Section 3.5 - 3.6

Wow the modular exponentiation thing is a cool trick. I can see this being very useful in optimizing certain algorithms. I understand Eulers and Fermat's theorem and there usefullness but the proff for Euler's might be beyond me. I just can't imagine coming up with the transformations they used in the proof.

Section 5.3 - 5.4

Nothing really difficult here. The seemlessness and simpliciy of decrypting AES is pretty nice. Its not a complicated or involved process. I don't understand exactly how the assumption the no weak keys exist because the encryption and decryption are different processes(pg161).

Section 5.1 - 5.2

The basic algorithm for AES looks pretty straight forward and easy to remember. The tough part here is the GF(2^8) property use for mixcolumn and the other steps especially with finding the inverse with regard to the S-Box but working out an example by hand can really help understand this.

Section 4.6 - 4.8

I still don't get why the meet in the middle attack works or what the properties of the double DES are that make it suck.
The use of a salt for password security seems very clever to me. Its a nice practical side to the crypto in the book. Sometimes little things added to the implementation of these systems can work out nicely and the salt is a novel example of making DES more secure without actually modifying the algorithm itself.

Section 4.5

The most interesting parts here were definitely the feedback methods. The way the output from the encryption would be XORed or shifted along with the use of the differing keys is a nice way to solve the problem of transmitting data of varying sizes. Even more interesting is the fact that the mode of operation plays a part in the cryptanalysis of DES and things beyond the algorithm can cause it to perform better or worse. I also wonder what the affects would be if the various modes were used together. Coming up with a cryptanalysis of the counter mode strikes me as a difficult task especially compared to the codebooks, once again its interesting how much of a role the mode of operation for DES plays in breaking it.

Section 4.3 - 4.4

I'm still unclear to how exactly differential cryptanalysis works. Just like DES it seems very magical and things "just work" without any formal proof. I don't understand how all the XORing manages to remove the key from the message and are we assuming that the adversary has access to our S-box or is the S-box universal? This was something I wasn't sure about either while reading the DES section. The lemma regarding the cycle of length n was cool because of the way it was used to proof DES is closed under composition. It didn't strike me as obvious at first but now I see how it makes sense.

Section 4.1 - 4.2

The most difficult part here was understanding exactly how the S-Box works. Its almost magical there should be a proof of some sort to show that this is actually as secure as it claims to be. That being said its pretty nice how a bunch of simple operations in DES can result in something that is believed to be secure.

Section 3.11

Wow this was some weird stuff. I had seen finite fields and their properties before in a linear algebra class but the field of integers mod n are strange. Especially the polynomials of degree 8 some of those properties were not very easy to understand. In particular the effects of division are kind of weird. However I do see how this allows a simplification for the calculations to make things like Rijndael fast.

Section 3.3 - 3.4

The explanation of how to do the Chinese Remainder theorem in the book was difficult to follow. However the general form given at the end seemed to make more sense. I guess at the heart of it, it is basically the same thing as solving a system of equations in linear algebra, you just keep substituting up.

The proofs using congruences were quite nice, they are very simple but elegant. It also looks like congruences are pretty powerful even though there isn't much to them.