Wednesday Dec 1 Section 16.2

   Today was on elliptic curves and encrypting messages.  The problem is similar to the discrete logarithm problem.  With the added complication that there is a chance that your message will be unable to be encrypted.  The message is encypted by taking the message, turning it into a number and that number becomes the x coordinate of the point that represents the plaintext.  But I can't find out how the message is encoded.  Elliptic curves can be used to factor polynomials.
  So the method of encryption has to do with the fact that if B=kA, for a given B and A, k is hard to find.

Section 16.1 Monday November 29th

  Today we read about the abelian group that can be formed from the points on an elliptic curve.  One thing that we learned was that the term elliptic curve is named such because the equations involved are also involved in computing the arc length of ellipses.  This section was not to hard to understand, there is a little algebra when computing P1+P2, but not too bad.  The next section looks worse, when you stsart creating these modular groups.  The way I understand it, it appears that in a curve mod n you might have many more points than n, in fact, it looks like you have to have more points than n.  Section 16.2.1 talks about this and I find it interesting.
  Section 16.2.1 contradicts what I thought and the section after that gives a more precise method of predicting the number of points in E.
  I forgot how to make a variable substitution to turn x^3+ax^2+bx+c into x^3+b'x+c'. It is taught in 372 I think.  I will be taking that class next semester.  I should look up the substitution.

Tuesday Nov 23 Section 2.12

  This was a really fun reading; Enigma is one of the things that legends are made from.  There were so many neat stories in the reading, like the enigma technician who encrypted all of his messages with his girlfriend's name, the German Admiral who wrote to High Command with his suspicions that Enigma was not secure, and who modified his enigma machines so that the Allieds were unable for years to crack his fleet's messages, even though the German Army and Air Force had completely transparent communications as far as the English were concerned.  The one paper said that the Bombe machines that cracked Enigma were named that because the Polish mathematician who came up with the idea was eating a "bomba" when he thought about it, a Polish ice-cream-like dessert.
  The book describes how the front panel, three rotors and reflecting panels work together, and it isn't really all that hard to understand.

Section 19.3 and an article, November 22

  So we now know the basic philosophy of a quantum computer, it is really interesting that looking at data restricts the output.  Something that is obvious when you think about it, but I still didn't think of it before this chapter.  I really liked the clock analogy in the article you asked us to read.  It makes me want to buy an analogue clock and corkboard.
  I still don't know what a quantum fourier analysis is, but I suppose that that falls under the statment in the book that we would have to trust that the quantum computer can do what the book says it can.
  So, since the book didn't really describe this material in any real depth, what are we expected to know about this?  I don't think that we could use the quantum method to actually solve anything, the information to do that isn't in the book.  Is it like AES where we just know the name of the steps?

Friday Nov 19th Sections 19.1 and 19.2

  Today's reading was on quantum computing, The polaroid filter thing is really cool, I have see that in my physics classes before, and every time I go to get new glasses I play with the polarized sunglasses doing the same thing.
  Using the quantum effects of measuring photons to test to see if someone was evesdropping blows my mind, such a cool idea.  I am taking physics 222 right now and the class is basically all quantum mechanics, excepting the first three weeks on general relativity.  I am still not sure how there is a probabilistic algorithm that factors integers.  But I think it might have to do with solving the central potential spherical shrodinger equation.  The answers to those solutions are integers, and there might be a way to perturb the system so that there is a relation between the two perturbation states?  A relation that has to do with primes?  Well, the next section might answer that so I am going to go read that instead.

Nov 17 Section 14.1 and 14.2

14.1 is on zero knowledge systems, which are really cool, and the diagram of the tunnel with the door really helps to understand the philosophy behind it.  So, I claim that I can find square roots modulo n, I compute x1 and x2 and then send them to someone, who then asks me to tell him the square root of one of the numbers.  I tell him the square root because I know it.  If I did not know it, then he would know that I did not have the key, and would deny me access.  If I am trying to fake it, I have a 50-50 shot of doing being able to fake it, but that is why the test is done multiple times.  Because the chance of faking it decreases like powers of one half.

14.2 is the FFS method of this, which is the same except that it is done in parellel, where I send lots of x1,x2 pairs and am asked for the square roots of xi_k, where i_k is ramdomly a one or a two.   Same chances as the previous scheme, 1/2 to the power of the number of square roots checked.

Monday Nov 15th Capter 12.1 and 12.2

  Today's reading was about secret splitting and threshold schemes, it was not too hard to understand.  It is based on the number of points needed to define a polynomial.  The method of recovery is the chinese remainder theorem for a matrix equation.  The really cool part is the situation of multiple companies having a system that requires representatives from each company present to figure out a secret.  That one is way cool.  It seems similar to the linear combination of solutions to a differential equation or finding a basis to a vector space.
  To be truthful, I feel that the most difficult thing in this section is knowing that the test is tomorrow and this is on the test after that.  But I thought it was really cool and I look forward to having a homework assignment about threshold schemes.

Friday 12th post

• Which topics and ideas do you think are the most important out of those we have studied?

Probably the number theory stuff.  The algorithms can only really be tested to those, asking us to use them would require a computer, but we might be asked to explain them. 

• What kinds of questions do you expect to see on the exam?

Number Theory questions, maybe questions about the steps in an algorithm.  not too much of actual breaking of codes.

• What do you need to work on understanding better before the exam?

I plan on speading a lot of time with chapter 3, that seems like the most important stuff.  I will try to look over the diagrams for the encyption systems too.  those seem like likely targets for questions.

• Are there topics you are especially interested in studying during the rest of the semester? What are they?I

You said that we would learn about quantum computing, that sounds really cool.  I would like going over what we learned already, if we could.  I bet that that will happen for the test on Monday.  But Sometimes it feels like I get the stuff that we are working on now, but I don't remember the stuff we did the week before.

Monday November 8 Sections 9.1-9.4

  So today was about the uses of signatures and hash funtions, and was fairly similar to the lecture on Friday.  The first section was on how to use RSA as a way of signing electronic contracts, the next on ElGamal's version of that, the third was on hash functions and how they make signatures shorter and easier to compute and the last section was on the birthday attack on hash functions.  I thought it was clever how Alice foiled the birthday attack by changing a comma.
  The ElGamal algorithm seemed less intuitive than the RSA version, but this may be because RSA is somthing I had heard about before taking this class and ElGamal is not.  I plan on looking over ElGamal more thouroughly before the next test. It is not as straightforward as RSA.  Which is more common to use?  Do they have different strengths and weaknesses?  It seems that there are mor attacks on RSA, because we have spent a lot of time on RSA attacks.

Sections 8.1 and 8.2 November 3 Wednesday

  Today's reading was on Hash functions.  To me they seem a lot like the one way trapdoor functions that were used in RSA and ElGamal.  Except that there is no trapdoor?  Is that the difference?  There are many hash functions mentioned, but none of them are described.  Are they going to be explained in a later chapter?  The relation between the discrete log problem and the discrete log hash function is interesting.
  So the reason for using hash functions is that they are faster than RSA and ElGamal. But it isn't as functional as either is it?  This would be usable for password verification, or error correction, but not for sending messages right?
  I think that the uninvertibility of a hash function is due in large part to the number of collisions that the function has.  So what was hard was to see how and why one would use a hash function instead of RSA or ElGamal.  Weighing the differences out would be a good idea.