Section 6.3, due 20 October 2010

What was the most difficult part of the material for you?

Starting with the Miller-Rabin test, I couldn't really make sense of the material at all, even after reading it several times....

What was the most interesting part of the material? How does this material connect to something else you have learned in mathematics? How is this material useful/relevant to your intellectual or career interests?

It's interesting that we can prove that something's composite without actually factoring it.

Section 3.10, due 18 October 2010

What was the most difficult part of the material for you?

I thought the point of the symbols was that they tell you whether or not a is a square mod n, but it turns out they don't always?

What was the most interesting part of the material? How does this material connect to something else you have learned in mathematics? How is this material useful/relevant to your intellectual or career interests?

I thought the whole thing was gross. Maybe part of it is that I'm trying to do too much of the reading in one sitting and I'm just getting sick of it, but I'm getting married on Thursday, and I'm really not going to have any other time to get this done.

Section 3.9, due 15 October 2010

What was the most difficult part of the material for you?

I'm not sure I understand why finding the solutions to x^2 = y mod n allows you to factor n, or how you actually find the square roots of a number mod a prime. Is it + or - y^((p+1)/4) mod p?

What was the most interesting part of the material? How does this material connect to something else you have learned in mathematics? How is this material useful/relevant to your intellectual or career interests?

I think it's interesting that finding square roots ends up being related to factoring, even if I don't really see how it works.

Section 6.2, due 13 October 2010

What was the most difficult part of the material for you?

I thought the entire section was kind of difficult to follow, but especially the timing attacks. I don't see how knowing the total time it takes to decrypt a message would let Eve know whether a bit in the binary representation of d was 0 or 1. And sometimes my computer at least will decide to be really slow for a little while, so it seems like that would invalidate that sort of attack.

What was the most interesting part of the material? How does this material connect to something else you have learned in mathematics? How is this material useful/relevant to your intellectual or career interests?

I think it's interesting to see that there are attacks on all of these encryption systems that people use. It makes me wonder if, in practice, there are a lot of encrypted transmissions that could be broken but most of the time, no one bothers.

Section 3.12, due 11 October 2010

What was the most difficult part of the material for you?
I thought the section was fairly straightforward in terms of how to calculate the continued fractions, but I'm not sure I see how this will be useful exactly.


What was the most interesting part of the material? How does this material connect to something else you have learned in mathematics? How is this material useful/relevant to your intellectual or career interests?
I thought it was cool that we got the quotients obtained from using the Euclidean algorithm to find the gcd of 12345 and 11111 in finding the continued fraction.

Section 6.1, due 8 October 2010

What was the most difficult part of the material for you?
I didn't really have any trouble with any of the material because I've written a paper with a several page section describing RSA.

What was the most interesting part of the material? How does this material connect to something else you have learned in mathematics? How is this material useful/relevant to your intellectual or career interests?
I like the idea that we can make all the information about how to encrypt a message publicly known, but it doesn't help an attacker decrypt the message at all.

Sections 3.6-3.7, due 6 October 2010

What was the most difficult part of the material for you?

I had to read the description of the Euler-phi function and Euler's theorem a couple of times, but I think it makes sense now.

What was the most interesting part of the material? How does this material connect to something else you have learned in mathematics? How is this material useful/relevant to your intellectual or career interests?

I thought the three-pass protocol was interesting, and it really helped to have the locked box example in understanding how the math works.

Sections 3.4-3.5, due 4 October 2010

What was the most difficult part of the material for you?

I'm not sure I quite understand how to split up a congruence mod a composite number into congruences mod primes (or powers of primes).

What was the most interesting part of the material? How does this material connect to something else you have learned in mathematics? How is this material useful/relevant to your intellectual or career interests?

I thought it was cool that we can find ways to raise a number to a power mod n without actually having to multiply it all out and then reduce mod n.

Test Review, due 1 October 2010

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

I think the chapter on AES was probably the most applicable to real life because that's the only cipher system that's still in use (we even learned to break the rest of them besides DES, which just needs the chips mentioned in the textbook), but it's good to have a solid background on classical cryptography and how to break it so we appreciate modern cryptography and have an idea of how it might be attacked.

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

I think we'll probably have to decrypt some classical ciphers--I hope not a Vigenere or one time pad used twice because that would be time consuming to do by hand, and the online applets are much more fun--and maybe implement a simplified DES or AES and/or give some definitions.

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

I think I understand everything from chapters 2-5, but I need to make sure I remember what everything is and how to use them, and maybe get a bit faster at figuring things out.

Sections 5.1-5.4, due 29 September 2010

What was the most difficult part of the material for you?

I read the stick figure explanation first, and it made the textbook a lot easier to understand. I'm a little fuzzy on exactly how the s-boxes were constructed, and what InvAddRoundKey is exactly, but I think I have the general idea anyway.

What was the most interesting part of the material? How does this material connect to something else you have learned in mathematics? How is this material useful/relevant to your intellectual or career interests?

I really liked the stick figure explanation--it made the material a lot less intimidating, and it reminded me of xkcd. :)

Reflection, due 27 September 2010

I didn't see the new reading assignments before I left campus Friday afternoon, and I'm still trying to get the internet set up at my apartment.

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

I usually spend about three to four hours on the homework assignments. The lecture and reading prepare me fairly well, though there have been a couple questions that we discussed the theory behind, but then I wasn't sure how to actually apply it, particularly the question on the most recent homework about finding two plaintexts that encrypted to the same ciphertext. I knew that the reason there would be problems was that the determinant of the matrix was 2, which is not coprime to 26 like it needs to be so the matrix could be inverted mod 26, but I wasn't sure how to go about finding two plaintexts that went to the same ciphertext, so I ended up kind of doing a guess and check sort of thing.

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

I think the homework has probably contributed most to my learning so far--it helps a lot to try to work problems out for myself, and I think the problems where we're decrypting an actual message are fun.

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

I really don't like that the blogs are due at midnight the night before class. If I do the reading too far in advance, I start forgetting some of the details, and I have to do it on campus or at a friend's apartment, so I'm usually either several days early or a little late, and I'd much rather do it in the gap I have between my 9:00 class and cryptography at 1:00, because then it's still fresh in my mind.

Section 3.11, due 24 September 2010

What was the most difficult part of the material for you?

I didn't understand the part about LFSR sequences at all. I'm not even sure what phenomenon from Section 2.11 they're trying to explain.

What was the most interesting part of the material? How does this material connect to something else you have learned in mathematics? How is this material useful/relevant to your intellectual or career interests?

I've taken Math 371 (abstract algebra), so I'm familiar with group (and field) theory, but it seems like it'd be a lot easier to just use fields with p elements instead of trying to make things work for p^n.

Sections 4.5-4.8, due 22 September 2010

What was the most difficult part of the material for you?

I thought the most difficult part of the reading were the cipher feedback (CFB), output feedback (OFB), and counter (CTR) modes of operation. The electronic codebook (ECB) and cipher block chaining (CBC) were pretty straightforward, but the last three took me some time to try to figure out, and I'm still not sure I see how CFB and OFB are different.

What was the most interesting part of the material? How does this material connect to something else you have learned in mathematics? How is this material useful/relevant to your intellectual or career interests?

I thought the sections about breaking DES and password security were interesting, especially that people weren't really sure that DES was secure for the last 10 years of its use and it could be broken in four and a half days by the last few years it served as a standard. I also think it's cool that people have thought about how most computer users actually choose passwords and try to make weak passwords more secure for them.

Sections 4.1, 4.2, and 4.4, due 20 September 2010

What was the most difficult part of the material for you?

I had some trouble understanding the proof about DES not being a group--that double encrypting with two keys was not the same as encrypting with a third key.

What was the most interesting part of the material? How does this material connect to something else you have learned in mathematics? How is this material useful/relevant to your intellectual or career interests?

I thought it was interesting that a lot of the structure of DES ended up depending on the technology available at the time, particularly the limits on how much information could be put on a computer chip.

Sections 2.9-2.11, due 17 September 2010

What was the most difficult part of the material for you?

Again, I had the most trouble with how and why decryption works (and/or how to break the system), this time for the LFSR sequences. I'm having some difficulty seeing how to set up the recurrence given some part of the key.

What was the most interesting part of the material? How does this material connect to something else you have learned in mathematics? How is this material useful/relevant to your intellectual or career interests?

I think it's cool that the one time pad is totally unbreakable, though it seems highly impractical since you need a secure way to send the key before you send the message, and the key is just as long as the message.

Sections 3.8, 2.5-2.8, due 15 September 2010

I forgot to do this yesterday before I left campus, and then my internet at my apartment was down and it was my birthday, so I didn't really want to come back on campus to do it, but I did the reading before midnight...

What was the most difficult part of the material for you?

I had some trouble following the decryption method/how to break the Playfair and ADFGX ciphers.

What was the most interesting part of the material? How does this material connect to something else you have learned in mathematics? How is this material useful/relevant to your intellectual or career interests?

I imagine this will probably be everyone's favorite part of the material, but I really liked the part about cryptography in Sherlock Holmes. I like Agatha Christie (particularly the Miss Marple books) better than Sherlock Holmes, but I still rather enjoy murder mysteries.

Section 2.3, due 13 September 2010

What was the most difficult part of the material for you?

I didn't understand *why* the first method of finding the key length works exactly. I reread the explanation several times and I'm sure I could use it, but I'm still not quite understanding why it works.

What was the most interesting part of the material? How does this material connect to something else you have learned in mathematics? How is this material useful/relevant to your intellectual or career interests?

I think it's interesting that using a Vigenere cipher makes the frequencies of the letters in the ciphertext close to 1/26, but once you've determined the key length and divided the message into parts, you still use frequency analysis (or something closely related to it) to break the cipher.

Sections 2.1-2.2 and 2.4, due 10 September 2010

What was the most difficult part of the material for you?

I think, of the three ciphers, the affine is the most difficult to understand, particularly as regards decryption, but on rereading that section, I think I have it now. As long as alpha is coprime with 26, the cipher will map every letter of the alphabet to a distinct letter of the ciphertext alphabet, making decryption possible.

What was the most interesting part of the material? How does this material connect to something else you have learned in mathematics? How is this material useful/relevant to your intellectual or career interests?

I thought it was interesting to see the most common digraphs, and which could be reversed (ER, for example) and which couldn't (TH).

Guest Lecturer, 8 September 2010

What was the most difficult part of the material for you?

I thought the deseret alphabet looked rather intimidating because of all the unfamiliar characters, but I thought it was kind of silly of people to try to use it to hide information when they'd published the key.

What was the most interesting part of the material? How does this material connect to something else you have learned in mathematics? How is this material useful/relevant to your intellectual or career interests?

I thought it was interesting that people hadn't found out who the unusual names were really in section 82 of the Doctrine and Covenants until so recently. There's kind of a fine line between writing down keys for codes in too many places (making it more likely that someone would find out the key) and not writing it down enough (and having people forget what the code actually means). I also thought it was cool that the early Saints used codes not necessarily for secrecy, but just to save money when sending telegrams.

Sections 3.2 and 3.3, due 3 September 2010

What was the most difficult part of the material for you?

I learned everything in these sections in Math 190 (or I guess it's 290 now?), so there wasn't really anything difficult for me, but I think I don't always use the extended Euclidean algorithm the most efficient way, so I think I'll try to see if I can streamline that so I can find inverses mod n more quickly. It also made me wonder if there was a better way to solve congruences with a power of x than just guessing and checking.

What was the most interesting part of the material? How does this material connect to something else you have learned in mathematics? How is this material useful/relevant to your intellectual or career interests?
I think it's interesting that you can have d solutions to a congruence when the gcd(a,n) = d (and d|b).

Sections 1.1-1.2 and 3.1, due 1 September 2010

What was the most difficult part of the material for you?

As the first reading assignment of the semester, I thought it was a pretty straightforward introduction to the material we'll be covering, but the part about the objectives of cryptography made me wonder if there is a system that fulfills all four of the main objectives and is still fast enough to be useful, or if people use different systems for different purposes.

What was the most interesting part of the material? How does this material connect to something else you have learned in mathematics? How is this material useful/relevant to your intellectual or career interests?
I think it's fascinating that we can have public key systems where everyone knows how to encrypt a message to Bob, and even know how to find the decryption key, but it's still not feasible to find the decryption key without more information.

Introduction, due 1 September 2010

What is your year in school and major?
Senior, Mathematics

Which post-calculus math courses have you taken? (Use names or BYU course numbers.)
Math 190, 214, 343, 334, 315, 316, 371, currently taking Math 352

Why are you taking this class? (Be specific.)
because I had to write a paper for English 316 about something related to my major, and I chose cryptography and became interested in the subject

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?
I don't really have any experience with those systems, but I have a TI-89 calculator, which can do a lot of the same things. I kind of know Java because I took CS 142.

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?
My Math 315 professor was very effective because he knew the material extremely well, and he was very patient in explaining it, and he was very approachable and was available to help with homework anytime he was in his office, which was most of the day.

Write something interesting or unique about yourself.
I'm getting married October 14th this semester.

If you are unable to come to my scheduled office hours, what times would work for you?
I can't come to your scheduled office hours, but I can come to the TA office hours.