5.1-5.4, due October 2

Difficult:
     I think the most difficult part to understand was the mix columns and the key schedule. I'm not really sure why the mix columns is helpful other than it just reorganizes the columns differently. I also don't fully understand how the key schedule is made. The text seemed a little confusing of how they got each key. 

Reflective:
     It seems like this method is much more complicated than anything that we have looked at before. It seems pretty intense that for every 128 bits we have to do at least 10 rounds to obscure the data. I think this would be very time consuming if we had a decently long plaintext. I was wondering if all algorithms need to be longer in order to be more secure. 

Q & A, due Sept 30

• How long have you spent on the homework assignments? Did lecture and the reading prepare you for them?
• I generally spend between one and two hours on the homework assignments. Usually lecture and reading prepares me for the homework,  but some of the questions with more complex math I still have a harder time with. 
• What has contributed most to your learning in this class thus far?
• Lecture has definitely been the most helpful. The reading is pretty dry and usually somewhat difficult to understand.  
• What do you think would help you learn more effectively or make the class better for you?
• I think more examples during lecture would be most helpful. I think I really understand a concept a lot better once I've seen an example of it. I think going over some of the more difficult homework problems would also be helpful. 

3.11-3.11.2, due Sept 27

Difficult:
      I don't understand the need for the irreducible polynomials. I know what they are but I don't know why we use them, or what makes them important. It seems that just changing the mod changes which polynomials are irreducible and which ones are not. 

Reflective:
     It is interesting seeing where some of the math that we learned is actually useful. In some of the math classes I've taken it always seems that the math isn't used by anyone other than math professors. It's good knowing that the math we are learning is directly applicably to the specific field of cryptography. 

4.5-4.8, due Sept 25

Difficult:
     I didn't really get the Triple DES method. A longer key would make the cipher harder to crack so why don't we just use longer keys instead of using more than one key. It seems that it would be less expensive to use a longer key as opposed to using going through the entire DES method more than once. 

Reflective:
     I think it's interesting how cryptography algorithms have to get better as software and hardware improves. It seems that DES was broken mainly using a brute-force method. They had to check a lot of keys before they found the right one. I wonder if there will come a time when cryptography can't quite live up to increasing hardware and we have to resort to something else. 

4.1, 4.2, and 4.4, due on Sept 23

Difficult:
     I didn't really understand how the expander function worked. It makes sense that it scrambles the data up more and makes it a harder to decipher. I'm not quite sure how we input the 6 bits and get 8 bits out. I don't know where we got the S-box from. I know how it works but I'm not sure who decided what the S-box was filled with. 

Reflective:
     So I learned about AES in my Computer Security class this semester. It's interesting how differently it's explained in the different ways. I think it made more sense in the Computer Security class because it was a much more formulaic approach it seemed. 

2.9-2.11, due on Sept 20

Difficult:
     I would like a bit of clarification on pseudo-random number generators. Some of them seemed to make a lot sense while I wasn't really clear what the others did. I also got lost on the linear shift register sequences. I understand how it requires you to have less bits in advance I was unclear as to how the proofs that were in the book completely applied to the actual encryption of the data.

Reflective:
     I think it is interesting that we actually have a cipher that is unbreakable. The OneTimePad Cipher seems so simple it's a bit hard to see how it can be so good. It makes sense that we can't really use it in practice as much because of it requires that your key be as long your text which is reasonably unfeasible if you want to encrypt something very long.

3.8, 2.5-2.8, due on Sept 18

Difficult:
     I don't think I really understood how the Playfair Cipher works. I think it's interesting that we first change the plaintext into different plaintext before we actually encrypt it. I'm not great with matrices so that will take some practice to really understand that. I just have to get used to matrix operations again.

Reflective:
     I think it's amazing that as technology has increased we've been able to come up with better and better encryption methods. Even in WWI there encryption methods weren't at all difficult compared to some of the encryption methods we have now. With the power of the computer we are now able to do so much more encrypting and decrypting quickly that our ciphers can be much more complex.

Guest Lecture, due on September 11

Difficult: 

     I think the most difficult part would be understanding how people didn't break these codes more easily. A lot of the old ways to encode were fairly simple and it seems today would easily have been solved. I suppose it is a pain to have to try and figure out some of the substitution ciphers but still  be possible. I suppose it seems that if someone really wanted to break the cipher they could have.

Reflective: 

   I think it is really interesting how some people wanted to use codes but some did not. Today, I think we are much more likely to want to do cipher things because we care much more about security. In the past they also just had less things they would need to encode. Today we have much greater access to private documents and with more access we need better security and so we want to encode things. 

2.3, due on September 16

Difficult: 

     Although I think I understand the Vigenere Cipher pretty well and how it works, I didn't' really understand how we could guess the key length. It did say that it was just a best guess. It seems by increasing the key length it would make the encryption that much harder to break. However, I guess you don't want the key length to be comparably sizable to the text itself.

Reflective: 

    We essentially used the Vigenere Cipher for our project. I just made up the algorithm before I read this chapter but I think it is funny how when I wanted to come up with a simple cipher it is so similar to another cipher that has already been done. I think that is partly why cryptography can be so difficult because it's difficult to create something that is completely new because cryptography has been around for so long. 

2.1-2.2 and 2.4, due on September 13

Difficult: 

     I don't really understand the affine ciphers. I understand that it is to strengthen the key but I don't get really how it works. The substitution ciphers and shift ciphers are logicial but I don't understand the math behind the affine ciphers that makes it different.

Reflective: 

    I thought is was interesting how long people have been using ciphers. In today's world we don't think much about it when something is encrypted. But I think that is mostly because we are so used to computers today. Computers have drastically changed how cryptography works because of things being accessible and just pure computing power. 

3.2 and 3.3, due on September 9

Most Difficult Part of the Reading:
     I didn't understand the working with fractions and modulo. I'm not really clear of when we should use fractions and when we shouldn't use fractions. I would also like some clarification on the Euclidean Algorithm and some examples. I don't quite get how we used it for inverse and modulo. 

Something Reflective:
    I think it is interesting how we use modulo in order to avoid using to large of numbers. We want to limit the space that it would take up on a computer and also make problems easier to solve. Other than those two reasons I'm not sure why we use modulo as much as we do. 

1.1-1.2 and 3.1, due on September 6.

Most Difficult Part of the Reading:
     I had a difficult time understanding the proofs behind the Prime Number Theorem. It makes since that all positive numbers are made up of prime numbers and I've been taught that often. I understand the proofs on a logical level that makes them believable but the actual lemmas of the proof were difficult to follow.

Something Reflective:
    I thought the most interesting part of the material was the discussion about public key encryption. I have learned a bit about RSA in one of my CS courses but I look forward to getting a better understanding of how it works. I also thought the discussion about making an encryption process that not only pays attention to how difficult it is to crack but also how quickly it can be done so it isn't burdensome.

Introduction, due on September 6

• What is your year in school and major?
• Senior, Computer Science
• Which post-calculus math courses have you taken?  (Use names or BYU course numbers.)
• Math 313
• Why are you taking this class?  (Be specific.)
• I need one more class to get a math minor and this class seemed like it would be most relevant to my field and could be helpful if I went into computer security. 
• Do you have experience with Maple, Mathematica, SAGE, or another computer algebra system? 
• No, but I have coded with Jave and C++ quite a bit so using code to solve math isn't too bad. 
• Programming experience?  How comfortable are you with using one of these programs to complete homework assignments?
• I am a senior in computer science so I can code in Java, C++, and C# decently well. I can probably use SAGE well enough for the purposes of the class. 
• 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?
• I had Professor Lang for Math 313. I like how he handed out typed notes because it was easier to follow the lecture without having to worry about scribbling everything down as fast as I can. I disliked how he didn't give partial credit on tests. If you had a small mathematical error that you couldn't find, which caused you to get the wrong answer, you immediately lost 75% of the points for that problem even though you knew how to do the problem. 
• Write something interesting or unique about yourself.
•  I speak the African dialect of Twi. 
• If you are unable to come to my scheduled office hours, what times would work for you?
• After 4 pm Monday through Friday are the only times I have available.