Lecture 7: Introduction to Galois Fields for the AES by Christof Paar
Introduction to Cryptography by Christof Paar3 HN recommenders · 2017–2020
278K views · lecture · evergreen · Uploaded 2014-01-30
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.
9:52Vectors | Chapter 1, Essence of linear algebra
3Blue1Brown
1:03:43How to Speak
MIT OpenCourseWare
57:151. Introduction to Human Behavioral Biology
Stanford
19:42But what is the Fourier Transform? A visual introduction.
3Blue1Brown
1:21:52LEADERSHIP LAB: The Craft of Writing Effectively
UChicago Social Sciences
1:11:40MIT's Pathway to Fusion Energy (IAP 2017) - Zach Hartwig
MIT Plasma Science and Fusion Center
52:29Stanford's Sapolsky On Depression in U.S. (Full Lecture)
Stanford
54:56Justice: What's The Right Thing To Do? Episode 01 "THE MORAL SIDE OF MURDER"
Harvard University
4 comments from Hacker News
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.
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.
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]
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).