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.

What Is the Role of the “Elliptic Curve” in the Security of ECDSA?
What Mathematical Operation Is Equivalent to ‘Scalar Multiplication’ on an Elliptic Curve?
What Are the Three Main Steps in Generating an ECDSA Signature?
What Is the ‘Base Point’ in the Context of Elliptic Curve Cryptography?
What Is the Mathematical Relationship between a Private Key and a Public Key?
Why Is Key Derivation Considered a One-Way Street?
Why Is It Computationally Infeasible to Derive the Private Key from the Public Key?
How Does a Point on the Curve Relate to the Public Key?

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