What Is the Computational Problem That Makes This Derivation Hard? ▴ Learn

What Is the Computational Problem That Makes This Derivation Hard?

The computational problem is the Elliptic Curve Discrete Logarithm Problem (ECDLP). Given two points on the curve, P and G, where P = d × G, the problem is to find the integer scalar d (the private key).

For the secp256k1 curve used in Bitcoin, the size of the number d is so large that there is no known efficient algorithm to solve for it in a reasonable amount of time, even with massive parallel computing.

Can the Private Key Be Derived from the Public Key, and Why Is This Crucial?

How Is the Public Key Mathematically Derived from the Private Key in ECDSA?

What Computational Resources Are Typically Required for ZKP Verification?

What Is the Role of the ‘Generator Point’ (G) in This Derivation?