Lecture 7: Introduction to Galois Fields for the AES by Christof Paar

While we're here, Christof Paar's 'Introduction to Cryptography' lecture series (freely available on YouTube here in English: [LINK] , originally delivered at Ruhr University Bochum) is a really excellent explanation of the internals of a number of crytographic algorithms. The lecture on Galois Fields ( [VIDEO] ) is especially useful in understanding AES, and explains where some of the operations described in the blog linked here actually come from (i.e: S-Boxes used in AES are derived from inversion in finite fields).

Galois fields are used in crypto a bit, and I recommend this lecture to understand it in the context of crypto [VIDEO] PS: He has an entire series of lectures on his channel. Highly recommend.

if you want to learn finite fields somewhat more formally, but not so formally, this is a pretty good introduction (yes, it's for AES, but the principles are the same): [VIDEO]

in practice these polynomials won't be over integers or rationals, they will be over finite fields. [VIDEO] they're also used extensively in reed-solomon coding.