Lecture 7: Introduction to Galois Fields for the AES by Christof Paar
Why Hacker News recommends it
Recommended as a moderately formal, clear introduction to finite fields, useful beyond AES.
What it is
Christof Paar's university lecture introducing Galois fields and finite-field arithmetic as used in AES. It covers the mathematics behind the AES S-box.
Recommended by 3 HN commenters across 3 different months, 2017 to 2020.
What Hacker News said
Strong rec opheliate · 2020-12 · on “Understanding how AES encryption works”
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).
Recommends ktta · 2017-07 · on “Galois Theory for Beginners (2010) [pdf]”
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.
Recommends dnautics · 2019-02 · on “Reed Solomon codes are cool”
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]
Cites dnautics · 2017-11 · on “STARKs, Part I: Proofs with Polynomials”
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.