Section 16.1, due on December 2

This section on elliptic curves is fascinating as well as being understandable.  The only main part that didn't make sense were some of the computations that were done in finding the third point in the addition algorithm.  Other than that, everything else made sense.  I am getting the feeling though that some things in here will use some more difficult concepts from abstract algebra.

This seems like a really interesting subject, and I'm interested to see how these curves will be applied to cryptography.  It seems like they aren't that connected, but I'm sure I'll see how wrong that thought is soon.

Assignment 37

Error correcting codes were rather hard for me to understand.  It makes sense why we need them, but how they work in practice did not make sense to me.  I don't understand how the error detecting and correcting algorithms work.

It was interesting to see how necessary these codes are.  I had never thought about the dangers of a noisy channel, but it makes sense that such error correcting codes would be needed in order to ensure clear communication.

Assignment 36

The enigma machine is quite an enigma to me.  I understand that it's mechanically generated, but I don't quite understand how the rotors produce different permutations of letters.  I understand that the rotors move, but I don't get how that creates different possibilities.

It is interesting to see an example of using technology in encrypt.  It's also amazing to see how much encryption has advanced, technology-wise, just in the past 70 years.

Assignment 35

Shor's Algorithm is very hard to understand, even from the nonmathematical perspective provided by the blog I read.  I especially don't understand the quantum Fourier transform.  This transform, and how it revealed the exponential period, didn't really make sense to me.

However, it was interesting to read about how quantum principles can be used to factor large numbers, especially since the advance isn't just in computing power, it's in how the computing is done.

Assignment 34

I'm not very clear on how these vectors in the complex plane work, or how the qubits are changed by the way in which they are measured.  It make sense that the particles are altered by the way they are measured, but I still don't get the nitty-gritty details behind all of this.

It was interesting to finally learn about the basis behind using a quantum computer, and the thought behind them.  I've always heard about them in science fiction books, but never have quite understood the theory behind them.

Assignment 32

What topics do I think are most important?  I think the basic principles behind RSA and the ElGamal encryption systems, as well as the principles of public key cryptography in general are important.  Also, the potential weaknesses of these systems are rather important to understand.

What kind of questions do I expect?  Perhaps using simplified versions of the cryptosystems we have studied recently, as well as applying the number theory we have learned behind the systems. I can also see primality testing being used.

What do I need to work on understanding?  I need to remember the continued fraction attack, as well as our methods for computing discrete logarithms.  I also need help with primality testing.

Assignment 31

I mainly got confused by the various names associated with the different methods.  The methods made sense, but the names and terminology associated with each of them was a little difficult to decipher.  Perhaps as I work through examples it will make more sense.

What was interesting about this section was that I had read about something similar in a Math Education magazine a week or two ago.  They talked about they system of creating lines so two people would be needed to find the secret.  It gave me a nice quick start into understanding this section.

Assignment 30

I am a little confused by the birthday attack on signatures.  I'm still not sure how that works in practice, or how one would do it.  I do understand that it is probabilistic, but I'm still not completely sure how it works.

Signatures in general are very interesting.  I'm surprised to see how much our public key encryption systems can be used in clever ways to produce signatures.  I was also surprised to see how a small change to a document could protect the signing.  I'll have to remember that trick to protecting one's self against fraudulence in an electronic document.

Assignment 29

In reading this section, I didn't quite understand how the birthday attack was to be used on weak hash functions, or how the multicollisions described would occur with such frequency.  Also, the reasoning behind why concatenating weak hash functions doesn't increase the strength was rather mysterious to me.

Still, it was interesting to see how hash functions could be applied crytographically.  I think the it's interesting to try to find things that are pseudorandom or appear random, and thus can be used in cryptography.

Assignment 28

I am still surprised by the nature of one way functions.  I'm a little confused though as to how the exponential hash function example provides a way for us to solve the discrete log problem, and how the parts of it are so correlative to it.  I'm not sure if they're providing a way to solve that is computationally unfeasible or just unlikely to occur.

Hash functions are quite interesting because they are not technically bijections, but they behave like them, and it is in computational power that they become difficult to break.  It's interesting how we can use computational prowess to get around logical difficulties.

Assignment 27

This sections was interesting in its conceptual implications.  However, bit commitment was a bit confusing to me.  I'm don't completely understand how the discrete logarithm is applied to ensure bit commitment.

As a whole, this section was rather interesting in its practical applications.  Bit commitment and key generation are important things to do in cryptography; it's interesting to see these practical problems solved in a clever, mathematical way.