Elliptic Curve Group Law
Visualize point addition and doubling on Weierstrass curves.
Welcome
Elliptic curves provide a mathematical group where the 'discrete log' problem is harder than in finite fields. This allows smaller keys with equivalent security.
Short Weierstrass Form
A Weierstrass elliptic curve: y² = x³ + ax + b (mod p)
Condition: 4a³ + 27b² ≠ 0 (non-singular)
The set of all (x,y) satisfying this equation + a 'point at infinity' forms a group.