6.5-7.1 for 28 October

1. The application to treaty verification was not initially clear. It involves the idea of authentication but I wasn't sure exactly how that takes place.

2. I liked the idea of using functions with trapdoors as a way to make a public key system. I also found the idea of discrete logarithms interesting. It reminded me a little bit of complex logarithms since there could be multiple solutions unless we make it clear which solution to default to.

6.4.1 for 26 October

1. The book doesn't explain why linear dependencies mod 2 in the matrix imply that the products of the numbers are squares.

2. I thought that this was an interesting approach to trying to factor a number. The theorem about square roots mod n has proved to be very useful in factoring numbers.

6.4 for lecture 23 October

1. The p-1 factoring algorithm was a little difficult, I am still not totally sure why it works, but I did find the idea very interesting.

2. I had thought of something like the Fermat factorization method over the summer, but realized as the book stated that the algorithm could take a long time if you pick your primes carefully.

6.3 for lecture 21 October

1. The most difficult part was understanding why the Miller-Rabin Primality test works. It seems to be an extension of the basic principle in the chapter, so it just took some time to internalize it.

2. I think this chapter is very interesting. I have always wanted to find a faster way to check that a number is prime since dividing by the primes up to the square root gets slow very quickly.

3.9 For lecture 16 October

1. The most difficult part was making sure that I understood the application of the theorem in the example, but it eventually made sense.

2. I thought it was interesting to use the proposition in the chapter to find a square root mod p, and then use the Chinese Remainder Theorem to find a square root mod a composite number. The application to RSA seems like it will be rather straightforward.

Sections 3.12 and 6.2 for 14 October

1. The OAEP was a little difficult to understand. There were just a lot of details and steps and I wasn't fully sure why it worked.

2. I liked the idea of attacking RSA by looking at how long it takes to decrypt a message. It used some statistical ideas, so it was interesting to see the mathematics and statistics mix in order to break an RSA message.

Chapter 6.1 due 9 October

1. The most difficult part was trying to remember all the number theory we had talked about before dealing with finding powers mod n and the phi function.

2. I really like seeing how some of the fun things that we can do in number theory have useful applications, like RSA. It was also fun to finally understand what is actually going on in this algorithm that I have heard so much about.

Post for lecture on 2 October

1. The most important topics have been the ones to do with number theory, such as finding inverses mod n and finite fields since they have a big role in the cryptosystems.
2. I would expect to see a fair amount of computational questions with number theory and some theoretical questions testing the ideas of how certain cryptosystems work and how they can be attacked.
3. I should put in some more time working with the finite fields and ECB and other methods for implementing block ciphers.