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.

Sections 6.5-7, 7.1, due October 28

I think that it is cool that PKC can be extended just a little more to provide digital signatures and verifications. I guess I never thought of using d to encrypt and e to decrypt, but of course it works exactly the same.

I am also very interested in learning about discrete logs. I don't exactly understand how they are used yet, or why it is hard to do them in reverse. I suppose, though, that we will be spending plenty of time on them in the future.

Section 6.3, due October 21

Oops. I read the wrong section last time. But I really liked this reading on primality testing. We talked about the jacobi symbols, but not really what they meant. It was neat to see how they fit into primality testing.

I am not really sure what "probably prime" means. I understood that if these tests told us a number was composite, then we knew that for sure. When using primes for an RSA encryption, I doubt that they just use a number that is pseudoprime, or even strong pseudoprime. What other tests do they do? Are they very complicated? I remember reading this last summer about some primality tests and they went way over my head.

Section 6.4.1, due October 19

I think that it is really interesting the methods that are devised to break any cryptological system. It takes a lot of ingenious thinking. It is the same in this case. My hat is off to whoever invented the Quadratic sieve.

Are we just going to be talking about the quadratic sieve? Or will we be talking about number field sieves as well. I get the concept of the quadratic sieve, but there is no way that I would be able to employ it to break a system.

Section 6.1, due October 9

I think that RSA is very elegant. I think it interesting it is from AES. While they are both secure encryption methods, they have almost nothing in common. While AES relies on confusion, RSA relies on only one thing: the difficulty of factoring large numbers.

I am pretty sure that they will talk about this in later chapters, but is it hard to find new primes to use. Obviously, a computer couldn't run through them all because there are so many. I just wonder if there are so many that you could not document them all.