7.2, due november 1

there was a ton of mathematics in these sections, and i got really lost. i think we may have gone over one of the methods in class, but the book must do it differently because i got lost. it was really hard for me to follow these methods in the book, but it will really help once i can work through examples to see how these methods work.

i think it’s really interesting that these methods can be used to encrypt and decrypt messages. to be honest, i don’t think i can really see how they can be used. but i’m sure we’ll see that soon. i know they wouldn’t put these methods in a cryptography book unless they could be used for cryptography. it will be interesting to see how these methods really work and how they work in cryptography.

6.5-6.7 and 7.1 due october 30

i got a little lost in the description of the public key cryptosystem and how it works, but i’m sure i will be able to follow it when working with an actual example. i was also a little confused by the discrete logarithms, but i think i just remembered this late and was rushing. it’s usually a little rough when i try to learn things by reading in a textbook. i do much better if i can work through an example.

when i was reading through that challenge, it took me a second before i realized that we can actually figure that out (we can right?). it really amazes me how far we have come and how far technology has come. we have given ourselves the ability to do so many things because we have created computers that will do so much more than we could ever imagine. for example, we can continue to deal with those ridiculously large numbers and it’s not even a big deal. math is awesome.

6.4.1 and 6.4.2, due october 28

i was little confused about how the matrices play into the quadratic sieve method. i got a little lost when the book explained how to create the matrices and how to use the numbers in the matrix (linear dependence—i also don’t really remember what that is.) i also just get lost in all the numbers and explanations, but i understand it better when i work through examples. the homework really helps me to solidify my understanding.

i am in a constant state of awe-ness because we can find factors (if any) of these massive, many-many-digit numbers. i still can’t wrap my brain around how huge these numbers are, but i feel a little more comfortable handling them on a figure-out-if-it’s-prime-or-not basis. i actually don’t know if i’ve ever dealt with a number that big, but i’m sure we could do it. math is amazing.

6.4 until just before 6.4.1, due october 25

i never found out how to choose B. the book mentioned that it’s kind of crucial to pick a good B because it will determine the chance of success and how fast the algorithm goes. it said that B would depend on the situation, but i didn’t read any more about how to choose B. i probably just need to see an example.

i kinda think it’s ridiculous that we even think about numbers with 100s of digits. however, i do think it’s super cool that there are ways to factor these massive numbers (and be able to find out if these huge numbers are prime). i’m blown away that people have discovered that.

section 6.3, due october 23

i was trying to understand how the primality tests work and how we know they work. i got a little lost in the notations and mathematics of it all. it will be helpful to see/work with examples. also i have a hard time wrapping my brain around 200-digit numbers. i can’t even begin to fathom it. that always throws me off.

even though i didn’t understand how we know they work, i think it’s super interesting that we have these primality tests. i also think it’s interesting that for there tests, we can pick a random a. there are no restrictions on a, and they are literally completely random (with a restriction…it has to be between 1 and n-1) but it can still prove whether n is prime or composite.

3.10, due october 21

i’m a little confused about the jacobi/legendre symbols. i really did get confused in all the mathematics of the examples and proofs in this section. it will be really helpful to see lots of examples and to work through examples on my own. that way i can familiarize myself with these symbols.

i think it’s so cool that we can calculate those “fractions” (i was also a little confused by those and if they really were fractions) by using all the different properties. i also think it’s so cool that we can use all these different methods to calculate squares mod p. math always blows my mind and it’s so interesting to learn new things!

3.9, due october 18th

i was a little confused about how a negative number could have a square root if the positive of it didn’t have one. i was pretty sure that negative numbers don’t have real square roots. but then i read through an example and i realized that it was the negative number (mod n) so it makes sense how it would have a root. again, it’s hard for me to just read through examples and understand them. these seem pretty simple, but i probably won’t really understand them until i do some examples by hand.

i think it’s so interesting what we can do with math.it’s also interesting to me how helpful modular arithmetic can be. we can find all solutions of x^2 congruent to b(mod n). it’s also interesting that if there isn’t a root for a number, then its negative will have a root. i love math!

6.2, due october 16

i got a little lost in the explanations and procedures in the short plaintext section. really, i just get confused whenever the word “bits” is used (i think that’s just a personal problem). there are a lot of steps and i keep getting them mixed up. i need to see/work on an example so that i can solidify these concepts.

i thought it was interesting that timing attacks could actually work. i don’t think i would have ever thought that timing how long it took to do the calculations (along with all the calculations—i didn’t really understand all that…) could be a way to decrypt a message. i didn’t really understand the process behind it (or the explanation of why it works), but the premise is mind-blowing to me.

3.12, due october 14

i got a little lost in all the fractions. i think i might have an idea of how to find them and how it all works, but i need to see more examples of this/work with the concept myself. also i was a little confused with the theorem in the section; i don’t think i see how that theorem is helpful. maybe when i have to use it i will see that it really is helpful.

i think it’s so interesting that we can use continued fractions to better approximate real numbers (with lots and lots of decimals). it makes a ton of sense when you think about it, but i never had. i always knew that if i wanted to accurately represent a number with crazy decimals, it was better to stick with the fraction. however, i never really thought about using a different fraction that would be a better, more exact representation/approximation of all those decimals. it makes so much sense.

6.1, due october 11

i got a little lost in all the calculations. the calculations didn’t look too complex, but there were some pretty big numbers. the order in which all the calculations need to be done was a little daunting, and i might have some trouble remembering which step happens when. but then again, maybe i don’t have to be responsible for knowing each step. i’m not sure. but doing examples will definitely help me solidify all this.

we’ve learned so many different methods for encrypting messages, but all of them would require a key in order to decrypt. i think it’s so interesting that this algorithm doesn’t require a key for decryption. also, it’s interesting how useful prime numbers can be.

3.6-3.7, due september 9th

i was a little confused about the three-pass protocol, especially about why alice and bob would send that box back and forth. it seemed a little excessive. but reading through the mathematical explanation made me realize that it probably increases security for the message. i was also a little confused by the mathematical steps alice and bob needed to do in order to properly send the message. i just got a little lost in the notation.

i had never heard of primitive roots before, and i think it’s so cool that that happens. it is so interesting to see all the different things people have discovered about numbers and how numbers behave. i also think the modular arithmetic is fascinating. it’s amazing to me that primitive roots exist and that someone noticed them. numbers are so cool!

3.4-3.5, due october 7th

i was a little confused on how to use the chinese remainder theorem. i think i kind of understand what it is, but i remember being a little confused when i learned about it in 371. it’s always easier for me to understand these math processes when i actually do them myself.

it was really interesting to see how easy it can be to work with modular exponentiation. i probably would have just multiplied it all out and then reduced it and it would have taken me forever. it makes sense that the method from that section would work, and it makes me feel better to know that i can reduce as i go instead of being stuck with a huge number.

questions, due october 4th

i think the most important ideas we’ve learned are the ones that have taught us how to solve mathematical and algorithmic problems, just like the learning outcomes said. to me, the most important ones are the ones that cannot be done on a computer/technology, because we won’t always have access to those. i think those other ones are important as well though.

i expect this test to be pretty similar to the homework we’ve been given, without the ones that required a CAS or something similar. i think there might be some questions like the ones we’ve done in class as well. maybe even a couple where we have to decode a bunch of jumbled letters.

to be honest, i haven’t really started studying for the exam, so i don’t know what i still need to study. but i do know that i need to go over the most recent material. i feel pretty confident with finding the generator and putting that stuff into binary, but once matrices are put in the mix, i get a little confused.

5.1-5.4, due october 2

the most difficult part of this section was just keeping all the abbreviations straight and separate from each other. as i was reading, i would realize that i wasn’t exactly sure what was going on, and i realized it was because i read over an abbreviation but didn’t recall what it was! as i continue to use them, i will be able to keep them separate and know what each stands for and what they mean.

the coolest part for me was just knowing that after doing all this stuff, the code is still unbreakable! reading through about all the bytes and matrices and inverses made me want to not even try to break the code. but it’s just so amazing to me that someone (or something) can still break this.