Elliptic Curve
Compute quadratic residues and their roots, enumerate the rational points of an elliptic curve, and save them to a file. Test curve generation, point addition, and doubling.
p is assumed prime; primality is not tested. The browser accepts p ≤ 10000 to keep output manageable. QRₚ contains nonzero squares; zero and its root are listed separately.
01 / QRₚ
Quadratic residues
Find each residue and all its roots modulo p.
02 / E(𝔽ₚ)
Rational points
y² ≡ x³ + ax + b (mod p). The count includes (0, 1, 0).
Elliptic curve arithmetic
Integers up to 2048 bits. Use decimals and points (x, y, 1); infinity is (0, 1, 0). Addition and doubling assume prime p and check that points belong to the curve.
Generate a curve
Miller–Rabin: 32 rounds, probable prime. Classroom randomness. The seed repeats a run in the same environment.