Cryptography Question

How long do I spend on the homework?  Well it depends but it usually takes me about an hour or so to get through the reading and blogging to try and make sense of it, and then about another 2 hours for each assignment.  They have been getting longer as the coursework gets harder but I think thats to be expected.  The reading has helped me get ready, and especially the diagrams but the lectures have been much better in preparing me.  I find if i pay attention in class and take notes that I am much better prepared to work on the homework.  The concepts are explained more fully in terms that I can understand.  That would be the thing that has been most helpful in my learning.

Reading 4.5-4.8

I guess that it's important to focus on the things that we do know and understand... What I thought was interesting out of this reading was 4.8, the section on password security.  I thought that there is a much larger thought process that goes into passwords than I had realized.  Also the salt factor seemed like it would greatly improve security, but yet again they say that they already have to work on new ways to keep passwords secure as these encryptions will soon become obsolete.

What I had a harder time understanding, were several things.  First I just had a small question on how you could build up a codebook, would it only work for people sending the exact same message? Because otherwise wouldnt the block cipher change more than just one letter in the corresponding ciphertext?  Also the output feedback mode confused me a little bit with when you split and XOR everything.

Sections 4.1, 4.2, 4.4

After an initial reading about DES encryption my head started to spin a little bit.  I have tried to back up and read through section 4.2 a few more times to at least understand the concept.  However the confusing part lies in 4.4.  Talking about splitting up and sending different parts of the plaintext different places was often hard to follow.  Also the part about using different S-boxes wasn't overly clear to me.

Something that I DID understand, and thought was interesting was how companies like banks might use two different types of encryption for their data.  We read about how they might send the key to the next cryptosystem via a previous one.  I had been wondering how different companies might receive keys from the senders without loss of security.  Using public key encryption to send it was something that I had not thought of before.

Reading 2.9-2.11

Something that I dont understand is what makes the one time pad system unbreakable as opposed to other systems, this seems to be almost simpler than some of the other ones that we have read about, but the book just bluntly states that it is unbreakable.  Will we be susceptible to mockery in later years as new people figure out a way to solve our "unbreakable" code?  Also I got pretty lost reading about LFSR sequences.

The part that i liked was going through the realization that what we think is random may not be random.  That in fact if I for example were to make up a "random" sequence of ones and zeros that not only would it not be very random you could probably predict where I was going, and be able to tell that a person had done it.  True randomness is hard to come by.

Reading 3.8 and 2.5-2.8

What I found interesting, (along with the entire story about Sherlock Holmes) was that the block cipher method made genuine sense to me, being able to invert matrices seems to have finally come in handy.  It also makes sense how it is so much harder to use frequency analysis because of how changing on letter of plaintext will manipulate a much larger portion of cipher text than with other ciphers that we have been using.

The hard part of this reading was understanding how someone would break the adfgx cipher without the keyword.  The book just said if you know the keyword then its easy.  But don't we only assume that they know the method not the key? It seems like without that, that it would be difficult to come to any kind of conclusion.  I guess that is why they thought it was strong at the time.

Reading 2.3

I found it interesting that they have discovered not only a logical problem solving way to solve Vigenere ciphers but also a mathematical approach as well.  And as usual, math seems to bring us closer to the answer faster.  Also it was a good reminder that we can never be content with what we have already done, just as people used to think that these were strong codes and now we can break them easily, it is the same with everything we do, we should always try and push ourselves to do bigger and better things.

What i didnt understand particularly well, was how they decided that finding how many times you get the same letter after shifting the cipher text would yield the key length.  I don't seem to be able to see the correlation between the letters matching up and the length of the key.  Is it maybe because you hope to have letters like e make appearances in both pieces of the cipher text and you will be shifting letters the key length apart similarly? (I don't think that that made sense outside of my head, I guess thats what a blog is for...)

2.1-2.2 and 2.4

Some of the things that I found most interesting, were just thinking about how all throughout history, lots of people, famous people, people I've heard of and read about, have used codes to deliver information.  I also hadn't realized, or thought about completely how much knowledge and mastery of other peripheral things would matter in cryptography.  For example in substitution ciphers, the more you know about the language you are working in the better, knowing things like h often precedes e but hardly follows it, are some of the cruxes that code breaking is based on.

What is hard for me to stomach a little, is how much guesswork needs to be done.  Cryptography has proven to be  very different kind of math, it's not just every time you see this kind of problem, apply this formula.  But in essence you have to be willing to try many different things and several kinds of attacks.  The approaches are still very logical, which appeals to me, but I am afraid that the guesswork that needs to be done will be ever increasing as we move into harder types of codes.

Guest Speaker Ardis Parshall

What I thought was the most interesting was when she was talking about the pigpen code.  Even though it isn't a code that would be very strong if anyone was trying to break it, it seems like it would be fun to use with friends.  Kerckhoff's principle seems to ruin all the fun of that kind of code...

Something that wasn't necessarily difficult to understand but that did spark questions, was the use of codes through other people.  It seems that the more people that are involved in the use of a code the more chance there is of it being broken.  For example Ardis was talking about how people would send messages through telegram, and normally that the person who was sending the message would have to have someone else actually send the telegram.  At some point, wouldn't the person who was sending gibberish get curious enough to try and find out what was being sent?  I wonder if there is some kind of formula or idea about how quickly code breaks down depending on the number of people using it.  Maybe that is the idea behind public key encryption.

Reading 3.2 and 3.3

The most interesting things in these sections were how you can run the Euclidean algorithm forwards and backwards to not only help you to find quotients but also to help you find the gcd of different and even large numbers.  Also it was interesting how addition, subtraction, and multiplication in Mod n seemed to be pretty straight forward but that division was the operation that is tricky.  Then you have to make sure that the gcd of n and your divisor is 1.

The pieces that I found the most difficult in this section were first the very last step of the proof for the first proposition, it made sense all the way until it just stated that b is congruent to c.  I feel like I am missing a step, or there is something that I'm not seeing there.  Also trying to wrap my head around non-linear congruences seems a little strange.

Reading 1.1-1.2 and 3.1

The hardest part of this section for me to understand was the piece about public key algorithms.  It is hard for me to understand what exactly it is that Bob knows that lets him decrypt the message when everyone has access to the message and the key.  I am still having a hard time seeing how this would solve the problem anyways because Bob needs extra information given to him somehow to be able to decipher the message.

The most interesting parts of this section were the real world applications of plaintext attacks in World War II.  It was interesting, (and a little scary) to see how using a little logic and a few interceptions that the Allies could become aware of entire encryption keys and all the while the German outpost never even realized they were feeding information to their enemies.  And to think that that one little slip could have such large ramifications.  It was also interesting to read about how the more that cryptography develops the more information we are willing to let Eve see.

Sept 4. Introduction

My name is Spencer, and I am currently a senior at BYU studying math.
I have taken Math 290, 313, 314, 341, 371.  And I am currently in 342 as well as 485 and have taken some stats classes as well.
I am taking this class because when I was in Math 371 I took it with a group of friends and we decided that it would be fun to take this together as well.  Having other people in the class I knew and would talk to made it easier to study and to get homework done.  It helped me understand more and I hope to be able to do just as well in this class.
I haven't used any of those programs hardly at all, and have little experience with any other mathematical program.  I have limited programming experience, I have taken a few classes in high school and here at BYU, but can general navigate my way through computer programs.
The most effective math professor that I have had, worked hard to make himself available to me, so that I could get the help that I needed on concepts that I did not understand they also taught in such a way as to allow me to feel like I was going to be able to make it if not excel. He helped me to feel not so overwhelmed even though the material was challenging.
Something unique about me is that I was on a national math team in high school (I wish that I still felt that smart) and am usually confident in my ability to get things done.
I will be attending your office hours as often as I can, luckily they are right when my classes end.