Skip to content
Hallway
0:00 / 0:00

#aes#galoisfields#finitefields

Lecture 7: Introduction to Galois Fields for the AES by Christof Paar

Introduction to Cryptography by Christof Paar

71K subscribers • 1 video on Hallway

YouTube
  • Recommended by 3 people: 3 on Hacker News.
  • A classic. People kept recommending it from 2017 to 2020.
  • Presented by Christof Paar

Intermediate. Assumes working knowledge.

278K views12 years ago3 recommendations

SecurityComputer scienceCryptographyMath for programmers

Christof Paar introduces Galois fields and finite-field arithmetic, explaining the mathematical foundations behind the AES S-box.

Interested in studying cybersecurity at the highest level? Bochum offers one of the most advanced academic environments for cybersecurity in Europe. The Max Planck Institute for Security and Privacy (MPI-SP) collaborates closely with the Horst Görtz Institute (HGI) at Ruhr University Bochum (RUB), where leading experts from across the field contribute through excellent teaching and pioneering research. Find out more at informatik.rub.de/en/studies/its/. We are also continuously seeking outstanding young researchers interested in joining our growing teams at both the MPI-SP and RUB. Opportunities at MPI-SP: ► Internships – A great way to explore research and potential Ph.D. opportunities. ► Ph.D. and Postdoc – Fully funded positions to pursue research in the broad area of computer and information science. ► Tenure-Track (Group Leader) – Lead your own group and establish your research profile (W2 German Federal Civil Service Remuneration Act). ► Detailed information: mpi-sp.org/53451/why-join-us Opportunities at HGI/RUB: ► Ph.D. & Postdoc Positions – Open to excellent graduates and researchers in computer science, engineering, mathematics, psychology, or related fields. ► CASA Jump.Start Program – Supports outstanding postdocs in developing independent research agendas (E14 TV-L, no teaching duties). ► Detailed information: casa.rub.de/en/jobs Discover why Bochum is a leading hotspot for cybersecurity: bochum-international.com/cybersecurity

Why it's here

3 people recommend this

What people say. Highly recommended as an exceptionally clear explanation of the finite-field mathematics used in AES and other cryptographic algorithms.

opheliateon Hacker News • Recommends

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 ( link to 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).
View on Hacker News

kttaon Hacker News • Recommends

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 link to this video PS: He has an entire series of lectures on his channel. Highly recommend.
View on Hacker News

dnauticson Hacker News • Recommends

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): link to this video
View on Hacker News

dnauticson Hacker News • Mentions

On “STARKs, Part I: Proofs with Polynomials”

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