9.1-9.4 For 9 November

1. The most difficult part was working out the details of how the el-gamal signature scheme works. The elgamal encryption is still a little new so it was good to see it in another setting to get a better idea of how it is secure.

2. I thought that this was an interesting way to get a secure way of verifying that someone sent something. I thought that it was very interesting that the message could be known and the source of the message be known with certainty.

8.1-2 for 4 November

1. The difficult part was understanding the details of the second example and the proposition in 8.1. There were enough details that it didn't come at a first reading.

2. I think the idea of a hash function is interesting because of signatures and error checking. I also liked the idea of being strongly/ collision-free, since even though the function is not injective it is hard to find two elements that map to the same thing.

7.3-7.5 for 2 November

1. Something difficult from this chapter was how to solve the football prediction predicament, but I did think it was a interesting way to solve the problem.

2. The Diffie-Hellman Key Exchange provided a nice way to exchange keys over a public key system. I thought it was interesting because in the previous chapters about AES and DES they said that the key could be exchanged over some public key system, and this method of doing it seems to be efficient and safe.

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.