3.4-3.5 due October 1

The most difficult part of the reading was trying to figure out how to actually do examples using the Chinese Remainder Theorem.  Seeing one or two in class would be super helpful.  The theorem and the proof are not that bad.

I really liked seeing how modular exponentiation can be used to find congruences for a massive power of 2 mod some number, without ever using a very large number.  It's just a really neat mathematical "trick", and I'm guessing one that will come in handy when we discuss the RSA algorithm.

Questions about the exam, due September 28

• Which topics and ideas do you think are the most important out of those we have studied?
• I think the most important thing to know for the exam will just be to have a general idea of how each of the encryption algorithms we have discussed work.  This might seem obvious, since it's the core focus of the class, but this will the first thing I study for the exam.  I want to be explain simply to myself how each of the encryption and decryption algorithms work.  Also, I will make sure to study the ideas of number theory we have covered thus far, especially properties of modulo arithmetic and the Euclidean algorithm.
• What kinds of questions do you expect to see on the exam?
• I expect there will be computation questions dealing with modulo arithmetic, such as finding the inverse of a number (mod n) or solving equations involving modulo arithmetic.  I also expect there will questions where I will be required to correctly implement certain encryption algorithms, as well as questions where I will have to decrypt simple messages by hand.  Basically I expect the exam to lean heavily toward computation and algorithm implementation, as well possibly some basic proofs of theorems from number theory.
•  What do you need to work on understanding better before the exam?
•  I think the concepts I understand the weakest are finite fields, LFSRs (how to generate and decrypt them), as well as the DES and AES algorithms.  Otherwise I feel  fairly confident in the material that we have covered thus far.

5.1-5.4, due September 26

Rijndael has a pretty involved algorithm, but I felt like I understood the encryption algorithm well enough.  I think the most difficult part to understand was certain aspects of the decryption algorithm, and how to invert some of the processes from the encyption algorithm.

I was glad to see that the authors mentioned others algorithms that were submitted as replacement standards for data encryption.  I would be interested to look them up and see how the algorithms work.  I also found it interesting that Rijndael is vulnerable to certain attacks up to six rounds, but that any amount greater than seven has no known attacks.  Adding rounds to the encryption seems simple, but apparently adds a lot security to the system.

Questions, due September 24

I have spent on average about 4 hours on the homework assignments.  The reading and lecture have been preparing me to work on the assignments, but I just haven't putting in enough effort to work on them.  Also going to Chris's office hours would really help me.

I think the examples are the most helpful thing we do in class.  I understand the algorithms that are part of our reading assignments well enough, though a little extra explanation in class helps, and then actually going through examples is VERY helpful.

I think the things I need to do most are just not procrastinating the homework assignments, and going to office hours to get help on the homework. 

3.11, due September 21

I felt the most lost in this reading when the authors were explaining the application of finite fields to LFSR sequences.   

This section was a good review for some material from abstract algebra.  Just like the authors, I found the analogous relationship between integers mod a prime and polynomials mod an irreducible polynomial to be pretty remarkable.  If I learned that in 371, I did not remember it.

4.1-4.2,4.4, due September 17

The most difficult part of the reading, which also happened to be a big part of the reading, was the overview of the DES algorithm.  I just don't think I followed it very well.  A slower walkthrough of the algorithm would definitely be helpful.

The most interesting part of the reading was the part about how DES is not a group.  I enjoy abstract algebra, so it was interesting to see how abstract algebra can be applied to a consideration of the DES algorithm.

3.8 and 2.5-2.8, due September 12

The most difficult part of the material covered in these sections was probably just the concept of inverting a matrix mod n.  I've never really considered modulo arithmetic for anything other than integers, so the reading definitely expanded my understanding of the power of modulo arithmetic.

Something in the reading that I found to be quite interesting was the introduction of block ciphers, and the way in which they add complexity to the encryption of a plaintext message.  This is evident from the fact that changing one letter in the plaintext will result in a change of n letters in the ciphertext (depending on the size of the blocks of text, n).  Since the use of blocks of size greater than 3 is resistant to frequency analysis, this method can be much more powerful then substitution or Vigenere ciphers.  It's a pretty simple method in the context of today's methods, but it laid the foundation for powerful ciphers such as DES, AES, and RSA cryptography.

2.3, due September 10

I like the Vigenere cipher more than the other "primitive" methods of encryption that we've talked about thus far.  It seems to be a little more robust, since it requires both frequency analysis, as well as some vector algebra to be broken.  The fact that one has to determine the key length as well as the shifts of each character in the key seems to add a little bit more to the strength of the method, though I'm sure it could be broken easily by a computer nowadays.  The second method of finding the key is a little hard to follow at first, but the summary at the end of the section made it much easier to understand.

2.1-2.2, and 2.4, due September 7

Shift ciphers and substitution ciphers were simple enough to understand, but I had never encountered an affine cipher before.  The principle behind it seems simple enough, but I think I'll just need to work out a few examples to better understand the way to encrypt and decrypt it, as well as how to attack it.  These are really simple methods of encryption that are really easy to break now, but they're interesting to me in a historical sense, since these seem to be some of the oldest methods of encryption.  This is evidenced, for instance, by the fact that Julius Caesar was purported to have used the shift cipher.

Guest Lecture, due on September 7

The lecture wasn't all that difficult to understand, considering most of the techniques of cryptography used by people in the early days of the church were fairly simple.  Though I was really glad to finally see what the actual code names used in those certain sections of the D&C were.  I have wondered about that for years.  I also had never heard of the Deseret alphabet, which I think is a very interesting fact about church history.  I think overall the lecture just helped me to understand that in any group or culture where secrecy of information is needed, cryptography will be useful.