The ECDSA Half Point Calculator allows you to divide a public point by two on the secp256k1 curve. By utilizing the modular inverse of 2 over the curve order (n), this tool instantly computes the half-point coordinates (P/2) required for deep cryptographic security research, key verification, and elliptic curve mathematics optimization.
Formula:
Main Halving Formula:
Q = ((n + 1) ÷ 2) · P (mod p)
Variable Explanation:
- Q: The computed Half Point coordinates (xq, yq)
- P: The starting ECDSA Public Key point coordinates (x, y)
- n: The multiplicative order of the curve field (For secp256k1: FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141)
- p: The prime field modulus (For secp256k1: 2256 - 232 - 977)
- ·: Elliptic curve scalar point multiplication
Underlying Point Arithmetic Formulas (Double-and-Add Method):
1. Point Doubling (When adding a point to itself, where x1 = x2):
λ = (3x12 + a) ÷ 2y1 (mod p)
2. Point Addition (When adding two distinct points, where x1 ≠ x2):
λ = (y2 - y1) ÷ (x2 - x1) (mod p)
3. Output Target Coordinates (x3, y3):
x3 = λ2 - x1 - x2 (mod p)
y3 = λ(x1 - x3) - y1 (mod p)