What Is the Basic Mathematical Operation Used to Derive the Public Key?

The basic mathematical operation is elliptic curve point multiplication. This is an operation defined by the elliptic curve group law.

It involves repeatedly adding the base point (G) to itself, a number of times equal to the private key (d). This is not a simple linear multiplication but a geometric and algebraic operation on the curve.

This repeated addition is the source of the one-way nature of the function.