6.4.1-6.4.2 due on October 22

What was the most difficult part of the material for you?

In the Universal Exponent Factorization Method, there are a log of conditions and checks. Keeping track of all the conditions and checks is the most difficult part of the material.

What was the most interesting part of the material?

I think it is very interesting to see the linear algebra application in the Quadratic Sieve method of factorization. I think it is a clever way to do it, and I always enjoy seeing connections of linear algebra to number theory.

6.3, due on October 17

What was the most difficult part of the material for you?

The Miller-Rabin Primality test was the most difficult part of the material for me. There were a lot of details as to why the test usually works. Following all these steps was difficult.

What was the most interesting part of the material?

I think it is very interesting that probabilistic methods are used in determining the primality of big numbers. It seems that RSA and other algorithms perhaps rely on these methods? If so then I wonder if there is anything exploitable with that. If not, then I guess that polynomial time deterministic algorithm is what is used in RSA implementations.

3.10, due on October 15

What was the most difficult part of the material for you?

As the book said, "it can be rather difficult to use by hand". Following all the by hand calculations was the most difficult part.

What was the most interesting part of the material? 

I really like the new ideas of Lengendre and Jacobi symbols. I think that they have interesting properties, and there are some cool tricks you can do with them.

6.2, due on October 10

What was the most difficult part of the material for you?

The section on "Low Exponent Attacks" had a lot of details. Keeping track of what everything means and how it all fits together was difficult.

What was the most interesting part of the material? 

I thought the hardware timing attack was very interesting. It shows that math and computer application are not quite the same. You can have a perfect algorithm, but somewhere in the implementation there could be a flaw that dissolves the security.

3.12, due on October 8

What was the most difficult part of the material for you?

Seeing the connection between the gcd and what was going on previously was intuitive, but hard to rigorously connect. It is a need connection though.

What was the most interesting part?

I think it is very interesting to be able to represent an arbitrary real number effectively in this way. It is cool that you can do better than just taking n decimal places over 10^n.