16.5, due december 11

i got pretty lost in all the mathematical explanations, which was kinda funny because i already knew the methods discussed in the section. i think i had forgotten some of those methods, but it started to come back to me. it will really help to see how these elliptic curves play into those methods and how the two can work together. it will also help to work through examples.

i don’t know why i doubted that elliptic curves could be used with encoding/decoding. of course they can! i thought it was so interesting that we have these methods for coding, and we have so many different ways we can use them. i thought they were hard enough when we were just using integers, and now we’re using elliptic curves! i just think it’s so cool that we can do so many things with math. i love math.

16.4, due december 9

this section didn’t seem too confusing. i think that means that i don’t actually get it. it seems easy enough, but i will definitely need to see examples and learn about it in class so that i really do understand it. i also don’t really see how this could help with encoding/decoding.

i thought the laws for GF(4) were pretty interesting. i really enjoy using different fields that have different laws. sometimes they can be confusing and hard to remember, but these laws are different than any of the ones i’ve ever learned about. i wonder how these laws came about—was it because someone decided that those were the laws or did someone notice the laws? math is so crazy and so interesting.

16.3, due december 6

i’m a little confused as to how factoring with elliptic curves works. i reread the section to see if i could make any more sense of it, and i think i understood it a little better. i’m not completely confident with these elliptic curves. actually working through an example will be very helpful for me.

i don’t know why, but i really liked that if an integer has only small prime factors that are less than or equal to B then that integer is called B-smooth. that name just made me laugh. also, even though i don’t really understand it all, i think the math behind these elliptic curves is pretty interesting. it’s so cool that this has all been discovered and that it can be useful!

16.2, due december 4

i was a little confused by the representing plaintext section. i couldn’t quite understand how the encoding process works. i do get lost in mathematical explanations in this book, so i probably just need to see an example and i’ll get it.

it was really helpful that we went over this section in class before i read it. i know i would have been confused by the math, but since i’ve already seen it and gone through examples, i was able to follow most of the section. i was reminded how cool i thought the math was. this was the first time i had been introduced to elliptic curves like this (at least that i can remember) and i really enjoyed adding points together.

16.1, due december 2

i got a little lost in the math of this section. it probably doesn’t help that i’m not very comfortable with ellipses. but i was also a little confused as to how this will be useful in cryptography. with other sections that are all about math, i’ve been able to see how the math in those sections might be used for encrypting messages. but i have no idea with this stuff. it will be interesting to see how it relates.

i thought it was really interesting that we use infinity as a value. most of the time, i just ignore it or avoid it because it is so big and you can’t really do anything with it. i was surprised to see how often that point is referred to and used. that will take some getting used to, honestly. but the context that it will be used makes perfect sense. i was a little surprised that it is even defined or placed on the axes.

18.1 and 18.2, due november 26

i was a little confused by the parity check and two-dimensional parity code examples. i guess i am confused because parity means positive or negative, but i can’t see how that applies to either example. i felt like those examples were making sure the message was odd or even so that it would be easy to detect an error. maybe there’s another meaning of parity there that i’m not getting. that was a little confusing for me. i think i followed everything else pretty well though.

the error correcting codes were super interesting to me. it was cool to think about how we can change a vector into a codeword by changing the fewest places possible and that will allow us to detect errors. so far we have just learned about different encrypting methods, but we haven’t focused on how to protect against or anticipate errors in the coding. i think that’s an important thing to consider and i haven’t even thought about that.

2.12, due november 25

i think i kind of understood this section. of course, as soon as we talk about it in class i’ll probably be totally lost. i am a little confused as to how this method works, as in exactly how the rotations and steps encrypt messages. i got a little lost when the section described the encryption process itself, but i think it will be helpful to hear the teacher explain this method. but i really do think i kind of understand this enigma stuff.

if i understood this stuff right, i think this is a really interesting idea. it was also interesting to read about the attack on the enigma. it seems like it would take a really long time to decrypt a message, but to me it seems like using this enigma method is pretty secure.