16.5, due on December 5

The Interesting

I like that elliptic curves make it possible to use smaller prime numbers. It's fun learning how to use the Diffie-Hellman and ElGamal methods applied in a new way. 

The Challenging

What does "analog" mean? Does it mean that it's basically the same idea? My other question is less related to the reading and more related to this information in general. How do we do these types of things in Sage? I've looked at the sheet you put up and I remember that you did it a really cool way in class, but could you consider showing us again?

16.3, due on November 30

The Interesting

I think it's cool that we did the example in class today with n = 2773 and we got to read about the case you mentioned in class. I really liked class on Wednesday and feel like I had a pretty good understanding of the material, but it was hard to understand the follow-up information in the chapter. 

The Challenging

So in class we found 2P and the book found that 3P factored n, but if you haven't factored n by 3P, do you just keep going and hope to find a factor?

13.1 was pretty fuzzy for me. I guess I don't understand what it means to have multiple roots, because I thought we were looking for the roots. 

16.2, due on November 28

The Interesting

I like that we are finally getting to learn about using these elliptic curves to factor because we've read about the method for ages. I do find it interesting that we are just pretending that n is prime, though, when we know that n is a product of two prime numbers (and is therefore composite and not prime.)

The adding of points in these elliptic curves are crazy. I can't believe that (1,2)+(4,3)=(4,2). 

The Challenging

I would love to see why adding two points together gives such non-intuitive results. I guess I'm not familiar enough with elliptic curves to know why this works the way it does. The book mentions that we can use methods like Baby Step, Giant Step and the Pohlig-Hellman attack can be used on elliptic discrete logarithm problems, but I don't really understand how these elliptic discrete logarithm problems work so I can't see how I would apply these methods. 

16.1, due on November 26

The Interesting

I was excited to finally read this section because we have read in so many of the other sections that one day we would learn about elliptic curves in cryptography. I haven't seen eliptic curves in a long time, so this was a nice exposure.

The Challenging

I tried to understand why p+infinity = p, but I don't really know if I'm convinced that I understand why. Is it because they call the top of the y axis infinity, so it just jumps down to the bottom? I didn't think that I was understanding the example on page 350 (why were they adding things to each other in the first place, why were they substituting it into the Elipse equation, why were they solving for a third point, etc.) But then on page 352 when it gave the simple procedure, I at least think I understand what they were trying to show, but I wouldn't say that I understand why it works. 

2.12, due on November 20

The Exhilerating

The sneaky British, selling Enigma machines to colonies so they can read their messages while the other countries thought the messages were secure. This is a pretty cool concept. I liked trying to picture the machine and how it worked. 

The Educationally Exhausting 

It was hard trying to follow how they could break the Enigma machine without an example. They did a small example in the end, but didn't really show how they used that information to break the code. I think I could probably explain how the machine worked, but I don't think I could explain why and how to break it. 

Shor & 19.3, due on November 19

Interesting

I was telling my husband that we are starting to apply a little quantum science to cryptography and he then asked me if we had learned about Fourier transforms yet. I looked at him with one of those blank faces that conveys that I have no idea what he is talking about, so it was fun for me to find that Fourier transforms were covered in our reading tonight. Next he asked about convolutions, so we'll see if they're in our reading for tomorrow!

Challenging

-What does the Shor author mean by "superposition?" What's a superposition?
-I think I wrapped my brain around the idea of the Fourier transform from the article we read, but I think I need to see some sort of an example to apply this more thoroughly to cryptography. Is it just used to find a factor of phi(n) so that we can eventually factor n?

from the book:
-I'm embarrassed to admit this but I don't really understand the |100> notation. I understand that the 100 on the inside is three bits, 1 0 and 0, but what does the | > mean? To be honest, I didn't understand much of what the book was talking about.  And when we do the continued fractions on 427/512, I thought 5/6 wouldn't work because 6 is not odd.....

19.1 & 19.2, due on November 16

Interesting

My husband and his brother talk about Quantum science all the time. They think "Flatland" by Dr. Quantum is fantastic, so I've watched it with them many times. It was fun seeing the quantum science being used for cryptography!

Challenging

I didn't relate very much to the polaroid example because I don't know what it means for the filters to have vertical or horizontal polarization, but it was still really cool. Also, what does orthogonal mean? By the end of the first section, I was basically reading another language.

To be honest, the key distribution of 19.2 seems really magical and mythical; I don't really understand how it works and why Alice would be able to see Bob's string any differently than Eve would observe.