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.