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.
Why Hacker News points people here: Recommended as a moderately formal, clear introduction to finite fields, useful beyond AES.
“this is a pretty good introduction (yes, it's for AES, but the principles are the same)”HN comment, 2019
“is a really excellent explanation of the internals of a number of crytographic algorithms.”
Explains finite field origins of AES S-Boxes
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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).
RecommendskttaJul 2017
“I recommend this lecture to understand it in the context of crypto”
Lecture on Galois fields in crypto context
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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.
RecommendsdnauticsFeb 2019
“this is a pretty good introduction (yes, it's for AES, but the principles are the same)”
Moderately formal introduction to finite fields
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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 itdnauticsNov 2017
Finite fields background
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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.
