How do these curves help the internet be secure? - Elliptic Curve Cryptography

Subtitles (hopefully) available! Legendas em português disponíveis :) This was my late entry to the #SoME2 contest. As I've said, this obviously glosses over many of the specifics of ECC, but if all goes well it can still serve as a decent primer to the subject :) This video's animations were made using Manim Community. Source Code: https://gist.github.com/arskiy/35f76c9b960871ad29a820ebd63d033b Resources I've used in the making of this video: Elliptic Curve Cryptography: A Gentle Introduction - https://andrea.corbellini.name/2015/05/17/elliptic-curve-cryptography-a-gentle-introduction/ Quantum resource estimates for computing elliptic curve discrete logarithms - https://arxiv.org/abs/1706.06752 Safe Curves - https://safecurves.cr.yp.to/ Weak Curves In Elliptic Curve Cryptography - https://wstein.org/edu/2010/414/projects/novotney.pdf Explicit Addition Formulas, elliptic curves notes - https://crypto.stanford.edu/pbc/notes/elliptic/explicit.html Evaluation of discrete logarithms in a group of p-torsion points of an elliptic curve in characteristic p - https://www.ams.org/journals/mcom/1998-67-221/S0025-5718-98-00887-4/S0025-5718-98-00887-4.pdf An Elementary Proof of the Group Law for Elliptic Curves - https://arxiv.org/abs/1710.00214 Other cool resources: Cryptohack - https://cryptohack.org/ Abstract Algebra, Theory and Applications