Poll, Sept 30

• How long have you spent on the homework assignments? Did lecture and the reading prepare you for them?
  I probably spend between 30 minutes to an hour actually solving the problems. Sometimes I feel like typing them up in latex or what have you, so presenting it takes a little bit longer. I'd say that the reading gives me a first pass at the information we learn, and then the lecture is rather important in solidifying those concepts (I'm thinking of DES right now...). Together, I feel prepared.
  
• What has contributed most to your learning in this class thus far?
  I'd say the book. See above for more explanation.
  
• 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 get better at the blogging on time. (I forget until its too late and then don't think I'll get credit, so I don't even try.)

§ 2.3, due Sept 16

This section dealt with the Vigenère cipher. Basically, it partitions the letters into their position (mod n), and performs a caesar shift on each of the groups of letters. We discussed how to defeat this method of encryption.

1. (Difficulty) I was a little hazy at first why a vector (representing the distribution of letters in the English language) dotted with itself is higher than a dot product with a "displaced" version of it:
   After thinking about it for a bit, I am satisfied with the explanation of the book. Perhaps I should show more it rigorously, but this is okay for me for now.
2. (Reflective) I liked the "second method" for breaking the Vigenère cipher. It is more algorithmic and a little less exciting than figuring out by hand how much of a shift the letters had. However, I was trying to think of a similar kind of method earlier.An analogy is having a broken piece of pottery or something. Two small pieces can be placed together in many ways, but by shifting them for a while, you finally find a "sweet spot" where they fit snugly. So it is with this cipher—the distribution of letters in the ciphertext and the English language will fit nicely (i.e. have a large dot product) when you find the right shift of the letters.

Guidelines for Blog Posts

This is for personal reference, as I can't find the syllabus anywhere, and having it here is helpful.

1. (Difficulty) Answer the question "What was the most difficult part of the material for you?" Note that "nothing" is not an acceptable answer. If nothing challenges you, then you should think about the material at a deeper level and generate some honest questions.
2. (Reflective) Write something reflective about the reading. This should be the answer to the question "What was the most interesting part of the material?" or "How does this material connect to something else you have learned in mathematics?" or "How is this material useful/relevant to your intellectual or career interest?" or something else.

The blog posting is due by 11:59PM on the day before lecture, so you should really get on it peter.

§§ 2.1-2 and 2.4, due Sept 13

My difficulty with the material: In 2.4, about substitution ciphers, there is a lot of (slightly boring) frequency analysis. It seems rather similar to the breaking of the code in the first day of class. I think it is interesting, however, that they talk about digrams (pairs of letters) and their frequency as well.

Reflective: I was trying to come up with some way of codifying a subset of the substitution ciphers (for this group project due today), but couldn't come up with anything past caesar shifts. Having read the section about affine ciphers would've been helpful. Ah well.

However, there has to be more ways to represent subsets of the 26! substitutions. However, they will all break in the same way due to frequency analysis.

§§ 3.2-3.3, due on Sept 9

My difficulty with the material: this is pretty standard number theory stuff that I've encountered so far (extended euclidean algorithm and modularity, etc&). I guess the hardest part is paying attention to how to keep track of the quotients and coefficients that yield \(ax + by = gcd(x,y)\). On some level I know how this works, but I have to re-figure-it-out every time including doing the reading just now.

The most interesting part, I guess, has to do with them mentioning quadratic residues. I don't know too much about it, but I wonder how hard it is to solve higher degree polynomials \(\pmod n\).

Mathjax test $x^2$ \(x^2\) \[x^2\] $$x^2$$ `x^2`. okay just imagine these worked up above, until I figure it out.

§§ 1.1-1.2, 3.1

My reading summary of Introduction to Cryptography with Coding Theory

I'm not entirely sure what to write here.

Section 1.1

Public key encryption sounds interesting. The book mentioned that it is based off of "hard questions" of math. Why? I guess we'll see.

How do we distinguish between the key and the encryption method? I sortof intuitively understand, but is there some kind of definition?

Section 1.2

The four main objectives of cryptography:

• Confidentiality (passing messages without "Eve" understanding)
• Data integrity (Bob wants to check that Alice's message arrived correctly)
• Authentication (Bob wants to check that Alice indeed sent the message)
• Non-repudiation (we'd like to prove to the world that Alice sent this message)

Section 3.1

A (re-)introduction to number theory. We covered divisibility, primality (and the approximate rate of primes), factorization, and the gcd. 

Friday Sept 6 (administrivia)

Hi Dr. Jenkins (plus the internet)

Here's my blog. its for BYU Math 485 homework.

• What is your year in school and major?
• I'm a junior, going for a Math degree.
• Which post-calculus math courses have you taken? (Use names or BYU course numbers.)
  Hmmm...
• Multivariable Calculus
• Linear Algebra
• 290 (Fundamentals of Math)
• 334 (ODE)
• 371/2 (Abstract Algebra I/II)
• 341/2 (Analysis I/II)
• 352 (Complex Analysis)
• 451 (Linear Topology)
• Why are you taking this class? (Be specific.)
• Hmmm. sounded interesting, counts as a math class. generally want to knwo about the subject material.
• 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?
• Hmmm... I used Matlab some time ago, but otherwise have no experience. I've programmed quite a bit, as my summer jobs for the past two years, and just on my own. I think I'll be fine.
• 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 so well/poorly?
• Its a little late right now and this is beyond my ability to analyze.
• Write something interesting or unique about yourself.
• I once fit 12 grapes in my mouth. This is not that impressive of a feat, but I did count them.
• If you are unable to come to my scheduled office hours, what times would work for you?
• 无