Section 16.1, due November 30

I thought that was a very good introduction to elliptic curves. I did not realize that the form for an elliptic curve was y^2=x^3+... They only showed a couple of graphs of what elliptic curves can look like. I know that they said that it only makes sense graphically in the rationals or reals, but could you show more example graphs of elliptic curves in class so we could have an idea of the different possibilities they can look like.

The book said that elliptic curves can be thought of rational points, reals, or even mod p. Can you have elliptic curves in the complex plane? The book did not mention that. Would the form still be the same as a standard elliptic curve and would it look the same, too?

Section 19.3 and blog, due November 23

I must admit I did not understand a lot of this. I even found the explanation on the blog kind of confusing. I did understand, though, that we need to find the period and then can use universal exponent factorization method to factor n.

I think that this is very interesting. For a while, before I learned about PKC I wanted to be quantum physicist. I really do want to understand this better and I am glad we will be going over it in class tomorrow.

19.1-2, due November 20

Quantum cryptography is pretty cool. It is definitely the future of cryptography. I hope that we get to learn how factoring works with quantum computers. It will be fun to see the light filters tomorrow in class.

This section didn't seem very difficult. I am sure that the specifics of it are a lot more complicated. From what I have read about quantum mechanics, there are a lot of things happening that just goes against all common sense.

Section 14.1-2,due Nov. 18

The idea of a zero-knowledge protocol is very interesting. You need to be careful that you don't inadvertently give away some information in your "proof." I definitely do not like the loose application of "proof" in this section.

While the concept is easy to understand, the application seemed a bit more complicated. I had some trouble understanding what 14.2 was doing. I understand that we want to do this process in the fewest amount of applications as possible.

Section 12.1-2, due November 16

I thought that this whole idea was really interesting. Before I read the section I tried to think of how one would go about solving the problem of letting any t people know that secret, but I could not think of one. But the method is so simple that it almost seems obvious afterward.

Nothing in these sections seemed that difficult and the implementation seemed pretty straightforward.

Test Review Questions

Which topics and ideas do you think are the most important out of those we have studied?
Probably discrete logarithms and how to factor big numbers, and hash functions to a lesser extent.

What kinds of questions do you expect to see on the exam?
I figure there will be questions on there asking about jacobian and legendre symbols. Maybe there will be stuff on how to use El Gamal.

What do you need to work on understanding better before the exam?
I understand how the El Gamal system works, but I am not for sure who sends what to whom and how to encrypt m and decrypt c.

Are there topics you are especially interested in studying during the rest of the semester? What are they?
I am really interested in elliptic curves and how they are used in the field of cryptography.

Section 8.3 and 9.5, due November 11

I thought that it was kind of hard to understand how exactly the SHA-1 algorithm works. It reminds me a lot of DES and AES where we are just doing a bunch of operations to make things hard to compute backwards.

The Digital Signature Algorithm was a lot easier and simpler to understand. I was wondering if there are any algorithms for digital signatures that don't depend on modular arithmetic. They also talked about the NIST adopting it as a standard. Did they have one before 1991? This book is three years old, so are there other algorithms being considered to replace it currently?

Section 7.3-7.5, due Novemeber 2

I think that it is kind of cool that we can use discrete logs for other things besides sending messages. I think that bit commitment is close to the same thing if Alice sent Bob her secret p and q, the factorization of n. He could then decrypt he message she had sent previously.

ElGamal makes sense mathematically but it might take a bit to remember how to use it. The key used in it is a lot different than RSA. Then again, the algorithm has a lot of similarities and also a lot of differences.