Galois Finite Fields and the Advanced Encryption Standard (AES) (cs.uaf.edu)
67 points by ankitg12 3 days ago
mmozeiko 5 minutes ago
> Inverses exist for each operation, which makes decryption possible.
It is worth mentioning that in modern AES usage this feature does not really matter, because block cipher is used in CTR mode. In CTR block cipher is used to create long keystream bytes (pretty much one-time-pad key). This keystream gets xor'ed with plaintext to get ciphertext. Then getting from ciphertext back to plaintext is exactly the same xor operation with same keystream, no inverse AES operations needed.
dboreham 3 hours ago
I don't know that "Weirdly" is right for the polynomial equivalence -- isn't that what Galois was trying to do in the first place (prove things about polynomials such as the impossibility of analytic solutions to higher order polynomials, and the impossibility of constructing a heptagon)?
tomsmeding 34 minutes ago
I read the "weirdly" as "unexpectedly", i.e. "you might not see this coming, but it's still true (and there's deep theory behind it)".
bananaflag 2 hours ago
A bit, yeah. I deleted a comment where I said it's not quite the same but it kinda is, and figuring it out is very rewarding.