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 ( ▶ this 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).

in “Understanding how AES encryption works” · View on HN

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): ▶ this video

in “Reed Solomon codes are cool” · View on HN

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

in “Galois Theory for Beginners (2010) [pdf]” · View on HN

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

in “STARKs, Part I: Proofs with Polynomials” · View on HN