19.1 and 19.2, Due on November 19

One big question I have is regarding the strange physics notation. I have never seen vectors represented that way and I'm a little confused as to what they mean. Another question I have is: What does this have to do with cryptography? I was so confused by the reading that I didn't even see it's application to cryptography.
The thing I'm most looking forward to in this unit is the actual experiments in class. I get that we are representing light as a vector but I think it will make more sense in class when we actually do the experiment. I also like the idea of using light as a medium for sending hidden messages, even if I don't understand why or how.

14.1 and 14.2, Due on November 17

The first sections was the most easily understood by me. I enjoyed reading about the Zero-Knowledge Protocol and the Tunnel diagram was very helpful. It's interesting to me how useful different mathematical ideas are in real contexts. The notion of finding square roots as a tool to secure information is really cool to me.
The second section was less easy for me to follow. I didn't catch all the steps, such as what Peggy and Victor need to check. I am wondering if this Feige-Fiat-Shamir identification scheme is meant to be a cryptosystem. I think it is not. I am also curious to know where else I might see Zero-Knowledge Techniques in place. It seems like an interesting idea and a quick Wikipedia search taught me a little more about it. I found it not so ironic that the example on Wikipedia used Victor and Peggy as well. Those must be real mathematical terms.

12.1 and 12.2, Due on November 15

One confusing part for me was in the example at the bottom of page 299-300. By using the Lagrange interpolating polynomial they came up with some numbers but I don't understand where the numbers came from. I'm not sure why they divided some of the large integers by 5 either. I understood most of the example except for that part. I also didn't understand the Vandermonde Matrix. That probably led to me being confused about the Lagranfe interpolating polynomial.
The interesting part of these sections for me was the different approaches to solving the same problem. As a mathematics education major we are always taught to represent things in multiple ways. The book did a nice job of explaining how to break this secret in three different ways. I also liked the first section because it was explained well and not too difficult.

Exam II Review

I will admit Dr. Jenkins, I am pretty nervous for this second exam. To try and alleviate that stress I'm doing my best to be well prepared and studying early. As I have been studying the topics I feel the least sure about are:

• The Pollard Rho Factorization Method
• Diffie-Hellman Key Exchange
• Encryption with Hash Functions
• Digital Signatures

Those are the concepts that make me scared. As far as the problems we should be able to know, I have no idea what to expect in regards to:

• Signing documents using RSA or ElGamal
• Describe strengths, weaknesses, and attacks for algorithms we have studied in class.

As I have been studying I am consistently pleased with how much more sense the mathematics makes the second time around. There are many ideas that I understand now that I didn't know when I first read and learned about them. That is making me more confident in my ability to do well on the test and I'm hoping that as I keep studying they will continue to make more sense as opposed to me just memorizing what to do.
As far as questions that I expect to see on the exam, I am guessing there will be a problem regarding finding a square root, a problem regarding calculating exponentials modulo n, and calculating Jacobi or Legendre symbols. I bet there will also be a problem where we are asked to describe one of the primality tests or factorization tests, and one where we are given a cryptosystem ans asked to describe a weakness or strength of it.

8.3 and 9.5, Due on November 10

I did not enjoy reading section 8.3. Hash functions have been a struggle for me from the start and this section only added to my woes. I don't understand the SHA-0 process, why letters such as A and B equal 1010, 1011 respectively, or what the 'W' variables are. My brain just does not think like a computer.
I enjoyed reading section 9.5 much more. You discussed it briefly on Monday and it's always easier to read something when the ideas have already been introduced. I like the idea of having alpha^q =1 mod p instead of using alpha as a primitive root.
I have one small suggestion regarding the homework. It would be nice if there was a key to selected problems posted online. I can usually solve all ten problems but I get the feeling there is often a better way than the method I chose. If it's too much work don't worry about it, and the grader is pretty good about catching and marking individual errors, but if you already have a key for the grader it would help my test preparation to see other ways of solving the problems.

9.1-9.4, Due on November 8

I enjoyed reading about the Birthday Attacks on Signatures. I believe you touched on it in class on Friday because it sounded very familiar. I also liked reading about the ElGamal Signature Scheme because it sounded familiar from what we have already learned studied.
Now, there are a few things I am still confused about. One big item is hash functions. I know that hash functions do not compose a cryptosystem but they are obviously used in cryptosystems. Once something has been sent through a hash function how do you get the message out again? I am very confused about them and their place in cryptosystems. Another question I have is about digital signatures. Are digital signatures anything special besides a specific message? It seems to me that they are essentially just messages that are unique to a sender. I'm not sure why the entirety of chapter nine is dedicated to digital signatures if they are just certain types of messages.

8,4-8.5, 8.7, Due on November 5

The section on the Birthday Paradox (and Birthday Attack) was the most interesting to me. I have learned that paradox before, and even put the mathematical probability to the test. I was at a party and counted 22 people so I went around and asked everyone for their birthday. Unfortunately there were no matches, making me look pretty foolish, but I told them if one more person showed up they would have the same birthday as someone already there. However, I realize now even with 23 people the probability is still only slightly better than 50%. Maybe next time I'll try it with 60 people. With the Birthday Attack I am wondering why anyone would use it instead of the Baby Step Giant Step method. The book claims that it doesn't provide a guarantee of a match, and that the BSGS method is generally faster anyway.
The last section on using hash functions to encrypt was hard for me. It looked a lot like the example you did on Wednesday but I'm still a little confused. I keep thinking hash functions are going to look like nice algebra functions but it's becoming increasingly more obvious that they are a whole different breed of functions.