I'm able to apply it.  However, I do understand that time may be an issue in putting that into practice.

Assignment 11

I have never worked with fields before, so this whole discussion about Galois fields was pretty crazy to me. The definition of a field makes sense to me, though.  I'm struggling with seeing how the Euclidean Algorithm will work on these binary polynomial fields, but I suspect as I work with them more, I'll figure them out.

It was good to finally read a good discussion about a field.  Fields are things I've heard about in other math classes, but I've never had one rigorously defined for me.  I'm excited to learn more about fields, and how they apply to cryptography.  I'm worried my lack of experience with group theory might make things difficult, but I'm sure things will work out in the end.  This is getting interesting; the mathematics are definitely ramping up from what they've been before.

Assignment 10

It was difficult for me to understand OFB.  I understand that it is a way of implementing DES, but I don't get it.  I know it's good for error correction.  I didn't understand most of this DES section, but it was all very interesting.  The five methods of implementing DES were confusing to me, though it made sense that we would sometimes need to correct for messages that were not perfect multiples of the block length.

I did not realize how much computers have improved when it comes to an ability to do calculations.  It really shouldn't surprise me, just with all the graphics available, but it's amazing how much a well-programmed computer can do.

Assignment 9

Perhaps the most difficult part of this reading assignment was the proof at the end, where we proved that DES is not a group.  I didn't quite understand that proof, but I assume that is mostly because I have not taken abstract algebra yet.  In general, I understood the section, but barely.  I feel like I have a tenuous hold on what the text was trying to say.

What was quite interesting to me was actually the proof I didn't understand.  The last part of the proof, where they show that m has to be greater than 10^(277), thus making DES not closed under composition was very interesting to me.  The proof used mainly a numerical method to show a theoretical result, or at least that's how it seemed to me.  Perhaps I misunderstood the proof, which is entirely possible, but either way, the method for doing this proof was quite interesting to me.  There are definitely more ways to prove things than I had before imagined.

Assignment 8

I will be completely honest.  I didn't really understand this reading assignment at all.  Specifically, I had trouble understanding a linear feedback shift register.  I understand that it's supposed to be a fast form of encryption, but it did not make sense to me.

On the flip side, it was interesting to learn about the one-time pad.  I have heard a lot about this cipher, and have always wondered what makes it so unbreakable.  The concept is fascinating, and it makes sense why it is so hard to use and thus often not used.  I think a lot of the mathematics of the coming sections are about to get more interesting than the mathematics we have dealt with so far.

Assignment 7

This reading was a little more difficult than past readings.  Maybe it's because it's been awhile since I've taken linear algebra, but block ciphers just did not make sense to me.  Maybe it's because I didn't quite get how matrix inverses mod n work, but I think I'm getting there.  I can tell it has to do with finding the adjugate matrix, which I may have to review in order to figure this out.  But this looks interesting.

I liked learning about the Sherlock Holmes cipher, and the errors the author made in the dancing-man ciphertext.  I think that's a good warning to us, to be sure not to take our codes too lightly.  It can be easy to get too confident and mess things up.  Also, it reminded me of the code we had to break for homework, where in breaking one of the letters we found that the frequency of e in that string was actually lower than usual.  Things are not always what they seem in cryptography; that's what makes it such an interesting field of study.

Assignment 6

This sections was very interesting to read, though the methods of decrypting a Vigenere cipher are still a little fuzzy to me.  It makes sense how the cipher works, but the method of finding the key using dot products still doesn't exactly make sense to me.  I kind of get it, but it's a little confusing why the maximum dot product appears when the proper shift is found.

However, this code seems very usable to me.  It sounds quite familiar, actually.  I think it might have been used the movie "The Prestige" to encode a journal.  I'm not sure, though.  It makes sense now how a cipher can be developed that uses multiple keys.  In fact, encryption keys in general make a lot more sense because of this cipher.  I like it.  I kind of want to start sending messages with this cipher.

Assignment 5

Probably the things I least understood about the readings in section 2.1-2.2 was how the attack method of chosen plaintext and chosen ciphertext work.  The other methods of attack made sense, especially those in the affine section, since they were related to how one would find the equation for the line, given two points.  The only difficulty in the known plaintext method of attack for me was the problem that arose when there were two solutions, I didn't quite understand that method.

Section 2.4 was especially interesting to me, since it showed me the power of a properly used substitution cipher.  I would have never thought to use digrams to help crack a substitution cipher, but it makes so much sense to do so.  There is much more to cryptography than I realize.

Assignment 4: Guest Lecturer

This guest lecturer was actually not my first introduction to cryptography in LDS history.  A few years ago, I read a fictional novel called The Moroni Code, which discussed codes used by prominent church leaders.  The main code discussed in that book was the masonic code we discussed in class.  Still, it was enlightening to see the variety of codes that have been used throughout history.

It makes sense that such codes would need to be used, especially considering the persecution experienced by church leaders.  What was interesting to me about this lecture was how cryptography was used in the Doctrine and Covenants.  I had always seen the section headings that discussed unusual names, but never knew what said unusual names were, and whose names they hid.

In the current day, I wonder what codes the churches use.  I'm sure there are sensitive documents and messages that the church does not want to be intercepted and read.  Thus, the Church must still be using some sort of encryption system, if not more than one.

Assignment 3

The most difficult thing about this section for me is understanding the extended Euclidean algorithm.  The method for using the extended Euclidean algorithm was a little confusing to me.  I supposed if I had to practice using the algorithm it would make more sense.  But, the thing that bothers me more is I still don't fully understand why the extended Euclidean algorithm works.  I like knowing the proofs of things, oddly enough.  I like seeing why something works.

It was interesting to read more about number theory.  I had forgotten how much I love learning about greatest common factors and number theory in general.  Maybe I need to take a number theory class.  I remember working with number theory in a math education class, and seeing how different methods students used to find GCDs turned out to be mathematically correct, and the reasons behind the methods.  I don't think I will use the number theory used in this class much in my future professional life, but I know I will need to understand the number theory in this course in order to properly teach it to my future students.

Assignment 2

Probably the most difficult about this material was understanding how the proof of the theorem about ax + by = d, where d = gcd(a,b), works.  I know I have seen the proof before in 290, but the proof in this book for some reason isn't clicking for me, especially since the proof makes the theorem more general.  It makes sense to me that a and b must differ by a multiple of the gcd, but the proof seems to take a different route than I have before seen in proving this fact.

The part about primes was probably the most interesting to me because that was the part that I could understand the most.  The parts in chapter one about the basis for cryptography were interesting, but I wasn't quite sure how the mathematics would come into play, especially in talking about how the magnitude of the number n correlates to log(n).  The part about prime numbers and greatest common divisors reminded me about discussions we had in my first math education class about finding greatest common divisors and least common multiples.  For some reason, I found prime factorizations fascinating.  I was surprised by all of the methods for finding both the LCM and the GCD, especially in seeing how each method was related.  I'm curious to see if finding LCMs will show up in this class.

Assignment 1: Introduction

I am a junior at BYU studying math education.  Post-calculus, I have Math 290, Math 313, Math 314, Math 341, and Math 362 (Geometry).  I am taking cryptography to fill the Math Ed requirement for a higher math class and it sounded more interesting than the other available classes.  I also have some friends taking this class, which makes it nice.  I have no experience with Maple, Mathematica, or SAGE outside of using Wolfram Alpha.  However, I tend to be a fast learner.  In working on the first homework assignment, SAGE started to make sense to me.

A math professor that had a great effect on me was Dr. Pace Nielson, my Math 313 professor.  I think his effectiveness is best illustrateded by something he did after I was done with his class.  I ran into him while I was walking home from campus, and he asked me about my life and we just talked.  He still remembered my name and was interested in my life.  During his class, I could tell that Dr. Nielson wanted us to succeed.  He tried to make sure we as students could succeed while still challenging us.  His tests were not easy, but he always tried to make sure we were prepared for them.

Something interesting about me is that I am a proud member of the BYU Marching Band.  This is my third season with Cougar Band and I love it.  The Cougar Marching Band owns my heart every fall.  I love the camaraderie and the excitement of the band.  I especially love how the band director has the vision of the Cougar Band bringing people to Christ.  We don't play hymns all the time, but we seek to play with precision and accuracy so people can see in us disciples of Christ seeking to excel.

I can come to the office hours listed on the syllabus, though if need be Monday, Wednesday, and Friday at 10 am are also great times for me.