yeah, i just have a very visual brain. when you use these words i get pictures of processes, and i naturally see scales and vectors, symmetries and inversions.
a lot of what seems absurd is just a reflection of what is sane.
random number generators, for example. people like to split hairs about whether it's really random if you can model it, but taht's teh thing, you can't model it until after it's happened. it's because the main mechanism of PRNGs relates to rounding errors and overflows being sent around in a circle, asymmetric cryptography is entirely built on top of the entropy caused by clockwork arithmetic, which in practise just means that bits fall off the left and they are gone, but because of the permutations and the rules of arithmetic, you don't get zero straight away, you get less... something... which we call entropy. to make it secure, you need good entropy, and then it's hard to figure out what was lost because it was more complicated than the thing it was added to.
haha. anyway. i love arithmetic. i first fell in love with it via the mandelbrot set but cryptography is even cooler. and the related coding systems, the principles of representation, integers, dimensions...
Still have small issues with your framing of crypto, but can't get into it now. Another time!
Oh, and one other thing I can't let go of, I think you once described finite fields inaccurately. They're entirely classsified, and all of order p^n for any n>=1
i may have been confusing them with arithmetic groups, which are a consequence of finite fields.
i just think of finite fields like the old school games where you go across the edge on the right and come back around on the left. the rules about what happens to you in that process though, that's where the devil is. does it wrap around? in what way, let's say it's binary, and we sequence the operation as one pass across the bits, then you can say "yes, this divide threw all the bits to the right one, so we can bring a new bit back from the left now" or if you add two numbers, and it overflows, how do you decide what way those overflowed bits go around the circle? is it a circle, or is it a mirror thing, so if 1010 overflows does it become 0101 on teh other side?
Thread collapsed
Thread collapsed
