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.