21K School / Calculators / Elliptic Curve Point Addition Calculator

Elliptic Curve Point Addition Calculator

Compute P+Q on an elliptic curve y²=x³+ax+b mod p using modular arithmetic.

mod p

ARITHMETIC

SLOPE

Steps

SHOWN

Elliptic Curve Point Addition Calculator

Compute P+Q on an elliptic curve y²=x³+ax+b mod p using modular arithmetic.

Number Type

Curve Parameters

p (prime)

Point P

P.x

P.y

Point Q

Q.x

Q.y

—

Result point—

Curve—

Computation Steps

How it works

Set curve parameters a, b and prime p.

Enter coordinates of points P and Q on the curve.

Calculator computes slope λ and result point using modular arithmetic.

Formula

λ = (Qy-Py)·(Qx-Px)⁻¹ mod p

Rx = λ²-Px-Qx mod p

Ry = λ(Px-Rx)-Py mod p

ECC Properties

Commutative: P+Q = Q+P

Identity: P + O = P

Inverse: P + (-P) = O

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