6.5-6.7 and section 7.1 due October 28

1) I am just not 100% sure what kind of crypto system uses discrete logarithms.  Is stand RSA or something similar?  It's probably a silly question, but perhaps it will make more sense in the lecture.
2) It is interesting to me that we can only compute discrete logs for primes that are about as large as the primes that we can factor.

6.4.1 and 6.4.2, Due October 26

1) This might be a silly question, but I was wondering if it is hard to factor something, is it also hard to find the square root of that really big number?  Supposing that we really did want to check every prime up to its' square root?
I don't understand how they got the matrix they did on pg. 184.
2) I think its cool that the linear dependency will help us understand whether or not we have factorization.  But I would like to understand better how to look for linear dependencies in different moduli.

6.3, Due October 21

1)  I can't really follow the Miller-Rabin Primality Test.  What does it mean for something to be a pseudoprime for the base a?  Why would we even want to know if something is prime?  Why is that an advantage to us?  Does composite mean factorable?  Why is the success of these two methods not guaranteed?
2)  I think it is fascinating that we have these different tests to test if something is prime or not.  The fact that we can do it with such giant numbers is amazing, and that our computers can do it so quickly.  I am still trying to figure out why this would be of so much use to us.

3.9, Due Friday October 16th

1) Actually, the reading was pretty clear and straight forward.  I understand the actual operations but I am not exactly sure that I understand the reasoning and justification behind it.
2) I am just excited to see how we are going to use this in the context of cryptography.

6.2, Due October 14th

1)  How could someone come to know the first m/2 or the last m/4 digits of p if it is not part of the public key?  Same for d?  I don't fully understand the short plaintext attack on RSA.  And I still don't really understand why the fraction approximation of decimals works.  I understand how to do it, but I don't get why.  Do we need to understand that?
2) I am impressed with all of these attacks on RSA but I am wondering if they are ever REALLY used in real world.  Are these the only known attacks?  Are people still studying RSA and trying to find different attacks?  Or is it futile until we have quantum computers?

3.12, Due October 12

1)  This is a really cool idea but I am wondering how we will be able to find the closest fraction that looks like the decimal if the irrational number.  Is there something we can do on sage or on the computer to find fractions that seem to look a lot like those decimals?
2)  I will be interested to see how we use this in cryptography.  What are the applications?

6.1, October 9

1) I don't exactly understand how Bob makes n and e public.  What does it mean to have a public key crypto system?  In what way would he make it public?  And would it make it easier to decrypt?  Less unsafe?  And although we have been practicing working with really really big exponents, how in the world are we going to deal with ones this big..?
2) I think it is cool that we can use this basic number theory for encryption.  I was trying to imagine how we would use Euler's equation for a cipher, but I like to see the application.  I also think it is funny their is a method called PGP (Pretty Good Privacy).  Why does it not matter if e-mail is that secure?  Why do we encrypt e-mails?  For security?  Or to make sure what is sent stays true to what was intended to be sent?

3.6-3.7, Due October 7

1) I honestly don't really understand the proof for format's theorem but I think it is really cool how it works and how it is so helpful for us to evaluate somewhat complicated expressions in mod(n).  I am also not completely understanding the general idea of Euler's theorem.  What is that notation on pg. (81) half-way down?

2) I love learning all of these new ways to re-write expressions and magically simplify.  I also think it is cool that such ancient discoveries have proved to be so useful in cryptography and with computers.  No longer is it just cool for math-sakes.  It actually has application.

3.4-3.5, Due October 5

1)  I guess I still don't fully understand what it means to just write one congruence into a system of congruences mod factors of n.  If this system of congruences is not like an addition of the two congruences, how do they relate to one another.  It is a pretty cool idea.
2)  I love to see all the different things that we can do modulo.  I also think it's cool to see the cross between linear algebra and this class.  I think overtime we see the material cross over between subjects, it just makes it that much more meaningful and applicable.

Due October 2, 2015

As I was looking over the list of things that we have learned over the semester, I honestly feel that most of what we have learned is important.  But I think for me, a lot of the number theory that we have learned is important (modulo, divisibility, GCD, Finite Fields, etc.)  I think it is important to really solidify our understanding for these different concepts so that we can actually apply them to the ciphers.  I think that it is important to understand generally how DES and AES work because they are actually used today, or in more recent years.  However, these are some of the hardest topics for me to understand.

I expect to see questions that are conceptual, asking about the actual cipher, strengths, weaknesses, and how to encrypt and decrypt.  I think this because a lot of the ciphers that we have learned about require computers to decipher.  I also expect to see questions that require us to practice various algorithms and procedures, like the Euclidean algorithm,  finding solutions to linear congruences, etc.

I REALLY need help understanding ECB,CBC, and CTR.  I missed a few on the homework and I have a very superficial understanding.  I also don't really remember the reasoning behind decryption of LSFR.  Meet in the middle attacks!  Those are the biggest things.  However, I do need to continue reviewing everything.