arkanaElliptic Curves In-Depth
A deeper dive into elliptic curves
Module 0133 min
Fundamentals
Defining elliptic curves, point addition, finite fields, projective coordinates, and the group structure that makes them useful in cryptography.
Module 0241 min
Elliptic Curves And Functions
Homomorphisms, isogenies, and curve twists, then divisors and the Mordell-Weil group, ending with rational points and the Birch–Swinnerton-Dyer conjecture.
Module 0340 min
Pairings
Torsion groups, the Weil and Tate pairings, Miller's algorithm for computing them, and the pairing types used in practice.
Module 0416 min
Curves In Practice
A tour of real-world curves - secp256k1, Curve25519, Ed25519, and pairing-friendly BLS12-381 - and the alternate curve forms behind their speed and security.