Exam Study Questions, Due October 1

Which topics and ideas do you think are the most important out of those we have studied?

I think that the most important ideas of those we have studied are the methods for making secure encryption systems and the reasons why the systems we have studied are, or are not, secure. To throughly explain why the systems are or are not secure, you need to understand how the systems work. This is a major chunk of what we have studied up until now since you will need to know the encryptions systems, functions, and also the underlying mathematics.

What kinds of questions do you expect to see on the exam?

I expect to see questions dealing with how some encryption systems work (especially Vigenere, Hill, and DES. Probably Rajindahl also.), different encryption modes and how to diagram them (and therefore use them) and decrypt from them. I defiantly expect to see some questions dealing with modular arithmetic, both involving integers and polynomials. To a lesser degree, I expect some questions involving ring theory (but not difficult ones as that is not the focus of the class) and maybe some "encode this" or "decode this" type questions, but again not difficult ones because we will have no resources but one small calculator and a pencil.

What do you need to work on understanding better before the exam?

I need to understand DES and Raindahl better, and I need to get the modes straight (I mix up CFB and OFB sometimes, and I forget the decoding procedures.) Otherwise, I feel pretty prepared.

Sections 5.1-5.4, Due September 29

Difficult: I found the key schedule algorithm particularly confusing, I would very much like an example of it. Most specifically, I am having trouble with the instance when i is a multiple of 4, the other instances actually are not so bad since they are just recursive. Also, the section never really explained the selection of the matrix used for MCT. Is there something special about that one, or could we use almost any 4X4 matrix with entries in GF(2^8)?

Reflective: The description of why the MC was left out in the final round made me laugh. They took almost a whole page justifying this decision, but all it really seems to boil down to is "one less step and it looks better". Really, I don't think it needs justification. I mean, this is a created system and leaving out the final MC doesn't complicate the procedure, so why should you justify yourself?

Class Evaluation Questions, Due September 27

How long have you spent on the homework assignments? Did lecture and the reading prepare you for them? I generally spend about two hours a week on homework assignments, though this latest one (assignment 4) is a bit more difficult. The lectures have helped me prepare for homework, mainly by showing me how to implement the methods shown in the book. The reading is excellent preparation for most of the homework. Also, though you didn't ask, the online decrypting tools have come in handy.

What has contributed most to your learning in this class thus far? Thus far I think that the reading itself has contributed the most to my learning. Lecture is helpful to round out things that I might have found a little difficult in the reading, but homework has mostly been a way to help me assess my understanding and decide what you think is important rather than a learning tool.

What do you think would help you learn more effectively or make the class better for you? I think that the current methods in class are aiding my learning just fine. The only thing I would change right now is the timing of posting reading assignments. I have missed two assignments not because I haven't been reading the book, but because they were posted at some time after I had checked on Friday, and so I did not know they were assigned for Monday. Maybe reading assignments could be posted further in advance?

Section 3.11, Due September 24

Difficult: I've had Modern Algebra already, so most of this section is review. I did get a bit lost following the discussion of LFSR Sequences in part 3.11.3. I think this arose from mixing in the linear algebra with the polynomial group. Truthfully, I think I have it worked out now though.

Reflective: Though this was a review for me, I feel it actually cleared up some Abstract Algebra for me. Galois fields have always been a struggle for me, but this section explained them differently than I have seen before and I think it helped me to get a better handle on what is going on.

Section 4.5-4.8, Due September 22

Difficult: I found the Cipher Feedback mode a bit difficult to understand, and along with that the Output Feedback mode, so apparently my struggle has to do with the part that is similar between the two. I think I do not fully understand how to get X_2 from X_1. It seems like we concatenate the ciphertext from encoding the first 8 bits onto the end of X_1, and then drop the first 8 bits from X_1 to obtain X_2. Am I understanding this right? If I am, then it seems that what we are doing with OFB is concatenation of the first 8 bits of X_1 to the last 8 bits of X_1, and then dropping the first 8 bits, to get X_2. That should be a cyclic process though, so it would seem undesirable.

Interesting: Section 4.6, about breaking DES was quite interesting. I think that now that a method has been found, then it will be a better idea for there to be a new standard rather than the triple DES that seems to be what the book favors. The book says there are just many more possible keys for a triple DES, but fails to take into account that technology is still advancing rapidly. What took many computers to do in the 90's can already be done with just one now, and processing speed and memory storage is still being increased.

Sections 2.9-2.11, due on September 17

Difficult: Wow! This was by far the most difficult section so far. If I had to pick a most difficult part, I suppose it would be section 2.11, about Linear Feedback Shift Register Sequences. I think the main problem started because I do not understand the equivalence describing the first relation. It seems to say that the n+5th term is given by adding the nth term to the n+2nd term, but then how do you find the nth term? The nth term would have to be the n+5th term minus the n+2nd term, but you haven't gotten those yet, because you are trying to get the nth term! Possibly this is the misunderstanding that carries over so that I do not understand the know plaintext attack.

Reflective: Earlier, I mentioned that I did not see how anyone could make a code that was "unbreakable". Now that the one time pad system has been explained, and I know a bit more, I can see how this would work. It seems that would be a great idea in general, but the great foil to the method seems to be the necessity of the courier to transport the one time use key. That is expensive (because you have to pay the guy) and dangerous (he could be intercepted). Other than that, it doesn't seem like it would be too hard to create a one time pad cipher. It seems to me that even with the weakness of random number generators and LFSR sequences, if you had one of these generate a key that was as long as your message and then used, say, a Vigenere style cypher, you would still not have enough patterns to mount an attack on your cyphertext.

Section 3.8 and 2.5-2.8, Due on September 15

Difficult: I didn't understand the point of the short section on ASCII. It seems like whether we use the "A=0, B=1, C=2...Z=25" method or ASCII to turn our letters into numbers, it is hardly different. The first method can be easily modified to include numbers 0-9, and so build any number we want, and also has been modified for various punctuation, according to the alphabet conversion applet. Maybe ASCII is useful just because not as many people are familiar with it? I also had some trouble with the decryption method for the ADFGX cypher. I would like to see that in action with an example.

Reflective: I've really enjoyed the substitution cyphers we have studied up to section 2.7, but it seems that the block cypher is indeed a better idea. The good thing about most substitutions, I think, is that they are very easy to understand. But block cyphers were not difficult to understand (with a little knowledge of linear algebra and modular arithmetic), and they are more difficult to break. It seems like a know plaintext or known cyphertext attack would be easier to prevent than a direct unknown cyphertext attack.

Section 2.3, due on September 13

Since we hadn't been assigned reading over the weekend before, I neglected to check the assignment site to see that this had been assigned. Really I had read this section earlier because I found it interesting. I'm going to blog about it despite the fact that I missed credit, just for completeness.

Difficult: When I first read this section, I found the cyphertext attack method difficult to understand. It seemed that they were only succeeding because they already knew the length of the key word. After the class discussion, I now understand how the frequency counts were used to good effect, showing how to find the length of the key word.

Reflective: I was fascinated by this cypher. It seems that it should be easily possible to modify this method so that the cypher is not so easily breakable. Possibly just giving messages in short pieces would be enough. My partner and I actually tried this as the code for our project, changing the shift cypher part to an affine cypher instead, and adding some more rules. I realize now that, should Eva know our method, then ours is only slightly harder than Vigenere's, since affine cyphers are only slightly harder than shift cyphers, but since then I've had some new ideas I'd like to see how to break based on this cypher. Maybe I'll write them up and attach them to this blog, if I have time later.

2.1-2.2 and 2.4, Due on September 10

Difficult: The most difficult part of today's reading for me was understanding the frequency analysis counting diagram idea in section 2.4. It seemed like they were successful in decoding the message mainly because of "lucky" guessing, or probably more because they were the ones who encoded it. I am still trying to follow the logic in this section. One of the hang ups I have is, what happens when the frequency is wrong? For example, the book mentions entire novels carefully written with no e's, couldn't a secret message be purposely written the same way? This would throw off the frequency analysis. Another example I noticed of frequency analysis being wrong was in our homework (number 3). The most frequently used letter there was t, not e.

Reflective: I was very interested in the use of affine ciphers. In particular, I enjoyed the discussion of using a known plaintext attack to decode them. The text said this could be accomplished with "a bit of luck", but the procedure it outlined seemed to show that you would have to have luck to hit letters that did not help you. As the text says "The...procedure works unless we get a gcd of 13 (or 26)". This seems really specific circumstances to me. I also enjoyed seeing the use of modulus, which has always seemed a mostly useless concept, to make ciphers.

Guest Lecture, Due on September 10

Difficult: Truthfully, I had trouble finding much of difficulty in the guest lecture. The codes the Mormons used seemed pretty simple, with the exception of Larrabee's cipher used by George Q. Cannon. The method of implementation for this code confused me in class, but when I read the speaker's notes (posted on the readings assignment site) afterwards it made perfect sense. Despite the author saying the code was the "most perfect ever invented", I couldn't help but notice that this code very strongly resembles the Vigenere Cipher presented in our book. The major difference seems to be that instead of having the key word represent a vector, you have to have the list to match the keyword with the code you want. This seems to be less secure to me, if you are using the list posted in the book that Larrabee wrote, then it only becomes a problem of discovering your key word. Possibly they used their own cipher keys.

Reflective: While the codes used by early mormons were not difficult to understand how to use, it was fascinating that they even had them! I had never heard of this before, nor did I know that there was research in this field. I had to wonder how one would go about decoding the telegraph cipher where words stood for ideas. I think that an outsider would really have no hope of deciphering such a message. I had also never heard of the "Deseret Alphabet" before, nor had my native Utahn wife. Why were they trying to make a new written language? The codes and their uses interested me. I also want to find out more about George Q. Cannon now. He sounds more awesome than previously imagined.

Difficult: The calculations used to find the a and b such that ax+by=d will be difficult to remember, even if they are just based on the Euclidean Algorithm. I believe this works because I can see it, but I do not readily see how it works. I think I can see the connection to the discussion of using primes to generate cyphers from chapter 1, but of course I am not sure. Would it be harder to find a and b if d is large? Or maybe if a and b are large? The examples work out quickly, thought the numbers involved are not small. How can we be sure to increase (or decrease) the number of steps in the Euclidean algorithm to increase (or decrease) the complexity of this calculation?

Reflective: Still using some ring theory, though I don't think I've ever used fractions in a modulus problem before. It's pretty interesting to me how that works, just interpreting the fraction as an inverse of some other number.