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.
Glossar
Elliptic Curve Discrete Logarithm Problem
Complexity ⎊ The Elliptic Curve Discrete Logarithm Problem (ECDLP) represents a foundational challenge in cryptographic security, particularly relevant to securing digital assets and transactions within cryptocurrency systems and increasingly, complex financial derivatives.
Public Key
Address ⎊ The public key mathematically derives the wallet address used to receive funds, collateral, or option contract payouts on the blockchain.
Secp256k1 Curve
Standard ⎊ Represents the specific set of parameters defined by the Standards for Efficient Cryptography Group, widely adopted for Bitcoin and many other digital assets.
Private Key
Ownership ⎊ The private key is the definitive proof of non-custodial ownership over the associated cryptocurrency or the collateral securing a derivative position.