7.2 due November 1

1. I was a little confused about the equation we were given where b = a^x, and a^(p-1)=1(mod p) implies that a^(p-1)/2 = +- 1(mod p). why is this true? Was it a rule we learned already? I can't remember if it was or not.
2. Reflectively, I was wondering to myself how they come up with these names for different methods. At the beginning of the chapter, it talks about the important birthday attack. Really? Who comes up with this? Before we had Rijndael and LUCIFER. I know they usually mean something specific, but I am pretty sure in some cases, like LUCIFER, they will change around words so that it will become that anagram.

6.4.1 and 6.4.2 due October 28

1. In 6.4.1, they start showing us a relation 17078^2 = 2^6 * 3^2 * 11 ( mod 3837523) gives the row 6,2,0,0,1,0,0,0. Where did this "row" come from? I know in the book it says each base gives a row in a matrix where the entries are the exponents of the primes, but it still feels like they just got these out of thin air.
2. A couple homeworks ago, we had to find x^2 = y^2(mod n) and x ≠ y(mod n). I had a hard time with that homework, and i think I actually just gave up on that specific question. This section really helps explain a little more to me at least how to come up with those numbers. I was just so confused before and couldn't even think of how to do that problem.

6.4 due October 25

1. I guess I am still a little confused when it comes to this kind of stuff because a lot of it all the sudden is "often we use this - choose random this - go until you decide to stop" I know that it is because of how difficult everything is, but I am just so used to math being exact always. How will I decide when I should stop?
2. It's a little crazy how hard it really is to factor large primes. In this age of computers, it surprising th think that it really is an issue. I feel like I just grew up thinking computers could do anything you wanted. The book mentions a quantum computer being used to help factor primes quickly. I am pretty sure that is what everyone thinks they have done at the NSA facility here in Utah. That would definitely be interesting if they had.

6.3 due October 23

1. I was a little confused with the Miller-Rabin Primality Test. Near the end of the test, we are told to continue finding new b's until stopping or reaching b k-1. I don't know where the k came from. I am pretty sure they are just saying to stop after a while, but maybe I'm wrong. It just feels like they came up with a k out of nowhere.
2. We learned about pseudoprimes a long time ago in my number theory class, but I definitely liked how this book described it more. It was way more obvious what they were in this text, while in my other text I was pretty confused. It's funny how some stuff is easier in this book, while other material makes sense in the other book.

3.10 due October 20

1. I already learned about this in my number theory class. I think the only thing was was confusing me when I first learned about it was when we were going from a big number to a small number, like for example (9|24). When you flip it, sometimes the examples given were (24|9) and others were -(24|9). How do we know when it is negative and positive? I kept messing it up sometimes.
2. I really like taking this class and number theory at the same time because the classes are very similar. It is nice because number theory shows more just the basic theory and proofs of what we are given, and cryptography uses them for more specific and "real life" examples. I T.A. for a college algebra class, and that's the question I get over and over, "Will we use this in real life?" I just tell them I'm still in college and not real life yet. But I am happy I am taking a class that I will hopefully use in real life.

3.9 due October 18

1. I wasn't too confused with this section because I already went over this in number theory. But, I was wondering why we had to use p = 3(mod 4) for our prime in the proposition. Is it because of something specific? I've seen it a couple times, but I don't know why it works.
2. It's interesting to see after going back and forth from chapter 3 to chapter 6 how they are building us up for RSA. They mention in this section about how we choose n=pq, and I think about how we are using that already! I think this means stuff is going to get a little harder in RSA!

6.2 due October 15

1. One thing that was taking me a lot of time to understand was the Low Exponent Attacks. They were trying to show if d<(1/3)N^(1/4), then d could be calculated quickly. They then go on to prove this, but it was super confusing with lots of different integers, roots, and powers. I think it was just looking really abstract to me, so it wasn't making much sense.
2. They mention in the book that these attacks to RSA are more because of mistakes. It made me think of what happened to Adobe recently. They were hacked, and the hackers got a bunch of account and credit card information. I don't know if they use RSA or something else, but I was really surprised to hear that a high up company like that getting hacked. I wonder if they just made a small mistake that allowed hackers to exploit, or if they were super super lucky.

6.1 due October 11

1. RSA seems pretty straightforward compared to stuff we've learned previously like DES. I think the only thing I wasn't following was why we had to make sure de = 1(mod(p-1)(d-1)) and 1 = gcd (e, (p-1)(q-1). But I'm sure its just so that it's actually easy do decrypt for Bob.
2. Like I said before, I am just happy this isn't quite as complex as DES. That section killed me. This seems easy, which makes it seem like it should be easy to attack, but I'm sure it's not. I was blown away  by how big the primes are though, 100 digits! That's crazy! I just hope we don't have to use super large primes for homework!

3.6-3.7 due October 9

1.  The Three-Pass Protocol was a little complex to me. I understood the nonmathematical example that they give to demonstrate how the Three-Pass Protocol worked, but when we got to the real math, I was barely grasping it. I think it was mostly just the different K1, K2 and K3. Is that a new K each time? How does that give us the real K? I think that maybe it just doesn't make too much sense because we don't have plaintext or ciphertext, just K.
2. Everything but the Three-Pass Protocol is stuff we just went over in my Number Theory class. I actually feel that this book does a better job at explaining it then my Number Theory book or professor does, which is kind of sad. But I like that these sections have been a little similar to each other so that I can understand everything a lot better. It's like taking 2 hours to understand 1 hour of stuff!

Review due Oct 4

• Which topics and ideas do you think are the most important out of those we have studied?
• I think the most important topics were the DES and chapters beyond that, since they seem the most applicable to "real life". It is something I expect to see more of if I get a job that uses cryptography.
• What kinds of questions do you expect to see on the exam?
• I am expecting that we will have to solve basic cyphertexts that can be done by hand. Probably coding and decoding for the different types of systems we learned.
• What do you need to work on understanding better before the exam?
• During the last part of this unit I was super busy with some family issues, so I think that I need to review DES and the last two units we went over before the test. I just struggled trying to do the homework and didn't have time to get help so I think reviewing the last couple chapters and the harder concepts will do me well.