Introduction to Cryptography by Christof Paar
3 HN recommenders · recommended in 4 months, 2017–2020
1:30:50 · 278K views · Jan 30, 2014
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 as a moderately formal, clear introduction to finite fields, useful beyond AES.
4 comments from Hacker News
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).
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.
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 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.