Testing

This is a test.

Dec 8 Section 16.5

  What is a basepoint? the term is used on page 365, line two.  So the analogy of a in ElGamal is a, the random number k is k.  The method seems pretty straightforward.  But, is it like ElGamal in that Alice cannot pick the same random integer several times over?  What would the dangers of this be?
  Is there an RSA implimentation using elliptic curves?
  I am looking forward to tomorrow's lecture and learning about identity based encryption.  It was somewhat revelatory when I read that even though a message can be signed by a system, the person might deny that it is their system, that someone else made a system and ascribed it to them.

16.4 Monday December 5th.

  Today we read about elliptic curves over finite fields.  This seemed really complicated.  I don't understand a model for why the derivatives disapear in a finite field mod 2.  I mean, yes the derivative of y^2 is 0*y*y' mod 2 but what does this look like?  further, is there a way to visualize what a polynomial in a finite field looks like?  the same way that we can graph a polynomial in the reals?  I am not sure that I understand this and it has been a while since 371.
  When are we going to start the final?  Will it be like the group project where we get to break all kinds of cool systems, or will it be more along the lines of the other tests, but we get to take it home?

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?