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.

14.1 & 14.2, due on November 14

The Interesting

I have always wondered how the little card swipers keep my information secret, so this is cool. I like the idea of the tunnel/hallway with the door in the back.

The Challenging

I don't understand why knowing that r1 and r2 factors of s mod n makes it so we know that x1 is r1^2 and x2 is r2^2. This seems like it's going to be really easy once I hear you explain it, but right now it's confusing! That made it hard for me to understand the Feige-Fiat-Shamir identification scheme and the following identification scheme they explained

12.1 & 12.2, due on November 12

The Interesting

When I first glanced at these two sections, I was a little nervous seeing all of the capital pi nutation, but then the first section made it seem manageable. This entire time reading it though, I just thought to myself, what's stopping his kids from coming and just trying all of the different numbers? They could still totally hack this and it doesn't seem very secure. 

I liked that we get to use matrices, they've always been a favorite. 

The Challenging

I cannot see why the determinant of the matrix is the product of the difference of the different x values. 

If two people tried to break the example with their numbers, why do they get a quadratic polynomial and why does that mean that any secret can still occur?

I don't understand how the Shamir method makes some people more important than others. 

Test 2 Preparation, due on November 9

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

 I think that RSA is a huge part of this exam: using it, knowing how it works, knowing how to do it, its weaknesses and strengths, etc.

I also think that knowing the methods for factoring, determining primality, and cracking the posed discrete log problems will be important. 

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

I expect that we will be decrypting RSA messages.
I bet we do a Chinese Remainder Theorem question. 
I think we'll test numbers to see if they are prime (and factor if they aren't).
I bet there will be a question about the birthday attack somehow, because it's fun.

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

I need to memorize the rules of the Jacobi symbol manipulation. I'll need to remember how to find square roots Mod n. I need to review the ElGamal methods and how to do them, as well as the primality determination methods. I will also really need to spend some time trying to understand signing documents in RSA, because that's still pretty fuzzy for me.

8.3 & 9.5, due on November 7

The Intriguing

I feel like it's really hard to just read about SHA-1 and understand what's happening until I actually have a message and am either watching it get encrypted with the method or if I'm trying it myself. I am sure we'll try them for homework and am excited. This was a fun reading because we talked about the DSA in class today a little so it made sense. 

The Challenging

What is a "Message Digest"? The book refers to the final Xl of SHA-1 as a message digest and I'm not sure what that means. .....And then I kept reading and was even more baffled by page 225. It seems hard to understand the SHA-1, but like I said in the intriguing, I think I will understand more by trying it out. 

9.1-9.4, due on November 5

The Captivating

I think it's crazy that there's such a thing as a blind signature. I don't know that I would ever feel comfortable signing a hash without knowing what I'm signing.

The Challenging

So in the ElGamal, Eve can solve it if both Bob and Alice use the same value for k?
I think it's crazy that changing one comma or space a bunch of times can result in finding a message with the same hash. Cool! I don't really know if I believe that this is possible, but it's still cool. To be honest, I don't really understand why the ElGamal system works with the multiple exponents.