Unlocking the Secrets of Group-Based Cryptography 🔐

Goal.
I would like to tell you a bit about my favorite subfields of mathematics (in no particular order), highlighting key theorems, ideas or concepts and why I like them so much. This is a variation of “My favorite theorems” and I park the videos on that list as well.

This time.
What is...group-based cryptography? Or: Subfields of mathematics 25.

Disclaimer.
Nobody is perfect, and I might have said something silly. If there is any doubt, then please check the references.

Slides.
http://www.dtubbenhauer.com/youtube.html

TeX files for the presentation.
https://github.com/dtubbenhauer/My-TeX-files

Thumbnail.
Picture from https://www.youtube.com/watch?v=MI9WD3LydXs

Main discussion.
https://en.wikipedia.org/wiki/Diffie%E2%80%93Hellman_key_exchange
https://en.wikipedia.org/wiki/Braid_group

Background material.
https://en.wikipedia.org/wiki/End-to-end_encryption
https://www.gbnews.ch/what-is-end-to-end-encryption-e2ee/
https://en.wikipedia.org/wiki/Key_(cryptography)
https://en.wikipedia.org/wiki/Key_exchange
https://en.wikipedia.org/wiki/Discrete_logarithm
https://www.iacr.org/archive/crypto2000/18800166/18800166.pdf
https://en.wikipedia.org/wiki/Public-key_cryptography#Examples
https://en.wikipedia.org/wiki/Elliptic-curve_Diffie%E2%80%93Hellman
https://en.wikipedia.org/wiki/RSA_(cryptosystem)
https://en.wikipedia.org/wiki/Cramer%E2%80%93Shoup_cryptosystem
https://en.wikipedia.org/wiki/ElGamal_encryption

Computer talk.
https://demonstrations.wolfram.com/StrongRSACryptosystem/
https://demonstrations.wolfram.com/RSAEncryptionAndDecryption/
https://en.wikipedia.org/wiki/Diffie%E2%80%93Hellman_key_exchange#/media/File:Diffie-Hellman_Key_Exchange.svg

Pictures used.
https://en.wikipedia.org/wiki/Diffie%E2%80%93Hellman_key_exchange#/media/File:Diffie-Hellman_Key_Exchange.svg
Picture from https://www.youtube.com/watch?v=MI9WD3LydXs
Another picture from https://www.youtube.com/watch?v=MI9WD3LydXs
Picture from https://www.youtube.com/watch?v=DSU7jmaVVjY
A variation of https://en.wikipedia.org/wiki/Semigroup#/media/File:Magma_to_group4.svg

YouTube and co.
https://www.youtube.com/watch?v=NmM9HA2MQGI
https://www.youtube.com/watch?v=pa4osob1XOk
https://www.youtube.com/watch?v=YEBfamv-_do
https://www.youtube.com/watch?v=MI9WD3LydXs (Shameful selfpromotion)

#crypthography
#grouptheory
#mathematics