19.4

The book is over...These are just exercises...

19.3

This part explained a bit more about quantum computing and how it works to do things in parallel by using a linear combination of states for the input and it gets a set of states as an output. I really still don't understand how this works or why. Also, I pretty much missed how the factoring algorithm works. I understand that they perform a fourier transform on the data points, but I'm not sure what the transform's result means in the context of finding a root.

19.1-19.2

I liked the intro to quantum cryptography since it explained how light is used and I found it quite fascinating. I thought it was interesting that they used the polarity as a measurement of the bit. I didn't understand how quantum security is more secure at all since someone could perform a man in the middle attack quite easily.

7.4-7.5

The Diffie-Hellman key exchange was a really nice surprise since it's so simple, and it's easy to understand how it works. I like how it seems like it would be easy to break, but in reality it's very very hard. I didn't understand the ElGamal crypto system. I'm not sure what they are trying to do in it, and it seems kind of strange. I see why it works with the identity, but I'm not sure on the rationale behind it.

6.6-6.7

I thought that the idea of using public key cryptography to confirm who sent a message is really neat idea since it allows you to use the encryption for verification. I never thought of using the private key to decrypt as a way of verifying who sent a message. It's really quite clever. I didn't quite grasp the example they used for the two countries and how that would work.

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.

3.11

The finite fields are kind of neat in this chapter since you can divide by any of the numbers from [1,(p-1)] mod p. I really didn't understand what they were going over in the book. Maybe it was just a little too long winded, or maybe it was just confusing. I kind of got lost after the first few things about the properties of a vield and the X polynomial.

3.3-3.4

The interesting part of this was the chinese remainder theorem. It seemed kinda cool how they found the number based on the congruences. It was also somewhat difficult to understand since the book wasn't quite clear enough for me.

3.1-3.2

The most intersting part of this section was the pi function. I didn't know that there were x/ln(x) primes from 1 to x. I thought it was interesting since it's not obvious that the distribution acts like it does. The extended Euclidian algorithm isn't exactly explained completely in why it works. I could probably use a better explanation of this.

2.8-2.11

I found the one time pad as the most interesting part of this section. It's interesting how the one time pad is impossible to break. This appeals to me since it's pretty cool to see something that is concrete like this in it's security. The only downside that they indicated was that the pad can only be used once, so generating them can be prohibitive. One part I didn't get completely was the linear feedback shift register. I'm not quite sure how it works and what the matrices that were int he book were used for.

2.5-2.8

One thing that I thought was somewhat vague was how to decrypt the ADFGX cipher. It left it up in the air how to deterministically figure out the boundaries for each column in the example listed in the book since one column has one more letter than the rest. I thought the matrix based block cipher was really interesting since it can be expanded to multiple letters easily and has many possibilities, but it also fails so easily once one plaintext is discovered.

2.1-2.4

One of the interesting things from the reading was the vigenere cipher which shifts a variable amount since it is a clever modification of the shift cipher. The first method for attacking the cipher is interesting since finding the key length seems somewhat incredible since it just involves counting coincidences. Finding the key was expected since it just analyzed letter frequencies. One thing that was not quite explained was how a combination of several ciphers could be solved. For example if a vigenere cipher was applied to a random substition cipher or the other way around, would it need new methods for an attack?

Name? Year? Major?
Brian Kennedy
Fifth Year
Computer Science Major

What courses have you taken post-calculus (please include course names and not numbers)?
Math 115 (Linear Algebra)
Math 151A (Applied Numerical Methods)

Why are you taking this course?
I need to take one more math course to satisfy my major's "Pick three upper division courses from some other department" requirement, and this class looked interesting.

Tell me about the math professor/teacher you've had whose been most effective. Tell me what s/he did that worked so well.
It was the professor for applied numerical methods. He posted his notes online, and when he would go over the material, he was always excited about what he was teaching. He would also have small 'quizzes' during class where now and then. Just after he had introduced something new, he would have us take out a piece of paper and work on one or two problems and then switch papers, grade and go over the answers. If I remember correctly, the quizzes didn't count against you, and it could help improve your grade by participating. It seemed to help us know whether or not we really got what he was teaching us.

Tell me about the math professor/teacher you've had whose been least effective. Tell me what s/he did that worked so poorly.
It was the professor for math 115A. This was the first math class where I had to prove things for homework and the exams. He never went through the different methods of mathematical proofs and just guessed that we knew how without asking. He would also go through the proofs for various things during class, but not really give us any idea for the rationale behind them. He also called us all stupid after the midterm since everyone except for one person scored less than 50%.

You wouldn't know it by looking at me, but ...
I like to play racquetball.