8.4-8.5 & 8.7, due on November 2

The Interesting

I really liked learning about the Birthday Paradox. The entire time I was reading it I felt interested, I would have a question, and then the book would immediately after answer that question I had. I think I want to play the licence plate game in the car and test it out.

It was fun reading 8.7 because we talked about it in class today so it made sense. Hooray! 

The Challenging

To be honest, I understood the Birthday attack when they were using specific examples but it started getting fuzzy when they were generalizing the idea. I don't think I understand it as well as I could. However, I definitely understood them much more than I understood the section on multiple collisions. I read it three times and still didn't understand what was going on. 

8.1-8.2, due on October 31

The Thrilling

I was excited to see that this chapter heading was "Hash Functions" because the first thing my husband said when I told him I was enrolled in this cryptography class was something about hash functions. I had no idea what he was talking about, but now, I'm semi-knowledgeable! Plus, it's cool that they're used for digital signatures so all of my signatures on checks that get scanned are securely documented, but safe from being hacked into.

The Haunting (October 31... get it?)

I'm assuming that "array" means matrix...
So we learned how to get our Hash Function by XORing the different columns of the matrix (sometimes after rotations) but how do we use it? Is it supposed to be the one-way function we'd use in another system?

7.3-7.5, due on October 29

The Interesting

I think it's cool that there are machines with the sole purpose of deciding the validity of ElGamal ciphertexts and solving Diffie-Hellman problems. That seems pretty crazy, but I'm sure they're really important. Also, I like the Bit Commitment methods; they were pretty cool.  

The Challenging

I don't get how in the ElGamal Public Key Alice can send her pair (r,t) to Bob without them being intercepted by Alice. Everything else is so secretive and sneaky, but this isn't which makes me worry that it's not very secure. 

7.2, due on October 26

The Interesting

I thought the Baby Step, Giant Step section was really interesting and I was excited that I actually understood what they were talking about. It almost reminds me of a meet-in-the-middle attack where we start forwards and backwords then look for matches. 

The Challenging

This chapter was harder than most of the others for me to understand. I had a really hard time understanding what was going on with everything, especially with the introductory proof, the workings of the Pohlig-Hellman algorithm, and with the Index Calculus. In the index calculus, why are they substituting things into various congruences?

6.5-6.7 & 7.1, due on October 24

The Interesting

I think it's crazy that the time it takes to factor primes has gotten faster; technology and our factorization methods just improve! Also, I never would have guessed to try the words "squemish ossifage" so they definitely picked correctly. I think the idea of a trapdoor is really cool, and it's good that a requirement of it is that it's easy to do. 

The Challenging

I am so excited to be working with Discrete Logarithms because I've tried to work with them in the past on homework and didn't know how. I don't really understand how we're just supposed to know that 2^6 = 2^16 = 1^26 = 9 mod 11 (= is congruence....).

Also, I don't understand why it matters if alpha is a primitive root. 

6.4.1 & 6.4.2, due on October 22

The Interesting

I thought the Quadratic Sieve method seemed really cool. I like that it used matrices, and logically it seemed to make sense. 

The Challenging

Even though the book details how to pick the numbers for the quadratic sieve, I still don't really think I could come up with those numbers on my own. 

6.4.1 Introduction, due on October 19

The Interesting

I really liked the Fermat Factorization method. It made a lot of sense to me and I would like to try one out. I hope there's one of these on the homework.

The Challenging

What is a "Bound"? 

It was hard for me to understand how the p - 1 Factoring Algorithm worked (and why it worked). And if we have B!, wouldn't that be a huge number? So then why would p - 1 divide B!?

6.3, due on October 17

The Interesting

It's really weird to me that the Fermat Primality test is only quite accurate, rather than precicely accurate. The majority of the mathematics that I encounter is proved to always work, so I find it intriguing that we're working with something that has unpredictable results. 

The Challenging

The Miller-Rabin Primality test doesn't make much sense to me. I tried following the example, but I don't really understand why we do it that way. There's just been a lot of theorems about these unfamiliar concepts lately so I'm still working on keeping them straight so I can notice and understand why when they're applied and used. I much prefer the Solovay-Strassen Primality Test at this point because I at least understand mostly how it's done. 

3.10, due on October 15

The Exciting

When I first read the example of (6/11)(7/11), I couldn't figure out why (6/11) was -1, but then I was able to spend a minute thinking about it and was able to figure out why. Exciting to understand something new! Most of the properties in this chapter seemed to make sense which is very comforting. 

The Challenging  (dun dun dun)

I am ashamed to admit that I don't really understand the proof we did in class today about the primitive roots, and didn't realize that I didn't get it until I was looking at the proof in the book. 

I wish I could understand how the book calculated that nasty fraction! It seemed crazy the way they sequenced it. 

3.9, due on October 12

The Cool

I think it's cool that finding the factors of n is just as easy as finding the solutions of a square exponent. 

The Hard

For 5 mod 11, why is (p + 1)/4 = 3? I would think that 5 is our prime, so (5+1)/4 = 3/2, not 3. Then I thought that if p = 11, then (11+1)/4 = 3, but I'm not sure if I'm right.

Also, I don't really understand why 2 has no square root in mod 11 and why it matters if the number is negative or positive. 

6.2, due on October 10

The Interesting

I can't believe you can use continued fractions to factor n knowing only n and e. This baffles my mind because on the last homework problem for this week, I am decrypting an RSA problem and I know what everything is, but I still can't decrypt the message! Whoever came up with this is brilliant. I think the timing method is pretty neat too, but probably not as realistic in this class because we don't have that type of hardware to measure the timing. 

The Challenging

I can't seem to grasp the purpose of the first theorem in the section.

The book says that to guard against having a small m to put random digits at the front and back and then later someone can easily take the extra digits off. How will that person know to take off the digits when the whole thing is just some big long number?

To be honest, I don't really think I understood any of the procedures for breaking RSA just from reading the book. 

3.12, due on October 8

The Interesting

We just learned about this Continued Fraction algorithm in Math History. It's so cool for me to see it applied and I can't wait to see it applied to Cryptography. 

The Challenging

I don't really understand what the theorem on 103 is talking about. Is it there to tell when you've got a good approximation? 

6.1, due on October 5

The Interesting

- I am amazed that using the quadratic equation could yield p and q so easily. I don't think I would have ever thought to apply it in that way
- I loved the PGP method of encrypting emails. I never stopped to think about how the email messages were sent, I guess I just assumed they were sent in plaintext. Now that I think about it, though, this is such a cool and safe method and I'm glad that email companies do this. 

The Challenging

- I think I have a pretty basic understanding of RSA after reading this section, however, I had a hard time understanding how to figure out what d should be. It said to use the extended Euclidean algorithm, but with what?
- I don't particularly understand how to plug numbers into the different formulas on page 168 to get p and q because I'm having a hard time keeping all of the numbers straight. 

3.6-3.7, due on October 3

The Cool

I thought it was really  neat how they easily solved 2^53 and I would like to try that out myself. I think that if I tried it out a few times, that it might help me to understand Fermat and Euler's theorems better. 

I also thought it was cool that I didn't think I understood Fermat's theorem until I saw a few examples of it. It's nice to say that I understand how to use it, even if I don't understand the proof of it. 

The (really) Tough

How do we know that the Euler's function of 1000 is 1000(1-1/2)(1-1/5)? I completely didn't deduce how to solve that from the reading. I looked back a few times trying to see where they got that, and I couldn't find an explanation that made sense.

I also thought the proposition about Primitive Roots was really confusing, but normally these propositions tend to make more sense after class so I'm excited for my understanding after class tomorrow. 

3.4-3.5, due on October 1

The Interesting

I haven't ever seen the trick where 2^4 is congruent to 4^2 mod 789. I thought that was a really neat trick and I bet that will save me a lot of time in the future. It was really neat how we can find the exponents of large numbers using binary. 

The Challenging

I feel like the Chinese Remainder Theorem is familiar, but it wasn't just popping back into my head like the Extended Euclidean Algorithm did. I cannot see how the flow works in solving these, or how the steps given actually lead us to a solution. I think I could benefit from seeing a quick example in class.