5.1-5.4, Due September 30

1) Ok, I know you explained this in class but for some reason I don't understand XOR.  I mean, I guess I understand the operation, but I am not 100% sure why it works.  Also, in the S-Box, is the matrix by which you multiply just randomly chosen?
2) I am so impressed that someone even came up with this cipher.  I am curious about how secure it is?  Are we still using AES today?

Questions Due Monday September 28th, 2015

I spend 1-2 hours on each reading assignment.  The lecture definitely prepares me for the homework. I am frustrated because I feel like I have a very superficial understanding of the reading, but I probably need to take more time to really internalize and digest what I am reading instead of rushing through it.  That will probably be one of my goals for the rest of the semester.

I think the exploration of the homework is where I really learn the very most because that is where I need to make sure I understand the concepts enough to actually problem solve.  This class is my favorite this semester, and when I finally understand it and successfully decrypt or solve it is that much more fulfilling.

I think the biggest thing I need to work on is giving more time to the readings, but it is hard because I feel like I have such limited time with all of my homework for my class and work.  But I will still try to manage my time more so that I can take more time to read and understand.

4.1, 4.2, and 4.4 Due Monday September 21

1)  The notation is pretty confusing to me.  I think that I am following the diagram, but I am wondering if the first half of the message, or in their example case, the first 6 bits are also dependent on the second half, or the the last 6 bits.  Because it looks like it is adding terms from both the L and the R (after it has been through the function) in order to get the next R bit.  I follow the diagram but I don't completely understand the notation.  I also don't completely understand the meaning of a permutation.

2) After looking at the DES algorithm and reading a little bit about it, I am impressed that people came up with such a secure and somewhat fast encryption method.  I also think it is pretty cool that although the DES algorithm is too long to discuss in the previous chapters, they could teach the same idea through a more simple example.  I am curious to learn more about differential analysis and how it works in order to break certain encryptions.

2.9-2.11, due Friday September 18

1)  To be completely and utterly honest, I just don't understand binary numbers and how they work.  I am still trying to understand 2.8 which explains them and how you can represent everything in 0's and 1's.  Why is it more advantageous for us to do this?  For one time pads, I understand how it is so efficient and secure, but isn't the key extremely long?  I mostly just don't understand the binary system which I think is causing the big gap in my understanding for the rest of the sections.
2)  I do think it is interesting that this can work and somehow we can encrypt and decrypt so speedily.  I  am happy because I understand modulo much better now than I did while taking Math 290 and now I can see why it is actually so useful and applicable to us in our world today.

3.8, 2.5-2.8 Due September 16th

1) I don't understand how the frequency analysis is usually successful for play fair ciphers because the blocks of two letters are two small.  Then for block ciphers, do you just pick a random matrix M to begin with?  I also can't remember how to take the determinant of a 3x3 matrix.  But I can look that up before class.  I am confused on the description of this whole cipher.  Binary numbers????
2) The play fair cipher was clever to me.  I like to see the creativity in all of the different cipher methods.  The story about Sherlock holmes was awesome and refreshing.

2.3, Due on September 14th

1. I understand the first method of decryption but I don't understand their explanation of why it works.  For finding the key length, why would the number of coincidences tell us that the number of displacements is also the number of digits in the key?  Similarly, once we find how many digits are in the key, why do we count by that? (i.e. 1, 6, 11, etc.)  I do not even understand the second method of decryption and how to calculate it, but I will read that section again before class.

2.  I just think it is so amazing to see the correlation between cryptography and linear algebra.  I never imagined that I would be using the dot product to decrypt a message.  I also think it is pretty amazing that the decryption solutions have been found for all of these encryptions.

2.1,2.2, and 2.4, Due on September 11

1.  I feel like I have a very superficial understanding of shift ciphers and how they relate to modular arithmetic.  I don't understand how they found the multiplicative inverse for 9(mod26) is 3.  Are there multiple multiplicative inverses?  I also don't completely understand how you can have a function or an encryption that is not one to one.  Why do we need to make sure that the gcd(z,26)=1?

2.  I think it is pretty amazing that you can make a cipher text so hard to break if the adversary only has the cipher text available.  But then again, if you just know a little bit of plaintext with the cipher text, depending on the cipher, description becomes so much easier so suddenly.  I still don't understand the Affine Ciphers completely, but I would like to know why they are so much more secure.  I would like to continue practicing decrypting substitution ciphers since it uses so much wit and cleverness.

Guest Speaker Lecture, Due on September 11

1.  To be honest, the hardest thing for me to understand was the fact that someone actually forgot the code names and what they stood for.  Personally, I thought that they would take better care of that information.  It is also ironic that someone stepped forward explaining that they did remember the missing names, but that information was filed away and they didn't find it until 1987.  Especially when this is referring to scripture, you would think they would take better care of that information.
2.  I loved hearing all of this history because until the lecture, I had no clue that cryptography would have a connection to the church but it totally makes sense now.  One of my favorite ciphers was the one where there is a grid with three letters in each square.  Each letter has either none, one, or two '.  I thought it was really clever and it looks a lot cooler and more foreign when you don't know the code. Overall, the lecture just made me a lot more interested in Cryptography and it's place not just in history, but in our society now.  It helped me to see more relevance of the subject and helped instill a desire within me to keep working hard, even though it is sometimes difficult for me and it is just the beginning of the semester!

3.2 and 3.3, Due on September 4

1.  I simply could not follow the extended Euclidean algorithm.  I am not sure if it is because I don't understand the operation, but even after going over their example several times, I am having a hard time conceptualizing it or even understanding the steps and logic behind each operation.  Why is it useful to us?

I had an easier time understanding the basic idea behind congruences, but I guess I don't yet see how it will be helpful to us in this course or in real life.  I am sure that will become more obvious as the class goes on.

I had a hard time understanding how they solved the last example on pg. 73.  How is 4/11111 the same as working with mod 12345?

I also don't completely understand how to work with fractions.  Is there a logical way to keep track of when I need certain integers to be relatively prime or when their gcd(a,n)=1.


2. When we studied congruences in Math290 I was curious as to what discipline or sector of math to which it is helpful.  I am excited to see how it is a part of cryptography and keeping messages safe.

I think my favorite part was in the second example on page 73 when they show how 7 is congruent to 18 which is congruent to 29 which is congruent to 40 and as we find all the different congruencies it makes it possible for us to divide.  It's an interesting way to think and sort of reminds me of how our number system is base 10, but how you can do math in different bases.

1.1-1.2 and 3.1, due on September 2

1)  In section 1.1.1, I didn't completely understand the description of airplanes determining if another airplane is a friend or a foe.  It says, "send a random message to the plane, which encrypts the message automatically and sends it back.  Only a friendly airplane is assumed to have the correct key.  Compare the message from the plane with the correctly encrypted message.  if they match the plane is friendly.  If not, it's the enemy."
This could be very elementary, so bear with me, but I guess I just don't understand the system.  Anytime you send a message to a plane, it will be sent to their plane and they will encrypt it using their encryption machine and send it back?  Or do they send their response in an encrypted message? I guess I just don't understand what exactly the cipher text would be in this case... the plain text that you just sent them now encrypted?  Or is their response that is encrypted?

I am also not 100% sure on the difference between a key and an algorithm.  What does it mean to keep the algorithm the same but to just change the key?  Does algorithm just mean the type of key?  Like the equation for it?

In sections 3.1.2

I am having a hard time wrapping my head around the Prime Number Theorem.  Why are we trying to prove that pi(x) is the number of primes less than x?  How does this prove that there are infinitely many prime numbers?

I have a surface understanding of the Lemma on pg. 65, and I definitely could not replicate the proof.

Lastly, I just can't understand the Theorem and Corollary on pg. 68, but I will continue trying to read and understand it before class tomorrow.  I don't understand it to the point that I can't even really identify the reason I don't understand it.



2) I loved chapter 1 because it really illustrated the application of this material in our world today.  I am very surprised because I didn't realize how cryptography is so widely used and severely needed in our world of technology, despite the fact that I use it every day.  I like that in 1.2 it broke the applications into four different, clear sections.  I have used and appreciate each part.  I am also interested to see the connection between cryptography and games.

In chapter 3, I felt like I was back in my Math 290 class.  The proofs are simple and beautiful for the most part and I find myself wanting to work out the proof myself before I read the solution.  I am very intrigued by the Euclidean algorithm and I am curious as to how it was discovered.  I am amazed at how quick it is and the fact that you don't need to factor.

Introduction, Due on September 2

Haley Rasmussen - Math 485 Mathematical Cryptography

1. I am a Math Education Major.  I am a Senior and will student-teach Fall 2016.
2. I have taken Math 313, 334, 290
3. I am taking this class because it seems interesting and fulfills a credit for my major.  I also have little to no experience with programming, so I would like to learn.
4. I don't have any experience and at the moment I am not very comfortable at all, but I am willing to put in the time to learn and work with you or the T.A.
5. The best and most effective math professor that I had was extremely interested in the student and ensuring that they understood.  They didn't just talk at us the whole time, but helped us to work through it ourselves so that we could learn more completely.

The worst math professor that I had was completely disconnected from the student, lectured at us the whole time, and that was it.

6.  I majored in Ballet at the University of Utah for two years but I decided to transfer to BYU so that I could become a Math Teacher.

7.  I can't make it to your office hours, but I could come MWF 2:00-3:00 pm or later in the afternoon at about 4:00 pm