The Animated Elliptic Curve
10 hours ago
- TLS 1.3 key exchange uses elliptic curves, with Curve25519 being the most popular.
- Elliptic curve point addition is associative and commutative, enabling scalar multiplication through repeated addition.
- Finite field arithmetic (modulo a prime) defines operations like addition, multiplication, division via multiplicative inverses, and square roots.
- A toy curve (Curve61) over a small finite field demonstrates the key exchange process: Alice and Bob compute a shared secret by exchanging scalar multiples of a base point.
- The real Curve25519 uses a large prime (2^255-19) and a base point with a huge order, providing security against attacks.
- Double-and-add method allows efficient computation of scalar multiplication for many point additions.