16.5 for 9 December

1. The difficult part was understanding the elliptic curve Diffie-Hellman Key Exchange. It gave an example and threw out some numbers, so it took some time to understand what was going on.

2. I though that the similarity between the ElGamal Digital Signitures and the Elliptic Curve version was very interesting, since they basically look the same.

16.4 for 7 December

1. The most difficult part was understanding the example using an elliptic curve over GF(4). I was not completely sure why some of the polynomials that resulted from plugging in elements of GF(4) had no solutions.

2. Using elliptic curves over GF(2^n) seems like it should be useful for computer applications since computer scientists always seem to like things to be in powers of 2.

16.1 for 30 November

1. The example on page 350 was difficult to understand dealing with adding the points and talking about roots. I was a little unsure about what exactly was going on.

2. I thought the idea of points on an elliptic curve forming an Abelian group with an identity being the point at infinity was an interesting concept.

14.1-2 for 18 November

1. The tunnel example did not make much sense to me. The example of the similar idea with the Feige-Fiat-Shamir Identification scheme at first was a little hard to figure out how step four verified that Peggy knew s_i, but then I reread it and it made more sense.

2. I thought that the idea of a zero knowledge proof was interesting, since it was a way of avoiding the ATM scam mentioned at the beginning of the book.

12.1 12.2 for 16 November

1. I was a little unsure of how the Vandermonde matrix was set up and why it worked exactly.

2. I thought the idea of secret sharing was interesting, that the secret could be split among 7 people but a minimum of 3 people would be needed to uncover it (as an example). The idea of an interpolation polynomial seemed like a creative way to go about it.

13 November

1. RSA is definitely a major topic, and how to attack it if it is not applied well. That would also include primality testing and factorization. Also discrete logs I would expect to have a significant portion.

2. I would expect to see some computational questions that would use techniques discussed in class to factor or find discrete logs, and some ciphers similar to what we have done in class that may have some weakness that can be exploited.

3. I feel like my weakest area is some of the more complicated algorithms such as Pohlig Hellman and the Quadratic Sieve.

4. Anything that would relate to number theory somehow I would find interesting, but there is nothing in particular I can think of.

8.3,9.5 For 11 November

1. There were a lot of steps and details in the SHA-1 algorithm. The difficult steps for me were steps 1 and 3d. I was a the function was a little strange that is used in 3d and then the first step just didn't come clearly to me.

2. I thought it was interesting to see some actual hashes and signing algorithms now that we have talked in detail about what they are and some possible uses and weaknesses.

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.

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.

Chapters 5.1-5.4 for lecture 30 September

1. The most difficult part of the section was bout how to reverse MC and then ARK by making some IMC and InvAddRoundKey. I wasn't really sure why this worked.

2. Having seen something like DES previously, understanding AES was definitely easier. It was nice to see a clear reason for why some of the things were derived, like the S-box. This is such a complicated, secure system that I wonder how someone would come up with it!

Post for lecture on 28 September

1. So far the assignments have taken me about as long as they should for a BYU class. The lecture and the reading have been very helpful in answering the problems.
2. The Jeremiah project was a little weird. On the other hand I have enjoyed learning about how to break weak ciphers. The best contribution to my learning is examples and working out the problems myself.
3. The most difficult thing so far has been the DES, which is getting more understandable, so that would be what I should spend more time studying before the test.