Section 19.3 - 19.4

I wonder if Shor's algorithm could changed to somehow work on modern multi processor machines. The need for measuring frequencies scares me though it seems like a lot more opportunities for errors.

Section 19.1 - 19.2

Wow this stuff is weird. The issue of a practical implementation of the basis strikes be as a problem. Also the error issues involved with eavesdropping make it nice for crypto but impractical for implementing other computer components were signals are usually monitored and split up a lot. Qubit are pretty cool though, I can see how they provide more powerful computation in the long run.

Section 74 - 7.5

I don't see the point of the beta requirements for the Decisional Diffie Hellman Problem. Also I get the feeling that Diffie Hellman and Discrete Log should be equivalent but I guess since there is no proof then it could be so otherwise too. The DDH <=> El Gamal and CDH <=> El Gamal proofs are pretty nice, they remind be of a lot of Comp Sci proofs from my algorithms class.

Section 7.1 - 7.3

Baby step/Giant Step is a pretty cool application of divide and conquer find discrete logs I think is a cute solution. Index calculus on the other hand works but I don't quite see how to come up with the relationships it looks for. Also bit commitment is useless if there was a trusted third party then alice and bob could rely on the third party.

Section 6.6 - 6.7

Hurray for public keys, its extremely useful!! Its just nice to see how easily that RSA fits into the concept of public keys. The only weird thing in this section was trapdoor stuff. Coming up with things that have trapdoors or checking if something doesn't have a trapdoor is probably extremely difficult.

Section 6.5

Its a shame that they didn't come up with a way to avoid the creation of repetitions when calculating the congruence relations. I wonder what percentage of six hundred people's calculations had repetitions that would've been a total waste. Also the reasoning for using two large primes and the motivation for wanting to find the q squared relation was unclear to me. Why limit the scoope of the large primes?

Section 6.3 - 6.4

The Miller-Rabin Primality test is quite interesting, its a simple solution that could pretty easily be turned into a computer program. The quadratic sieve on the other hand really confuses me. I really don't see how the linear dependencies fit in. Well actually I can sort understand how it works, its just I could never imagine being able to come up with it on my own.

Section 6.1 - 6.2

The timing attack is awesome, its a very interesting and different approach from the way we have attacked other encryption methods in the past. I'm not sure how easy it would be to do though. I also wonder if there is any weakness from the fact that RSA takes its input from only a small subset of numbers (ie printable ascii) if we were to use RSA to just encrypt arbitrary numbers, I wonder what difference it would make. I also don't completely understand the proof that shows that knowing n and phi(n) gives away p and q.

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.

Section 3.1 - 3.2

The Euclidean Algorithm is pretty intuitive ad its cool how relatively simple and powerful it is. I'd like to see a better proof of the theorem that every positive integer is a product of primes. The proof in the book seems too trivial to be complete, but maybe I'm just paranoid about it.

Section 2.9 - 2.11

The fact that something as simple as a one time pad is so strong is pretty interesting. I wonder if functions other then XOR could be used.

The construction of the LFSRs are sort of complicated I like to see a simpler example worked out in class.

Section 2.5 - 2.8

The modular arithmetic involved in inverting the matrices for the hill cipher was sort of hard to follow. After reading the appropriate section in chapter 3 it became much clearer. I would still like to go through the example step by step using a computer to check the matrix operations in order to make sure its correct.
The Sherlock Holmes story was entertaining but it felt a bit too contrived. I under the authors desire to emphasize the importance of frequency analysis and mastery of the language but that example even though entertaining felt out of place.
The ease in breaking the playfair cipher was interesting I wonder how larger values of n would effect things.

Section 2.1 - 2.4

The first method for breaking the Vigenere cipher was slightly difficult to understand though the second method was much clearer. Just trying random letters for frequencies in the vector seemed very akward.

I thought the affine ciphers were pretty cool and it would be interesting to see what would happen if a gamma and delta were added to the function. Also the digram method seemed very cumbersome but it was interesting to see how the proximity of certain letters could be used to crack substitution ciphers.

First Post

Shant Hovsepian, 4th year Senior Computer Science

Discrete Math
Linear Algebra
Differential Equations
More Linear Algebra
Applied Stats/Probability

I'm taking Math 116 because I'm extremely interested in crypto both theoretically and applied to computer systems.

The most effective math professor I had actually provided very clear and detailed solutions to all the homework problems assigned.

The least effective math professor I had would give extremely convoluted lectures that involved only greek variables and no actual numbers. He would lecture at a very rapid pace and insist on giving detailed proofs for a intro calculus class. His exams were always discouragingly difficult.

You wouldn't know it by looking at me, but I'm obsessed with penguins.