6.4-6.5

The RSA Challenge seemed somewhat straightforward except for the part about how people attacked it. I wasn't clear on the whole thing about how people worked with a distributed network to make a sparse matrix that they later reduced to a nonsparse matrix.

6.3-6.4

The primality testing was the most interesting thing in this section because it enables testing primes with a given probability. I found it interesting because it lets you guess if a number is prime without actually dividing by all numbers less than a certain number. I didn't understand how any of the factorization methods work at all. It wasn't quite clear how they work step by step for their algorithm.

6.1-6.2

I thought the whole way that the RSA algorithm worked was really cool. It seemes sort of magical how it is able to give you the plaintext by taking the ciphertext to an exponent. I'm curious as to whether the decryption exponent is unique (mod (p-1)(q-1)) for a given encryption exponent. I didn't understand how the attacks against RSA work since I got lost in the reading for all of it.

3.9-3.10

I did not understand at all what section 3.9 is trying to convey. I understood how to find the square root, but I didn't undrstand how it works. I thought the method for whether a number is a square mod p is pretty cool since it gives a simple definition for it.

3.5-3.7

I thought the cool part about this section was fermat's little theorem and how it applies to numbers modulo another number that have gcd of 1 respective to each other. It was really neat how you can do a really big exponent modulo that number much faster by using the theorem to reduce the number significantly. I wasn't quite too strong on how the theorem works since I didn't really get how it went from the prime to just the gcd of one part.

5.3-5.4

In this section, I didn't quite completely understand the whole Rijndael decryption still since I never completely understood the encryption. I sort of get it, but I'm not sure if it is 100% correct. One really cool thing came in 5.4 where they showed how they designed each portion of the cipher to be resistant to something and also had a strict definition for the S-Box. That made it really nice since there isn't really any confusion on how it works.

5.1-5.2

The Rijndael cipher looks much simpler than DES in terms of how the steps work. I thought the cipher was easier to visualize since the steps were linear and there was no switching back and forth of the halves of the cipher. I didn't understand why they chose to create the sbox the way they did since it referes to GF(2^8) which I don't have much intuitave sense on.

4.6-4.8

The part about how different people cracked a DES password through distributed, and then custom aproaches was interesting. I thought that the EFF project was interesting since they managed to produce a machine which could crack DES in a matter of days on a relatively small budget. Additionally, it made me wonder how fast someone could crack DES encryption today with custom hardware. On part of it I felt like the book was incorrect in stating that adding salt to the UNIX one way password function made it so that a chip would have to try all 4096 possibilites. It seems like the people who wrote the book have never used an FPGA since it would be easy to just have an input for the salt and then switch the bits based on the salt.

4.5

I found it intersting that a block cipher could be attacked by a dictionary if the same key is reused since it isn't that intuative because there are several characters per block, and there are so many possible combinations of 8 letters that it would be hard to analyze it in the same way one might attack a random substitiution cipher. I wasn't too clear on how counter mode works for the encryption system.

4.3-4.4

In this section I really didn't understand differntial cryptanalysis at all. It looks like it could be really cool if someone explained it to me, but all the figures and numbers made it confusing. A sentence or paragraph explaining what was going on might have worked a bit better. On the other hand I thought that the thing about how if a crypto system is in a group then double encryption becomes equivelant to single encryption, but if it isn't then the double encryption effectively doubles the key length.

4.1-4.2

I liked learning how DES works since I have read things on it before and I never really understood what went on in the DES encryption process. I'm not quite clear on how the different sboxes can be distinguished from each other on decryption since they are two rows and going backwards they are not distinguishable. I'm guessing it has to do with the key, but it isn't obvious.