Why Is This One-Way Function Computationally Infeasible to Reverse?
The function is infeasible to reverse because it is based on the Elliptic Curve Discrete Logarithm Problem (ECDLP). In simple terms, while point multiplication (d G = P) is fast, finding the scalar (d) when given the two points (G and P) is computationally equivalent to guessing a needle in an enormous haystack.
The large number of possible private keys makes brute-forcing or efficient mathematical inversion impossible with current computing technology.
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.
Point Multiplication
Elliptic Curve Operation ⎊ This fundamental mathematical procedure involves calculating the coordinates of a resulting point on a specific elliptic curve after adding a given point to itself a specified number of times, a core operation in public-key cryptography used for key generation and verification.
Computationally Infeasible
Threshold ⎊ Computationally Infeasible describes the state where the resources required, typically time or energy, to reverse a cryptographic operation or brute-force a private key exceed any practical or economically viable limits given current technological capabilities.
Mathematical Inversion
Derivation ⎊ Mathematical inversion, within cryptocurrency and derivatives, represents a process of reconstructing underlying parameters or states from observed market data, often employing techniques from quantitative finance and stochastic calculus.